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Resonance fluorescence in a laser-produced AL XII plasma

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Title:
Resonance fluorescence in a laser-produced AL XII plasma
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Back, Christina Allyssa, 1961-
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English
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xi, 207 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Crystals ( jstor )
Fluorescence ( jstor )
Ionization ( jstor )
Ions ( jstor )
Laser beams ( jstor )
Lasers ( jstor )
Photons ( jstor )
Plasmas ( jstor )
Pumps ( jstor )
Resonance lines ( jstor )
Laser plasmas ( lcsh )
Plasma spectroscopy ( lcsh )
Radiative transfer ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 199-206).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Chjristina Allyssa Back.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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RESONANCE FLUORESCENCE IN A LASER-PRODUCED AL XII PLASMA


By

CHRISTINA ALLYSSA BACK
















A DISSERATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1989





























Copyright 1989

by

Christina Allyssa Back














ACKNOWLEDGMENTS


Charles F. Hooper, of course, made this dissertation work possible. He

oversaw my progress and didn't laugh when I discovered the obvious. Despite the

obvious problem of being removed on the opposite coast, he made a deliberate effort to

stay in touch.

I thank Richard Lee for guiding me in the proper direction. In particular, he

was instrumental in the development of the set of experiments for my dissertation. He

also kept me from going too far afield in the analysis.

The laser facility staff of James Swain and William Cowens made heroic efforts

to keep the laser operating. Though over-taxed, they sacrificed their personal time to

stay late a few nights to make up for the temperamental laser. Some of the best data was

taken during those evenings.

I would also like to thank C. Chenais-Popovics, who lent her expertise to the

excecution of the final photopumping experiment, J.D. Kilkenny, who also helped in

formulating the experiments, and J. I. Castor for the many discussions I had with him

about radiative transfer. Many others were kind enough to share their knowledge with

me and I have appreciated their wisdom.

Finally, I would like to thank my parents, Sangho, Flora, and Alice, my brother,

Tony, and Doug Shearer for being so supportive.















TABLE OF CONTENTS



ACKNOWLEDGEMENTS .................................. ..............................

LIST OF FIGURES..................................... .................................... vii

ABSTRACT ................................................................ .............. x

CHAPTERS

1 INTRODUCTION................................ .............................. 1

2 REVIEW OF LITERATURE ...................................................... 9
Identification of Highly Ionized Species............................................ 9
Emission Spectroscopy ................................................ ............... 10
Point Projection Spectroscopy ..................................................... ... 13
Absorption Spectroscopy ....................................................... 14
Outstanding Problems.................................... ....................... 15

3 PLASMA MODELS........................................... .................... 18
Thermodynamic Equilibrium (TE)................................ ............ .. 19
Local Thermodynamic Equilibrium (LTE)....................................... 21
Coronal Model .................................................. ................ 22
Collisional Radiative Models (Kinetics or Rate Models)......................... 25
Rates and Atomic Cross Sections........................................... ... 27
Radiative Rates (bound-bound) -(Z,i) + hv <---> E(Z,j)................ 28
Radiative Rates (bound-free) E(Z,i) + hv <---> E(Z+l,j) + e-.......... 29
Collisional Rates (bound-bound) E(Z,i) + e- <---> E(Z,j) + e-........ 31
Collisional Rates (bound-free)
E(Z,i) + e- <---> E(Z + 1,j) + e- + e- ............................... 32
Radiative Rates Involving Metastable States (bound-free)................ 33

4 FLUORESCENCE EXPERIMENT ................................................... 34
Design of Fluorescence Experiment................................................. .... 34
Target Design--Front Plasma............................... ........... 41
Target Design--Pump Plasma ............................................... 42
General Laser Parameters........................................... ... 44
Overview of the Experiments .................................................. 47
Description of JANUS Laser Facility .................................................. 48
Experiment I............................................. ........................... 54
Diagnostics ........................................................................... 56
Procedure .............................................................................. 58
Experiment II............................................. .......................... 59
D iagnostics.................. ................. ................ .............. 60
Procedure.............................................................................. 60









Experimental Series III............................................ ................ 62
Diagnostics .................................................................. 66
Procedure.......................................... ....................... 68
Problems..................................................... 71

5 ANALYSIS ................................................ ...........................7 72
Data Reduction ...................................................................... ..72
General Discussion of Spectral Analysis ......................................... 75
Line Identification ................................................. ........... 78
Line Ratios .................................................... 78
Line Shapes ................................................................. 81
Absolute Flux ................................................................ 86
Experimental Results ............................................................ 86
Experiment I.............................................. ................. 86
Line ratios from time-integrated data.............................. 87
Line widths............................................................ 89
Absolute flux......................................................... .... 99
Target parameters...................................... ............. 102
Source size ..........................................................102
Experiment II................................................................ 103
Identification of control shots ......................................... 103
Line ratios of time-resolved data................................... 108
Determination of laser energy needed to create the front
plasm a................................................... ..... ........ 109
Time behavior......................................................... 119
Target overcoat.......................................... .............120
Experiment III................................................................. .... 120
Confirmation of experiment I ......................................121
Confirmation of experiment II ........................................ 126
Time dependence of the pump plasma .............................. 127
Source size ..........................................................132
The photopumping shots--preliminary tests.........................132
Identification of photopumping ...................................... 133
Ratio ............................................................... 146
Absolute flux of fluorescence ..................................... 147
Potential problems.................................................... 150
V ariations............................................... ................ 151

6 RADIATIVE TRANSFER THEORY............................................... 152
D efinitions......................................................................... ... 152
Macroscopic Coefficients............................................ ................ 155
Transfer Equation............................................. .....................156
Source Function ............................................................... 158
The Formal Solution ................................................. ........ 159
Analytic Approximations ..................................... ................. 159
Numerical Solutions............................................ ...............162
Non-LTE Line Transfer....................................................... ...163
Analytic Model of the Experiment ........................................... 166

7 COMPUTER SIMULATION........................................................170
Atomic Model ........................................................................... 170
Atomic Physics Codes......................................................... 170
Aluminum Model ............... ............................................ 171
Radiative Transfer Simulation............................................................ 173








ALTAIR Computer Code ..................................................... 173
General considerations........................................................ 174
Constant density case ................................... ................... 176
Linear temperature gradient and logarithmically decreasing
density gradient .................................................... ......... 179
Summary of results.............................................................. 179
Limitations........................ .....................................183

8 CONCLUSIONS......................................................................... ...184

APPENDICES

A DIAGNOSTICS ......................................................................... ... 187
Dispersion Elements...................................................... 187
Other Elements................................................................................... 192

B CRYSTAL CALIBRATION.......................................................... 195

REFERENCES ................................................................................. 199

BIBLIOGRAPHICAL SKETCH.................................................................207
















LIST OF FIGURES


Figure ag


1-1 The temperature and density regime of some plasma sources...................... 2

1-2 A comparison between a line spectrum for neutral helium and one of
helium-like aluminum. ............................................................ 3

1-3 Schematic energy level diagram for ionized aluminum. The completely
stripped ion has zero energy. The energy level of the first ionization
potential for each ion is represented by the hatched bar.............................. 4

1-4 Two-level atom diagram illustrating photopumping................................... 6

3-1 Ionization balances of Saha and Coronal models for aluminium at an
electron density of 1020 cm -3 .......................................... ........... 24

4-1 Laser intensity vs electron temperature...................... ........................... 46

4-2 JANUS laserbay ......................................... ...................... 50

4-3 JANUS target room. .................................................. .............. 53

4-4 Experim ental set-up I .................................................... ................. 57

4-5 Experimental set-up II ............................................................... 61

4-6 Diagram of the full target used in the photopumping experiments. The
alignment of the target with the Ta shield and the focal spots is not to
scale. ....................................... .......................... 64

4-8 Target and tantalum shield mount ...................................................... 65

4-9 Set-up for experiment III. The diagnostics are labelled as follows................ 67

5-1 Synthetic spectra at 200 and 1000 eV ............................................. 82

5-2 A spectrum including Stark broadening convolved with a instrument
w idth of 3 eV .............................................................................. .... 84

5-3 Sample spectra recorded on the minispectrometer ..................................... 90

5-4 Time-integrated temperature intensity ratios........................................ 91









5-5 RATION plots for temperature ratios...................................... ........... .. 93

5-6 RATION plots for temperature ratios.................................... ............ 95

5-7 Time-integrated intensity ratios for density............................................ 96

5-8 RATION plots for density ratios....................................................... 98

5-9 Absolute photon flux vs. laser energy................................................. 101

5-10 Line identification for a time-resolved spectrum of He-Al........................... 104

5-11 Line identification for a time-resolved spectrum of Li-Al........................... 105

5-12 Line identification for a time-resolved spectrum of K-shell carbon
em mission ........ ......................... .............................. ................ 106

5-13 Line identification for a time-resolved spectra from ................................ 107

5-14 Line intensity ratios taken from the 20-50A time-resolved spectra.................110

5-15 R A T IO N plots ............................................................................ 112

5-16 RATION plots................................................................. ...114

5-17 He-like Al spectra 5-8A for different laser energies. A distinct increase in
emission is visible for laser energies greater that 2.5 J. The target was an
embedded Al microdot 1500 A thick that was overcoated with 1000A of
parylene-N. The energy in the laser is given. Please see figure 5-10 for
line identification..........................................................................116

5-18 The corresponding spectra in the 20-50 A region from the Harada grating
streak camera spectra for the same shots shown in figure 5-17. Please see
figure 5-13 for line identification...... ..................................................118

5-19 Sample curved crystal spectrometer (CCS) spectra.................................. 122

5-20 Time-integrated CCS intensity ratios for temperature .............................. 123

5-21 Time-integrated CCS intensity ratios for density..................................... 124

5-22 Absolute photon flux vs. laser energy from the CCS and the fit to the
data. The data from experiment I is shown for comparison........................ 126

5-23 Li-like Al intensity vs. wavelength for different times. These spectra
show that the ionization balance is not significantly changing for the time
period over which the photopumping occurs. All times are relative to plot
(d).......................................................................................... 128

5-24 Intensity ratios from the 20-50A wavelength range..................................130

5-25 Intensity vs. time for the pump plasma. The duration of the He-like Al
resonance line is -250 ps full-width-half-maximum................................... 131









5-26 Data of front and pump plasma with no shielding of the pump plasma............. 137

5-27 Raw data of the three classes of photopumping two-beam shots. The
photographs on the left hand side are from the crystal streak camera and
the photographs on the right hand side are from the Harada grating streak
camera. The laser energy and focal spot is given for the front and pump
plasmas. The pairs of data were recorded simultaneously ............................. 139

5-28 Intensity vs wavelength plots for the raw data in figure 5-27. The crystal
streak camera plots are taken at the peak of the intensities of the self-
emission and fluorescence. The Harada streak camera plots are ~ 0.4 ns
apart. ..................................................................................... ... 141

5-29 Example of the intensity plots used to determine for background emission........ 143

5-30 He-like Al resonance line vs time for photopumping shots. Table 5-1
gives the laser focal spots............................. ................................ 145

7-1 A comparison of the ionization balance with and without detailed radiative
transfer.................................................................................. .. 175

7-2 The constant density case. The x-axis corresponds to the distance, z,
measured in units of cm.................................................................178

7-3 The temperature and density gradients versus z (cm) before the
photopumping for the second simulation. ........................................... 180

7-4 The ionization balance as a function of z (cm) for the case with
temperature and density gradients shown in figure 7-3. The curves a
through e correspond to the C-like through fully stripped ions..................... 181

7-5 The source function versus z (cm) for the second simulation .................... 182

A-1 Geometry of the minispectrometer. Three rays corresponding to x-rays of
three different wavelengths are shown..............................................189

A-2 Diagram of the x-ray streak camera. The dispersion direction is
perpendicular to the plane of the page. The sweep of the electrons in time
is shown. .............. ...................... ............. ..........................191

B-1 Schematic diagram of crystal calibration set-up. The center of rotation for
the crystal and proportional counter was the center of the crystal................. 196















Abstract of Dissertation Presented
to the Graduate School of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy

RESONANCE FLUORESCENCE IN A LASER-PRODUCED AL XII PLASMA

By

Christina Allyssa Back

December 1989

Chairman: Charles F. Hooper, Jr.
Major Department: Physics

A new direction for laser-plasma spectroscopy is explored--the study of

fluorescence due to controlled radiative pumping. The active probing of the plasma can

yield new information that can test radiative transfer theory as well as atomic theory.

This study is relevant to x-ray lasing schemes which depend on photopumping to create

population inversions. This thesis begins to investigate the process of resonance

fluorescence itself.

A detailed analysis of the requirements of the photopumping system is discussed

in order to optimize the system chosen. A line coincidence scheme was used to observe

the fluorescence of the resonance line of Al XII. The resonance transition involves the

ground state, 1 1S1, and the first dipole allowed excited state, 2 IP1. In these

experiments, two distinct and independent plasmas were created. One plasma serves as

the plasma to be photopumped. The second plasma serves as the bright x-ray source to

photopump the first plasma. Both were aluminum plasmas. Hence, in this system, the

fluorescence of the 1SO-1PI transition was due to photopumping by photons of the same

Al XII ISO-1P transition from the second plasma.









A description of the experiments follows. Three experiments were necessary to

demonstrate the photopumping. The first experiment characterized the radiative pump.

The second experiment characterized the plasma to be pumped. The third experiment

was the x-ray fluorescence experiment involving both plasmas. Two independent laser

beams at 0.53 and 1.06 pm were used to create the plasmas.

The first direct observation of fluorescence in laser-produced plasmas was

obtained. An x-ray streak camera provided time-resolved data in which the fluorescence

signal was observed unambiguously. The fluorescence signal was quantified also. The

time-integrated and time-resolved data were analyzed by using spectroscopic methods.

In particular, line ratios generated by a collisional-radiative kinetics model and

measurements of absolute flux are discussed.

Finally, radiative transfer theory is reviewed and a simple analytic model is

proposed to give an order of magnitude estimate of the emission due to photopumping

relative to the self-emission of the plasma.














CHAPTER 1
INTRODUCTION



A plasma is a hot gaseous state of matter whose constituent atoms are ionized.

The plasma, as a whole, is electrically neutral, but is composed, at least in part, of

charged particles, ions, and electrons that are no longer bound. As a result, internal

electrostatic fields, called microfields, are strong enough to perturb the ionic energy level

structure. The interactions between charged particles can create plasma effects such as

collective motion or continuum lowering. For these reasons, plasmas behave differently

than hot gases or collections of neutral particles.

Plasma sources include vacuum sparks, stars, z-pinch plasma, theta-pinch

plasmas, shock tubes, tokamaks, and laser-produced plasmas. Figure 1-1 shows the

temperature and density regimes of some plasmas. The earliest studies of plasmas could

be considered to be spectroscopy of astrophysical sources. Spectroscopy has proven to

be a very powerful tool in the study of plasmas. In fact, the existence of helium was

postulated by Lockyer in 1868 based on his study of the lines of the spectra from the

sun. The development of laboratory plasma sources has allowed the study of plasmas in

a "controlled," reproducible environment.

Laser-produced plasmas are characterized by temperatures on the order of

1000 eV, electron densities of 1018 to 1022 cm-3, and copious x-ray emission. X-rays

can be divided into the approximate categories of "soft" x-rays, 18 50A, and "hard" x-

rays less than 1 A. This distinction is a historical one referring to the penetrating

power of the radiation: "soft" x-rays have less penetrating power than hard x-rays. In

this thesis, the spectroscopy of "soft" x-rays will be used to study laser-produced

plasmas.










108

107
Magnetic Fusion
106 \ Ite a Plasmas
Solar coronaaser Plasmas




10 108 1012 1016 1020 1024
10 -



--
T (K( 104)
Z Pinch





To illustrate some of the characteristics of spectra from highly ionized plasmas






the case of an aluminum plasma will be considered. In figure 1-2, the spectra of neutral
helium and helium-like aluminum are presented. The spectrum of neutral helium shows
the resonance lines, those lines that arise from allowed transitions involving the ground
level ls. The resonance lines in both of the spectra have essentially the same structure.
The spectral lines become more closely spaced as they approach the series limit. The
spectrum of the highly ionized aluminum typically contains lines from the helium-like
resonance series as well as lines corresponding to transitions from hydrogen-like ions
103 Medium


100 104 108 1012 1016 1020 1024
ne (cm3)

Figure 1-1. The temperature and density regime of some plasma sources.


To illustrate some of the characteristics of spectra from highly ionized plasmas,
the case of an aluminum plasma will be considered. In figure 1-2, the spectra of neutral
helium and helium-like aluminum are presented. The spectrum of neutral helium shows
the resonance lines, those lines that arise from allowed transitions involving the ground
level ls2. The resonance lines in both of the spectra have essentially the same structure.
The spectral lines become more closely spaced as they approach the series limit. The
spectrum of the highly ionized aluminum typically contains lines from the helium-like
resonance series as well as lines corresponding to transitions from hydrogen-like ions
and satellite lines. The principal resonance lines are indicated in the figure. The
unmarked lines appearing in the ionized spectra on the red wavelength side of the
resonance lines are the satellite lines. These lines arise from the preceding ionization










Spectrum of neutral He

2
s ls2p
ls2- ls 3p
is2- ls4p

_____iL,


Spectrum of Al XII and Al XIII


Al XIII
Al XII


Figure 1-2. A comparison between a line spectrum for neutral helium
and one of helium-like aluminum.


















I.












E- 0
N "

N








,--' *
11 ,N












I 0-




E cd
















-- .E
"r d >3 >
s s sl
w o^ en'
cs 2 2
i Tt ^
^33UJI~ ^0









stage of the ion. For instance the satellites to the helium-like lines are from the lithium-

like ion stage. Satellite lines are formed by radiative transitions from discrete states

above the first ionization limit, to ground, or excited, states of the ion. The upper level

is a metastable state having an electron configuration with two or more excited electrons.

These doubly excited states only exist in non-hydrogenic ions. In general, as the

principal quantum number, n, of the spectator electron increases, the satellite wavelength

decreases (i.e. the ls2p3p 1s23p lies closer to the parent line, 2p Is, than 1s2p2 -

ls22p line). By n=4, the satellite can be on either the red or the blue side of the

resonance line. The following figure, 1-3, is a schematic energy level diagram for the

H-like, He-like, and Li-like ion stages of aluminum. The resonance transitions are

indicated by solid lines, while the satellite transitions are indicated by dotted lines.

The spectra shown in figure 1-2 are only schematic. In reality, the individual

lines have an intrinsic natural width and can be affected additionally by mechanisms

such as Stark broadening. Moreover, the spectra can be affected by radiative transfer

effects such as radiative trapping. Radiative trapping occurs if a transition is optically

thick, meaning that a photon has a high probability of being reabsorbed by another ion

before leaving the plasma. In this case, the photons emitted at line center in the interior

of the plasma cannot escape. These photons are either thermally destroyed or their

frequencies diffuse into the line wings where the opacity is smaller and they can escape.

Therefore, the photons emitted at line center primarily escape from the cooler outer

layers of the plasma, whereas photons in the line wing can have a substantial

contribution from photons emitted in the hot core of the plasma. The result can be that

the spectral line may become broader and have a dip in the center of the line profile.

Hence, the spectoscopist's challenge is to extract an understanding of the atomic

physics, plasma conditions, and interaction between radiation and matter, from the

spectrum.














plasma to be pumped


radiative pump
J L.0 1


I" -


/I


' I


Figure 1-4. Two-level atom diagram illustrating photopumping.
a) Ionized atom in its ground state before the photopumping;
b) Photons from the radiative pump are absorbed by the ions;
c) The excited state radiatively decays back to the ground state.


-* W


p p
-----


------~--









The motivation for this thesis research is to explore the fundamental process of

photopumping, i.e. using photons to selectively excite ions. Figure 1-4 shows a

schematic diagram of photopumping that involves two levels of an ion. Also shown in

the figure are schematic diagrams of the plasmas at each step of the experiment. Part (a)

shows the ion in an initial state which, for convenience, is the ground state. The

radiative pump provides photons having an energy that matches the energy necessary to

excite an electron. Part (c) shows the atom relaxing to a lower state, in this case its

original ground state, by radiative decay. The emission of photons due to the radiative

decay of a state that has been achieved by the absorption of radiation is called

fluorescence. Only the photons that are involved in the process of photopumping or

fluorescing are indicated.

The study of fluorescence due to a radiative pump would be a promising next

step in the development of laser plasma spectroscopy for the following reasons. First,

photopumping has never been directly observed or studied in the x-ray regime. Its

effects on x-ray spectra have not been experimentally verified. Second, if a known

radiative pump is used, the pump would serve as a controlled probe that perturbs the

plasma and causes it to fluoresce. The study of this fluorescence would yield detailed

information about radiation transport, level populations, and competing rate processes in

the plasma. Finally, the study of photopumping is directly relevant to x-ray lasing

schemes that depend on this process to create population inversions.15

The work presented has been both experimental and theoretical. A basic review

of the relevant advances in plasma spectroscopy is given in chapter 2. Chapter 3 is an

introduction to the analytic models used in plasma spectroscopy. Chapters 4 and 5

discuss a photopumping experiment that was designed to observe and quantify the

fluorescence. Chapter 6 discusses radiative transfer in more detail and presents a simple

analytic model of the plasma emission. The results of computer simulations of the







8

radiative transfer in a planar slab having plasma conditions similar to that of the

experiment are discussed in chapter 7. Final conclusions are given in chapter 8.














CHAPTER 2
REVIEW OF LITERATURE



Spectroscopy is an essential tool in the study of laser-produced plasmas because

of its non-perturbative nature. In the last ten years, the advances in spectroscopy of

laser-produced plasmas have been accompanied by the development of x-ray lasers and

inertial confinement fusion. High speed computers have enabled complex calculations

of atomic and plasma models that are necessary for analysis. As a result, the

understanding of plasmas has become more sophisticated as the methods to observe and

diagnose plasmas have become more refined and specialized. In order to set this thesis

in context, the main developments in the study of laser-produced plasma will be

highlighted. This chapter will be a descriptive history; it is by no means exhaustive.

The underlying equations and assumptions of the field will be introduced in the next

chapter. Two notable references on soft x-ray spectroscopy of plasmas are the review

by De Michelis and Mattioli 6 and the textbook on plasma spectroscopy by Griem.7



Identification of Highly Ionized Species



The identification of transitions from highly ionized species in the x-ray regime

was done using high-voltage vacuum sparks in the 1939 by Edlen and Tyren.8

However, the earliest observations of x-rays from a plasma were obtained in 1949 by

the U.S. Naval Research Laboratory when soft x-ray emission of the solar corona was

detected.9 The study of x-rays originating from laser-produced plasmas began in 1973

with Galanti and Peacock who irradiated polyethelene with a neodymium laser.10









By 1974, as more powerful lasers have become available, the spectra of ionized

rare earth elements has been obtained from laser-produced plasmas. 11 Recently

interest has been generated in the nickel and neon isoelectronic sequences of these

elements due to the development of x-ray lasing schemes.12,13 This research has

spawned more papers identifying lines in these sequences from various ions.14,15

The standard reference for the wavelength of transitions is a publication by the

National Bureau of Standards. It is a compiled list of the observed lines from the

literature and is commonly referred to as the "finding table." 16 The satellite lines of

He-like ions from astrophysical sources were classified by Gabriel and Jordan. 17,18

Their classification scheme for He-like satellite lines has carried over to high density

laser-produced plasmas. A comprehensive listing of the spectral satellite lines in the 1.5

to 15.0 A wavelength range is compiled by Boiko, Faenov, and Pikuz. 19 The lines,

primarily from laser-plasma sources, are identified by comparison to theoretical

calculations using a perturbation theory expansion in powers of Z"1 or by Hartree-Fock

calculations.



Emission Spectroscopy


The analysis of emission spectra to make detailed measurements of temperature

and density has evolved as the experimental and computational methods have been

developed. Gabriel and Jordan identified the usefulness of line ratios of dielectronic

satellites to determine densities of astrophysical plasmas.20 Their methods have been

extensively cited and extended to laser plasmas.

An instructive paper discussing the use of the emission lines for diagnostics of

laser plasmas is that of Aglitskii, Boiko, Vinogradov, and Yukov.21 They analyzed the

spectra of H-like and He-like magnesium and aluminum ions for intensity ratios

sensitive to temperature and density. Their discussions of the mechanisms populating









the upper levels of the transitions give a physical understanding of the diagnostics.

Subsequent papers have used similar applications of the same line ratios.22,23

Dielectronic satellites have been a continual subject of laser plasma studies. An

early paper that systematically compared the satellite spectra of He-like ions of C, F,

Mg, and Al in laser-produced plasmas is by Peacock, Hobby and Galanti.24 In this

paper, they identify the satellite spectra in He-like ion emission by comparing them to

Hartree-Fock calculations. They noted an anomalous increase in intensity of the "jkl"

satellite as the ion charge increases. An explanation for this effect has been proposed by

Weisheit.25 He suggests that at higher ion charges, collisional ionizations that

depopulate the autoionizing states decrease and therefore the satellite intensity increases.

Other studies have investigated the impact of dielectronic recombination in plasmas.26,27

Lineshapes are also an important diagnostic for dense laser-produced plasmas.

A fundamental text by Griem, "Spectral Line Broadening by Plasmas", gives the general

formalism of line broadening.28 Theoretical lineshapes are the convolution of the

natural broadening, Doppler broadening, and Stark broadening. In high density laser

plasmas, Stark broadening can be particularly sensitive to electron density and therefore

has received the most attention. The development of accurate microfield theories

enabled extensive calculations of Stark line widths. 29-32 The work has concentrated on

hydrogenic species since Stark broadening is the most pronounced for these ions. A

calculational method which is used here, for line broadening of hydrogenic species at

laser plasma densities is given by Lee.33 He extends the formalism and presents sample

calculations for Si XIV. Line broadening continues to generate interest in the field.34-37

The standard techniques of line ratios and line widths are also applied to space-

resolved spectra.38,39 Boiko, Pikuz, and Faenov, in one of the first papers reporting

on spatial distributions, used a 65 gm slit to collimate the radiation from the source that

is Bragg diffracted by a crystal.40 In this paper, the electron density profile was









obtained as a function of distance from the target surface. By 1978, spatial resolution to

10 pm had been achieved.41

A prime example of a quantitative measurement of the bound-free continue is

given in the work of Galanti and Peacock.42 They used an absolutely calibrated grating

to measure the carbon emission from a polyethylene target. Space-resolved spectra was

used to investigate the recombination continue. Direct measurements of the H-like and

He-like carbon ion populations were made and compared to a theoretical collisional

radiative model. Their measurements also found no evidence for non-Maxwellian

velocity distributions for 1.06 .tm laser having an intensity of 5.0 x 1012 W/cm2. A

later work by Irons and Peacock gives a good example of a method to measure

recombination rates for bare and H-like carbon.43

The development of x-ray streak cameras allowed time-resolved spectra. In the

paper by Key et al., the first time histories of the resonance line widths and the satellites

were reported.44 The emission spectra of plane aluminum targets and neon-filled

mircroballons was analyzed for time-dependent line intensity ratios and possible cooling

mechanisms were proposed. The length of time a laser-produced plasma emits x-rays is

typically 100 ps to 3 ns, depending on the laser pulse. Time resolution on the order of

tens of picoseconds allows the time-dependent study of plasmas. Now, even sub-

picosecond resolution is being pursued.

Determination of temperature and density by comparison to ionization

calculations has also been done.45 Recently a paper by Goldstein et al. has used the Na-

like satellite to the Ne-like resonance line to determine the electron temperature and

charge state distribution in a bromine plasma.46 In this analysis, the relative abundances

of the Na-like and Ne-like ions were adjusted in a model of the plasma emission until the

synthetic spectrum fit the experimental spectrum. The advantage of this method is that it

does not depend on hydrodynamic modeling. The result is, however, critically

dependent on the atomic model.









A variety of methods described above must be used to diagnose a plasma well.47

A particularly clear discussion of a consistent use of the methods presented here is

contained in the paper by Kilkenny et al.48 An x-ray pinhole camera and space-

resolving minispectrometers were used in the spectroscopic analysis of microballoons.

The determination of electron temperature and density were deduced from the

recombination continue of the spectra. These measurements were corroborated by the

electron temperature, as determined from the ionization state of the plasma, and density,

as derived from a line width fitting procedure to all the observed members of the the

hydrogenic line series. The size of the emitting plasma was determined also.

There are two significant limitations on emission spectroscopy. First, the

emission depends directly on the excited state populations. These excited states do not

give direct information about the ground state populations, which are the most important

in determining ionization balance since the overwhelming proportion of the total

population resides in the ground states. Second, if the plasma is not hot enough, the

emission is too low to make an accurate diagnosis or to even be detected. These

limitations led to the development of techniques to image and probe the plasma.


Point Projection Spectroscopy



This technique was developed in a response to the needs of laser fusion to

determine the dynamics, size, and symmetry of laser-driven implosions. The feasibility

of this technique was reported by Key et al. in 1978.49 In this experiment, a separate

laser-produced plasma served as a source to image an imploding microballoon. This

source is called a backlight. The microballoon, imploded by six orthogonal laser beams,

was backlit at different delay times during its implosion in order to determine the

compressed density. The technique was elaborated in later papers.50,51 Eventually









streaked radiography was used to measure ablation pressure, implosion velocity, and

other hydrodynamic quantities.

Since the technique is dependent on the development of bright backlight sources,

it became clear that studies of the backlight source itself were needed. One of the

fundamental papers characterizing laser-produced plasma sources has been that of

Matthews et al.52 The absolute conversion efficiency of line sources in the 1.4 to

1.8 keV range were studied as a function of laser wavelength, intensity, and pulse

width. Other conversion efficiency studies have investigated different wavelengths53-55

and/or different elements for potential backlight sources.56-59

Other source studies have focused on the optimization of the source for x-ray

yield, source size, and spectral characteristics. The paper of Lampart, Weber, and

Balmer reports on a systematic study of the emission from elements having atomic

number 9 through 82.60 Using a 0.53tm wavelength laser, planar targets were

irradiated with 1 J, 800 ps laser pulses. The resulting 5-15 A x-ray emission varied

from pronounced line emission from K-shell and L-shell emitters to nearly continuous

emission. Thus they showed that the spectral characteristics of the source could be

controlled by a judicious choice of target and irradiance conditions. A paper by Zigler et

al. has reported on optimizing the intensity while minimizing the size of the backlight

source.61 A novel multi-layered target is introduced. The target is initially pitted by a

pre-pulse from the laser to expose the target element of interest. When the full laser

pulse is incident on the pitted target, the ablation of the initial layer keeps the target

plasma localized.


Absorption Spectroscopy


More recently, absorption techniques have been developed so that the

experimenter can probe the plasma as well as passively observe it. Lewis and









McGlinchey first coupled Bragg crystals with x-ray streak cameras in order to obtain

"quasi-monochromatic" probing of material.62. In absorption spectroscopy, a "warm"

plasma is irradiated from behind, typically by a broad-band photon flux. The "warm"

plasma will absorb the radiation from the backlight at frequencies corresponding to

particular transitions. Thus absorption features appear in the spectrum. Analysis of the

absorption profiles yields the number of ground state ions. A good example of this

technique is given in the paper by Balmer et al.63 One laser beam irradiates a foil target.

The tip of a fiber is irradiated to create a point backlight. The spectrometer was aligned

perpendicular to the face of the foil so that the time-integrated data simultaneously

recorded the backlight spectrum, the shadow of the foil, and the absorbing plasma

spectrum. The data reduction involved subtracting the direct backlight spectrum from

the absorbing plasma spectrum to reveal the absorption lines. The transmission at line

center of optically thin lines and an equivalent width of optically thick lines were

measured to determine the absorption. This example illustrates how backlights can be

successfully used as probes of laser heated targets,64 x-ray heated targets,65 and shock

heated targets.66, 67


Outstanding Problems


For plasmas that are significantly affected by opacity, these techniques do not

give enough information to fully interpret the spectra. Hear examined the effects of

radiative transfer of resonance lines and noted that even in plasmas having uniform

temperature and density, the line profile does not reach the black body limit at line

center.68 Earlier Osterbrock found that the diffusion of photons in frequency can be an

even more pronounced effect since the optical depth in the wings is much less than at

line center.69 Holstein introduced the idea of an escape factor to correct for the effects

of radiative transfer in resonance lines.70,71 In addition to references in some of the









papers already mentioned, papers noting the effects of radiative transfer in laser-

produced plasmas are plentiful.72-76

The tools and techniques of producing and analyzing laser-produced plasmas are

now sophisticated enough to begin exploring radiative transfer. The advent of computer

codes that can solve the formidable radiative transfer equations now make it possible to

generate synthetic spectra. At the same time, experimental techniques have been

developed that enable experiments which are sophisticated enough to be able to address

these questions. As yet, though, there has been no concerted effort to resolve the

questions related to radiative transfer effects. The following is a discussion of recent

research related to photopumping.

The attempts at photopumping have not been conclusive. A paper by Mochizuki

et al. investigates the radiative heating of a layered foil.77 They use a double foil, one of

which is irradiated directly by the laser, while the other is radiatively heated by x-rays

from the first foil. They attempted to study the ionization bum-through phenomenon in

which x-ray pre-heating reduces the opacity of the sample and causes a strong radiative

transport of energy to the rear of the foil. However this study fails to adequately

characterize the x-ray heating source. The use of two foils eliminates neither the

possible heating due to the physical contact of the ablating laser irradiated foil with the

second foil, nor the possible direct heating of the second foil by the laser itself.

Another attempt has been to try photoresonant excitation of the ls-3p H-like

fluorine line by the 2p-3d line of Be-like manganese .78 The purpose of this research

was to create a population inversion and observe the lasing of the 2p-3d level of H-like

fluorine. However, the frequency mismatch between the pump ls-3p transition as well

as the physical configuration of the target presented problems.

A recent paper by Monier et al. has explored the photoresonance of the ls-3p

resonance line of A1XIII and the 2p6 (1S0) 2p53d (3D1) line of Sr XXIX.5 This

scheme was designed to explore the possible use of photopuming as a mechanism for







17

population inversions. This research, as the others, fall short of characterizing the

radiation of the pump. However, none of the mentioned studies intended to study the

fundamental process.














CHAPTER 3
PLASMA MODELS



In this chapter, before launching into the experiment and results, a general

discussion of plasma models that are frequently used to help characterize and study

plasmas is presented. Since the spectra from a plasma is a manifestation of atomic

processes, this thesis will focus on the nature of plasma constituents as opposed to the

fluid properties.

The emission of a photon depends on the transition probability, the population of

the upper state of the transition, and the probability that the photon escapes the plasma

medium. The first quantity is intrinsic to the ion and requires complex atomic structure

calculations. The population distribution is essentially determined by the kinetics

equations, also known as the rate equations, which describe how all the atomic

processes couple the states. The probability that the photon escapes requires the

solution of the radiative transfer equation which describes how the radiation interacts

with matter. Unfortunately, the population distribution and the radiation field are

interdependent. Consequently, a fully consistent model must involve simultaneously

solving both sets of equations.

Valuable physical insight can be gained by decoupling the radiative transfer

equation from the kinetics equations. This approach assumes that the detailed radiative

transfer does not significantly affect the ionization and population of the states. This

treatment is valid for plasmas that are optically thin, meaning that photons escape the

plasma without being reabsorbed, or for plasmas in which the radative processes are









dominated by the collisional processes. To a first order approximation, radiation

trapping can be incorporated into kinetics models by the addition of escape factors.

The models that will be discussed are thermodynamic equilibrium, local

thermodynamic equilibrium, coronal model, and collisional radiative model. For the

purpose of this thesis, a collisional radiative model was primarily used to diagnose the

temperatures and densities of the plasmas. A radiative transfer code was used to

investigate the effects of radiation transport. Important atomic physics results will be

quoted and used but not explicitly derived.



Thermodynamic Equilibrium (TE)


In thermal equilibrium, the state of the matter can be entirely specified by the

thermodynamic quantities. The most convenient thermodynamic quantities to choose are

temperature and density. The ion, electron, and radiation temperature are all the same.

The radiation is homogeneous and isotropic hence the specific intensity, Iv, is equal to

its black body value, the Planck function.


3
S=B = 2hv 1 erg
2 h 2 sr hz sec
c (exp() 1) 1 J



where h is the Planck constant, c is the speed of light, and k is the Boltzmann constant.

The population distributions and ionization balance are determined by the Boltzmann and

Saha equations which will be described in the next section.

This limit is never physically realized; however, it provides one of the most

powerful concepts in the calculation of rate coefficients: detailed balance. In

thermodynamic equilibrium, every atomic processes must be balanced by its inverse









process. The principle of detailed balance is based on the microscopic probability of the

transition to a state. Microscopic laws are time invariant or "reversible." Thus, this

concept can provide relationships between reciprocal processes regardless of the

surrounding plasma conditions because transition probabilities are intrinsic to the atom

or ion itself.

An interesting set of relationships between the Einstein coefficients, A and B,

can be obtained. If we equate the number of transitions from a lower state i to an upper

state j to the number from the upper state to the lower state.


niBij Iv= njAj,i+ njBj,iIv



were ni stands for the number of ions in state i. The left hand side of the equation

represents the number of upward transitions due to stimulated absorption. The right

hand side represents the sum of the spontaneous decays and the stimulated emissions.

This equation can be solved for Iv. In TE, Iv equals the Planck function. Therefore,

the relationships between the coefficients can be found to be


3
Aij 2hv ]
c[ NJ 2 sec
c

cm hz sr
giBi,j=gjBj,i [2 erg



where gi is the statistical weight of state i. Even though these relationships are derived

from a condition of thermodynamic equilibrium, they are always valid. The Einstein B

coefficient given here has units such that B times Iv is in sec-1. If the radiation density,

p = 4xI/c, is used, then B must be multiplied by c/47.









Local Thermodynamic Equilibrium (LTE)


The Local Thermodynamic Equilibrium model assumes that the plasma is

governed by the local temperature and density at each point in the plasma. The state of

the plasma can still be described by the thermodynamic quantities of T and n, but the

temperature and density structure can be non-uniform.

By using the laws of statistical mechanics, we find that the levels are populated

according to the Boltzmann prescription.


nj = gj I- Ej,il
exp( l
ni gi ex kT)


where k is the Boltzmann constant, g is the statistical weight of the level, and Ej,i = Ej -

Ei, the energy difference between the upper level j and the lower level i.

The relationship between the ground states of successive ions is determined by

the Saha equation, which can be understood as an extension of the Boltzmann

expression to free particles.


"nz+1,gne gz+1.g ( 2mkT 3/2 xp zg
nz,g gz,g h2



where h is Planck's constant, and Xz,g is the ionization potential of an ion of charge z.

The Boltzmann and Saha equations can be combined to relate a ground state to any

excited state of another ion


3/2
n zj = nz+,ge \- 9 exp z2 /
gzj 1 h .nep jg
nz'J= nz+l'gne gz g2 )2'mkT exp E )









The particles will have a Maxwellian velocity distribution

2
3/2 2
f(u)du = 2 exp 2 4x du


where u is the velocity and m is the mass of the particles.

The equations above describe a plasma in LTE. The power of LTE lies in the

fact that the temperature T used in the velocity distribution functions and the population

distributions is the same at each point in the medium. The statistical arguments obviate

the need to know atomic cross sections and coeffficients in order to determine the kinetic

temperature and density of the plasma.

The significant difference between TE and LTE is that the macroscopic radiation

field is not in equilibrium. This deviation is caused by temperature and density

gradients. The radiation field must be obtained by solving the radiative transfer

equation.

A sufficient condition for LTE to exist is if the collisional processes are the only

processes important in determining the population densities. In this case, radiative

processes do not significantly affect the ionization balance and population densities.



Coronal Model


The Coronal model is based on coronal equilibrium in which collisional

excitation processes are balanced by radiative deexcitation processes. It is so named

because this condition was found to exist in the corona of the sun. This model is valid

for aluminum plasmas at temperatures of 100eV and electron densities on the order of

1018 cm-3. In this section, the equations given by McWhirter are quoted.79 The

population distribution of the number of ions in an excited state, x, to the number of

ions in the ground state, g, is determined by











n n Ag,x
-.= ne g'X
ng Ax,q
q< x


where ne is the electron density, Xg,x is the collisional excitation rate coefficient from the

ground to excited level, and the sum appearing in the denominator is the total radiative

rate from the excited state to all states, q, lower than the excited state.

Likewise, ionization balance is primarily determined by collisional excitation and

radiative recombination. A simple argument shows that at low densities, radiative

recombination is stronger than 3-body recombination, the inverse of collisional

ionization. Collisional recombination is a three body process involving an ion and two

electrons one electron recombines, while the other absorbs the excess energy. Hence it

is proportional to ne2. Radiative recombination only involves one free electron and is

therefore proportional to ne. The analog of the LTE Saha equation that relates the

ground states of adjacent ionization stages is

nzg zz+l,g
nz+l,g S z,g


where the additional subscript z denotes the ionic charge, a is the radiative

recombination coefficient, and S is the 3-body recombination coefficient.

Using analytic hydrogenic expressions for the respective coefficients, an

expression showing the functional dependence on T and ne can be found. Here, we

assume only recombinations and ionizations between ground states, because at these

lower densities, the excited state populations of ionization stages will be insignificant

compared to the ground state populations. Details about the atomic coefficients will be

given later in Rates and Atomic Cross Sections. The ratio of the number of ions in the

ground state of successive ionization stages is















Saha Equilibrium Ionization Balance


Coronal Equilibrium Ionization Balance


----
-4---
I
8 -o-
-*--

-A-

-U-

-U-
---N--


Temperature (K')


Figure 3-1. Ionization balances of Saha and Coronal models for aluminum
at an electron density of 1020 cm3.


neutral Al
Mg-like Al
Na-like Al
Ne-like Al
F-like Al
O-like Al
N-like Al
C-like Al
B-like Al
Be-like Al
Li-like Al
He-like Al
H-like Al


108









3/4
n-g = 7.87x109 (Xz, ) exp (k
nz+l,gkTkT

where X, is the ionization potential of the ion having ionic charge z. Notice that the

ionization balance is independent of electron density, but is now strongly dependent on

the atomic rates which are strong functions of temperature. Figure 3-1 shows a

calculation of ionization balance of a coronal plasma based on the equation given above.


Collisional Radiative Models (Kinetics or Rate Models)


Laser-produced plasmas having densities from 1018 cm-3 or above can fall

between the two previous models. At these densities the radiative and collisional rates

are comparable, so a rate equations, or kinetics, model must be used. In a kinetics

model, all the important radiative and collisional rates that connect the levels of the

atomic energy levels are included. The rates together with an equation conserving the

total ion density can be written in matrix form and solved for the populations of all the

levels.

A rate is the number of transitions per unit time. In a volume of medium, the

number density of particles will change in time according to the net flux of particles

through the volume and the net rate at which particles are brought from other states by

radiative and collisional processes. If there are no temperature or density gradients, then


jni
= .= .(j Pj,i-ni Pi~j)


where Pij is the total rate from i to j.

The total rate Pij is composed of radiative and collisional rates. The form of

these rates can be expressed as follows. The bound-bound rates for radiative line









transitions can be written with the Einstein coefficients. The number of stimulated
absorptions in a transition with line shape O(v) is


niRi,j = niB ij (v)J(vdv


where J(v) is the mean intensity, i.e. the intensity integrated over all solid angles. The
number of emissions is

n Rj,i= njAj,i4(v) dv


Like the stimulated absorption rate, the photoionization rate is proportional to the
mean intensity. The number of photoionizations is



J(v)
ni Ri,k = ni47 i J(vdv
hv



The radiative recombination rate, which does not depend on the incident radiation, is
expressed so that the explicit dependence on the electron density, ne, is shown.


nj Rj,i= nj ne


where the rate coefficient a is defined by



a = f oj (u) f(u)u du



where f(u) is the electron velocity distribution and oj(u) is the radiative recombination
capture cross section.









All the collisional rates can be expressed in the following form

ni Cij = nine ao(u) f(u) u du = nineXij


where a is the cross section for the process being considered and f(u) is the velocity

distribution. Xij is the rate coefficient with units cm3sec-1. It is sometimes written as

.

An example of a collisional radiative model for K-shell ions is RATION, a code

written primarily by R. W. Lee.80 It constructs the energy levels from semi-empirical

formulae, calculates and fills a rate matrix, then inverts the matrix to solve for the

populations. It will be described in more detail in chapter 5.



Rates and Atomic Cross Sections


Since the results of a numerical model cannot always be easily generalized, a list

of the basic rates and their dependencies will be given. In addition to revealing the

important processes that are included in typical models, this section will define a

consistent set of expressions that will be referred to throughout the rest of this thesis.

The Z, ne, and Te dependencies of rates and cross sections will be emphasized, but the

details of the calculations are left to the references. Unless otherwise noted, cgs units

are used, except for explicit energy factors X, E, and R shown in the equations which

are in eV.

Since the hydrogenic atom can be solved analytically for wavefunctions and

energy levels, hydrogenic approximations will be given in order to show basic trends.

In this section, the units of rate coefficients used by Mihalas will be used.81 The

monograph edited by Bates and the texts by Mihalas, Zel'dovich and Raiser, and

Cowan, are extremely useful references.82-84











Radiative Rates (bound-bound) S(Z, i) + hv <- > (Zi)



In this process a photon of energy hv is absorbed or emitted by an ion

represented by the symbol E The net charge of the ion is Z. The indices i and j stand

for the lower and upper levels, respectively. From quantum mechanics, the dipole

matrix elements can be calculated and expressed in the form of an electric dipole line

strength or an oscillator strength, fij. The absorption cross section is given by 81


B ij hv
4n
where


2
Ste 4n7
Bij= -e- fij 4v
m 1e hv


By using the Einstein relations between A and B, the hydrogenic A rate can be

analytically expressed as

2 2
Aji = 8.01 x 109 4( f i [se--
ni nj nj


where ni is the principal quantum number of level i, and the expressions for the energy

and the statistical weight for hydrogenic ions, gi = 2ni2, have been substituted. The Z4

dependence comes from the energy dependence of the rate. The helium-like rates do not

have a corresponding analytic form, but there are fits to the rates such as those of Drake,

and Drake and Dalgaro.85-87









Radiative Rates (bound-free) (Zi) + hv <- > E(Z+1.i) + e-


Free bound processes affect the ionization balance of the plasma. The ion E
absorbs a photon of energy hv and ionizes to a charge state of Z+1. The photoionization
cross section can be found by using Kramers semi-classical result

4 10 4
64rc me Z [2]
o- = --- [cm
i 3 ch6 n53


Notice that at threshold energies En=R Z2 n -2, the threshold cross section, aithresh is

3
thresh -18 n Vn
oi =7.91 x 10
S2 3
v


The exact quantum mechanical result differs from the classical result by a multiplicative
factor dependent on v, called the Gaunt factor, which is on the order of 1 near threshold.
The semi-classical result differs from the exact result by approximately 20 %.
An analytic expression for this rate coefficient from the ground state is given for
I>>kT in Zeldovich and Raiser where the radiation field is approximated by the Wien
expression.

19 2 thresh ( x21 -
Rg(v) = 3.40x 1019 TX g2 (v) exp cm[ e


where og is the photoionization cross section of the ground state.
The cross section for radiative recombination can be found from detailed balance
from the photoionization cross section .

64 410 z4
644 e1 Z34 2 3hf
3 c 3h3 n5 2
m)ch









where the captured electron has energy 0.5mu2 and the energy of the emitted photon,

hv, is

2
m) R Z
hv(emitted photon) = + --
2 2
n

where R is the Rydberg energy. Notice that the cross section is inversely proportional

to the electron energy and also to the energy of the emitted photon, hv. Again, the

relation can be corrected by the Gaunt factor for the quantum mechanical result of the

cross section.

In the coronal approximation, the total recombination rate is approximately equal

to the rate coefficient (cm3/sec) for recombination into the ground state, which is 79


az,g(T) = 2.05 x 10-12 Xz-1, g
T 1/2 [Esec


This expression includes the result of an integration over the electron distribution. It is

useful for plasmas that have a thermal energy kT that is much smaller than the ionization

potential. A more general expression for recombination into a shell of principal quantum

number, n, is 88

4 3/2 [3
z,g(T) = 5.2 x 10-14 Z 4 R3/2 1 exp(xn) Ei(xn)
(kT)3/2 n3

where only the leading term of the gaunt factor is taken and


R Z2
xn-- --
kT n

Ei is the exponential integral. The total recombination rate coefficient for an ion must be

summed over all the states into which the electron can recombine.










Collisional Rates (bound-bound) E(Z,i) + e- <- > (Zi) + e-


In this process an ion in lower state, i, is excited to an upper state, j, by a
collision with an electron. The calculations for collisional cross section are difficult to
generalize by a representative cross section because of the different regimes in which
approximations are valid. An excellent review by Seaton discusses the various
methods.89 The cross section, Q, is of the form
f E/2
Q= E/2(e,Ei) de [cm2]
0

where a is the cross section, Ei is the incident electron energy, E = Ei X, and e is the
energy of the ejected electron.
An approximation for the cross section of optically allowed transitions is given
by Seaton

S4712 fji
Qj = 2 (E Ei)


where g is the Kramers-Gaunt factor and 0.5mu2 is the energy of the incident electron.
The rate coefficients are found by integrating the collisional cross section over a
velocity distribution. The temperature dependence of the collisional excitation rate is due
to the integration over the Maxwellian velocity distribution. The analytic collisional rate
coefficient of excitation for hydrogenic bound-bound states is

-6.5 x 104 Eji cm3
Xi.) = 0 fij exp (
Eji f Esec









For transitions between lower level i to upper level j, detailed balancing of the
collisional rates implies

gi E EjEi"
i Xj exp ~)
Xi g ijkT

So the deexcitation coefficient can calculated to be

gi6.5 x 104 cm
J = gj Ej,iT sec


Numerous calculation of rate coefficients can be found in the literature and references
therein.90-96


Collisional Rates (bound-free) E(Z.i) + e- <- > E(Z + ,i) + e- + e-


Collisional processes are dependent on the velocity distribution of the electrons.
Electrons can ionize an ion of charge Z to a final state in which the ion has charge Z+l.
A study of electron-impact ionization cross sections using variations of the Coulomb-

Born and distorted wave approximations has been done by Younger.97 A good overall
review has been done by Rudge.98

For collisional ionization, the coefficient for hydrogen-like ions is 79


-ep1/4 _XT 3]
S z,(T) = 2.34 x 107 7/4 exp
X Z,g
based on the work of Burgess.99 The inverse process is three-body recombination. It
can be calculated by detailed balance.







33
Radiative Rates Involving Metastable States (bound-free)
E(Zi) + e- > E(Z-l.i *) > E(Z- 1, m) + hv


A rate that is important in laser-plasmas is dielectronic recombination. It is a two

stage process. First an electron is captured by an ion of charge Z creating a doubly

excited state denoted by j*. This state can then stabilize by a radiative transition to a

lower state m. The rate coefficient, ad, is given by

3/2 3,m gA' [M31
a = 47 2a0 ex g) A P
T


where ao is the Bohr radius, G is the sum of statistical weights over the index level m,

Aa is the autoionizing rate, and P is the probability of radiative stabilization which

depends on the branching ratio of radiative decay rates.84 Tabulations of wavelengths

and transition probabilities have been calculated by Vainshtein and Safronova100 and

Gabriel13














CHAPTER 4
FLUORESCENCE EXPERIMENT


Having given a background discussion of plasmas and processes of importance,

now a specific system of plasmas that can demonstrate photopuming will be discussed.

Resonance radiative pumping is the process by which the first dipole allowed excited

state is selectively populated by a photon source tuned to the transition energy between

the ground and the excited state. The system chosen for this experiment was a line
coincidence scheme to observe the fluorescence of the Al XII 11SO-21P1 transition due

to photopumping by photons produced by the Al XII 11SO-21p1 transition from a

spatially distinct plasma source. Thus, this photopumping experiment involved two

independent plasmas. Since the photopumping effect has never been directly observed

in a laser-produced plasma, considerable thought was given to the design of the system

and target. The first half of the chapter will justify the choice of this system and

consider the factors that influence the experimental conditions. The second half will

describe the experiments. The spectroscopic notation that will be used throughout this
thesis is [ n (2S+1) L j ], where n is the principal quantum number, S is the total spin, L

is the total angular momentum, and J =L+S.




Design of Fluorescence Experiment


The design for the experiment was developed according to the following

guidelines. First, the spectroscopic analysis was to be as unambiguous as possible.










Second, the design had to maximize the fluorescence effect. Third, the plasma

expansion should be as one-dimensional as possible.

From a spectroscopic point of view, K-shell spectra are the most straightforward

to study because of the relatively simple energy level structure. The line series structure

is prominent and the number of overlapping lines is minimized. Isoelectronic sequences

behave similarly to the neutral atom with the same number of electrons because the

electron structure is similar. Therefore, estimates of the hydrogenic energy levels can be

made from a Bohr model of the atom that has been scaled by a factor of Z2


Z2 R
2
n



where R is the Rydberg constant, Z is the ion charge, and n is the principal quantum

number of the level. Z equals one for hydrogen.

For helium-like ions, the energy levels can be estimated by


(Z-1)2 R
2
n



where x is the ionization energy of the ion. The ionization energy is larger than would

be predicted based on the assumption that the ground state energy Eo = -(Z-1) 2 R

because the electrons are in a closed shell. In 1930, Hylleraas calculated the ionization

energy to within the experimental error by using a modified Ritz method.101 Often in

semi-empirical formulas, experimental data provides the values for the ionization

potentials.

As more electrons are added, the bare charge of the nucleus is screened and

electron-electron interactions become important. The atom becomes a many-body









system that must be numerically solved. In order to concentrate on the photopumping

effect, K-shell ions were an attractive choice because an analytic approach to

understanding the results could be attempted.

Several factors influence the strength of the fluorescence signal. First we will

consider the plasma that will be pumped. This plasma needs to be in a state that

maximizes the number ions that are available to be pumped. In a laser plasma, several

ionization stages may exist at a given time, depending on the ionization balance of the

plasma. In order to make a judicious choice of the plasma state, we consider the

ionization energy of the ion being pumped. As we can see from the ionization balance

of charge states in figure 3-1, the helium-like ion is the dominant species over a larger

temperature range than the other ions because of the large ionization energy required to

remove an electron from the K-shell. Moreover, a rough calculation shows that the

excitation energy between the ground state and the first excited state will be

approximately 75% of the ionization potential. Hence, the helium-like ground state can

be preferentially populated to create a large pool of ions in the proper state to be

photopumped.

To detect photopumping, the radiative excitation rate must be significantly larger

than the collisional excitation rate. Since the collisional and radiative rates are both

proportional to the oscillator strength, a simple expression for a lower limit on the

photon flux necessary to perturb the plasma can be found


C..
I > Ci
Ipump >
o Bi, j



where Cij is the collisional excitation rate, B ij is the Einstein coefficient, and 0o is the

line profile at line center, and Ipump is the intensity of the external radiative pump. For a

temperature of 200 eV, this expression implies that the intensity must be greater than









6 x 1014 ergs cm-2 sr1sec-1 for the resonance line of He-like Al. For typical backlight

plasmas, the burst of radiation lasts about 100 ps, so the irradiance of the pump would

need to be 8 x 10-2 Watts cm-2.

After laser pulse has ended, the deexcitation mechanism in laser-produced

plasmas is generally due to radiative decay. For instance, for bound-bound transitions,

we can define E to be the ratio of the collisional deexcitation rate to the spontaneous

decay rate. After manipulating the relevant expressions from the previous chapter, we

find


1.4 x 1013
e= ne
E


where E is the energy of the transition, ne is the electron density, and T is the electron

temperature. In a He-like Al plasma, having a density of 10 21 cm-3 and a temperature
of 107 K, e = 10-5 for the resonance line. Once a level is photopumped, the strength of

the fluorescence signal will primarily depend on the number of ways in which the

excited state can radiatively decay. It is therefore advantageous to choose an excited

state that is dominated by one decay route.

Next, we will consider the pump radiation. To efficiently photopump, the

wavelength of the pump must match the wavelength of the transition or transitions to be

pumped, and the pump must be as bright as possible. To pump the transition, either a

broad band source such as M shell radiation from dysprosium (Z=66) or an appropriate

line source could be used. X-ray sources are characterized by their x-ray conversion

efficiency, which is measured by the percentage of laser energy converted into the

energy emitted by the x-rays. Typically, broad band sources have a higher total x-ray

conversion efficiency over the whole band, but over the frequency range of a particular

line, the conversion efficiency is smaller than for a correctly chosen line source. In the









case of a line pump, the frequency overlap of the pump and the transition to be pumped

must be large. If the frequencies are mismatched, Stark broadening could serve as a

mechanism to broaden the pump line, however, at densities 1020 cm-3, it is not a

pronounced effect The most likely candidate for line pumping is the same transition

itself.

Preliminary calculations were done to estimate 1.) if the photopumping effect

would be observable and 2.) to determine whether a line coincidence scheme or a

continuum pumping scheme would be better. Some elementary principles about

radiative transfer must be introduced here. A more detailed discussion will be presented

in the Radiative Transfer Theory chapter.

The energy transported by a radiation field in a frequency interval (v + dv), into

a solid angle d., in a time dt, and across an area dA is

dEv = Iv cos( 0) dA dv dQ dt


where Iv is the specific intensity. The energy that is absorbed from the radiation field

can be expressed as

(dEv, abs = Ky Iv cos( 0) dA dv dR dt di


where Ky is the absorption coefficient with units of 1/cm and dfrepresents the path

length of the radiation through the material. The absorption coefficient, or opacity, is

the product of the number of absorbers (#/cm3) times the absorption cross section

(cm2). Its inverse can be considered the mean path length of the photon before it is

absorbed or scattered.

We will now consider the simple radiative transfer in one-dimension through a

slab of plasma. If we assume that the plasma only absorbs radiation (i.e. no scattering

or self-emission) and the plasma is homogeneous (i.e. K is a constant), then the radiative

transfer equation has a simple solution









I= Iiexp( -K )

where Ii is the radiation incident on the slab of plasma.
In this approximation, the energy absorbed from a plasma of length f is given by

the difference in the energy transported by the radiation field before and after it passes
through the plasma.


Eabs = ( exp (i-K)) fi cos( ) dA dv dQ dt

If the medium is homogeneous, then the absorption fraction, (1 exp( iK ), is

essentially constant. Now, if we assume that all the energy absorbed will be re-emitted
at the same frequency as the incident radiation, then the equation


Efluor = Ei(l- exp (- t))


is an estimate of the total energy emitted into 47t by fluorescence. The quantity Ei
represents the energy incident on the slab. Certainly, this equation will give an upper
limit of the energy since no photons are destroyed by themalization. However, it is
sufficient to roughly estimate the photopumping effect and to determine the relative
efficiency of line versus continuum pumping.

For a comparison, we will consider the pumping from helium-like ground state
to the first excited state versus the pumping the same ground state to the continuum.
The absorption fraction depends on the product Kt. If we assume that the initial plasma

conditions, the ion density, and absorption length, are identical for the two cases, then
the critical factor in determining the absorption fraction is the absorption cross section.
If we approximate the absorption cross section for radiative pumping of a bound-bound
transition by its value at the frequency of the transition, then







40
2
7Ke f
Bound -meij

where o is the value of the line profile at line center. The photoionization cross section

can be estimated by its value at threshold, also given in chapter 3. For an aluminum

plasma at a temperature of 500 eV, the values of the cross sections are 1.4 x 10-17 cm2,

and 4.7 x 10-20 cm2, respectively. Therefore, the absorption fraction for the line

pumping is over a factor of 100 larger than for the continuum pumping.

In order to quantitatively estimate the photopumping effect, we need the incident

energy Ei. The conversion efficiency in the Al K-shell lines has been measured to be

1.2 % of the laser energy. The continuum pumping can be done with a broad band

source. The M-band emission of Au, a well-studied element, has conversion

efficiencies of 4 %. These estimates are taken from the published literature.52

A simple calculation of the maximum energy emitted by the fluorescence for line

pumping of the 1 1S0 2 1P1 line by the K-shell lines gives approximately 0.7 J / sr for

a laser with 10 J of energy at a wavelength of 0.53 gim. This value is well above the

limit of detection for time-integrating crystal spectrometers of 1.0 x 10 -6 J / sr.

In summary, the experiment described in this thesis uses a line coincidence

scheme involving the resonance line of Al XII because it offered the highest detectable

fluorescence signal. There are four main reasons for choosing the resonance line in Al

XII, ls2 1S0 ls2p IP1, for the study of photopumping. As discussed in the

beginning of this chapter, He-like systems have a much simpler level structure than many

electron ions. The spectra are therefore simpler to analyze qualitatively and

quantitatively. Second, because excited electrons will primarily decay back to the

ground state, the photons resulting from resonance fluorescence will be in a well-

defined energy range. Third, the high oscillator strength enhances the photoabsorption

cross section. A large cross section increases the probability that a photon will be

absorbed and thus maximizes the observable fluorescence signal. Finally, the most









important reason is that the large ionization potential between the ground state of Al XII

and the ground state of Al XII provides a relatively large temperature regime in which

the plasma can exist in the ground state of the Al XII without significant emission of the

He-like lines. Thus, the result of photopumping should be the obvious enhanced

emission of photons at the frequency of the transition that was pumped.


Target Design--Front Plasma


Since, the plasmas are created by a laser beam irradiating a solid target, we now

discuss the target design. The goals of the design were to maximize the number of ions

available to photopump and to reduce the temperature and density gradients.

In order to reduce the gradients in the front plasma, an embedded microdot was

used. An embedded microdot is a localized "tracer" layer composed of the material of

interest, that is surrounded by a substrate. It is fabricated by depositing the tracer

element onto a substrate that has been masked with a metal plate having a hole that is the

desired shape and size of the microdot. After the tracer layer is deposited, a final

overcoat of a material such as plastic is deposited over the substrate and tracer dot.

Recent work by Burkhalter et al. have shown that a plasma created by irradiating an

embedded microdot is hydrodynamically confined.102 The advantages of microdots are

that the spectral lines for all states of ionization are emitted from the same known volume

of plasma.103 More recently, Young has completed a series of experiments that

investigates the behavior of the plasma density as a function of space after the microdots

are irradiated.104 Seeded targets also reduce opacity,105 but the low concentration

could make fluorescence hard to detect. For this experiment, an embedded microdot

was used.

Now we turn to the planarity of the plasma. Thermal conduction within the

plasma tends to keep the underdense plasma at a fairly uniform temperature in space.









The density scale length is determined by the hydrodynamics. When the physical

expansion of the plasma exceeds the lateral dimension, then the ablation surface

becomes bowed. Density and velocity gradients are determined by the divergence of the

flow. Therefore, to maintain a planar plasma, the scale length is the minimum of the

effective radius of curvature or the expansion distance, the speed of sound times the

pulse length. Max gives a semi-empirical formula for the limit on the focal spot size, R,

for planar geometry 106


1/2 1/2
Z T t
R > 150m [ ( ( ) ( ) ]



where T is the laser pulse length, Z is the atomic number, A is the atomic mass, and T is

the electron temperature. Even for focal spots that are twice the diameter of the

microdots, gradients have been detected.


Target Design--Pump Plasma


To obtain a simple estimate of the plasma temperature when maximum emission

will occur in the resonance line, one can determine when the He-like ionization stage

was maximized. The rate equation model, RATION predicts that at an Al plasma

temperature of 500 eV the mean number of bound electrons is 2. At higher

temperatures, a larger fraction of ions would be in the H-like stage, and conversely, at

lower temperatures, the ions would be in the Li-like and lower stages. The absolute

emitted flux also depends on the size of the He-emission region. This issue is

determined by the maximum laser energy available.

Now, we will discuss the geometrical constraints of the front and back plasma.

The pump and fluorescing plasmas must be irradiated in such a way as to keep the two









plasmas from mixing. In addition, the plasma being pumped must be exposed to the

pump as much as possible. Finally, the line of sight of the spectrometer must be able to

be shielded from the pump plasma. An important parameter here is the blow-off

velocity, v, since this determines the plasma size. It is estimated by the sound speed at

critical density. Again, using the equations from Max,106


1/2 1/2
v 3 x 10 [ (T) ] cm/sec



An Al plasma will expand in the direction of the incident laser at velocities

~ 3 x 107 cm/sec. Ablation rates have been measured by M. H. Key et al.107

After considering several geometries, a target coated on both sides was determined

to be the best compromise. This configuration keeps the plasmas distinct and separate.

This two-sided target will be called a full target. The ideal thickness of the target is

determined by conflicting restrictions. On one hand, the energy per unit area falls off as

r -2, where r is the distance between the pump and the plasma to be pumped, which

implies that the pump should be as close as possible to the plasma to be pumped. On the

other hand, shocks travelling though the medium can heat the plasma. For this

experiment, we used a substrate that was thicker than the shock transit speed multiplied

by the time delay between the pulses.

Possible target compositions include compacted powders such as MgO, P,S,
A1PO4,KC1, NaCI, CaO and CD2, or solid elements such as aluminum. The element

chosen for the target was aluminum for the following reasons. It has been well studied

in other plasma studies so this work could benefit from previous studies. The emission

lines for hydrogen-like and helium-like are in the range of 5 to 8 A, a convenient regime

for using crystal spectrometers. Target fabrication using Al is standard and relatively

easy. Composite powders, in particular, are difficult to fabricate.108










The substrate between the two Al layers was chosen to be a plastic whose

constituents were only carbon and hydrogen. The primary reason for this choice was

that the carbon and hydrogen spectroscopic lines do not interfere with those of He-like

aluminum. Another reason was that plastic could be used as an overcoat material for the

embedded microdot.



General Laser Parameters



To start the experimental section, an overview of laser-matter interactions is

presented. From laser studies done by Max89 and others,109 we can qualitatively

understand the deposition of the laser energy into a solid target.

The main mechanism for the absorption of laser energy at the critical density is

inverse bremsstrahlung. In this process, the electrons, oscillate with the laser electric

field. The interactions of the electrons with ions effectively damp the laser light wave

and the electromagnetic energy is thermalized. At densities greater than critical density,

the energy, which is now thermal energy, is propagated into the target by electron

thermal conduction.

When the laser beam irradiates a solid target, the surface of the material becomes

highly ionized. The transport of the laser energy into the material is then affected by the

free electrons so that the dispersion relation becomes


22 2
kLC CO
2 2(
OL OL

and
2 1/2
47te n e
S=(Me
p me









where wop is the plasma frequency in Hertz, ne is the electron density, me is the electron

mass, kL is the wavenumber, and OL is the laser frequency. From this relationship, we

can derive a critical density,



nc= 1.1 x 1021(11)2
XL



At this density, the laser light can no longer propagate (k = 0). Therefore, the energy

absorbed from the laser occurs at densities equal to or less than the critical density. The

critical electron density for 1.06 pm is 1.0 x 1021 cm-3. The laser light can also be

reflected or scattered so that typically, the percentage of laser energy absorbed is about

60% for 1.06 pm light.110

It is useful to estimate some of the plasma parameters to provide a guide for

choosing the experimental laser parameters that will be used. First of all, it is assumed

that nearly all the laser energy is deposited at, or near, the critical density. If we balance

the rate of thermal conduction away from the point of energy deposition by the rate of

laser absorption at the critical density, we find 89


2/3
2
T 1 I abs ( (c/se
1 keV f 104W/cm2 1 cm/sc



where f is a quantity determined by flux-limiting conditions, and labs is the absorbed

laser intensity. Interestingly, the temperature in the corona of the plasma only depends

on the intensity and wavelength of the laser. Figure 4-1 shows the temperature as a

function of intensity for the two laser wavelengths available, 1.06 and 0.53 pmn.









The laser conditions were chosen to enhance the x-ray conversion efficiency.

Backlight experiments have shown that a plasma created with frequency-doubled

wavelength has a higher x-ray conversion efficiency.52 First, the coupling of the laser

energy into the target is better. The critical density, where most of the laser energy is

deposited, is higher. Therefore the time necessary to ionize the Al is shorter and less of

the laser energy goes into the kinetic energy of the low density plasma. Second, the hot

electrons produced in laser-produced plasmas increases as IX2.54 Therefore, longer

wavelengths increase the probability that hot electrons could pre-heat the plasma and

cause emission. In this experiment, any non-radiative heating of the microdot plasma is

unacceptable because the emission would compete with the fluorescence signal. The

100 ps pulse length was used to achieve as high an irradiance as possible which is also a

factor in high conversion efficiency.





6000 -

T(eV) 5000 -
4000- X= 1.06 gm

3000 -

2000 -
X = 0.53 gtm
1000 -

0
2 4 68 2 4 68 2 468
11 12 13 14
101 101 101 101
Laser Intensity (W / cm 2)


Figure 4-1. Laser intensity vs electron temperature.









Overview of the Experiments


First a brief overview of the experiments will be given to make the logic behind

them apparent. In order to conclusively demonstrate photopumping, three separate

experiments were performed on the JANUS laser facility at LLNL. The first two

experiments were necessary to characterize each of the two plasmas. In this thesis, the

plasma that will be pumped is called the front plasma. The second plasma, which serves

as the radiative pump, will be called the pump plasma. The pump plasma was created

later in time than the front plasma.

The purpose of the first experiment was to characterize the pump plasma. The

temperature and density range of the plasma was bracketed. The primary measurement

was the absolute number of photons available to pump the front plasma. This

measurement was a critical test of the proposed system--if the photon flux was not

intense enough, then trying to detect fluorescence would be futile.

The purpose of the second experiment was to characterize the front plasma. The

ideal plasma condition was much more difficult to achieve because a plasma that is too

hot has strong self-emission that makes the fluorescence difficult to detect. On the other

hand, a plasma that is not hot enough, does not have a sufficient number of He-like ions

to pump. The technique used to determine this condition was to decrease the energy in

the laser until He-like emission was barely detectable and simultaneously monitoring the

Li-like emission to insure that the plasma was sufficiently ionized.

The final experiment was the photopumping experiment. One laser beam was

used to create the front plasma and a separate, independently-timed laser beam was used

to create the pump plasma. These laser beams irradiated opposite sides of a planar target.

The results from the first two experiments guided the laser conditions. Detecting the

fluorescence required timing of the laser beams with respect to each other and precise

alignment of the target and spectrometers.









Description of JANUS Laser Facility


Since laser physics is an entire field in itself, a relatively brief description of the

laser will be given here. From the experimentalist's point of view, the laser is a tool to

create the plasmas for experiments. In general, a staff of people operate the laser so that

it will deliver a pulse of energy and duration requested by the experimenter. This

description will only give a hint of the procedure required to deliver a laser pulse at the

desired parameters.

The JANUS laser at LLNL is a solid state pulsed laser which uses Nd:glass as

the lasing medium. The laser has two independent beams which can be used at a

wavelength of 1.06 p m, the wavelength of the lasing transition in Nd3+, or at 0.53 4pm,

the frequency-doubled wavelength. In this process, the beam is passed through a

potassium dihydrogen phosphate (KDP) crystal which converts the frequency of the
incoming light, defined as o10, into 20 light by harmonic generation. The dielectric

polarization induced in the medium by the electric field generated by the incoming laser
light oscillates with a frequency 20o in the form of a spatial wave. The polarization wave

generates a coherent electromagnetic wave at 20c. Under ideal conditions, the efficiency

of this nonlinear process can be as large as 80%. However, due to the quality of the

crystal, reflection losses and other limiting factors, the typical conversion efficiency at

JANUS is only 25%.

In its present configuration, a single beam can deliver up to 100 J in 1 ns, or

30 J in 100 ps. The frequency-doubled beam gives nominal energies of 30 J in 1 ns

and 10 J in 100 ps. The maximum repetition rate for full system shots is one shot

every forty-five minutes; it is limited by the time necessary for the amplifier optics to

cool. However, including time necessary for laser alignment and shot preparation, the

average number of shots per day is about five.









Figure 4-2 shows the layout of the laser components. The master-oscillator is a

Quantronix 416 that is an active mode-locked and Q switched laser. One of the

oscillator pulses is selected by the switchout for propagation and amplification through

the laser chain. There are three main types of components in the laser chain: amplifiers,

spatial filters, and isolators. The initial pulse has an energy of 50 p.J and a gaussian

profile in space and time. It is first double passed through a Quantel preamplifier which

increases the energy by a factor of 50. Subsequent amplification is achieved by using

two kinds of amplifiers in the JANUS system rods and disks. The lasing medium for

both are Nd doped glass. The alpha rod amplifiers have a gain of 20. The rods can be

pulsed every 10 minutes because they are immersed in cooled water. The beta rod

amplifiers have a gain of 7. The beta disk amplifiers consist of six 10.8 by 20.0 cm Nd

doped glass disks that are mounted at Brewster's angle in order to eliminate reflections.

These amplifiers have a gain of 3.5 and have refractive index matched coatings that

suppress parasitic modes. Although the disk cavity is flushed with cooled nitrogen gas,

the disks must be allowed to cool for forty-five minutes before they can be used again.

The spatial beam profile is shaped by an apodized aperture which is placed

between the first two alpha rod amplifiers. The aperture clips the wings of the spatial

profile to achieve maximum beam filling of the amplifying media. This component only

has a transmission of 10%, and therefore is the highest energy loss in the system. The

temporal profile is gaussian.

JANUS incorporates 5 spatial filters inserted in the laser chain at regular

intervals. They serve two purposes: First, they suppress beam break up and

filamentation. When the beam is focused through a pinhole, the high spatial

frequencies are eliminated and the beam is more uniform. Second, they expand the

beam to a larger diameter. The optics can only withstand approximately 5 GW/cm2, so

the beam must be expanded in diameter to avoid damaging them. Initially, the beam is

about 2 mm in diameter. At the entrance to the chamber, the diameter is 90 mm.









o I
S0-

ui









The isolators, Faraday rotators and Pockels cells, are components that eliminate

feedback and amplified spontaneous emission (ASE). They are usually found next to

the amplifiers since these components generate the ASE and also suffer the most damage

from retro-reflections. Faraday rotators and polarizers are used to eliminate retro-

reflections that could propagate backwards through the laser chain and cause damage.

The incoming beam passes through the first polarizer which linearly polarizes it, the

Faraday rotator rotates the polarization by 45 degrees, then it passes through the second

linear polarizer which is oriented 45 degrees with respect to the first one. When retro-

reflection comes back through the Faraday rotator it is again rotated 45 degrees, and is

now rotated a total of 90 degrees with respect to the first polarizer. The extinction of the

retro-reflected beam is high enough to alleviate amplification of the retro-reflected beam.

The two Pockels cells eliminate feedback and noise due to amplified fluorescence. The

pockels cell is gated "on" for 30 ns. Light can pass in either direction during this time.

However, when the cell is off, the extinction factor is on the order of 10-3.

The laser beam is directed out of the laser bay into the target chamber room. If a

frequency-doubled beam is desired, then the conversion crystal is placed at the entrance

to the target chamber. Figure 4-3 shows the general layout of the room and the beam

paths. Alignment of the laser optics and focussing are done by using continuous wave

(CW) YAG lasers that are propagated along the same optical path as the laser beam. The

same CW YAG laser is used for alignment of the beam onto the target. However, since

different wavelengths of light have different focal lengths through the lenses, a

frequency-doubled YAG laser light must be used for focussing the 2C beam on the

target.

The alignment for the beam onto the target is accomplished by using a

combination of mirrors and partially transmitting mirrors to reflect the beam, and lenses

to focus the beam. The beam path is shown in figure 4-3. Before doing shots, the laser

was aligned into the target chamber to a fixed fiducial which was placed at chamber









center. Unless there is reason to believe the optics have been moved or jarred, this

procedure is only done once per day.

The beam can be focused by viewing the target either in retro-reflection or in

transmission. If the target is reflective, focussing on the target in retro-reflection is

easiest. The laser light that is reflected off the target passes back through the focussing

lens at the entrance to the chamber. This reflected laser light is then refocussed into a

TV monitor. Since the same lens is used for the incoming laser light and the retro-

reflected light, the lens position for best focus of the laser is the same as for best focus

for the TV monitor.

To focus in transmission, two lenses must be used. A lens in front of the target

focuses the laser onto the target, while a lens in back collimates the transmitted laser

light into a TV monitor. The first step is to position the back lens with respect to the

target. Incoherent light from a lamp at the entrance of the chamber is used to project a

shadow of the target onto the TV monitor. To focus the shadow, either the target must

be moved to the point of focus for the back lens, or the lens must be moved so that it

focuses on a fixed target position. In general, choosing a fixed target position was

found to be the best since this choice does not require repositioning of the spectrographs

for every shot. Once the settings for target and back lens are known, the next step is to

focus the laser beam onto the target. The target is removed temporarily so that it does

not obscure the laser beam. Then the front lens is moved until the position of best focus

is found, which occurs when the focal spot of the laser appearing in the TV monitor is

minimized. Finally, the target is moved back to its original position.

The chamber pressure must be < 10 -3 torr to eliminate distortion and self-

focussing of the laser beam. However, when streak cameras are used, the target

chamber must be evacuated to pressures in the range of 10-5 torr. The target chamber is

evacuated by two pumps. An oil diffusion roughing pump begins pumping out the

chamber. When the vacuum reaches 10-3 torr, the roughing pump is assisted by a




















1-4
I.-=

II


04


.a
U
0*
S
Mft









turbomolecular pump to speed up the process. A liquid nitrogen trap was used also to

minimize the time necessary to pump down. Evacuating the chamber takes about fifteen

minutes if the chamber has been up to air for less than an half an hour.

Finally, JANUS provides a trigger, an electronic pulse that is used to time the

"shutters" of diagnostics. The trigger is formed by directing a small fraction of the laser

beam onto a photodiode. The diode generates a pulse that is propagated through a fiber

optic that has a shorter path length than the amplified laser beam. For JANUS, the

trigger pulse is created after the preamplifier and typically arrives approximately 30 ns

before the laser pulse arrives at the center of the target chamber.

The laser, the target focus, and the target itself, combine to make such a complex

system that absolutely identical experimental conditions are virtually impossible. The

plasma formed by the laser on any one shot is not exactly reproducible, so beam

diagnostics are extremely important. On each shot, the laser energy is measured by a

calorimeter. Additional diagnostics include an optical streak image for the temporal

shape and pulsewidth, a prepulse monitor, and an equivalent plane photograph of beam

quality.

When possible, alignment of spectrographs and shots for beam timing were

done with "rod" shots. These are shots in which only the alpha amplifiers in the laser
chain are used. Laser energies of up to 20 J in co can be achieved with a repetition rate

of one shot every five minutes. These so-called "rod" shots are more reliable than full

system shots and allowed increased repetition rate of the laser. For all the experiments,

f/4 lenses were used to focus the beam onto the target.



Experiment I


The primary purpose of this experiment was to measure the absolute number of

photons from the pump plasma. Any attempt at photopumping would be futile if the









photon flux was not intense enough to create a detectable signal. It was necessary to

experimentally verify that 1.) the laser energy was high enough to generate an intense

flux of photons through the target, and 2.) to prove that the field of view of the

spectrometer to be used to measure the fluorescence could be shelded by a knife-edged

block. In addition, the source was to be characterized by temperature and density as

well as in absolute photon number. This experiment was the most straightforward of

the three performed. The laser was focused on the target and the emission spectra was

recorded by time-integrating crystal spectrometers.

The targets used in this experiment were parylene-N(C8Hg)n sheets with Al

coatings of different thicknesses. These targets will be referred to as foils. Three types

of targets were used in order to obtain optimized pump emission:

1.) 3000A of Al on 20 pm of parylene-N;

2.) 4000A of Al on 20 pm of parylene-N;

3.) 3000A of Al on 30 pm of parylene-N.
Figure 4-4 (a) shows a simple drawing of the foil.

The targets were provided by EXITECH and LLNL. In general, the plastic

(CH) layer is created by coating glass microscope slides. Then the Al is vacuum

deposited. The procedure EXITECH used was to coat a 10pm CH layer on a

microscope slide, then the CH was released from the slide and was supported free-

standing and allowed to be coated on both sides, thus speeding the process since the CH

could be deposited on both sides. However, when the Al was deposited, the heat

involved in this process was enough to weaken the structure of the initial foil so that it

became warped. The foils were not planar; however, measurements by EXITECH

determined that the Al deposition was complete. The method LLNL used was to coat

the CH on the slide and then deposit the Al. These were flat. For all later experiments,

the CH substrate was supported entirely on the slide to avoid warping problems. With

the method of production decided, EXITECH supplied the targets.









The targets were mounted onto a brass target support that was specially designed

for the photopumping experiment. Figure 4-4 (a) shows a diagram of the brass mount

with and without a target. This support was a rectangular "washer" 8 mm x 2 mm x

15 mm. It had a 4 mm hole centered in the middle of the 8 mm side and 4 mm below

the top. A 1 mm deep channel that was as wide as the diameter of the hole was cut into

one of the 8 mm x 15 mm sides. The foil was mounted by stretching the foil across the

channel and gluing the ends above and below the channel. The Al side was mounted

against the brass over the hole. The hole in the brass support allowed the laser to

irradiate the Al side of the target and allowed the minispectrometer to view the plasma.

(The front plasma in the final experiment would be created on the opposite side.) The

foils were cut to a width of approximately two millimeters with a razor blade. After

experimenting a bit, the best way to cut the foils was to use several light strokes to score

the foil instead of a single cut which left a ragged edge. A fast setting epoxy

(Double/Bubble epoxy produced by Hardman, Inc.) which has a working time of 3 to 5

minutes, was used to glue the foil.

The laser irradiated the bare aluminum side of the target through the hole in the

brass target support. It was focused to a spot 250 gLm in diameter which was the

anticipated diameter of the embedded microdot. The laser was a 0.53 pgm wavelength

beam which had a 100 ps full-width-half-maximum (FWHM) pulse duration.

Focussing was done in retro-reflection.


Diagnostics


The diagnostics were two minispectrometers to record the absolute photon flux
from the back and front simultaneously. They will be referred to as MA and MB. Both

used PET crystals to diffract the x-rays in the range of 5 to 8 A. The spectra was

recorded on Kodak Direct Exposure Film (DEF). Appendix A gives a description of the











foil target n


Figure 4-4. Set-up for experiment I.
a) Diagram of the brass target support and the foil target
used in experiment I;
b) Experimental set-up I. The diagnostics are labelled as follows:
pinhole camera (PH), minispectrometer (MA) and (MB).


Laser beam
irradiating
target


(a) Brass support


100 ns
2c beam









geometry of the spectrographs and the dispersion relation for Bragg crystal. Figure

4-4 (b) shows the experimental set-up. Detector MA was placed on the side on which

the laser was incident. Detector MB was placed on the opposite side. It measured the

x-rays that were transmitted through the plastic substrate of the target--the flux that the

microdot would actually receive if it were in place. Pinhole cameras recorded the size of

the x-ray emitting region of the plasma.

The time-integrating crystal spectrometers are the only detectors currently used to

determine absolute flux with spectral resolution because the crystal's reflective

properties and the x-ray film can be calibrated with known x-ray sources. Although

other detectors, such as the streak cameras, are much more sensitive, they are difficult to

calibrate absolutely.



Procedure


Initially, the target was placed in the center of the chamber and the diagnostics

were aligned to the target by eye. Then set-up shots, using only rod amplifiers, were

done at best focus to produce a spectrum to check the alignment of the spectrographs.

These spectrographs view the entire source, however, the spectrographs do need to be

aligned directly facing the source otherwise the film exposure is not uniform.

The focal spot used in this experiment was 250 p.m in diameter. This diameter

was to match the diameter of the embedded microdot, the front plasma. Laser shots at

the maximum energy available at JANUS were needed to attain an irradiance of
1014 W/cm2. At 0.53ptm the maximum energy was < 12 J.

Since the absolute flux was the critical measurement, the film was developed by

the LLNL technical photography department where the environment is controlled and

chemicals are monitored. For the initial set-up shots, the film was developed in the

JANUS darkroom.











Experiment II


In this experiment, the laser energy needed for minimum emission of He-Al lines

and the time dependence of the emission was determined. This experiment explored the

optimal conditions for photopumping. The front plasma was created by irradiating an

embedded microdot. The data was taken by monitoring the front plasma with two x-ray

streak cameras. One viewed the helium-like Al emission, while the other viewed the

lithium-like Al emission. The Li-like ionization stage was monitored to check that the

plasma was hot enough for the He-Al ground state to be populated.

Three types of microdot targets were shot in this series. They had differing

thicknesses of overcoatings. A sample target is shown in figure 4-5 (a) mounted on the

brass support. Below is a list of the overcoatings on the microdots:

1.) No overcoating at all;

2.) 1000A of parylene-N;

3.) 2000A of parylene-N.
All the microdots were 270 nim in diameter.

The microdots with no overcoating were to be used as back-up targets in case the

overcoating caused focussing or low emission signal problems. They were used also

for initial alignment purposes. Microdots having different overcoating thicknesses were

chosen to allow latitude with the emission level and timing of emission. The

overcoating can be used to control the time of emission because the laser will take a

finite amount of time to bum through the overcoating.

A microdot is not easy to find in the limited field of view of the TV monitoring

system. In order to facilitate focussing, each microdot was mounted over the hole of

4 mm nut where the screw would usually enter. The microdots were centered in the

hole by eye. The nut was easily found in the laser focus, then the microdot was easily









centered at the position of the laser beam. Because of the use of the nuts, the targets

could be changed very easily by slipping the nuts in and out of the brass mount

described in the experiment I. In this manner, the targets could be mounted on the nuts

ahead of time. The amount of time needed to mount a new microdot target was kept to a

minimum. The nuts are not shown in the figure 4-5.

The laser conditions for the front plasma were chosen to be a 1.06 pm

wavelength for 1 ns. Fairly low energies of about 2 J were sufficient to create the He-

like Al plasma. Focussing was done in transmission.



Diagnostics


The diagnostics for this experiment were a crystal streak camera and a flat-field

Harada grating streak camera. For this experiment, both streak cameras were mounted

perpedicular to the laser axis. Figure 4-5 (b) shows the position of the spectrographs

with respect to the target. The crystal streak camera used a KAP crystal and covered a

wavelength region of 5 to 8 A. The resolving power was -200. This streak camera

monitored the emission from the hydrogen-like and helium-like ion stages of aluminum.

The Harada grating streak camera covered a range of 30 to 50 A. This spectrograph

primarily recorded the emission from the lithium-like aluminum ions as well as the

hydrogen-like and helium-like emission of carbon.



Procedure


Because of the sensitivity of the diagnostics to position, particularly the Harada

camera, the target was moved to a set position for the shots (nominally the center of the

chamber). Once the target was in place, the final focussing procedure took place.














Laser beam irradiating target


(a) Embedded mircrodot target
(a) Embedded mircrodot target


Figure 4-5.


Set-up for experiment II.
a) Schematic diagram of target being irradiated by a
laser beam that has a focal spot 2.2 times the
diameter of the microdot;
b) The experimental set-up.


1 ns
1 o beam






(b)


Harada grating
streak camera









The focal spot diameter was to be 600 pm, about -2.2 times the diameter of the

microdot. At best focus, the laser beam has a beam waist of about 30 pm in diameter.

The focal spot was expanded by moving the lens towards the target, the point of best

focus is then behind the target. A convenient way to check the diameter of the focal spot

was to compare its image to the image of the known diameter of the microdot as it

appeared on the TV monitor. This comparison confirmed that the laser focal spot was

600 10 p.m in diameter. While focussing the laser on the microdot, a filter attenuated

the master-oscillator pulse so that it did not ablate the overcoat of the microdot.

A solid aluminum target was irradiated in order to align the spectrographs.

These laser shots produced reference spectra for the identification of the lines.

Following the set-up shots, the method used in the experiment was to irradiate the

microdot and see it in emission first. Next, the focal spot was kept fixed, but the

energy in the laser was decreased until the emission could not be detected. Since the

laser energy required was < 2 J, "rod" shots could be used for this series of laser shots.



Experimental Series III


This third and final experiment combined the first two. The full target was a CH

foil with a bare Al dot on one side and an embedded microdot on the other. Instead of

coating the entire back side of the full target with aluminum as was done in experiment I,

an aluminum dot was deposited. This change was made in order to simplify the

alignment of the laser beams on the target. The most important addition was a Ta block

that shielded the crystal streak camera from the pump plasma. This block was critical to

the detection of the fluorescence.

For the final experiment, the plastic substrate in the target was changed to

polypropylene (C3H6)n. This substitution was made because of availability. The

properties of the polypropylene and parylene are roughly the same, except that the









molecular configuration is slightly different, which leads to a change in density.

Polypropylene has a mass density of 0.9 g/cm3 as opposed to 1.1 g/cm3 for

parylene-N. The ablation rate for polypropylene (- 5600 A/ns ) is slightly higher, so

the thickness was increased to 24 plm so that the substrate had the same bum-through

characteristics.

The different target combinations were: 1.) a target with a 550 pim diameter bare

dot of aluminum for the pump plasma, and 2.) a full target with an embedded microdot

on the front side and a dot on the other side. The full target consisted of a 24 pm thick

polypropylene substrate (CH) with an embedded microdot of 270 pm diameter on one

side and a 550 gpm diameter bare dot of aluminum on the other (see figure 4-6). The

embedded microdot, a 1500 A thick spot of Al overcoated with 1000 A of parylene-N,

was irradiated to create the front plasma. The other Al microdot, 3000 A thick, was

irradiated by the back beam and became the pump plasma. The centers of the embedded

microdot and bare dot were aligned.

The most efficient way to block the main diagnostic from the emission of the

pump plasma is to place a block as close as possible to the pump plasma. This method

minimizes the blocking of the front plasma emission. The special need to block the

pump from the diagnostics required an elaborate target mount. The relationship of the

target and shield are shown in figure 4-7. The Ta shield was 4 mm from the center of

the target. For a line of sight that was 90 degrees from the laser axis, the placement of

the block edge relative to the front edge of the full target had to be within 5 .m.

The mount consisted of a mechanical base that could accommodate two stalks. It

is shown in figure 4-7. The hole for one of the stalks was fixed, while the other was

actually a sleeve that could be manipulated by small jewelers screws. The tantalum

shield was mounted on a stalk and placed in the fixed hole. The brass target support had

a stainless steel stalk which then slipped into the adjustable sleeve. It was held in by a

dab of epoxy and could be "snapped" out by breaking the epoxy "seal" and twisting the













1500 A Al


1500 A Al
270 pm dia.





looo A CH


To Streak
Camera


/Ta shield


T4 4mm


Figure 4-6. Diagram of the full target used in the photopumping experiments.
The alignment of the target with the Ta shield and the focal spots
is not to scale.


3000 A Al
550 pim dia.

7


24 pm
CH





















Line of sight for alignment
of target and Ta block


-z








x


y y


Target mount


Figure 4-7. This mount enabled the target to be precisely aligned to the tantalum
shield. The coordinate axis is centered over the axis of rotation in the
x-y plane. The bold arrows indicate the position and direction of the
adjustment screws.


~,,~









brass support and stalk out of the sleeve. The important feature of the mount was that

the target could be precisely aligned to the tantalum block. By using the adjustable

screws, the height, pitch, and rotational position could be adjusted. These adjustments

gave the range of positions for the target relative to the block

The targets came on microscope slide size sheets. There were about 24 to a

sheet. These were carefully cut into strips about 1.5 2 mm wide with a very sharp

pair of scissors. The method of using a razor blade was abandoned for fear of

damaging the targets. The targets were mounted by putting a slight dab of epoxy on the

brass target support, and then carefully pressing the target onto it. Each brass support

had a stainless steel stalk that could be inserted into the target mount. Targets could be

carefully mounted in advance on the brass supports, and, during the experiment, were

popped into one of two mounts.

During the two-beam experiment, the beams irradiated opposite sides of a planar

target. A 1 ns beam of 1.06 pim wavelength at 1.0 x 1012 W/cm2 was used to prepare

the front plasma in the Al XII ion stage. A 0.53 pm wavelength laser beam with a

100 ps pulse length created the pump plasma. An irradiance of 1.0 x1014 W/cm2 was

used to generate x-rays in the pump plasma. The laser beams were focused and aligned

with f/4 lenses by viewing the target in retro-reflection. The peak of the laser beam that

created the radiative pump was delayed by 1.0 ns relative to the peak of the first laser

pulse. A 600 p.m focal spot was used to create the front plasma; a 270 gm focal spot

was used to create the pump plasma.


Diagnostics


The diagnostics included the full array of diagnostics used in the first two

experiments, but in a slightly different configuration. The spectroscopic diagnostics

used for the final experiment (see figure 4-9) covered the H-like through Li-like ion




























ins


1 ns
1o beam









(b)


100 ps
20 beam


I
Line of sight to
I align streak camera,
I target, and Ta block


Figure 4-8. Set-up for experiment III.
a) Close-up of the alignment of the target showing the line
of sight for the streak camera;
b) The diagnostics in the schematic diagram are labelled as
follows: pinhole camera (PH), minispectrometer (MB),
curved crystal spectrometer (CCS). The Harada
grating streak camera is not shown.









stages of Al. Time integrating spectrometers used Bragg crystals to cover a wavelength

range of 6 A to 8 A. These crystals were calibrated absolutely by measuring the crystal

rocking curve on a stationary x-ray anode source. Appendix B describes the method of

calibration. A time-resolving streak camera was used with a Harada flat-field variable

line spaced grating (2400 lines/mm) to measure the Li-like Al lines from the front

plasma. It viewed the plasma at an angle of 45' above the axis defined by the laser

beams (not shown in figure 4-8) and encompassed a spectral range of 32 A to 60 A.

The primary diagnostic, the crystal streak camera, overlapped the spectral coverage of

the time-integrating spectrometers by using a flat KAP crystal. Two pinhole cameras

were also used to monitor the consistency of the laser focal spots.

The main diagnostic addition was the use of a curved crystal spectrometer with a

space-resolving slit It was positioned perpendicular to the laser axis but did not have a

block. Instead it had a slit of 25 p.m which, when positioned correctly, should have

imaged both the front and rear plasmas onto different parts of the film. The advantage

of having both plasmas on the film would be that variations in film development would

not have affected the relative intensities. In addition to getting the absolute photon

number, the relative measure of the intensities would have been obtained.

Unfortunately, the front plasma emission was either not strong enough or the crystal

efficiency was too poor to record the front plasma emission. In fact, even the pump

plasma emission barely registered.

Finally, the streak speed of each of the streak cameras was timed. Since an

absolute timing fiducial was not available, the relative timing between the two signals

(self-emission and fluorescence) was important.

Procedure


The preparation for the two-beam shots was the following. The target was

aligned to the Ta shield. Then the target mount was placed in the chamber and aligned to









the crystal streak camera photocathode slit. Finally the laser beams were focused on

each of the microdots. Each one of these will now be discussed in turn.

The target to shield alignment procedure was critical to the success of the shots,

so it will described in detail. The foil was played and slightly stretched so that it was as

flat as possible. The first step was to align this clean edge with the Ta knife-edge. For

this procedure a special microscope was used. The target was clamped into a holder that

could only rotate. The stage of the microscope could be moved with micrometers in the

x-, y-, or z-direction. A conventional microscope allows the specimen to move in a

plane and the microscope lens to focus in the direction perpedicular to the plane. The

advantage of this special microscope was that the object remained stationary. This

microscope simplified the task of measuring the relative position of different parts in the

z-direction, even if the depth of field of focus in the x-direction changes.

To enable a clear discussion of the alignment, we will define the plane-of-

alignment as an imaginary plane passing through the center of the target and parallel to

the face of the target. The mount was adjusted until the knife-edge of the block is in this

plane-of-alignment First the axis of rotation was oriented parallel to the knife-edge of

the shield. The actual process of accomplishing the final alignment is a tedious iteration

between the rotation of the brass support and the rotation of the entire mount because the

axis of rotation of the brass support was not centered on the center of the microdot, and

the axis of rotation of the mount was about the fixed Ta shield. The error in this

alignment was 2 to 4 microns, due to the irregularity of the edge of the CH. The

microscope with a digital readout had a resolution of 1/1000 of a micron.

The alignment of this target mount inside the vacuum chamber was another

critical step. A Keuffel and Esser telescope was mounted on the target chamber opposite

the crystal streak camera. The line of sight was established so that the crosshairs of the

telescope were centered on the center of the streak camera photocathode slit. Then, the

target was first aligned rotationally by viewing the target surface and the knife-edge so









that the plane-of-alignment was parallel to the telescope line of sight, and vertical. The

z-axis shown in the target mount diagram (figure 4-7) was now parallel to the axis

defined by the direction of the laser beams. This positioning was done using an Oriel

rotational mount that could be operated by controls outside of the chamber. Then the

target was moved vertically so that it was aligned to the point of focus for the

instruments, the center of the chamber. The target was moved in the z-direction until it

was at the center crosshair. Final slight x-y adjustments were made at the end. In

essence, the y- and z-directions were determined by the telescope. There was no

absolute fix on the x-direction, however, it was not a critical dimension and was

observed experimentally not to drift more than 50 pm. Since the slit was 1 mm, the

error in alignment in the z-direction was judged to be 10 microns. The y-direction

error was not critical to within 0.25 mm.

The focussing of the laser beams was fairly complicated because it was

necessary to have the focal spots coincide on the same axis. The aluminum in each of

the microdots was reflective enough to focus in retro-reflection for both beams. The

optics for focussing would have been much more complicated if the embedded microdot

had to be focused in transmission because the focal length of the lens on the backlight

side would have to be moved for 1.06 gpm light and for 0.53pgm light. We checked the

focus of each beam just before the shot.

The philosophy for this set of shots was the following. We began by

confirming the results from the previous two experiments. This procedure allowed us to

check the laser conditions and characterizations of each of the two plasmas. Then, a

two-beam shot was made with both plasmas without using the block. The timing and

the line overlap of the He-like ISO IP1 transition of the back and front plasmas were

checked. Then one-beam shots to create the radiative pump blocked by the Ta shield

were done in order to prove that the fluorescence observed was not merely direct

emission from the radiative source.









Finally the two-beam shots on the full target were done. Variations of the laser

parameters included changing the focal spot size on the back and changing the relative

timing between the two laser pulses. Shots were also taken using a broad band source,

Sm (Z=62) for the pump plasma.


Problems


A danger of not focussing the beams back to back did exist. In focussing in

retro-reflection, initial focus was done with an incoherent light source that was focused

through the lens and reflected back. Obviously, the light cannot be in the middle of the

lens, otherwise it would obscure the light reflected back out. So, the focus was

dependent on the position of the incoherent source unless the lens was positioned at best

focus. The error, then, comes in the alignment of the lens that focuses the laser beam.

If the z-direction movement of the lens did not coincide with the laser axis, then moving

the lens to defocus the laser beam also would have affected the position of the beam on

the target. Once the lens was defocussed, the position of the beam on the target could

not be checked because the incoherent light source would give a false image, and the

retro-reflected light was found to be too weak to be detected by the TV monitor. The

observed error for the back beam that can be attributed to this drift was estimated from

the movement of the microdot on the TV screen using the incoherent light. At most, the

image of the dot moved by approximately 275 mrn. In most cases, the observed drift

was about 100 p.m. The drift for the front beam was not important because the beam

was defocussed to 600 gm--the drift might have introduced edge effects from the laser

beam, but the beam certainly did not miss the embedded microdot. The back beam was

not defocussed as much, so the drift would have been smaller, ~ 50 p.m. This problem

may have decreased the intensity of the fluorescence signal.














CHAPTER 5
ANALYSIS


Before analysis of the data begins, the raw data must be converted by detailed

data reduction procedures to yield meaningful units. First the data reduction for each

type of film will be discussed. Then, a discussion of the spectroscopic methods

follows. Finally, the results for each of the experiments will be discussed.



Data Reduction


All the data were recorded on two different kinds of film-- film sensitive to direct

x-rays and professional photographic film sensitive to visible light. First the film was

developed. Then it was digitized and computer software packages were used to process

the data. The image processing of x-ray film data involved removing the film fog,

converting film density to intensity, and removing background x-ray exposure.

Appendix A gives the details about the film.

For these experiments, a Perkin-Elmer PDS 1010GM microdensitometer was

used to digitize the data. The scanning process involves using an incandescent source,

imaged through an aperture onto the film. The light passing through the film is recorded

by a photomultiplier tube. The electrical signal from the tube is proportional to the

optical density of the emulsion. The result of this process is a numerical matrix of

numbers; each number represents the the film density for a pixel, which is the area of the

film illuminated during the scanning. The film density can be resolved in steps of

0.005, with a maximum of 5.11. A stepper motor controls the scanning to better than

1 gm.111









The digitized data were processed by the image processing software, XT,

provided by G. Glendinning of LLNL. XT can display a two-dimensional image of the

data on a Ramtek color monitor and the user can manipulate a cursor that can be moved

by means of a trackball. The software associates a cursor that is visible on the screen to

the data image. Typically, a calibration file data is folded in to convert the digitized data

from density to relative intensity. The resulting image is a record of the intensity

distribution as a function of space, or as a function of space and time. For direct x-ray

film, absolute calibration files were used. For streak camera data, a calibration file was

generated by scanning the calibration wedge on each piece of film.

By placing the cursor at a particular position, one can specify the area of data to

be studied and operations provided by the software are used to manipulate the data. One

of the operations of this program allows the user to generate profiles of the data. The

user specifies a slice of the data and the program plots an average of the intensity values

in the width of the slice versus the x or y axis of the image. These plots are called

"lineouts" and they correspond to intensity versus wavelength plots, intensity versus

time plots, or intensity versus space plots.

For direct x-ray film, the product of intensity and time is a reliable measure of

exposure.112 Therefore, for direct x-ray film, the film density is a linear function of the

number of photons striking the film. Absolute calibration of the film is obtained by

using known x-ray sources to generate calibration curves. Henke, et al. have done

extensive studies to model the film response and have measured known

exposures.113,114

Direct x-ray film has a film fog produced by any background x-rays such as

cosmic rays. The optical density of film is defined as logarithm to the base 10 of the

film opacity, where the film opacity equals the inverse of the transmission. Even film

that has not been exposed will be slightly opaque when developed. The calibration

curves are valid when an optical density of zero corresponds to unexposed film.









Therefore, before the film density is converted to relative intensity, this inherent density

is subtracted so that conversion using the calibration curve is not skewed.

In this experiment, DEF and Industrex M direct x-ray film was used. Both have

a useable density range of about 0.2 to 2 photons/pm2. Below a value of 0.2, the film

is not sensitive, while above a density of two, the film saturates and is no longer linear

with exposure. The development of the films was performed according to the times and

temperatures listed by Henke so that his calibration curves could be used.

Although filters were placed in between the crystal and film, the film became

fogged due to crystal fluorescence and stray radiation. The average of the background

fog was found by sampling the pixel intensities in the area of film near the data of

interest. Then, the average background intensity was subtracted from the data.

The film used with the streak cameras detects the light from the P-20 phosphor

on the back of the microchannel plate. Details of the streak camera are given in appendix

A. Some commercially available films are Kodak TMAX 400, RXP, and Tri-X. These

films have a much larger dynamic range than direct x-ray film and their densities are

linear with the log of the exposure.

In this experiment RXP and TMAX 400 film were used. A portion of each piece

of film was exposed to light from a Xenon flash lamp that had been attenuated by a

continuous calibration wedge placed on the film. The exposure time was chosen to be

one millisecond because the phosphor on the streak camera glows for about one

millisecond. The calibration wedge for a P-20 phosphor has a gradation of 0.6 optical

densities per cm. After the film was developed, this strip was densitometered to provide

a known density vs log(Exposure) curve for each particular piece of film. The streak

camera data were then corrected for background. Only relative intensities can be derived

from this data.









General Discussion of Spectral Analysis


The data are now in a form that can be analyzed. A spectrum, i.e. the intensity

as a function of wavelength, has been extracted from the raw data. The observables

contained in the spectrum are the intensities and line widths. The quantities that can be

deduced from the data depend on the experimental conditions. For instance, the plasma

can be characterized by its electron temperature and/or electron density by line ratios.

Further, individual line transitions can be analyzed for absolute flux and time-

dependence. Ionization balance can be inferred from the temperature and/or the ground

state populations measured by absorption lines. This section will explain the methods of

spectroscopic analysis used in this thesis.

There are three types of transitions: 1.) bound-bound, 2.) bound-free, and

3.) free-free. A comprehensive discussion of the intensities is given in Stratton.115

The intensities are given as follows.



Bound-bound transitions. These intensities involve the integration over the plasma
length, f. For the optically thin lines,


I = 1- fniAi,jhv d
47c
where A is the Einstein coefficient, ni is the ion density, and hv is the energy of the

transition.

For optically thick lines, the effects of radiation trapping can be accommodated by

reducing the spontaneous emission coefficient by an "escape factor." The effective

spontaneous decay rate is A*ij = Pe Aij. where Pe is the escape factor. It can be

defined in one of two ways. One way is to consider the intensity of the line as having a









negative contribution due to the stimulated absorption term. Then the escape probability

is
nlgu c I"
Pe=I nug 3Ivv dv
2hv

where the Einstein Bji coefficient has be reexpressed in terms of the Aji coefficient, u

stands for the upper level, 1 stands for the lower level, and (O, is the line profile.

An equivalent way to think of the photon escape factor is to define it as the

integration of the transmission of a photon through a medium over angle and space. In

this formulation the escape factor represents the mean probability that a photon emitted

anywhere in the plasma volume travels directly to the plasma surface and escapes in any

direction. This approach will be discussed in more detail in the context of radiative

transfer theory in the next chapter. The paper by Irons gives a complete discussion of

this process and cites a comprehensive set of references.116



Free-bound transitions. The intensities involving continuum states must be

summed over the different ion species ni and the levels, p, into which the electron can be

captured.

I, dv = ne ni hv dCfdv
47J i p

The energy of the photon and recombining electron are related by hv = 0.5mv2+X,

where X is the ionization potential, a is the recombination coefficient, and v is the

velocity of the electron. For hv > X, the spectrum is continuous. For hv < X, however,

there is no bound-free spectrum for this ion. This recombination can shift to lower

energies if the electron density is high enough to cause ionization potential depression.

Using the cross section given in chapter 2 for recombination into the nth shell of

H-like ions of charge i, the emission per unit frequency per unit time per volume is








( 3/2 / 2
dE X(h) X ex(in)p hv
d = Cneni h) g exp X(in) -T
dv k \(h)


where C = 1.7 x 1040 ergs cm3, is the number of places in the nh shell that can be

occupied by the captured electron, X(h) is the hydrogenic ionization energy, and X(i,n)

is the ionization energy from the initial state i to the final state n, and g is the bound-free

Gaunt factor.


Free-free transitions. For a plasma length, C, these intensities are given by

Ivdv= I ne niyhv dvdl
4ltl i

where y is the free-free transition probability. The sum over i accounts for different

ionization species, and ne is the electron density.

If the integration is over a Maxwellian electron velocity distribution using

Kramer's formulation, the emission is
1/2
dE X(h)/ 2 hv)
-= C ni'T Z gex -
dv kT kT
where C = 1.7 x 10-40 ergs cm3, X(h) is the hydrogen ionization potential, and Z is the

effective nuclear charge. The gaunt factor, g, has been tabulated by Karzas and Latter,
and is the quantum mechanical correction to the classical result.117 g = 1 for hv = kT,

g < 1 for hv > kT, and g > 1 for hv < kT. For long wavelengths, (i.e. hv<
spectral shape is independent of T; but for short wavelengths, the spectrum can be

useful as a temperature diagnostic

A general rule for the continuum emission is that for
kT > K XhZ2
free-free radiation exceeds the bound-free radiation for an atomic number Z.115 Here Xh

is the ionization potential of hydrogen. The ions become totally stripped.











Line Identification


To a first approximation, the structure of the spectra is determined by the energy

levels and the transition oscillator strengths. The energy level structure for K-shell ions

has already been discussed. Line identification is done by matching the experimental

dispersion to the dispersion that can be calculated for the spectrograph for wavelengths

given in the literature.


Line Ratios


Line ratios are frequently used to measure the temperature and/or density of a

plasma. A good temperature diagnostic should be constant for changes in density. A

good density diagnostic is constant in a given temperature range. Whether a line ratio is

a good temperature or density diagnostic depends on how the higher lying level is

populated (source of the population) and the lower state type (excited or ground).

In low density plasmas, the predominant population source is the ground state.

In general, collisional excitation is responsible for creating excited states, and

spontaneous decay depopulates those states. The line ratio, then, for transitions from

the same ion stage, are essentially density independent because the line ratio will reflect

the ratio of the collisional excitation rates. The electron density cancels out.

As the density increases to the point where levels become collisionally mixed,

the level with the highest spontaneous decay rate, Aij is the main depopulation

mechanism. For example the intercombination line has a low Aij value and, therefore,

at densities in which the collisional rate to the 1P1 level approximately equals the

radiative decay rate, the 3P1 level is depopulated by collisions more than radiative decay,

thus the intensity of the intercombination line decreases. The intercombination line is so







79

named because it is a transition which is spin forbidden, i.e. AS = 1. It appears in the

spectra of ionized species because pure L-S coupling is no longer an adequate

representation of the system.

One of the standard intensity ratios is found by combining the Boltzmann

population distribution and line intensity in LTE.

-1

kT=IEa-E Ib baa
Ia agb ]



where the subscripts a and b stand for different upper levels, X is the wavelength of the

transition, (Ea Eb) is the energy of the transition, f is the oscillator strength, and g is

the statistical weight.

For coronal equilibrium the temperature may be determined by

[ ga -1

kT= (Ea- E4 bb) (Ebb) gf

Ia(E gbfb



In the analysis performed in this thesis, the suite of computer codes RATION,

RATSHOW, and SPECTRA were used. These were written primarily by R. W. Lee to

serve as a tool in the study of plasmas.80 A complete plasma model must be quite

complex since it must incorporate the detailed atomic models of all the constituent ions

as well as the plasma effects. As conceived, these codes are meant to facilitate the study

of plasmas by using a complete but simplified atomic physics model. Hydrodynamic

effects and detailed radiative transport are not included. Hence the results of theses

codes are most applicable to spectra from plasmas that have small temperature and









density gradients, or are resolved in time or space. Even if the plasma does not satisfy

the above criteria, the code can bracket of the temperature and density of the plasma.

The first code, RATION, calculates the populations of the H-like, He-like, and

Li-like ion stages. The details of the atomic structure can be found in the paper

describing the codes. In general, the electron configurations of the ground state and first

excited state are represented in detail. For instance, the He-like ground state and the

four excited states of the form 1s21 are explicitly included. In addition, the model

includes the important doubly excited levels that are involved in the formation of

satellites to the resonance transitions of He-like and H-like ions. The preceding

ionization stages, Be-like to neutral, are represented only by their ground states. All the

rates mentioned in the chapter 3 are included.

The two other codes use the population file output by RATION. RATSHOW

calculates line ratios as a function of temperature and/or density. SPECTRA uses the

populations and theoretical or semi-empirical energies and oscillator strengths to create a

synthetic spectra for given a temperature and density. SPECTRA includes the

calculations of detailed Stark line shapes if desired.

The codes are used interactively in several ways. For a well-characterized

plasma, i.e. one in which independent measures of the temperature and density exist, the

code can be used to resolve discrepancies between differing theoretical rates that affect a

particular spectroscopic diagnostic such as a line ratio. The more common way to use

the codes is to diagnose the temperature and/or density of plasmas. In the following

analysis, the codes were used to determine temperatures and densities.

Figure 5-1 shows the spectrum of aluminum in the 20 to 50 A region for two

different temperatures. The dotted line is the spectrum at 200 eV. It is dominated by Li-

like emission. The character of the spectrum drastically changes as the temperature

increases because the Balmer lines of H-like aluminum become dominant.









Line Shapes


Line shapes are affected by the plasma environment and the resolution of the

spectrometer. They can be used to determine ion density or temperature. At high

densities, Stark broadening causes the energy levels which are essentially degenerate to

become shifted in response to the strong plasma fields. For hydrogenic species, the

electron density can be schematically represented by


3/2
ne= C(ne,T) AX

where C is a slowly varying function of density and temperature. This measurement is

not dependent directly on the atomic cross sections, and therefore, is a good complement

to measurements of the density by line ratios. In this thesis, the line shape codes of Lee

are used to estimate electron density.118 However, Stark broadening was not a

significant factor because the densities were not high enough.

At lower densities, the line width is usually dominated by Doppler broadening,

in which case it provides a measure of the ion temperature, Ti.


1/2
2 k Ti

\Mc2

where M is the mass of the ions, X is the wavelength of the line, c is the speed of light,

and k is the Boltzmann constant.

Figure 5-2 shows the 200 eV spectrum including Stark broadening which is

convolved with an instrument FWHM width of 3 eV. This synthetic spectrum shows

how drastically the line spectrum can be affected by instrument resolution as well as line

broadening mechanisms.




























































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Absolute Flux


This measurement depends on the collection efficiency of the detector. In

principle, the equation for line intensities can be used to calculate the number density of

the upper level. However, the line shape is not always well known, and the plasma

length is not usually well characterized. Only optically thin lines can be used for

calculating number densities by this method. Measurements of the absolute intensity of

the continuum can be used to calculate density; although in practice, it is very hard to

determine the absolute efficiencies of detectors.

In this thesis, the absolute flux was used to calculate the number of photons per

steradian emitted by the plasma source. It is a measurement of the conversion efficiency

from laser energy to x-rays. No attempt is made to determine the plasma conditions

from these numbers. The reduction of the recorded flux to the source flux is dependent

on the detector geometry and the crystal efficiency and therefore, will be discussed

below.



Experimental Results


Experiment I


Time integrated line ratio measurements in the preliminary experiment for the

pump plasma determined the temperature range, density range, and the absolute photon

number of the pump. An example of the spectrum is shown in figure 5-3 in which the

lines have been identified. The analysis of experiment I consisted of the following:

1.)line intensity ratios of the He-like dielectronic satellites to the Li-like dielectronic
satellites, and [Al XIII 12S1/2 22P1/2/ Al XII 11S0 21P1] for temperature, 2.) the

line intensity ratios of the [Al XII 1 1So 23P1 / Al XII 1 1S 21P1] and the width of







87

the He 11S0 51P1 line due to Stark broadening for density, and 3.) the absolute flux

calculation. To determine the source size, the width of the 11SO 23p1 line on the

minispectrometer were used.


Line ratios from time-integrated data



Figure 5-4 shows all the temperature sensitive line intensity ratios. Since bare

aluminum was irradiated, large temperature and density gradients would be expected in

the plasma. The line ratios for the [12Sl/2 22P3/2 / 11S 21P1] and the [He-like

satellites / Li-like satellites] decrease slightly with increasing energy. Within the error of

these measurements, this variation is not significant.

The ratio involving only the satellites is probably the most reliable diagnostic

since these lines are optically thin. The value for the ratio is 0.4 + 0.2. From the

RATION graphs given in figure 5-5, we find that this ratio implies a temperature range

of 400 to 600 eV.

The ratio of the Al XIII 12S i2 22P3/2 to the Al XII 1 So 21P1 is a

temperature diagnostic because the lines are from different ionization stages.

Unfortunately, these lines are vulnerable to opacity effects. Therefore, line ratios

involving these lines are difficult to interpret. The value of this ratio is 0.5 0.2 which

indicates a temperature of 200 to 600 eV for densities 1.0 x 1022 or less.

The two ratios involving the satellites to the resonance lines do not give as

conclusive a measure of temperature. As discussed in the introduction, satellite lines are

formed by discrete states above the first ionization limit. The intensity ratio of the

satellite line to its parent resonance line is generally a good temperature diagnostic

because the ratio can be expressed as a function of temperature multiplied by a term

depending on the decay rate (an atomic parameter) of the satellite line which is generally









a function of Z. The review paper by Dubau and Volonte,6 shows that the temperature

dependence of the ratio can be expressed by


Sexp((Eo-Es )/kT)
F(T) T


where E0 is the energy of the parent line and Es is the energy of the satellite line. The

exponential factor is usually a slowly varying function of T because in this case, the

energy (Eo Es ) << kT. Therefore, the ratio is proportional to the inverse of T.

The value of the [Li-like satellites / 11SO 21P1] ratio is approximately

0.27 + 0.04. This regime on the RATION plots shown in figure 5-6 tend to imply an

electron temperature of 200 to 400 eV for the same density range. However, the

observed intensity of the resonance line is depressed by radiative trapping. Hence, tt is

conceivable that the ratio could be too high by a factor of 4. The range of temperatures

indicated by a ratio that is 0.25 smaller, is again 500 to 600 eV which agrees with the
previous ratios. The ratio of the [He-like satellites / 12S 1 22P3/2] is 0.2 + 0.04.

Again radiative trapping probably inflates this ratio. In fact, if the same multiplicative

factor is used for both of these ratios, the temperature range indicated by both track each

other. Although the ratios are not conclusive, they are in the approximate range

expected.

Density was deduced from the ratio of the Li-like satellites to the Al XII
11SO 23p1 which is called the intercombination line, and from the intercombination

line to the resonance line. The figure 5-7 gives the density sensitive ratios as a function
of laser energy. The [Li-like satellites / 11S0 23p1 ] ratio has a value of 1.4 + 0.4 .

The plots in figure 5-8 show that this ratio implies the density should be in a range of

1021 to 1022 cm -3.

The [11S0 23P1 / 11S0 21P1] ratio is a better diagnostic because both of the

lines are emitted from the same region of the plasma. The intercombination line is









density sensitive because the population of this level is collisionally mixed with that of

the 1P1 resonance level which can decay much more quickly. The value of the ratio is

from 0.05 to 0.2. However, the resonance line persists about three times as long as the

intercombination line. Hence, it is reasonable to assume that the ratio could be wrong

by a factor of 3. From figure 5-8 we find that the upper limit of the ratio gives a density

is 5.0 x 1019. The lower limit implies densities near 1021 cm -3 which implies that the

lines are emitted over a density equal or less than the critical density at which the laser

energy is deposited.

A consistent determination of the temperature and density must take into account

measurements from all the ratios. Since gradients affect the individual line intensities

differently, the diagnostics that are presented bracket the plasma parameter regime

possible in the experiment. With this in mind, these ratios indicate that the plasma has a

temperature in the range of 400 to 600 eV and an electron density in the range of

5 x 1019 to 5x 1021 cm-3.



Line widths



To determine the line broadening resulting from the Stark broadening

mechanism, an optically thin line was first used to determine the line width contributions

due to the source size and instrument. Next, the line width at full-width-half-maximum

was taken of the highest order resolvable line. The spectra were considered

unresolvable at principal quantum number n = 6, so the 11SO 5 1P1 transition was

used. This measurement also assumes that the emission region of the optically thin

satellite is about the same as the region emitting the n=5 line. Although both lines are

probably emitted in the dense, hot region in the center, there was no independent method

used to confirm this fact. The electron density determined by this method was

- 5.0 x 1021 cm-3




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AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


RESONANCE FLUORESCENCE IN A LASER-PRODUCED AL XII PLASMA
By
CHRISTINA ALLYSSA BACK
A DISSERATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1989

Copyright 1989
by
Christina Allyssa Back

ACKNOWLEDGMENTS
Charles F. Hooper, of course, made this dissertation work possible. He
oversaw my progress and didn't laugh when I discovered the obvious. Despite the
obvious problem of being removed on the opposite coast, he made a deliberate effort to
stay in touch.
I thank Richard Lee for guiding me in the proper direction. In particular, he
was instrumental in the development of the set of experiments for my dissertation. He
also kept me from going too far afield in the analysis.
The laser facility staff of James Swain and William Cowens made heroic efforts
to keep the laser operating. Though over-taxed, they sacrificed their personal time to
stay late a few nights to make up for the temperamental laser. Some of the best data was
taken during those evenings.
I would also like to thank C. Chenais-Popovics, who lent her expertise to the
excecution of the final photopumping experiment, J.D. Kilkenny, who also helped in
formulating the experiments, and J. I. Castor for the many discussions I had with him
about radiative transfer. Many others were kind enough to share their knowledge with
me and I have appreciated their wisdom.
Finally, I would like to thank my parents, Sangho, Flora, and Alice, my brother,
Tony, and Doug Shearer for being so supportive.
iii

TABLE OF CONTENTS
paee
ACKNOWLEDGEMENTS i in
LIST OF FIGURES vii
ABSTRACT x
CHAPTERS
1 INTRODUCTION 1
2 REVIEW OF LITERATURE 9
Identification of Highly Ionized Species 9
Emission Spectroscopy 10
Point Projection Spectroscopy 13
Absorption Spectroscopy 14
Outstanding Problems 15
3 PLASMA MODELS 18
Thermodynamic Equilibrium (TE) 19
Local Thermodynamic Equilibrium (LTE) 21
Coronal Model 22
Collisional Radiative Models (Kinetics or Rate Models) 25
Rates and Atomic Cross Sections 27
Radiative Rates (bound-bound) E(Z,i) + hv <—> E(Z,j) 28
Radiative Rates (bound-free) E(Z,i) + hv <—> E(Z+l,j) + e- 29
Collisional Rates (bound-bound) E(Z,i) + e- <—> E(Z,j) + e- 31
Collisional Rates (bound-free)
—(Z,i) + e- <—> bZ,(Z + l,j) + e- + e- 32
Radiative Rates Involving Metastable States (bound-free) 33
4 FLUORESCENCE EXPERIMENT 34
Desi gn of FI uorescence Experiment 34
Target Design—Front Plasma 41
Target Design—Pump Plasma 42
General Laser Parameters 44
Overview of the Experiments 47
Description of JANUS Laser Facility 48
Experiment 1 54
Diagnostics 56
Procedure 58
Experiment II 59
Diagnostics 60
Procedure 60
tv

Experimental Series III 62
Diagnostics 66
Procedure 68
Problems 71
5 ANALYSIS 72
Data Reduction 72
General Discussion of Spectral Analysis 75
Line Identification 78
Line Ratios 78
Line Shapes 81
Absolute Flux 86
Experimental Results 86
Experiment 1 86
Line ratios from time-integrated data 87
Line widths 89
Absolute flux 99
Target parameters 102
Source size 102
Experiment II 103
Identification of control shots 103
Line ratios of time-resolved data 108
Determination of laser energy needed to create the front
plasma 109
Time behavior 119
Target overcoat 120
Experiment III 120
Confirmation of experiment I 121
Confirmation of experiment II 126
Time dependence of the pump plasma 127
Source size 132
The photopumping shots-preliminary tests 132
Identification of photopumping 133
Ratio £, 146
Absolute flux of fluorescence 147
Potential problems 150
Variations 151
6 RADIATIVE TRANSFER THEORY 152
Definitions 152
Macroscopic Coefficients 155
Transfer Equation 156
Source Function 158
The Formal Solution 159
Analytic Approximations 159
Numerical Solutions 162
Non-LTE Line Transfer 163
Analytic Model of the Experiment 166
7 COMPUTER SIMULATION 170
Atomic Model 170
Atomic Physics Codes 170
Aluminum Model 171
Radiative Transfer Simulation 173
v

ALTA IR Computer Code 173
General considerations 174
Constant density case 176
Linear temperature gradient and logarithmically decreasing
density gradient 179
Summary of results 179
Limitations 183
8 CONCLUSIONS 184
APPENDICES
A DIAGNOSTICS 187
Dispersion Elements 187
Other Elements 192
B CRYSTAL CALIBRATION 195
REFERENCES 199
BIBLIOGRAPHICAL SKETCH 207
vi

LIST OF FIGURES
Figure page
1 -1 The temperature and density regime of some plasma sources 2
1-2 A comparison between a line spectrum for neutral helium and one of
helium-like aluminum 3
1 -3 Schematic energy level diagram for ionized aluminum. The completely
stripped ion has zero energy. The energy level of the first ionization
potential for each ion is represented by the hatched bar 4
1-4 Two-level atom diagram illustrating photopumping 6
3-1 Ionization balances of Saha and Coronal models for aluminium at an
electron density of 1020cm-3 24
4-1 Laser intensity vs electron temperature 46
4-2 JANUS laserbay 50
4-3 JANUS target room 53
4-4 Experimental set-up 1 57
4-5 Experimental set-up II 61
4-6 Diagram of the full target used in the photopumping experiments. The
alignment of the target with the Ta shield and the focal spots is not to
scale 64
4-8 Target and tantalum shield mount 65
4-9 Set-up for experiment III. The diagnostics are labelled as follows 67
5-1 Synthetic spectra at 200 and 1000 eV 82
5-2 A spectrum including Stark broadening convolved with a instrument
width of 3 eV 84
5-3 Sample spectra recorded on the minispectrometer 90
5-4 Time-integrated temperature intensity ratios 91
vii

5-5 RATION plots for temperature ratios 93
5-6 RATION plots for temperature ratios 95
5-7 Time-integrated intensity ratios for density 96
5-8 RATION plots for density ratios 98
5-9 Absolute photon flux vs. laser energy 101
5-10 Line identification for a time-resolved spectrum of He-A1 104
5-11 Line identification for a time-resolved spectrum of Li-Al 105
5-12 Line identification for a time-resolved spectrum of K-shell carbon
emission 106
5-13 Line identification for a time-resolved spectra from 107
5-14 Line intensity ratios taken from the 20-50Á time-resolved spectra 110
5-15 RATION plots 112
5-16 RATION plots 114
5-17 He-like A1 spectra 5-8Á for different laser energies. A distinct increase in
emission is visible for laser energies greater that 2.5 J. The target was an
embedded A1 microdot 1500 Á thick that was overcoated with 1000Á of
parylene-N. The energy in the laser is given. Please see figure 5-10 for
line identification 116
5-18 The corresponding spectra in the 20-50 Á region from the Harada grating
streak camera spectra for the same shots shown in figure 5-17. Please see
figure 5-13 for line identification 118
5-19 Sample curved crystal spectrometer (CCS) spectra 122
5-20 Time-integrated CCS intensity ratios for temperature 123
5-21 Time-integrated CCS intensity ratios for density 124
5-22 Absolute photon flux vs. laser energy from the CCS and the fit to the
data. The data from experiment I is shown for comparison 126
5-23 Li-like A1 intensity vs. wavelength for different times. These spectra
show that the ionization balance is not significantly changing for the time
period over which the photopumping occurs. All times are relative to plot
(d) 128
5-24 Intensity ratios from the 20-50Á wavelength range 130
5-25 Intensity vs. time for the pump plasma. The duration of the He-like A1
resonance line is ~250 ps full-width-half-maximum 131
viii

5-26 Data of front and pump plasma with no shielding of the pump plasma 137
5-27 Raw data of the three classes of photopumping two-beam shots. The
photographs on the left hand side are from the crystal streak camera and
the photographs on the right hand side are from die Harada grating streak
camera. The laser energy and focal spot is given for the front and pump
plasmas. The pairs of data were recorded simultaneously 139
5-28 Intensity vs wavelength plots for the raw data in figure 5-27. The crystal
streak camera plots are taken at the peak of the intensities of the self¬
emission and fluorescence. The Harada streak camera plots are ~ 0.4 ns
apart 141
5-29 Example of the intensity plots used to determine for background emission 143
5-30 He-like A1 resonance line vs time for photopumping shots. Table 5-1
gives the laser focal spots 145
7-1 A comparison of the ionization balance with and without detailed radiative
transfer 175
7-2 The constant density case. The x-axis corresponds to the distance, z,
measured in units of cm 178
7-3 The temperature and density gradients versus z (cm) before the
photopumping for the second simulation 180
7-4 The ionization balance as a function of z (cm) for the case with
temperature and density gradients shown in figure 7-3. The curves a
through e correspond to the C-like through fully stripped ions 181
7-5 The source function versus z (cm) for the second simulation 182
A-l Geometry of the minispectrometer. Three rays corresponding to x-rays of
three different wavelengths are shown 189
A-2 Diagram of the x-ray streak camera. The dispersion direction is
perpendicular to the plane of the page. The sweep of the electrons in time
is shown 191
B -1 Schematic diagram of crystal calibration set-up. The center of rotation for
the crystal and proportional counter was the center of the crystal 196
IX

Abstract of Dissertation Presented
to the Graduate School of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
RESONANCE FLUORESCENCE IN A LASER-PRODUCED AL XII PLASMA
By
Christina Allyssa Back
December 1989
Chairman: Charles F. Hooper, Jr.
Major Department: Physics
A new direction for laser-plasma spectroscopy is explored-the study of
fluorescence due to controlled radiative pumping. The active probing of the plasma can
yield new information that can test radiative transfer theory as well as atomic theory.
This study is relevant to x-ray lasing schemes which depend on photopumping to create
population inversions. This thesis begins to investigate the process of resonance
fluorescence itself.
A detailed analysis of the requirements of the photopumping system is discussed
in order to optimize the system chosen. A line coincidence scheme was used to observe
the fluorescence of the resonance line of Al XII. The resonance transition involves the
ground state, 1 1Si, and the first dipole allowed excited state, 2lP\. In these
experiments, two distinct and independent plasmas were created. One plasma serves as
the plasma to be photopumped. The second plasma serves as the bright x-ray source to
photopump the first plasma. Both were aluminum plasmas. Hence, in this system, the
fluorescence of the ^o^Pi transition was due to photopumping by photons of the same
Al XII iSo-1?! transition from the second plasma.
x

A description of the experiments follows. Three experiments were necessary to
demonstrate the photopumping. The first experiment characterized the radiative pump.
The second experiment characterized the plasma to be pumped. The third experiment
was the x-ray fluorescence experiment involving both plasmas. Two independent laser
beams at 0.53 and 1.06 (im were used to create the plasmas.
The first direct observation of fluorescence in laser-produced plasmas was
obtained. An x-ray streak camera provided time-resolved data in which the fluorescence
signal was observed unambiguously. The fluorescence signal was quantified also. The
time-integrated and time-resolved data were analyzed by using spectroscopic methods.
In particular, line ratios generated by a collisional-radiative kinetics model and
measurements of absolute flux are discussed.
Finally, radiative transfer theory is reviewed and a simple analytic model is
proposed to give an order of magnitude estimate of the emission due to photopumping
relative to the self-emission of the plasma.
xi

CHAPTER 1
INTRODUCTION
A plasma is a hot gaseous state of matter whose constituent atoms are ionized.
The plasma, as a whole, is electrically neutral, but is composed, at least in part, of
charged particles, ions, and electrons that are no longer bound. As a result, internal
electrostatic fields, called microfields, are strong enough to perturb the ionic energy level
structure. The interactions between charged particles can create plasma effects such as
collective motion or continuum lowering. For these reasons, plasmas behave differently
than hot gases or collections of neutral particles.
Plasma sources include vacuum sparks, stars, z-pinch plasma, theta-pinch
plasmas, shock tubes, tokamaks, and laser-produced plasmas. Figure 1-1 shows the
temperature and density regimes of some plasmas. The earliest studies of plasmas could
be considered to be spectroscopy of astrophysical sources. Spectroscopy has proven to
be a very powerful tool in the study of plasmas. In fact, the existence of helium was
postulated by Lockyer in 1868 based on his study of the lines of the spectra from the
sun. The development of laboratory plasma sources has allowed the study of plasmas in
a "controlled," reproducible environment.
Laser-produced plasmas are characterized by temperatures on the order of
1000 eV, electron densities of 1018 to 1022 cm-3, and copious x-ray emission. X-rays
can be divided into the approximate categories of "soft" x-rays, 1Á - 50Á, and "hard" x-
rays , less than 1 Á. This distinction is a historical one referring to the penetrating
power of the radiation: "soft" x-rays have less penetrating power than hard x-rays. In
this thesis, the spectroscopy of "soft" x-rays will be used to study laser-produced
plasmas.
1

2
10
10
10
10'
Solar corona
T (K ) 4
10
10'
10
Interstellar
Medium
Magnetic Fusion
Plasmas
Z Pinch
Plasmas
10° 104 108 .o12 io>6 1020 1024
ne (cm3)
Figure 1 -1. The temperature and density regime of some plasma sources.
To illustrate some of the characteristics of spectra from highly ionized plasmas,
the case of an aluminum plasma will be considered. In figure 1-2, the spectra of neutral
helium and helium-like aluminum are presented. The spectrum of neutral helium shows
the resonance lines, those lines that arise from allowed transitions involving the ground
level Is2. The resonance lines in both of the spectra have essentially the same structure.
The spectral lines become more closely spaced as they approach the series limit. The
spectrum of the highly ionized aluminum typically contains lines from the helium-like
resonance series as well as lines corresponding to transitions from hydrogen-like ions
and satellite lines. The principal resonance lines are indicated in the figure. The
unmarked lines appearing in the ionized spectra on the red wavelength side of the
resonance lines are the satellite lines. These lines arise from the preceding ionization

Intensity (arb. units) Intensity (arb. units)
3
Spectrum of neutral He
Figure 1-2. A comparison between a line spectrum for neutral helium
and one of helium-like aluminum.

Total electron energy
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ls22p
1s22s
Al XIII (H-like)
Al XII (He-like)
Al XI (Li-like)
Figure 1-3. Schematic energy level diagram for ionized aluminum. The completely stripped
ion has zero energy. The energy level of the first ionization potential for each ion
is repesented by the hatched bar.

5
stage of the ion. For instance the satellites to the helium-like lines are from the lithium¬
like ion stage. Satellite lines are formed by radiative transitions from discrete states
above the first ionization limit, to ground, or excited, states of the ion. The upper level
is a metastable state having an electron configuration with two or more excited electrons.
These doubly excited states only exist in non-hydrogenic ions. In general, as the
principal quantum number, n, of the spectator electron increases, the satellite wavelength
decreases (i.e. the Is2p3p - ls23p lies closer to the parent line, 2p - Is, than ls2p2 -
ls22p line). By n=4, the satellite can be on either the red or the blue side of the
resonance line. The following figure, 1-3, is a schematic energy level diagram for the
H-like, He-like, and Li-like ion stages of aluminum. The resonance transitions are
indicated by solid lines, while the satellite transitions are indicated by dotted lines.
The spectra shown in figure 1-2 are only schematic. In reality, the individual
lines have an intrinsic natural width and can be affected additionally by mechanisms
such as Stark broadening. Moreover, the spectra can be affected by radiative transfer
effects such as radiative trapping. Radiative trapping occurs if a transition is optically
thick, meaning that a photon has a high probability of being reabsorbed by another ion
before leaving the plasma. In this case, the photons emitted at line center in the interior
of the plasma cannot escape. These photons are either thermally destroyed or their
frequencies diffuse into the line wings where the opacity is smaller and they can escape.
Therefore, the photons emitted at line center primarily escape from the cooler outer
layers of the plasma, whereas photons in the line wing can have a substantial
contribution from photons emitted in the hot core of the plasma. The result can be that
the spectral line may become broader and have a dip in the center of the line profile.
Hence, the spectoscopist's challenge is to extract an understanding of the atomic
physics, plasma conditions, and interaction between radiation and matter, from the
spectrum.

6
(a)
WSSSSSSSSA
plasma to be pumped
Figure 1-4. Two-level atom diagram illustrating photopumping.
a) Ionized atom in its ground state before the photopumping;
b) Photons from the radiative pump are absorbed by the ions;
c) The excited state radiatively decays back to the ground state.

7
The motivation for this thesis research is to explore the fundamental process of
photopumping, i.e. using photons to selectively excite ions. Figure 1-4 shows a
schematic diagram of photopumping that involves two levels of an ion. Also shown in
the figure are schematic diagrams of the plasmas at each step of the experiment. Part (a)
shows the ion in an initial state which, for convenience, is the ground state. The
radiative pump provides photons having an energy that matches the energy necessary to
excite an electron. Part (c) shows the atom relaxing to a lower state, in this case its
original ground state, by radiative decay. The emission of photons due to the radiative
decay of a state that has been achieved by the absorption of radiation is called
fluorescence. Only the photons that are involved in the process of photopumping or
fluorescing are indicated.
The study of fluorescence due to a radiative pump would be a promising next
step in the development of laser plasma spectroscopy for the following reasons. First,
photopumping has never been directly observed or studied in the x-ray regime. Its
effects on x-ray spectra have not been experimentally verified. Second, if a known
radiative pump is used, the pump would serve as a controlled probe that perturbs the
plasma and causes it to fluoresce. The study of this fluorescence would yield detailed
information about radiation transport, level populations, and competing rate processes in
the plasma. Finally, the study of photopumping is directly relevant to x-ray lasing
schemes that depend on this process to create population inversions.1'5
The work presented has been both experimental and theoretical. A basic review
of the relevant advances in plasma spectroscopy is given in chapter 2. Chapter 3 is an
introduction to the analytic models used in plasma spectroscopy. Chapters 4 and 5
discuss a photopumping experiment that was designed to observe and quantify the
fluorescence. Chapter 6 discusses radiative transfer in more detail and presents a simple
analytic model of the plasma emission. The results of computer simulations of the

8
radiative transfer in a planar slab having plasma conditions similar to that of the
experiment are discussed in chapter 7. Final conclusions are given in chapter 8.

CHAPTER 2
REVIEW OF LITERATURE
Spectroscopy is an essential tool in the study of laser-produced plasmas because
of its non-perturbative nature. In the last ten years, the advances in spectroscopy of
laser-produced plasmas have been accompanied by the development of x-ray lasers and
inertial confinement fusion. High speed computers have enabled complex calculations
of atomic and plasma models that are necessary for analysis. As a result, the
understanding of plasmas has become more sophisticated as the methods to observe and
diagnose plasmas have become more refined and specialized. In order to set this thesis
in context, the main developments in the study of laser-produced plasma will be
highlighted. This chapter will be a descriptive history; it is by no means exhaustive.
The underlying equations and assumptions of the field will be introduced in the next
chapter. Two notable references on soft x-ray spectroscopy of plasmas are the review
by De Michelis and Mattioli 6 and the textbook on plasma spectroscopy by Griem.7
Identification of Highly Ionized Species
The identification of transitions from highly ionized species in the x-ray regime
was done using high-voltage vacuum sparks in the 1939 by Edlen and Tyren.8
However, the earliest observations of x-rays from a plasma were obtained in 1949 by
the U.S. Naval Research Laboratory when soft x-ray emission of the solar corona was
detected.9 The study of x-rays originating from laser-produced plasmas began in 1973
with Galanti and Peacock who irradiated polyethelene with a neodymium laser.10
9

10
By 1974, as more powerful lasers have become available, the spectra of ionized
rare earth elements has been obtained from laser-produced plasmas.11 Recently
interest has been generated in the nickel and neon isoelectronic sequences of these
elements due to the development of x-ray lasing schemes.12-13 This research has
spawned more papers identifying lines in these sequences from various ions.14-15
The standard reference for the wavelength of transitions is a publication by the
National Bureau of Standards. It is a compiled list of the observed lines from the
literature and is commonly referred to as the "finding table." 16 The satellite lines of
He-like ions from astrophysical sources were classified by Gabriel and Jordan. 17-18
Their classification scheme for He-like satellite lines has carried over to high density
laser-produced plasmas. A comprehensive listing of the spectral satellite lines in the 1.5
to 15.0 A wavelength range is compiled by Boiko, Faenov, and Pikuz. 19 The lines,
primarily from laser-plasma sources, are identified by comparison to theoretical
calculations using a perturbation theory expansion in powers of Z1 or by Hartree-Fock
calculations.
Emission Spectroscopy
The analysis of emission spectra to make detailed measurements of temperature
and density has evolved as the experimental and computational methods have been
developed. Gabriel and Jordan identified the usefulness of line ratios of dielectronic
satellites to determine densities of astrophysical plasmas.20 Their methods have been
extensively cited and extended to laser plasmas.
An instructive paper discussing the use of the emission lines for diagnostics of
laser plasmas is that of Aglitskii, Boiko, Vinogradov, and Yukov.21 They analyzed the
spectra of H-like and He-like magnesium and aluminum ions for intensity ratios
sensitive to temperature and density. Their discussions of the mechanisms populating

11
the upper levels of the transitions give a physical understanding of the diagnostics.
Subsequent papers have used similar applications of the same line ratios.22’23
Dielectronic satellites have been a continual subject of laser plasma studies. An
early paper that systematically compared the satellite spectra of He-like ions of C, F,
Mg, and A1 in laser-produced plasmas is by Peacock, Hobby and Galanti.24 In this
paper, they identify the satellite spectra in He-like ion emission by comparing them to
Hartree-Fock calculations. They noted an anomalous increase in intensity of the "jkl"
satellite as the ion charge increases. An explanation for this effect has been proposed by
Weisheit.25 He suggests that at higher ion charges, collisional ionizations that
depopulate the autoionizing states decrease and therefore the satellite intensity increases.
Other studies have investigated the impact of dielectronic recombination in plasmas.26’27
Lineshapes are also an important diagnostic for dense laser-produced plasmas.
A fundamental text by Griem, "Spectral Line Broadening by Plasmas", gives the general
formalism of line broadening.28 Theoretical lineshapes are the convolution of the
natural broadening, Doppler broadening, and Stark broadening. In high density laser
plasmas, Stark broadening can be particularly sensitive to electron density and therefore
has received the most attention. The development of accurate microfield theories
enabled extensive calculations of Stark line widths. 29'32 The work has concentrated on
hydrogenic species since Stark broadening is the most pronounced for these ions. A
calculational method which is used here, for line broadening of hydrogenic species at
laser plasma densities is given by Lee.33 He extends the formalism and presents sample
calculations for Si XIV. Line broadening continues to generate interest in the field.34'37
The standard techniques of line ratios and line widths are also applied to space-
resolved spectra.38’39 Boiko, Pikuz, and Faenov, in one of the first papers reporting
on spatial distributions, used a 65 pm slit to collimate the radiation from the source that
is Bragg diffracted by a crystal.40 In this paper, the electron density profile was

12
obtained as a function of distance from the target surface. By 1978, spatial resolution to
10 fim had been achieved.41
A prime example of a quantitative measurement of the bound-free continua is
given in the work of Galanti and Peacock.42 They used an absolutely calibrated grating
to measure the carbon emission from a polyethylene target. Space-resolved spectra was
used to investigate the recombination continua. Direct measurements of the H-like and
He-like carbon ion populations were made and compared to a theoretical collisional
radiative model. Their measurements also found no evidence for non-Maxwellian
velocity distributions for 1.06 (im laser having an intensity of 5.0 x 1012 W/cm2. A
later work by Irons and Peacock gives a good example of a method to measure
recombination rates for bare and H-like carbon 43
The development of x-ray streak cameras allowed time-resolved spectra. In the
paper by Key et al., the first time histories of the resonance line widths and the satellites
were reported.44 The emission spectra of plane aluminum targets and neon-filled
mircroballons was analyzed for time-dependent line intensity ratios and possible cooling
mechanisms were proposed. The length of time a laser-produced plasma emits x-rays is
typically 100 ps to 3 ns, depending on the laser pulse. Time resolution on the order of
tens of picoseconds allows the time-dependent study of plasmas. Now, even sub¬
picosecond resolution is being pursued.
Determination of temperature and density by comparison to ionization
calculations has also been done 45 Recently a paper by Goldstein et al. has used the Na-
like satellite to the Ne-like resonance line to determine the electron temperature and
charge state distribution in a bromine plasma.46 In this analysis, the relative abundances
of the Na-like and Ne-like ions were adjusted in a model of the plasma emission until the
synthetic spectrum fit the experimental spectrum. The advantage of this method is that it
does not depend on hydrodynamic modeling. The result is, however, critically
dependent on the atomic model.

13
A variety of methods described above must be used to diagnose a plasma well.47
A particularly clear discussion of a consistent use of the methods presented here is
contained in the paper by Kilkenny et al.48 An x-ray pinhole camera and space¬
resolving minispectrometers were used in the spectroscopic analysis of microballoons.
The determination of electron temperature and density were deduced from the
recombination continua of the spectra. These measurements were corroborated by the
electron temperature, as determined from the ionization state of the plasma, and density,
as derived from a line width fitting procedure to all the observed members of the the
hydrogenic line series. The size of the emitting plasma was determined also.
There are two significant limitations on emission spectroscopy. First, the
emission depends directly on the excited state populations. These excited states do not
give direct information about the ground state populations, which are the most important
in determining ionization balance since the overwhelming proportion of the total
population resides in the ground states. Second, if the plasma is not hot enough, the
emission is too low to make an accurate diagnosis or to even be detected. These
limitations led to the development of techniques to image and probe the plasma.
Point Projection Spectroscopy
This technique was developed in a response to the needs of laser fusion to
determine the dynamics, size, and symmetry of laser-driven implosions. The feasibility
of this technique was reported by Key et al. in 1978.49 In this experiment, a separate
laser-produced plasma served as a source to image an imploding microballoon. This
source is called a backlight. The microballoon, imploded by six orthogonal laser beams,
was backlit at different delay times during its implosion in order to determine the
compressed density. The technique was elaborated in later papers.50-51 Eventually

14
streaked radiography was used to measure ablation pressure, implosion velocity, and
other hydrodynamic quantities.
Since the technique is dependent on the development of bright backlight sources,
it became clear that studies of the backlight source itself were needed. One of the
fundamental papers characterizing laser-produced plasma sources has been that of
Matthews et al.52 The absolute conversion efficiency of line sources in the 1.4 to
1.8 keV range were studied as a function of laser wavelength, intensity, and pulse
width. Other conversion efficiency studies have investigated different wavelengths53*55
and/or different elements for potential backlight sources.56*59
Other source studies have focussed on the optimization of the source for x-ray
yield, source size, and spectral characteristics. The paper of Lampart, Weber, and
Balmer reports on a systematic study of the emission from elements having atomic
number 9 through 82.60 Using a 0.53|im wavelength laser, planar targets were
irradiated with 1 J, 800 ps laser pulses. The resulting 5-15 Á x-ray emission varied
from pronounced line emission from K-shell and L-shell emitters to nearly continuous
emission. Thus they showed that the spectral characteristics of the source could be
controlled by a judicious choice of target and irradiance conditions. A paper by Zigler et
al. has reported on optimizing the intensity while minimizing the size of the backlight
source.61 A novel multi-layered target is introduced. The target is initially pitted by a
pre-pulse from the laser to expose the target element of interest. When the full laser
pulse is incident on the pitted target, the ablation of the initial layer keeps the target
plasma localized.
Absorption Spectroscopy
More recently, absorption techniques have been developed so that the
experimenter can probe the plasma as well as passively observe it. Lewis and

15
McGlinchey first coupled Bragg crystals with x-ray streak cameras in order to obtain
"quasi-monochromatic" probing of material.62. In absorption spectroscopy, a "warm"
plasma is irradiated from behind, typically by a broad-band photon flux. The "warm"
plasma will absorb the radiation from the backlight at frequencies corresponding to
particular transitions. Thus absorption features appear in the spectrum. Analysis of the
absorption profiles yields the number of ground state ions. A good example of this
technique is given in the paper by Balmer et al.63 One laser beam irradiates a foil target.
The tip of a fiber is irradiated to create a point backlight The spectrometer was aligned
perpendicular to the face of the foil so that the time-integrated data simultaneously
recorded the backlight spectrum, the shadow of the foil, and the absorbing plasma
spectrum. The data reduction involved subtracting the direct backlight spectrum from
the absorbing plasma spectrum to reveal the absorption lines. The transmission at line
center of optically thin lines and an equivalent width of optically thick lines were
measured to determine the absorption. This example illustrates how backlights can be
successfully used as probes of laser heated targets,64 x-ray heated targets,65 and shock
heated targets.66-67
Outstanding Problems
For plasmas that are significantly affected by opacity, these techniques do not
give enough information to fully interpret the spectra. Hearn examined the effects of
radiative transfer of resonance lines and noted that even in plasmas having uniform
temperature and density, the line profile does not reach the black body limit at line
center.68 Earlier Osterbrock found that the diffusion of photons in frequency can be an
even more pronounced effect since the optical depth in the wings is much less than at
line center.69 Holstein introduced the idea of an escape factor to correct for the effects
of radiative transfer in resonance lines.70-71 In addition to references in some of the

16
papers already mentioned, papers noting the effects of radiative transfer in laser-
produced plasmas are plentiful.72'76
The tools and techniques of producing and analyzing laser-produced plasmas are
now sophisticated enough to begin exploring radiative transfer. The advent of computer
codes that can solve the formidable radiative transfer equations now make it possible to
generate synthetic spectra. At the same time, experimental techniques have been
developed that enable experiments which are sophisticated enough to be able to address
these questions. As yet, though, there has been no concerted effort to resolve the
questions related to radiative transfer effects. The following is a discussion of recent
research related to photopumping.
The attempts at photopumping have not been conclusive. A paper by Mochizuki
et al. investigates the radiative heating of a layered foil.77 They use a double foil, one of
which is irradiated directly by the laser, while the other is radiatively heated by x-rays
from the first foil. They attemped to study the ionization bum-through phenomenon in
which x-ray pre-heating reduces the opacity of the sample and causes a strong radiative
transport of energy to the rear of the foil. However this study fails to adequately
characterize the x-ray heating source. The use of two foils eliminates neither the
possible heating due to the physical contact of the ablating laser irradiated foil with the
second foil, nor the possible direct heating of the second foil by the laser itself.
Another attempt has been to try photoresonant excitation of the ls-3p H-like
fluorine line by the 2p-3d line of Be-like manganese ,78 The purpose of this research
was to create a population inversion and observe the lasing of the 2p-3d level of H-like
fluorine. However, the frequency mismatch between the pump ls-3p transition as well
as the physical configuration of the target presented problems.
A recent paper by Monier et al. has explored the photoresonance of the ls-3p
resonance line of A1XIII and the 2p6 (lS0) - 2p53d (3Di) line of Sr XXIX.5 This
scheme was designed to explore the possible use of photopuming as a mechanism for

17
population inversions. This research, as the others, fall short of characterizing the
radiation of the pump. However, none of the mentioned studies intended to study the
fundamental process.

CHAPTER 3
PLASMA MODELS
In this chapter, before launching into the experiment and results, a general
discussion of plasma models that are frequently used to help characterize and study
plasmas is presented. Since the spectra from a plasma is a manifestation of atomic
processes, this thesis will focus on the nature of plasma constituents as opposed to the
fluid properties.
The emission of a photon depends on the transition probability, the population of
the upper state of the transition, and the probability that the photon escapes the plasma
medium. The first quantity is intrinsic to the ion and requires complex atomic structure
calculations. The population distribution is essentially determined by the kinetics
equations, also known as the rate equations, which describe how all the atomic
processes couple the states. The probability that the photon escapes requires the
solution of the radiative transfer equation which describes how the radiation interacts
with matter. Unfortunately, the population distribution and the radiation field are
interdependent. Consequently, a fully consistent model must involve simultaneously
solving both sets of equations.
Valuable physical insight can be gained by decoupling the radiative transfer
equation from the kinetics equations. This approach assumes that the detailed radiative
transfer does not significantly affect the ionization and population of the states. This
treatment is valid for plasmas that are optically thin, meaning that photons escape the
plasma without being reabsorbed, or for plasmas in which the radative processes are
18

19
dominated by the collisional processes. To a first order approximation, radiation
trapping can be incorporated into kinetics models by the addition of escape factors.
The models that will be discussed are thermodynamic equilibrium, local
thermodynamic equilibrium, coronal model, and collisional radiative model. For the
purpose of this thesis, a collisional radiative model was primarily used to diagnose the
temperatures and densities of the plasmas. A radiative transfer code was used to
investigate the effects of radiation transport. Important atomic physics results will be
quoted and used but not explicitly derived.
Thermodynamic Equilibrium (TE1
In thermal equilibrium, the state of the matter can be entirely specified by the
thermodynamic quantities. The most convenient thermodynamic quantities to choose are
temperature and density. The ion, electron, and radiation temperature are all the same.
The radiation is homogeneous and isotropic hence the specific intensity, Iv, is equal to
its black body value, the Planck function.
Iv= Bv =
2hv
1
c2 (exp(^)-l)
erg
cm sr hz sec
where h is the Planck constant, c is the speed of light, and k is the Boltzmann constant.
The population distributions and ionization balance are determined by the Boltzmann and
Saha equations which will be described in the next section.
This limit is never physically realized; however, it provides one of the most
powerful concepts in the calculation of rate coefficients: detailed balance. In
thermodynamic equilibrium, every atomic processes must be balanced by its inverse

20
process. The principle of detailed balance is based on the microscopic probability of the
transition to a state. Microscopic laws are time invariant or "reversible." Thus, this
concept can provide relationships between reciprocal processes regardless of the
surrounding plasma conditions because transition probabilities are intrinsic to the atom
or ion itself.
An interesting set of relationships between the Einstein coefficients, A and B,
can be obtained. If we equate the number of transitions from a lower state i to an upper
state j to the number from the upper state to the lower state.
niBi,JIv=njAj.i+njBJ,iIv
were n¡ stands for the number of ions in state i. The left hand side of the equation
represents the number of upward transitions due to stimulated absorption. The right
hand side represents the sum of the spontaneous decays and the stimulated emissions.
This equation can be solved for Iv. In TE, Iv equals the Planck function. Therefore,
the relationships between the coefficients can be found to be
3
giBi,j=gjBj,i
where gi is the statistical weight of state i. Even though these relationships are derived
from a condition of thermodynamic equilibrium, they are always valid. The Einstein B
coefficient given here has units such that B times Iv is in sec-1. If the radiation density,
p = 47tl/c, is used, then B must be multiplied by c/47t.
sec
cm hzsr
erg

21
Local Thermodynamic Equilibrium ÍLTEl
The Local Thermodynamic Equilibrium model assumes that the plasma is
governed by the local temperature and density at each point in the plasma. The state of
the plasma can still be described by the thermodynamic quantities of T and n, but the
temperature and density structure can be non-uniform.
By using the laws of statistical mechanics, we find that the levels are populated
according to the Boltzmann prescription.
where k is the Boltzmann constant, g is the statistical weight of the level, and Ej¡ = Ej -
Ej, the energy difference between the upper level j and the lower level i.
The relationship between the ground states of successive ions is determined by
the Saha equation, which can be understood as an extension of the Boltzmann
expression to free particles.
where h is Planck's constant, and Xz,g is the ionization potential of an ion of charge z.
The Boltzmann and Saha equations can be combined to relate a ground state to any
excited state of another ion

22
The particles will have a Maxwellian velocity distribution
,3/2
exP
2^
-mo
2kT
4ko do
where o is the velocity and m is the mass of the particles.
The equations above describe a plasma in LTE. The power of LTE lies in the
fact that the temperature T used in the velocity distribution functions and the population
distributions is the same at each point in the medium. The statistical arguments obviate
the need to know atomic cross sections and coeffficients in order to determine the kinetic
temperature and density of the plasma.
The significant difference between TE and LTE is that the macroscopic radiation
field is not in equilibrium. This deviation is caused by temperature and density
gradients. The radiation field must be obtained by solving the radiative transfer
equation.
A sufficient condition for LTE to exist is if the collisional processes are the only
processes important in determining the population densities. In this case, radiative
processes do not significantly affect the ionization balance and population densities.
Coronal Model
The Coronal model is based on coronal equilibrium in which collisional
excitation processes are balanced by radiative deexcitation processes. It is so named
because this condition was found to exist in the corona of the sun. This model is valid
for aluminum plasmas at temperatures of ~ lOOeV and electron densities on the order of
10^ cm'3. In this section, the equations given by McWhirter are quoted.79 The
population distribution of the number of ions in an excited state, x, to the number of
ions in the ground state, g, is determined by

23
=n,
X,., |
Iam
\q where ne is the electron density, Xg x is the collisional excitation rate coefficient from the
ground to excited level, and the sum appearing in the denominator is the total radiative
rate from the excited state to all states, q, lower than the excited state.
Likewise, ionization balance is primarily determined by collisional excitation and
radiative recombination. A simple argument shows that at low densities, radiative
recombination is stronger than 3-body recombination, the inverse of collisional
ionization. Collisional recombination is a three body process involving an ion and two
electrons - one electron recombines, while the other absorbs the excess energy. Hence it
is proportional to ne2. Radiative recombination only involves one free electron and is
therefore proportional to rie. The analog of the LTE Saha equation that relates the
ground states of adjacent ionization stages is
nz,g _ az+i.g
nz+l,g Sz>g
where the additional subscript z denotes the ionic charge, a is the radiative
recombination coefficient, and S is the 3-body recombination coefficient.
Using analytic hydrogenic expressions for the respective coefficients, an
expression showing the functional dependence on T and ne can be found. Here, we
assume only recombinations and ionizations between ground states, because at these
lower densities, the excited state populations of ionization stages will be insignificant
compared to the ground state populations. Details about the atomic coefficients will be
given later in Rates and Atomic Cross Sections. The ratio of the number of ions in the
ground state of successive ionization stages is

Normalized Ion Fraction Normalized Ion Fraction
24
Saha Equilibrium Ionization Balance
^ neutral A1
♦ Mg-like A1
â–  Na-like A1
■o— Ne-like A1
â– â–  F-like A1
â– a O-like A!
N-likeAl
C-likeAl
■m— B-likeAl
-t Be-like A1
-a Li-like A1
â– * He-like A1
H-likeAl
Figure 3-1. Ionization balances of Saha and Coronal models for aluminum
at an electron density of 1020 cm'3.

25
where Xz is the ionization potential of the ion having ionic charge z. Notice that the
ionization balance is independent of electron density, but is now strongly dependent on
the atomic rates which are strong functions of temperature. Figure 3-1 shows a
calculation of ionization balance of a coronal plasma based on the equation given above.
Collisional Radiative Models (Kinetics or Rate Models)
Laser-produced plasmas having densities from 10^ cm"3 or above can fall
between the two previous models. At these densities the radiative and collisional rates
are comparable, so a rate equations, or kinetics, model must be used. In a kinetics
model, all the important radiative and collisional rates that connect the levels of the
atomic energy levels are included. The rates together with an equation conserving the
total ion density can be written in matrix form and solved for the populations of all the
levels.
A rate is the number of transitions per unit time. In a volume of medium, the
number density of particles will change in time according to the net flux of particles
through the volume and the net rate at which particles are brought from other states by
radiative and collisional processes. If there are no temperature or density gradients, then
j *>
where Pi j is the total rate from i to j.
The total rate Pj j is composed of radiative and collisional rates. The form of
these rates can be expressed as follows. The bound-bound rates for radiative line

26
transitions can be written with the Einstein coefficients. The number of stimulated
absorptions in a transition with line shape (v) is
niRi,j =
ni Bitj (v) J(v) dv
where J(v) is the mean intensity, i.e. the intensity integrated over all solid angles. The
number of emissions is
nj Aj j <()(v) dv
Like the stimulated absorption rate, the photoionization rate is proportional to the
mean intensity. The number of photoionizations is
ni R¡,k= ní 4rc
m .
ct¡ dv
hv
The radiative recombination rate, which does not depend on the incident radiation, is
expressed so that the explicit dependence on the electron density, rie, is shown.
nj Rj,i= njnea
where the rate coefficient a is defined by
a =
CTj (o) f(o)o do
o
where f(o) is the electron velocity distribution and oj(o) is the radiative recombination
capture cross section.

27
All the collisional rates can be expressed in the following form
n¡ Cj j = n¡ne ja(u) f(-o) \) dt) = n^eXj j
where a is the cross section for the process being considered and f(o) is the velocity
distribution. Xy is the rate coefficient with units cm^sec'1. It is sometimes written as
.
An example of a collisional radiative model for K-shell ions is RATION, a code
written primarily by R. W. Lee.80 It constructs the energy levels from semi-empirical
formulae, calculates and fills a rate matrix, then inverts the matrix to solve for the
populations. It will be described in more detail in chapter 5.
Rates and Atomic Cross Sections
Since the results of a numerical model cannot always be easily generalized, a list
of the basic rates and their dependencies will be given. In addition to revealing the
important processes that are included in typical models, this section will define a
consistent set of expressions that will be referred to throughout the rest of this thesis.
The Z, ne, and Te dependencies of rates and cross sections will be emphasized, but the
details of the calculations are left to the references. Unless otherwise noted, cgs units
are used, except for explicit energy factors %, E, and R shown in the equations which
are in eV.
Since the hydrogenic atom can be solved analytically for wavefunctions and
energy levels, hydrogenic approximations will be given in order to show basic trends.
In this section, the units of rate coefficients used by Mihalas will be used.81 The
monograph edited by Bates and the texts by Mihalas, Zeldovich and Raiser, and
Cowan, are extremely useful references.82"84

28
Radiative Rates (bound-bound') E(Z. i) + hv < > E(Z.\)
In this process a photon of energy hv is absorbed or emitted by an ion
represented by the symbol E . The net charge of the ion is Z. The indices i and j stand
for the lower and upper levels, respectively. From quantum mechanics, the dipole
matrix elements can be calculated and expressed in the form of an electric dipole line
strength or an oscillator strength, fy. The absorption cross section is given by 81
where
2 .
Tte . 4k
By using the Einstein relations between A and B, the hydrogenic A rate can be
analytically expressed as
AJ.i
= 8.01 x 10'
z4(i-V
2 2
n;
n
f.
’■J 2
n¡
sec
where n¡ is the principal quantum number of level i, and the expressions for the energy
and the statistical weight for hydrogenic ions, g¡ = 2n¡2, have been substituted. The Z4
dependence comes from the energy dependence of the rate. The helium-like rates do not
have a corresponding analytic form, but there are fits to the rates such as those of Drake,
and Drake and Dalgamo.85'87

29
Radiative Rates (bound-free) S(Z.i) + hv < > E(Z+ Li) 4- e-
Free bound processes affect the ionization balance of the plasma. The ion E
absorbs a photon of energy hv and ionizes to a charge state of Z+l. The photoionization
cross section can be found by using Kramers semi-classical result
o- =
4 10 «V4
64tc me Z
3Í3
ch
5 -
n v
[cm2]
Notice that at threshold energies En=R Z^ n *2, the threshold cross section, o¡thresh , is
3
thresh
G. = 7.91 X 10 —
v
,-18 n n
,2 3
The exact quantum mechanical result differs from the classical result by a multiplicative
factor dependent on v, called the Gaunt factor, which is on the order of 1 near threshold.
The semi-classical result differs from the exact result by approximately 20 %.
An analytic expression for this rate coefficient from the ground state is given for
I»kT in Zeldovich and Raiser where the radiation field is approximated by the Wien
expression.
,q 2 thresh
Rg,/v) = 3.40x 10iy Tx og (v)
exp
x\
cm2 hz sr
rkTl
erg
where og is the photoionization cross section of the ground state.
The cross section for radiative recombination can be found from detailed balance
from the photoionization cross section .
4 10
G¡ =
6471 e
mi)
fc) [cn,2]
3 VJ 3, 3 5
J,Jch n

30
where the captured electron has energy 0.5m\)2 and the energy of the emitted photon,
hv, is
7 2
, , . , , . mt) RZ
hv(emitted photon) = —— +
where R is the Rydberg energy. Notice that the cross section is inversely proportional
to the electron energy and also to the energy of the emitted photon, hv. Again, the
relation can be corrected by the Gaunt factor for the quantum mechanical result of the
cross section.
In the coronal approximation, the total recombination rate is approximately equal
to the rate coefficient (cm3/sec) for recombination into the ground state, which is 79
a „(T) = 2.05 x 10'12 hdiA
z'8 Tl/2 l sec
This expression includes the result of an integration over the electron distribution. It is
useful for plasmas that have a thermal energy kT that is much smaller than the ionization
potential. A more general expression for recombination into a shell of principal quantum
number, n, is 88
3
az g(T) = 5.2 x 10
14 Z 4 R3/2 !
(kT)3/2 n3
exp(xn) E¡(xn)
cm
sec
where only the leading term of the gaunt factor is taken and
xn =
RZ
kT n ‘‘
Ej is the exponential integral. The total recombination rate coefficient for an ion must be
summed over all the states into which the electron can recombine.

31
Collisional Rates (bound-bound) E.(ZA) + e- < > E(Z.\) + e-
In this process an ion in lower state, i, is excited to an upper state, j, by a
collision with an electron. The calculations for collisional cross section are difficult to
generalize by a representative cross section because of the different regimes in which
approximations are valid. An excellent review by Seaton discusses the various
methods.89 The cross section, Q, is of the form
r E/2
Q= I o(e,E¡) de
•'o
where a is the cross section, Ej is the incident electron energy, E = Ej - and e is the
energy of the ejected electron.
An approximation for the cross section of optically allowed transitions is given
by Seaton
Qi.i =
4 71'
fj,i
2 (Ei - Ei)
mi) 13 ' J '
g
where g is the Kramers-Gaunt factor and 0.5mt)2 is the energy of the incident electron.
The rate coefficients are found by integrating the collisional cross section over a
velocity distribution. The temperature dependence of the collisional excitation rate is due
to the integration over the Maxwellian velocity distribution. The analytic collisional rate
coefficient of excitation for hydrogenic bound-bound states is
-4
y /rYr\ 6.5x10 ~ i 11
‘jm = ~É¡~fT iJ explTf)
Ej-il
3 '
cm
1 kT )
. sec .

32
For transitions between lower level i to upper level j, detailed balancing of the
collisional rates implies
So the deexcitation coefficient can calculated to be
Numerous calculation of rate coefficients can be found in the literature and references
therein.90-96
Collisional Rates (bound-free') 5fZ.fi + e- < > 5fZ + l.fi + e- + e-
Collisional processes are dependent on the velocity distribution of the electrons.
Electrons can ionize an ion of charge Z to a final state in which the ion has charge Z+l.
A study of electron-impact ionization cross sections using variations of the Coulomb-
Bom and distorted wave approximations has been done by Younger.97 A good overall
review has been done by Rudge.98
For collisional ionization, the coefficient for hydrogen-like ions is 79
based on the work of Burgess.99 The inverse process is three-body recombination. It
can be calculated by detailed balance.

33
Radiative Rates Involving Metastable States (bound-free)
E(ZÁ) +e- > ZCZ-l.i *) > EfZ - 1. ml + hv
A rate that is important in laser-plasmas is dielectronic recombination. It is a two
stage process. First an electron is captured by an ion of charge Z creating a doubly
excited state denoted by j*. This state can then stabilize by a radiative transition to a
lower state m. The rate coefficient, ad , is given by
a
3/2
T
where ao is the Bohr radius, G is the sum of statistical weights over the index level m,
Aa is the autoionizing rate, and P is the probability of radiative stabilization which
depends on the branching ratio of radiative decay rates.84 Tabulations of wavelengths
and transition probabilities have been calculated by Vainshtein and Safronova100 and
Gabriel13

CHAPTER 4
FLUORESCENCE EXPERIMENT
Having given a background discussion of plasmas and processes of importance,
now a specific system of plasmas that can demonstrate photopuming will be discussed.
Resonance radiative pumping is the process by which the first dipole allowed excited
state is selectively populated by a photon source tuned to the transition energy between
the ground and the excited state. The system chosen for this experiment was a line
coincidence scheme to observe the fluorescence of the Al XII1 1Sq-21Pi transition due
to photopumping by photons produced by the Al XII 1 ISq^Pi transition from a
spatially distinct plasma source. Thus, this photopumping experiment involved two
independent plasmas. Since the photopumping effect has never been directly observed
in a laser-produced plasma, considerable thought was given to the design of the system
and target. The first half of the chapter will justify the choice of this system and
consider the factors that influence the experimental conditions. The second half will
describe the experiments. The spectroscopic notation that will be used throughout this
thesis is [ n (2S+1) L j ], where n is the principal quantum number, S is the total spin, L
is the total angular momentum, and J =L+S.
Design of Fluorescence Experiment
The design for the experiment was developed according to the following
guidelines. First, the spectroscopic analysis was to be as unambiguous as possible.
34

35
Second, the design had to maximize the fluorescence effect. Third, the plasma
expansion should be as one-dimensional as possible.
From a spectroscopic point of view, K-shell spectra are the most straightforward
to study because of the relatively simple energy level structure. The line series structure
is prominent and the number of overlapping lines is minimized. Isoelectronic sequences
behave similarly to the neutral atom with the same number of electrons because the
electron structure is similar. Therefore, estimates of the hydrogenic energy levels can be
made from a Bohr model of the atom that has been scaled by a factor of Z2
z2r
E = -
2
n
where R is the Rydberg constant, Z is the ion charge, and n is the principal quantum
number of the level. Z equals one for hydrogen.
For helium-like ions, the energy levels can be estimated by
E = X-
(Z-1)2R
2
n
where % is the ionization energy of the ion. The ionization energy is larger than would
be predicted based on the assumption that the ground state energy E0 = -(Z-l) 2 R
because the electrons are in a closed shell. In 1930, Hylleraas calculated the ionization
energy to within the experimental error by using a modified Ritz method.101 Often in
semi-empirical formulas, experimental data provides the values for the ionization
potentials.
As more electrons are added, the bare charge of the nucleus is screened and
electron-electron interactions become important. The atom becomes a many-body

36
system that must be numerically solved. In order to concentrate on the photopumping
effect, K-shell ions were an attractive choice because an analytic approach to
understanding the results could be attemped.
Several factors influence the strength of the fluorescence signal. First we will
consider the plasma that will be pumped. This plasma needs to be in a state that
maximizes the number ions that are available to be pumped. In a laser plasma, several
ionization stages may exist at a given time, depending on the ionization balance of the
plasma. In order to make a judicious choice of the plasma state, we consider the
ionization energy of the ion being pumped. As we can see from the ionization balance
of charge states in figure 3-1, the helium-like ion is the dominant species over a larger
temperature range than the other ions because of the large ionization energy required to
remove an electron from the K-shell. Moreover, a rough calculation shows that the
excitation energy between the ground state and the first excited state will be
approximately 75% of the ionization potential. Hence, the helium-like ground state can
be preferentially populated to create a large pool of ions in the proper state to be
photopumped.
To detect photopumping, the radiative excitation rate must be significantly larger
than the collisional excitation rate. Since the collisional and radiative rates are both
proportional to the oscillator strength, a simple expression for a lower limit on the
photon flux necessary to perturb the plasma can be found
ipump >
Cid
OoBi.j
where Qj is the collisional excitation rate, B i j is the Einstein coefficient, and line profile at line center, and IpUmp is the intensity of the external radiative pump. For a
temperature of 200 eV, this expression implies that the intensity must be greater than

37
6 x 1014 ergs cnr2 sr^sec1 for the resonance line of He-like Al. For typical backlight
plasmas, the burst of radiation lasts about 100 ps, so the irradiance of the pump would
need to be 8 x 102 Watts cm-2.
After laser pulse has ended, the deexcitation mechanism in laser-produced
plasmas is generally due to radiative decay. For instance, for bound-bound transitions,
we can define e to be the ratio of the collisional deexcitation rate to the spontaneous
decay rate. After manipulating the relevant expressions from the previous chapter, we
find
e » n„
1.4 x 10
3
E YT
-13
where E is the energy of the transition, ne is the electron density, and T is the electron
temperature. In a He-like Al plasma, having a density of 10 21 cm'3 and a temperature
of 107 K°, e = 10'5 for the resonance line. Once a level is photopumped, the strength of
the fluorescence signal will primarily depend on the number of ways in which the
excited state can radiatively decay. It is therefore advantageous to choose an excited
state that is dominated by one decay route.
Next, we will consider the pump radiation. To efficiently photopump, the
wavelength of the pump must match the wavelength of the transition or transitions to be
pumped, and the pump must be as bright as possible. To pump the transition, either a
broad band source such as M shell radiation from dysprosium (Z=66) or an appropriate
line source could be used. X-ray sources are characterized by their x-ray conversion
efficiency, which is measured by the percentage of laser energy converted into the
energy emitted by the x-rays. Typically, broad band sources have a higher total x-ray
conversion efficiency over the whole band, but over the frequency range of a particular
line, the conversion efficiency is smaller than for a correctly chosen line source. In the

38
case of a line pump, the frequency overlap of the pump and the transition to be pumped
must be large. If the frequencies are mismatched, Stark broadening could serve as a
mechanism to broaden the pump line, however, at densities ~ 1020 cm'3, it is not a
pronounced effect. The most likely candidate for line pumping is the same transition
itself.
Preliminary calculations were done to estimate 1.) if the photopumping effect
would be observable and 2.) to determine whether a line coincidence scheme or a
continuum pumping scheme would be better. Some elementary principles about
radiative transfer must be introduced here. A more detailed discussion will be presented
in the Radiative Transfer Theory chapter.
The energy transported by a radiation field in a frequency interval (v + dv), into
a solid angle d£2, in a time dt, and across an area dA is
dEv = Iv cos( 0) dA dv dQ dt
where Iv is the specific intensity. The energy that is absorbed from the radiation field
can be expressed as
(dEv) abs = kv Iv cos( 0) dA dv dQ dt dt
where kv is the absorption coefficient with units of 1/cm and dfrepresents the path
length of the radiation through the material. The absorption coefficient, or opacity, is
the product of the number of absorbers (#/cm3) times the absorption cross section
(cm^). jts inverse can be considered the mean path length of the photon before it is
absorbed or scattered.
We will now consider the simple radiative transfer in one-dimension through a
slab of plasma. If we assume that the plasma only absorbs radiation (i.e. no scattering
or self-emission) and the plasma is homogeneous (i.e. K is a constant), then the radiative
transfer equation has a simple solution

39
I = Ij exp ( -k[ )
where I; is the radiation incident on the slab of plasma.
In this approximation, the energy absorbed from a plasma of length C is given by
the difference in the energy transported by the radiation field before and after it passes
through the plasma.
If the medium is homogeneous, then the absorption fraction, (1 - exp( - k C), is
essentially constant. Now, if we assume that all the energy absorbed will be re-emitted
at the same frequency as the incident radiation, then the equation
Efluo^Eii1 - exp [-k())
is an estimate of the total energy emitted into 4k by fluorescence. The quantity Ej
represents the energy incident on the slab. Certainly, this equation will give an upper
limit of the energy since no photons are destroyed by themalization. However, it is
sufficient to roughly estimate the photopumping effect and to determine the relative
efficiency of line versus continuum pumping.
For a comparison, we will consider the pumping from helium-like ground state
to the first excited state versus the pumping the same ground state to the continuum.
The absorption fraction depends on the product k[. If we assume that the initial plasma
conditions, the ion density, and absorption length, are identical for the two cases, then
the critical factor in determining the absorption fraction is the absorption cross section.
If we approximate the absorption cross section for radiative pumping of a bound-bound
transition by its value at the frequency of the transition, then

40
2
_ ti e f ,
^bound ~ jjj q M.j^o
where (j)0 is the value of the line profile at line center. The photoionization cross section
can be estimated by its value at threshold, also given in chaper 3. For an aluminum
plasma at a temperature of 500 eV, the values of the cross sections are 1.4 x 10'17 cm2 ,
and 4.7 x 10'20 cm2, respectively. Therefore, the absorption fraction for the line
pumping is over a factor of 100 larger than for the continuum pumping.
In order to quantitatively estimate the photopumping effect, we need the incident
energy Ej. The conversion efficiency in the A1 K-shell lines has been measured to be
~ 1.2 % of the laser energy. The continuum pumping can be done with a broad band
source. The M-band emission of Au, a well-studied element, has conversion
efficiencies of ~ 4 %. These estimates are taken from the published literature.52
A simple calculation of the maximum energy emitted by the fluorescence for line
pumping of the 1 !So - 2]Pi line by the K-shell lines gives approximately 0.7 J / sr for
a laser with ~ 10 J of energy at a wavelength of 0.53 Jim. This value is well above the
limit of detection for time-integrating crystal spectrometers of 1.0 x 10 '6 J / sr.
In summary, the experiment described in this thesis uses a line coincidence
scheme involving the resonance line of Al XII because it offered the highest detectable
fluorescence signal. There are four main reasons for choosing the resonance line in A1
XII, Is2 !S0 - ls2p iPj, for the study of photopumping. As discussed in the
beginning of this chaper, He-like systems have a much simpler level structure than many
electron ions. The spectra are therefore simpler to analyze qualitatively and
quantitatively. Second, because excited electrons will primarily decay back to the
ground state, the photons resulting from resonance fluorescence will be in a well-
defined energy range. Third, the high oscillator strength enhances the photoabsorption
cross section. A large cross section increases the probability that a photon will be
absorbed and thus maximizes the observable fluorescence signal. Finally, the most

41
important reason is that the large ionization potential between the ground state of Al XII
and the ground state of Al XIII provides a relatively large temperature regime in which
the plasma can exist in the ground state of the Al XII without significant emission of the
He-like lines. Thus, the result of photopumping should be the obvious enhanced
emission of photons at the frequency of the transition that was pumped.
Target Design-Front Plasma
Since, the plasmas are created by a laser beam irradiating a solid target, we now
discuss the target design. The goals of the design were to maximize the number of ions
available to photopump and to reduce the temperature and density gradients.
In order to reduce the gradients in the front plasma, an embedded microdot was
used. An embedded microdot is a localized "tracer" layer composed of the material of
interest, that is surrounded by a substrate. It is fabricated by depositing the tracer
element onto a substrate that has been masked with a metal plate having a hole that is the
desired shape and size of the microdot. After the tracer layer is deposited, a final
overcoat of a material such as plastic is deposited over the substrate and tracer dot.
Recent work by Burkhalter et al. have shown that a plasma created by irradiating an
embedded microdot is hydrodynamically confined.102 The advantages of microdots are
that the spectral lines for all states of ionization are emitted from the same known volume
of plasma.103 More recently, Young has completed a series of experiments that
investigates the behavior of the plasma density as a function of space after the microdots
are irradiated.104 Seeded targets also reduce opacity,105 but the low concentration
could make fluorescence hard to detect. For this experiment, an embedded microdot
was used.
Now we turn to the planarity of the plasma. Thermal conduction within the
plasma tends to keep the underdense plasma at a fairly uniform temperature in space.

42
The density scale length is determined by the hydrodynamics. When the physical
expansion of the plasma exceeds the lateral dimension, then the ablation surface
becomes bowed. Density and velocity gradients are determined by the divergence of the
flow. Therefore, to maintain a planar plasma, the scale length is the minimum of the
effective radius of curvature or the expansion distance, the speed of sound times the
pulse length. Max gives a semi-empirical formula for the limit on the focal spot size, R,
for planar geometry 106
R > 150(im [ Q
1/2 T 1/2
(FkeV) (T~ns) ]
where x is the laser pulse length, Z is the atomic number, A is the atomic mass, and T is
the electron temperature. Even for focal spots that are twice the diameter of the
microdots, gradients have been detected.
Target Design-Pump Plasma
To obtain a simple estimate of the plasma temperature when maximum emission
will occur in the resonance line, one can determine when the He-like ionization stage
was maximized. The rate equation model, RATION predicts that at an A1 plasma
temperature of 500 eV the mean number of bound electrons is 2. At higher
temperatures, a larger fraction of ions would be in the H-like stage, and conversely, at
lower temperatures, the ions would be in the Li-like and lower stages. The absolute
emitted flux also depends on the size of the He-emission region. This issue is
determined by the maximum laser energy available.
Now, we will dicuss the geometrical constraints of the front and back plasma.
The pump and fluorescing plasmas must be irradiated in such a way as to keep the two

43
plasmas from mixing. In addition, the plasma being pumped must be exposed to the
pump as much as possible. Finally, the line of sight of the spectrometer must be able to
be shielded from the pump plasma. An important parameter here is the blow-off
velocity, v, since this determines the plasma size. It is estimated by the sound speed at
critical density. Again, using the equations from Max,106
7 Z 1/2 T 1/2
v = 3 x 10 [ y (y-j^y) ] cm/sec
An A1 plasma will expand in the direction of the incident laser at velocities
~ 3 x 1()7 cm/sec. Ablation rates have been measured by M. H. Key et al.107
After considering several geometries, a target coated on both sides was determined
to be the best compromise. This configuration keeps the plasmas distinct and separate.
This two-sided target will be called a full target. The ideal thickness of the target is
determined by conflicting restrictions. On one hand, the energy per unit area falls off as
r '2, where r is the distance between the pump and the plasma to be pumped, which
implies that the pump should be as close as possible to the plasma to be pumped. On the
other hand, shocks travelling though the medium can heat the plasma. For this
experiment, we used a substrate that was thicker than the shock transit speed multiplied
by the time delay between the pulses.
Possible target compositions include compacted powders such as MgO, P,S,
A1P04,KC1, NaCl, CaO and CD2 , or solid elements such as aluminum. The element
chosen for the target was aluminum for the following reasons. It has been well studied
in other plasma studies so this work could benefit from previous studies. The emission
lines for hydrogen-like and helium-like are in the range of 5 to 8 Á, a convenient regime
for using crystal spectrometers. Target fabrication using Al is standard and relatively
easy. Composite powders, in particular, are difficult to fabricate.108

44
The substrate between the two A1 layers was chosen to be a plastic whose
constituents were only carbon and hydrogen. The primary reason for this choice was
that the carbon and hydrogen spectroscopic lines do not interfere with those of He-like
aluminum. Another reason was that plastic could be used as an overcoat material for the
embedded microdot.
General Laser Parameters
To start the experimental section, an overview of laser-matter interactions is
presented. From laser studies done by Max89 and others,109 we can qualitatively
understand the deposition of the laser energy into a solid target.
The main mechanism for the absorption of laser energy at the critical density is
inverse bremsstrahlung. In this process, the electrons, oscillate with the laser electric
field. The interactions of the electrons with ions effectively damp the laser light wave
and the electromagnetic energy is thermalized. At densities greater than critical density,
the energy, which is now thermal energy, is propagated into the target by electron
thermal conduction.
When the laser beam irradiates a solid target, the surface of the material becomes
highly ionized. The transport of the laser energy into the material is then affected by the
free electrons so that the dispersion relation becomes
and
2 2
k£c “D
-±—= 1 -(—P)
2 2
CO,
CO,
47te2n,
0>p=( f
p m„
1/2

45
where Cüp is the plasma frequency in Hertz, ne is the electron density, me is the electron
mass, kL is the wavenumber, and 0)l is the laser frequency. From this relationship, we
can derive a critical density,
nc= 1.1 x IQ21 (JiHü)
At this density, the laser light can no longer propagate (k = 0). Therefore, the energy
absorbed from the laser occurs at densities equal to or less than the critical density. The
critical electron density for 1.06 |im is 1.0 x 1021 cm'3. The laser light can also be
reflected or scattered so that typically, the percentage of laser energy absorbed is about
60% for 1.06 (im light.110
It is useful to estimate some of the plasma parameters to provide a guide for
choosing the experimental laser parameters that will be used. First of all, it is assumed
that nearly all the laser energy is deposited at, or near, the critical density. If we balance
the rate of thermal conduction away from the point of energy deposition by the rate of
laser absorption at the critical density, we find 89
T
1 keV
(cm/sec)
where f is a quantity determined by flux-limiting conditions, and Iabs is the absorbed
laser intensity. Interestingly, the temperature in the corona of the plasma only depends
on the intensity and wavelength of the laser. Figure 4-1 shows the temperature as a
function of intensity for the two laser wavelengths available, 1.06 and 0.53 (im.

46
The laser conditions were chosen to enhance the x-ray conversion efficiency.
Backlight experiments have shown that a plasma created with frequency-doubled
wavelength has a higher x-ray conversion efficiency.52 First, the coupling of the laser
energy into the target is better. The critical density, where most of the laser energy is
deposited, is higher. Therefore the time necessary to ionize the A1 is shorter and less of
the laser energy goes into the kinetic energy of the low density plasma. Second, the hot
electrons produced in laser-produced plasmas increases as IA.^.54 Therefore, longer
wavelengths increase the probability that hot electrons could pre-heat the plasma and
cause emission. In this experiment, any non-radiative heating of the microdot plasma is
unacceptable because the emission would compete with the fluorescence signal. The
100 ps pulse length was used to achieve as high an irradiance as possible which is also a
factor in high conversion efficiency.
Figure 4-1. Laser intensity vs electron temperature.

47
Overview of the Experiments
First a brief overview of the experiments will be given to make the logic behind
them apparent. In order to conclusively demonstrate photopumping, three separate
experiments were performed on the JANUS laser facility at LLNL. The first two
experiments were necessary to characterize each of the two plasmas. In this thesis, the
plasma that will be pumped is called the front plasma. The second plasma, which serves
as the radiative pump, will be called the pump plasma. The pump plasma was created
later in time than the front plasma.
The purpose of the first experiment was to characterize the pump plasma. The
temperature and density range of the plasma was bracketed. The primary measurement
was the absolute number of photons available to pump the front plasma. This
measurement was a critical test of the proposed system-if the photon flux was not
intense enough, then trying to detect fluorescence would be futile.
The purpose of the second experiment was to characterize the front plasma. The
ideal plasma condition was much more difficult to achieve because a plasma that is too
hot has strong self-emission that makes the fluorescence difficult to detect. On the other
hand, a plasma that is not hot enough, does not have a sufficient number of He-like ions
to pump. The technique used to determine this condition was to decrease the energy in
the laser until He-like emission was barely detectable and simultaneously monitoring the
Li-like emission to insure that the plasma was sufficiently ionized.
The final experiment was the photopumping experiment. One laser beam was
used to create the front plasma and a separate, independently-timed laser beam was used
to create the pump plasma. These laser beams irradiated opposite sides of a planar target.
The results from the first two experiments guided the laser conditions. Detecting the
fluorescence required timing of the laser beams with respect to each other and precise
alignment of the target and spectrometers.

48
Description of JANUS Laser Facility
Since laser physics is an entire field in itself, a relatively brief description of the
laser will be given here. From the experimentalist’s point of view, the laser is a tool to
create the plasmas for experiments. In general, a staff of people operate the laser so that
it will deliver a pulse of energy and duration requested by the experimenter. This
description will only give a hint of the procedure required to deliver a laser pulse at the
desired parameters.
The JANUS laser at LLNL is a solid state pulsed laser which uses Nd:glass as
the lasing medium. The laser has two independent beams which can be used at a
wavelength of 1.06 |im, the wavelength of the lasing transition in Nd^+, or at 0.53 qm,
the frequency-doubled wavelength. In this process, the beam is passed through a
potassium dihydrogen phosphate (KDP) crystal which converts the frequency of the
incoming light, defined as loo, into 2co light by harmonic generation. The dielectric
polarization induced in the medium by the electric field generated by the incoming laser
light oscillates with a frequency 2co in the form of a spatial wave. The polarization wave
generates a coherent electromagnetic wave at 2oo. Under ideal conditions, the efficiency
of this nonlinear process can be as large as 80%. However, due to the quality of the
crystal, reflection losses and other limiting factors, the typical conversion efficiency at
JANUS is only 25%.
In its present configuration, a single beam can deliver up to 100 J in 1 ns, or
30 J in 100 ps. The frequency-doubled beam gives nominal energies of 30 J in 1 ns
and 10 J in 100 ps. The maximum repetition rate for full system shots is one shot
every forty-five minutes; it is limited by the time necessary for the amplifier optics to
cool. However, including time necessary for laser alignment and shot preparation, the
average number of shots per day is about five.

49
Figure 4-2 shows the layout of the laser components. The master-oscillator is a
Quantronix 416 that is an active mode-locked and Q switched laser. One of the
oscillator pulses is selected by the switchout for propagation and amplification through
the laser chain. There are three main types of components in the laser chain: amplifiers,
spatial filters, and isolators. The initial pulse has an energy of 50 pJ and a gaussian
profile in space and time. It is first double passed through a Quantel preamplifier which
increases the energy by a factor of 50. Subsequent amplification is achieved by using
two kinds of amplifiers in the JANUS system - rods and disks. The lasing medium for
both are Nd doped glass. The alpha rod amplifiers have a gain of 20. The rods can be
pulsed every 10 minutes because they are immersed in cooled water. The beta rod
amplifiers have a gain of 7. The beta disk amplifiers consist of six 10.8 by 20.0 cm Nd
doped glass disks that are mounted at Brewster's angle in order to eliminate reflections.
These amplifiers have a gain of 3.5 and have refractive index matched coatings that
suppress parasitic modes. Although the disk cavity is flushed with cooled nitrogen gas,
the disks must be allowed to cool for forty-five minutes before they can be used again.
The spatial beam profile is shaped by an apodized aperture which is placed
between the first two alpha rod amplifiers. The aperture clips the wings of the spatial
profile to achieve maximum beam filling of the amplifying media. This component only
has a transmission of 10%, and therefore is the highest energy loss in the system. The
temporal profile is gaussian.
JANUS incorporates 5 spatial filters inserted in the laser chain at regular
intervals. They serve two purposes: First, they suppress beam break up and
filamentation. When the beam is focussed through a pinhole, the high spatial
frequencies are eliminated and the beam is more uniform. Second, they expand the
beam to a larger diameter. The optics can only withstand approximately 5 GW/cm2, so
the beam must be expanded in diameter to avoid damaging them. Initially, the beam is
about 2 mm in diameter. At the entrance to the chamber, the diameter is 90 mm.

Target room 1
Figure 4-2. JANUS laserbay
Target room 2
K
X^w
OSCILLATOR
ROD CHAIN
DOUBLE-PASS
DISK AMPLIFIER
DISK CHAIN
O
TARGET CHAMBER

51
The isolators, Faraday rotators and Pockels cells, are components that eliminate
feedback and amplified spontaneous emission (ASE). They are usually found next to
the amplifiers since these components generate the ASE and also suffer the most damage
from retro-reflections. Faraday rotators and polarizers are used to eliminate retro-
reflections that could propagate backwards through the laser chain and cause damage.
The incoming beam passes through the first polarizer which linearly polarizes it, the
Faraday rotator rotates the polarization by 45 degrees, then it passes through the second
linear polarizer which is oriented 45 degrees with respect to the first one. When retro-
reflection comes back through the Faraday rotator it is again rotated 45 degrees, and is
now rotated a total of 90 degrees with respect to the first polarizer. The extinction of the
retro-reflected beam is high enough to alleviate amplification of the retro-reflected beam.
The two Pockels cells eliminate feedback and noise due to amplified fluorescence. The
pockels cell is gated "on" for 30 ns. Light can pass in either direction during this time.
However, when the cell is off, the extinction factor is on the order of 10'3.
The laser beam is directed out of the laser bay into the target chamber room. If a
frequency-doubled beam is desired, then the conversion crystal is placed at the entrance
to the target chamber. Figure 4-3 shows the general layout of the room and the beam
paths. Alignment of the laser optics and focussing are done by using continuous wave
(CW) YAG lasers that are propagated along the same optical path as the laser beam. The
same CW YAG laser is used for alignment of the beam onto the target. However, since
different wavelengths of light have different focal lengths through the lenses, a
frequency-doubled YAG laser light must be used for focussing the 2co beam on the
target.
The alignment for the beam onto the target is accomplished by using a
combination of mirrors and partially transmitting mirrors to reflect the beam, and lenses
to focus the beam. The beam path is shown in figure 4-3. Before doing shots, the laser
was aligned into the target chamber to a fixed fiducial which was placed at chamber

52
center. Unless there is reason to believe the optics have been moved or jarred, this
procedure is only done once per day.
The beam can be focussed by viewing the target either in retro-reflection or in
transmission. If the target is reflective, focussing on the target in retro-reflection is
easiest. The laser light that is reflected off the target passes back through the focussing
lens at the entrance to the chamber. This reflected laser light is then refocussed into a
TV monitor. Since the same lens is used for the incoming laser light and the retro-
reflected light, the lens position for best focus of the laser is the same as for best focus
for the TV monitor.
To focus in transmission, two lenses must be used. A lens in front of the target
focusses the laser onto the target, while a lens in back collimates the transmitted laser
light into a TV monitor. The first step is to position the back lens with respect to the
target. Incoherent light from a lamp at the entrance of the chamber is used to project a
shadow of the target onto the TV monitor. To focus the shadow, either the target must
be moved to the point of focus for the back lens, or the lens must be moved so that it
focuses on a fixed target position. In general, choosing a fixed target position was
found to be the best since this choice does not require repositioning of the spectrographs
for every shot. Once the settings for target and back lens are known, the next step is to
focus the laser beam onto the target. The target is removed temporarily so that it does
not obscure the laser beam. Then the front lens is moved until the position of best focus
is found, which occurs when the focal spot of the laser appearing in the TV monitor is
minimized. Finally, the target is moved back to its original position.
The chamber pressure must be < 10tom to eliminate distortion and self¬
focussing of the laser beam. However, when streak cameras are used, the target
chamber must be evacuated to pressures in the range of 10"^ torr. The target chamber is
evacuated by two pumps. An oil diffusion roughing pump begins pumping out the
chamber. When the vacuum reaches 10'^ torr, the roughing pump is assisted by a

Figure 4-3. JANUS target room

54
turbomolecular pump to speed up the process. A liquid nitrogen trap was used also to
minimize the time necessary to pump down. Evacuating the chamber takes about fifteen
minutes if the chamber has been up to air for less than an half an hour.
Finally, JANUS provides a trigger, an electronic pulse that is used to time the
"shutters" of diagnostics. The trigger is formed by directing a small fraction of the laser
beam onto a photodiode. The diode generates a pulse that is propagated through a fiber
optic that has a shorter path length than the amplified laser beam. For JANUS, the
trigger pulse is created after the preamplifier and typically arrives approximately 30 ns
before the laser pulse arrives at the center of the target chamber.
The laser, the target focus, and the target itself, combine to make such a complex
system that absolutely identical experimental conditions are virtually impossible. The
plasma formed by the laser on any one shot is not exactly reproducible, so beam
diagnostics are extremely important. On each shot, the laser energy is measured by a
calorimeter. Additional diagnostics include an optical streak image for the temporal
shape and pulsewidth, a prepulse monitor, and an equivalent plane photograph of beam
quality.
When possible, alignment of spectrographs and shots for beam timing were
done with "rod" shots. These are shots in which only the alpha amplifiers in the laser
chain are used. Laser energies of up to 20 J in lco can be achieved with a repetition rate
of one shot every five minutes. These so-called "rod" shots are more reliable than full
system shots and allowed increased repetition rate of the laser. For all the experiments,
f/4 lenses were used to focus the beam onto the target.
Experiment I
The primary purpose of this experiment was to measure the absolute number of
photons from the pump plasma. Any attempt at photopumping would be futile if the

55
photon flux was not intense enough to create a detectable signal. It was necessary to
experimentally verify that 1.) the laser energy was high enough to generate an intense
flux of photons through the target, and 2.) to prove that the field of view of the
spectrometer to be used to measure the fluorescence could be shelded by a knife-edged
block. In addition, the source was to be characterized by temperature and density as
well as in absolute photon number. This experiment was the most straightforward of
the three performed. The laser was focussed on the target and the emission spectra was
recorded by time-integrating crystal spectrometers.
The targets used in this experiment were parylene-N(C8H8)n sheets with A1
coatings of different thicknesses. These targets will be referred to as foils. Three types
of targets were used in order to obtain optimized pump emission:
1.) 3000Á of A1 on 20 (im of parylene-N;
2.) 4000Á of A1 on 20 (im of parylene-N;
3.) 3000Á of A1 on 30 [im of parylene-N.
Figure 4-4 (a) shows a simple drawing of the foil.
The targets were provided by EXITECH and LLNL. In general, the plastic
(CH) layer is created by coating glass microscope slides. Then the A1 is vacuum
deposited. The procedure EXITECH used was to coat a 10|im CH layer on a
microscope slide, then the CH was released from the slide and was supported free¬
standing and allowed to be coated on both sides, thus speeding the process since the CH
could be deposited on both sides. However, when the A1 was deposited, the heat
involved in this process was enough to weaken the structure of the initial foil so that it
became warped. The foils were not planar; however, measurements by EXITECH
determined that the A1 deposition was complete. The method LLNL used was to coat
the CH on the slide and then deposit the Al. These were flat. For all later experiments,
the CH substrate was supported entirely on the slide to avoid warping problems. With
the method of production decided, EXITECH supplied the targets.

56
The targets were mounted onto a brass target support that was specially designed
for the photopumping experiment. Figure 4-4 (a) shows a diagram of the brass mount
with and without a target. This support was a rectangular "washer” 8 mm x 2 mm x
15 mm. It had a 4 mm hole centered in the middle of the 8 mm side and 4 mm below
the top. A 1 mm deep channel that was as wide as the diameter of the hole was cut into
one of the 8 mm x 15 mm sides. The foil was mounted by stretching the foil across the
channel and gluing the ends above and below the channel. The A1 side was mounted
against the brass over the hole. The hole in the brass support allowed the laser to
irradiate the A1 side of the target and allowed the mini spectrometer to view the plasma.
(The front plasma in the final experiment would be created on the opposite side.) The
foils were cut to a width of approximately two millimeters with a razor blade. After
experimenting a bit, the best way to cut the foils was to use several light strokes to score
the foil instead of a single cut which left a ragged edge. A fast setting epoxy
(Double/Bubble epoxy produced by Hardman, Inc.) which has a working time of 3 to 5
minutes, was used to glue the foil.
The laser irradiated the bare aluminum side of the target through the hole in the
brass target support. It was focussed to a spot 250 pm in diameter which was the
anticipated diameter of the embedded microdot. The laser was a 0.53 pm wavelength
beam which had a 100 ps full-width-half-maximum (FWHM) pulse duration.
Focussing was done in retro-reflection.
Diagnostics
The diagnostics were two minispectrometers to record the absolute photon flux
from the back and front simultaneously. They will be referred to as MA and MB. Both
used PET crystals to diffract the x-rays in the range of 5 to 8 Á. The spectra was
recorded on Kodak Direct Exposure Film (DEF). Appendix A gives a description of the

57
foil target
xWx
MM
a
(a) Brass support
Figure 4-4. Set-up for experiment I.
a) Diagram of the brass target suport and the foil target
used in experiment I;
b) Experimental set-up I. The diagnostics are labelled as follows:
pinhole camera (PH), minispectrometer (MA) and (MB).

58
geometry of the spectrographs and the dispersion relation for Bragg crystal. Figure
4-4 (b) shows the experimental set-up. Detector MA was placed on the side on which
the laser was incident Detector MB was placed on the opposite side. It measured the
x-rays that were transmitted through the plastic substrate of the target-the flux that the
microdot would actually receive if it were in place. Pinhole cameras recorded the size of
the x-ray emitting region of the plasma.
The time-integrating crystal spectrometers are the only detectors currently used to
determine absolute flux with spectral resolution because the crystal's reflective
properties and the x-ray film can be calibrated with known x-ray sources. Although
other detectors, such as the streak cameras, are much more sensitive, they are difficult to
calibrate absolutely.
Procedure
Initially, the target was placed in the center of the chamber and the diagnostics
were aligned to the target by eye. Then set-up shots, using only rod amplifiers, were
done at best focus to produce a spectrum to check the alignment of the spectrographs.
These spectrographs view the entire source, however, the spectrographs do need to be
aligned directly facing the source otherwise the film exposure is not uniform.
The focal spot used in this experiment was 250 (im in diameter. This diameter
was to match the diameter of the embedded microdot, the front plasma. Laser shots at
the maximum energy available at JANUS were needed to attain an irradiance of
10^4 W/cm^. At 0.53pm the maximum energy was < 12 J.
Since the absolute flux was the critical measurement, the film was developed by
the LLNL technical photography department where the environment is controlled and
chemicals are monitored. For the initial set-up shots, the film was developed in the
JANUS darkroom.

59
Experiment II
In this experiment, the laser energy needed for minimum emission of He-Al lines
and the time dependence of the emission was determined. This experiment explored the
optimal conditions for photopumping. The front plasma was created by irradiating an
embedded microdot. The data was taken by monitoring the front plasma with two x-ray
streak cameras. One viewed the helium-like A1 emission, while the other viewed the
lithium-like A1 emission. The Li-like ionization stage was monitored to check that the
plasma was hot enough for the He-Al ground state to be populated.
Three types of microdot targets were shot in this series. They had differing
thicknesses of overcoatings. A sample target is shown in figure 4-5 (a) mounted on the
brass support. Below is a list of the overcoatings on the microdots:
1.) No overcoating at all;
2.) 1000Á of parylene-N;
3.) 2000Á of parylene-N.
All the microdots were 270 |im in diameter.
The microdots with no overcoating were to be used as back-up targets in case the
overcoating caused focussing or low emission signal problems. They were used also
for initial alignment purposes. Microdots having different overcoating thicknesses were
chosen to allow latitude with the emission level and timing of emission. The
overcoating can be used to control the time of emission because the laser will take a
finite amount of time to bum through the overcoating.
A microdot is not easy to find in the limited field of view of the TV monitoring
system. In order to facilitate focussing, each microdot was mounted over the hole of
4 mm nut where the screw would usually enter. The microdots were centered in the
hole by eye. The nut was easily found in the laser focus, then the microdot was easily

60
centered at the position of the laser beam. Because of the use of the nuts, the targets
could be changed very easily by slipping the nuts in and out of the brass mount
described in the experiment I. In this manner, the targets could be mounted on the nuts
ahead of time. The amount of time needed to mount a new microdot target was kept to a
minimum. The nuts are not shown in the figure 4-5.
The laser conditions for the front plasma were chosen to be a 1.06 (im
wavelength for 1 ns. Fairly low energies of about 2 J were sufficient to create the He-
like A1 plasma. Focussing was done in transmission.
Diagnostics
The diagnostics for this experiment were a crystal streak camera and a flat-field
Harada grating streak camera. For this experiment, both streak cameras were mounted
perpedicular to the laser axis. Figure 4-5 (b) shows the position of the spectrographs
with respect to the target. The crystal streak camera used a KAP crystal and covered a
wavelength region of 5 to 8 Á. The resolving power was ~200. This streak camera
monitored the emission from the hydrogen-like and helium-like ion stages of aluminum.
The Harada grating streak camera covered a range of 30 to 50 Á. This spectrograph
primarily recorded the emission from the lithium-like aluminum ions as well as the
hydrogen-like and helium-like emission of carbon.
Procedure
Because of the sensitivity of the diagnostics to position, particularly the Harada
camera, the target was moved to a set position for the shots (nominally the center of the
chamber). Once the target was in place, the final focussing procedure took place.

61
Figure 4-5. Set-up for experiment II.
a) Schematic diagram of target being irradiated by a
laser beam that has a focal spot 2.2 times the
diameter of the microdot;
b) The experimental set-up.

62
The focal spot diameter was to be 600 pm, about ~2.2 times the diameter of the
microdot. At best focus, the laser beam has a beam waist of about 30 pm in diameter.
The focal spot was expanded by moving the lens towards the target, the point of best
focus is then behind the target. A convenient way to check the diameter of the focal spot
was to compare its image to the image of the known diameter of the microdot as it
appeared on the TV monitor. This comparison confirmed that the laser focal spot was
600 + 10 pm in diameter. While focussing the laser on the microdot, a filter attenuated
the master-oscillator pulse so that it did not ablate the overcoat of the microdot.
A solid aluminum target was irradiated in order to align the spectrographs.
These laser shots produced reference spectra for the identification of the lines.
Following the set-up shots, the method used in the experiment was to irradiate the
microdot and see it in emission first. Next, the focal spot was kept fixed, but the
energy in the laser was decreased until the emission could not be detected. Since the
laser energy required was < 2 J, "rod" shots could be used for this series of laser shots.
Experimental Series III
This third and final experiment combined the first two. The full target was a CH
foil with a bare A1 dot on one side and an embedded microdot on the other. Instead of
coating the entire back side of the full target with aluminum as was done in experiment I,
an aluminum dot was deposited. This change was made in order to simplify the
alignment of the laser beams on the target. The most important addition was a Ta block
that shielded the crystal streak camera from the pump plasma. This block was critical to
the detection of the fluorescence.
For the final experiment, the plastic substrate in the target was changed to
polypropylene (C3H6)n- This substitution was made because of availability. The
properties of the polypropylene and parylene are rougly the same, except that the

63
molecular configuration is slightly different, which leads to a change in density.
Polypropylene has a mass density of 0.9 g/cm3 as opposed to 1.1 g/cm3 for
parylene-N. The ablation rate for polypropylene (~ 5600 Á/ns ) is slightly higher, so
the thickness was increased to 24 pm so that the substrate had the same bum-through
characteristics.
The different target combinations were: 1.) a target with a 550 pm diameter bare
dot of aluminum for the pump plasma, and 2.) a full target with an embedded microdot
on the front side and a dot on the other side. The full target consisted of a 24 pm thick
polypropylene substrate (CH) with an embedded microdot of 270 pm diameter on one
side and a 550 pm diameter bare dot of aluminum on the other (see figure 4-6). The
embedded microdot, a 1500 Á thick spot of A1 overcoated with 1000 Á of parylene-N,
was irradiated to create the front plasma. The other A1 microdot, 3000 Á thick, was
irradiated by the back beam and became the pump plasma. The centers of the embedded
microdot and bare dot were aligned.
The most efficient way to block the main diagnostic from the emission of the
pump plasma is to place a block as close as possible to the pump plasma. This method
minimizes the blocking of the front plasma emission. The special need to block the
pump from the diagnostics required an elaborate target mount. The relationship of the
target and shield are shown in figure 4-7. The Ta shield was 4 mm from the center of
the target. For a line of sight that was 90 degrees from the laser axis, the placement of
the block edge relative to the front edge of the full target had to be within 5 pm.
The mount consisted of a mechanical base that could accommodate two stalks. It
is shown in figure 4-7. The hole for one of the stalks was fixed, while the other was
actually a sleeve that could be manipulated by small jewelers screws. The tantalum
shield was mounted on a stalk and placed in the fixed hole. The brass target support had
a stainless steel stalk which then slipped into the adjustable sleeve. It was held in by a
dab of epoxy and could be "snapped" out by breaking the epoxy "seal" and twisting the

64
Figure 4-6. Diagram of the full target used in the photopumping experiments.
The alignment of the target with the Ta shield and the focal spots
is not to scale.

65
Figure 4-7. This mount enabled the target to be precisely aligned to the tantalum
shield. The coordinate axis is centered over the axis of rotation in the
x-y plane. The bold arrows indicate the position and direction of the
adjustment screws.

66
brass support and stalk out of the sleeve. The important feature of the mount was that
the target could be precisely aligned to the tantalum block. By using the adjustable
screws, the height, pitch, and rotational position could be adjusted. These adjustments
gave the range of positions for the target relative to the block
The targets came on microscope slide size sheets. There were about 24 to a
sheet. These were carefully cut into strips about 1.5-2 mm wide with a very sharp
pair of scissors. The method of using a razor blade was abandoned for fear of
damaging the targets. The targets were mounted by putting a slight dab of epoxy on the
brass target support, and then carefully pressing the target onto it. Each brass support
had a stainless steel stalk that could be inserted into the target mount. Targets could be
carefully mounted in advance on the brass supports, and, during the experiment, were
popped into one of two mounts.
During the two-beam experiment, the beams irradiated opposite sides of a planar
target. A 1 ns beam of 1.06 pm wavelength at 1.0 x 1012 W/cm2 was used to prepare
the front plasma in the Al XII ion stage. A 0.53 pm wavelength laser beam with a
100 ps pulse length created the pump plasma. An irradiance of 1.0 xlO14 W/cm2 was
used to generate x-rays in the pump plasma. The laser beams were focused and aligned
with f/4 lenses by viewing the target in retro-reflection. The peak of the laser beam that
created the radiative pump was delayed by ~ 1.0 ns relative to the peak of the first laser
pulse. A 600 pm focal spot was used to create the front plasma; a 270 pm focal spot
was used to create the pump plasma.
Diagnostics
The diagnostics included the full array of diagnostics used in the first two
experiments, but in a slightly different configuration. The spectroscopic diagnostics
used for the final experiment (see figure 4-9) covered the H-like through Li-like ion

67
Figure 4-8. Set-up for experiment III.
a) Close-up of the alignment of the target showing the line
of sight for the streak camera;
b) The diagnostics in the schematic diagram are labelled as
follows: pinhole camera (PH), minispectrometer (MB),
curved crystal spectrometer (CCS). The Harada
grating streak camera is not shown.

68
stages of Al. Time integrating spectrometers used Bragg crystals to cover a wavelength
range of 6 Á to 8 Á. These crystals were calibrated absolutely by measuring the crystal
rocking curve on a stationary x-ray anode source. Appendix B describes the method of
calibration. A time-resolving streak camera was used with a Harada flat-field variable
line spaced grating (2400 lines/mm) to measure the Li-like A1 lines from the front
plasma. It viewed the plasma at an angle of 45° above the axis defined by the laser
beams (not shown in figure 4-8) and encompassed a spectral range of 32 Á to 60 Á.
The primary diagnostic, the crystal streak camera, overlapped the spectral coverage of
the time-integrating spectrometers by using a flat KAP crystal. Two pinhole cameras
were also used to monitor the consistency of the laser focal spots.
The main diagnostic addition was the use of a curved crystal spectrometer with a
space-resolving slit. It was positioned perpendicular to the laser axis but did not have a
block. Instead it had a slit of 25 pm which, when positioned coirecdy, should have
imaged both the front and rear plasmas onto different parts of the film. The advantage
of having both plasmas on the film would be that variations in film development would
not have affected the relative intensities. In addition to getting the absolute photon
number, the relative measure of the intensities would have been obtained.
Unfortunately, the front plasma emission was either not strong enough or the crystal
efficiency was too poor to record the front plasma emission. In fact, even the pump
plasma emission barely registered.
Finally, the streak speed of each of the streak cameras was timed. Since an
absolute timing fiducial was not available, the relative timing between the two signals
(self-emission and fluorescence) was important.
Procedure
The preparation for the two-beam shots was the following. The target was
aligned to the Ta shield. Then the target mount was placed in the chamber and aligned to

69
the crystal streak camera photocathode slit. Finally the laser beams were focussed on
each of the microdots. Each one of these will now be discussed in turn.
The target to shield alignment procedure was critical to the success of the shots,
so it will described in detail. The foil was layed and slightly stretched so that it was as
flat as possible. The first step was to align this clean edge with the Ta knife-edge. For
this procedure a special microscope was used. The target was clamped into a holder that
could only rotate. The stage of the microscope could be moved with micrometers in the
X-, y-, or z-direction. A conventional microscope allows the specimen to move in a
plane and the microscope lens to focus in the direction perpedicular to the plane. The
advantage of this special microscope was that the object remained stationary. This
microscope simplified the task of measuring the relative position of different parts in the
z-direction, even if the depth of field of focus in the x-direction changes.
To enable a clear discussion of the alignment, we will define the plane-of-
alignment as an imaginary plane passing through the center of the target and parallel to
the face of the target. The mount was adjusted until the knife-edge of the block is in this
plane-of-alignment. First the axis of rotation was oriented parallel to the knife-edge of
the shield. The actual process of accomplishing the final alignment is a tedious iteration
between the rotation of the brass support and the rotation of the entire mount because the
axis of rotation of the brass support was not centered on the center of the microdot, and
the axis of rotation of the mount was about the fixed Ta shield. The error in this
alignment was 2 to 4 microns, due to the irregularity of the edge of the CH. The
microscope with a digital readout had a resolution of 1/1000 of a micron.
The alignment of this target mount inside the vacuum chamber was another
critical step. A Keuffel and Esser telescope was mounted on the target chamber opposite
the crystal streak camera. The line of sight was established so that the crosshairs of the
telescope were centered on the center of the streak camera photocathode slit. Then, the
target was first aligned rotationally by viewing the target surface and the knife-edge so

70
that the plane-of-alignment was parallel to the telescope line of sight, and vertical. The
z-axis shown in the target mount diagram (figure 4-7) was now parallel to the axis
defined by the direction of the laser beams. This positioning was done using an Oriel
rotational mount that could be operated by controls outside of the chamber. Then the
target was moved vertically so that it was aligned to the point of focus for the
instruments, the center of the chamber. The target was moved in the z-direction until it
was at the center crosshair. Final slight x-y adjustments were made at the end. In
essence, the y- and z-directions were determined by the telescope. There was no
absolute fix on the x-direction, however, it was not a critical dimension and was
observed experimentally not to drift more than 50 (im. Since the slit was 1 mm, the
error in alignment in the z-direction was judged to be ± 10 microns. The y-direction
error was not critical to within 0.25 mm.
The focussing of the laser beams was fairly complicated because it was
necessary to have the focal spots coincide on the same axis. The aluminum in each of
the microdots was reflective enough to focus in retro-reflection for both beams. The
optics for focussing would have been much more complicated if the embedded microdot
had to be focussed in transmission because the focal length of the lens on the backlight
side would have to be moved for 1.06 p.m light and for 0.53|im light. We checked the
focus of each beam just before the shot.
The philosophy for this set of shots was the following. We began by
confirming the results from the previous two experiments. This procedure allowed us to
check the laser conditions and characterizations of each of the two plasmas. Then, a
two-beam shot was made with both plasmas without using the block. The timing and
the line overlap of the He-like ’So - ’Pi transition of the back and front plasmas were
checked. Then one-beam shots to create the radiative pump blocked by the Ta shield
were done in order to prove that the fluorescence observed was not merely direct
emission from the radiative source.

71
Finally the two-beam shots on the full target were done. Variations of the laser
parameters included changing the focal spot size on the back and changing the relative
timing between the two laser pulses. Shots were also taken using a broad band source,
Sm (Z=62) for the pump plasma.
Problems
A danger of not focussing the beams back to back did exist. In focussing in
retro-reflection, initial focus was done with an incoherent light source that was focussed
through the lens and reflected back. Obviously, the light cannot be in the middle of the
lens, otherwise it would obscure the light reflected back out. So, the focus was
dependent on the position of the incoherent source unless the lens was positioned at best
focus. The error, then, comes in the alignment of the lens that focusses the laser beam.
If the z-direction movement of the lens did not coincide with the laser axis, then moving
the lens to defocus the laser beam also would have affected the position of the beam on
the target. Once the lens was defocussed, the position of the beam on the target could
not be checked because the incoherent light source would give a false image, and the
retro-reflected light was found to be too weak to be detected by the TV monitor. The
observed error for the back beam that can be attributed to this drift was estimated from
the movement of the microdot on the TV screen using the incoherent light. At most, the
image of the dot moved by approximately 275 pm. In most cases, the observed drift
was about 100 p.m. The drift for the front beam was not important because the beam
was defocussed to 600 p.m--the drift might have introduced edge effects from the laser
beam, but the beam certainly did not miss the embedded microdot. The back beam was
not defocussed as much, so the drift would have been smaller, ~ 50 pm This problem
may have decreased the intensity of the fluorescence signal.

CHAPTER 5
ANALYSIS
Before analysis of the data begins, the raw data must be converted by detailed
data reduction procedures to yield meaningful units. First the data reduction for each
type of film will be discussed. Then, a discussion of the spectroscopic methods
follows. Finally, the results for each of the experiments will be discussed.
Data Reduction
All the data were recorded on two different kinds of film— film sensitive to direct
x-rays and professional photographic film sensitive to visible light. First the film was
developed. Then it was digitized and computer software packages were used to process
the data. The image processing of x-ray film data involved removing the film fog,
converting film density to intensity, and removing background x-ray exposure.
Appendix A gives the details about the film.
For these experiments, a Perkin-Elmer PDS 1010GM microdensitometer was
used to digitize the data. The scanning process involves using an incandescent source,
imaged through an aperture onto the film. The light passing through the film is recorded
by a photomultiplier tube. The electrical signal from the tube is proportional to the
optical density of the emulsion. The result of this process is a numerical matrix of
numbers; each number represents the the film density for a pixel, which is the area of the
film illuminated during the scanning. The film density can be resolved in steps of
0.005, with a maximum of 5.11. A stepper motor controls the scanning to better than
1 |im.ul
72

73
The digitized data were processed by the image processing software, XT,
provided by G. Glendinning of LLNL. XT can display a two-dimensional image of the
data on a Ramtek color monitor and the user can manipulate a cursor that can be moved
by means of a trackball. The software associates a cursor that is visible on the screen to
the data image. Typically, a calibration file data is folded in to convert the digitized data
from density to relative intensity. The resulting image is a record of the intensity
distribution as a function of space, or as a function of space and time. For direct x-ray
film, absolute calibration files were used. For streak camera data, a calibration file was
generated by scanning the calibration wedge on each piece of film.
By placing the cursor at a particular position, one can specify the area of data to
be studied and operations provided by the software are used to manipulate the data. One
of the operations of this program allows the user to generate profiles of the data. The
user specifies a slice of the data and the program plots an average of the intensity values
in the width of the slice versus the x or y axis of the image. These plots are called
"lineouts" and they correspond to intensity versus wavelength plots, intensity versus
time plots, or intensity versus space plots.
For direct x-ray film, the product of intensity and time is a reliable measure of
exposure.112 Therefore, for direct x-ray film, the film density is a linear function of the
number of photons striking the film. Absolute calibration of the film is obtained by
using known x-ray sources to generate calibration curves. Henke, et al. have done
extensive studies to model the film response and have measured known
exposures.113’114
Direct x-ray film has a film fog produced by any background x-rays such as
cosmic rays. The optical density of film is defined as logarithm to the base 10 of the
film opacity, where the film opacity equals the inverse of the transmission. Even film
that has not been exposed will be slightly opaque when developed. The calibration
curves are valid when an optical density of zero corresponds to unexposed film.

74
Therefore, before the film density is converted to relative intensity, this inherent density
is subtracted so that conversion using the calibration curve is not skewed.
In this experiment, DEF and Industrex M direct x-ray film was used. Both have
a useable density range of about 0.2 to 2 photons/jim2. Below a value of 0.2, the film
is not sensitive, while above a density of two, the film saturates and is no longer linear
with exposure. The development of the films was performed according to the times and
temperatures listed by Henke so that his calibration curves could be used.
Although filters were placed in between the crystal and film, the film became
fogged due to crystal fluorescence and stray radiation. The average of the background
fog was found by sampling the pixel intensities in the area of film near the data of
interest. Then, the average background intensity was subtracted from the data.
The film used with the streak cameras detects the light from the P-20 phosphor
on the back of the microchannel plate. Details of the streak camera are given in appendix
A. Some commercially available films are Kodak TMAX 400, RXP, and Tri-X. These
films have a much larger dynamic range than direct x-ray film and their densities are
linear with the log of the exposure.
In this experiment RXP and TMAX 400 film were used. A portion of each piece
of film was exposed to light from a Xenon flash lamp that had been attenuated by a
continuous calibration wedge placed on the film. The exposure time was chosen to be
one millisecond because the phosphor on the streak camera glows for about one
millisecond. The calibration wedge for a P-20 phosphor has a gradation of 0.6 optical
densities per cm. After the film was developed, this strip was densitometered to provide
a known density vs log(Exposure) curve for each particular piece of film. The streak
camera data were then corrected for background. Only relative intensities can be derived
from this data.

75
General Discussion of Spectral Analysis
The data are now in a form that can be analyzed. A spectrum, i.e. the intensity
as a function of wavelength, has been extracted from the raw data. The observables
contained in the spectrum are the intensities and line widths. The quantities that can be
deduced from the data depend on the experimental conditions. For instance, the plasma
can be characterized by its electron temperature and/or electron density by line ratios.
Further, individual line transitions can be analyzed for absolute flux and time-
dependence. Ionization balance can be inferred from the temperature and/or the ground
state populations measured by absorption lines. This section will explain the methods of
spectroscopic analysis used in this thesis.
There are three types of transitions: 1.) bound-bound, 2.) bound-free, and
3.) free-free. A comprehensive discussion of the intensities is given in Stratton.115
The intensities are given as follows.
Bound-bound transitions. These intensities involve the integration over the plasma
length, C. For the optically thin lines,
where A is the Einstein coefficient, n¡ is the ion density, and hv is the energy of the
transition.
For optically thick lines, the effects of radiation trapping can be accommodated by
reducing the spontaneous emission coefficient by an "escape factor." The effective
spontaneous decay rate is A*y = Pe Ay. where Pe is the escape factor. It can be
defined in one of two ways. One way is to consider the intensity of the line as having a

76
negative contribution due to the stimulated absorption term. Then the escape probability
is
where the Einstein By coefficient has be reexpressed in terms of the Ay coefficient, u
stands for the upper level, 1 stands for the lower level, and ((y is the line profile.
An equivalent way to think of the photon escape factor is to define it as the
integration of the transmission of a photon through a medium over angle and space. In
this formulation the escape factor represents the mean probability that a photon emitted
anywhere in the plasma volume travels directly to the plasma surface and escapes in any
direction. This approach will be discussed in more detail in the context of radiative
transfer theory in the next chaper. The paper by Irons gives a complete discussion of
this process and cites a comprehensive set of references.116
Free-bound transitions. The intensities involving continuum states must be
summed over the different ion species n¡ and the levels, p, into which the electron can be
captured.
The energy of the photon and recombining electron are related by hv = 0.5mv2+x,
where x is the ionization potential, a is the recombination coefficient, and v is the
velocity of the electron. For hv > x, the spectrum is continuous. For hv < x, however,
there is no bound-free spectrum for this ion. This recombination can shift to lower
energies if the electron density is high enough to cause ionization potential depression.
Using the cross section given in chapter 2 for recombination into the nth shell of
H-like ions of charge i, the emission per unit frequency per unit time per volume is

77
dE „
— = Cn^i
dv
#)
13/2
X(i.n) \ fc
X(h)
Jlgexp X(i,n)-S
where C = 1.7 x 10-40 ergs cm3, ^ is the number of places in the n111 shell that can be
occupied by the captured electron, %(h) is the hydrogenic ionization energy, and %(i,n)
is the ionization energy from the initial state i to the final state n, and g is the bound-free
Gaunt factor.
Free-free transitions. For a plasma length, [, these intensities are given by
t
Ivdv =
4tc
ne ^ n¡yhv dv d/
where y is the free-free transition probability. The sum over i accounts for different
ionization species, and ne is the electron density.
If the integration is over a Maxwellian electron velocity distribution using
Kramer's formulation, the emission is
dE _r n n to
dv CilenMkT
1/2
Z g exp
hv
FT
where C = 1.7 x KT40 ergs cm3, %(h) is the hydrogen ionization potential, and Z is the
effective nuclear charge. The gaunt factor, g, has been tabulated by Karzas and Latter,
and is the quantum mechanical correction to the classical result.117 g = 1 for hv = kT,
g < 1 for hv > kT, and g > 1 for hv < kT. For long wavelengths, (i.e. hv«kT ) the
spectral shape is independent of T; but for short wavelengths, the spectrum can be
useful as a temperature diagnostic
A general rule for the continuum emission is that for
kT>SCxhZ2
free-free radiation exceeds the bound-free radiation for an atomic number Z.115 Here Xh
is the ionization potential of hydrogen. The ions become totally stripped.

78
Line Identification
To a first approximation, the structure of the spectra is determined by the energy
levels and the transition oscillator strengths. The energy level structure for K-shell ions
has already been discussed. Line identification is done by matching the experimental
dispersion to the dispersion that can be calculated for the spectrograph for wavelengths
given in the literature.
Line Ratios
Line ratios are frequently used to measure the temperature and/or density of a
plasma. A good temperature diagnostic should be constant for changes in density. A
good density diagnostic is constant in a given temperature range. Whether a line ratio is
a good temperature or density diagnostic depends on how the higher lying level is
populated (source of the population) and the lower state type (excited or ground).
In low density plasmas, the predominant population source is the ground state.
In general, collisional excitation is responsible for creating excited states, and
spontaneous decay depopulates those states. The line ratio, then, for transitions from
the same ion stage, are essentially density independent because the line ratio will reflect
the ratio of the collisional excitation rates. The electron density cancels out.
As the density increases to the point where levels become collisionally mixed,
the level with the highest spontaneous decay rate, A¡ j , is the main depopulation
mechanism. For example the intercombination line has a low A¡j value and, therefore,
at densities in which the collisional rate to the !Pi level approximately equals the
radiative decay rate, the 3Pj level is depopulated by collisions more than radiative decay,
thus the intensity of the intercombination line decreases. The intercombination line is so

79
named because it is a transition which is spin forbidden, i.e. AS = 1. It appears in the
spectra of ionized species because pure L-S coupling is no longer an adequate
representation of the system.
One of the standard intensity ratios is found by combining the Boltzmann
population distribution and line intensity in LTE.
kT = (E,-Eb|
3
In
ItAbg/a
3
where the subscripts a and b stand for different upper levels, X is the wavelength of the
transition, (Ea - Eb) is the energy of the transition, f is the oscillator strength, and g is
the statistical weight.
For coronal equilibrium the temperature may be determined by
kT”(E.-Eb|
In the analysis performed in this thesis, the suite of computer codes RATION,
RATSHOW, and SPECTRA were used. These were written primarily by R. W. Lee to
serve as a tool in the study of plasmas.80 A complete plasma model must be quite
complex since it must incorporate the detailed atomic models of all the constituent ions
as well as the plasma effects. As conceived, these codes are meant to facilitate the study
of plasmas by using a complete but simplified atomic physics model. Hydrodynamic
effects and detailed radiative transport are not included. Hence the results of theses
codes are most applicable to spectra from plasmas that have small temperature and

80
density gradients, or are resolved in time or space. Even if the plasma does not satisfy
the above criteria, the code can bracket of the temperature and density of the plasma.
The first code, RATION, calculates the populations of the H-like, He-like, and
Li-like ion stages. The details of the atomic structure can be found in the paper
describing the codes. In general, the electron configurations of the ground state and first
excited state are represented in detail. For instance, the He-like ground state and the
four excited states of the form 1 s21 are explicitly included. In addition, the model
includes the important doubly excited levels that are involved in the formation of
satellites to the resonance transitions of He-like and H-like ions. The preceding
ionization stages, Be-like to neutral, are represented only by their ground states. All the
rates mentioned in the chapter 3 are included.
The two other codes use the population file output by RATION. RATSHOW
calculates line ratios as a function of temperature and/or density. SPECTRA uses the
populations and theoretical or semi-empirical energies and oscillator strengths to create a
synthetic spectra for given a temperature and density. SPECTRA includes the
calculations of detailed Stark line shapes if desired.
The codes are used interactively in several ways. For a well-characterized
plasma, i.e. one in which independent measures of the temperature and density exist, the
code can be used to resolve discrepancies between differing theoretical rates that affect a
particular spectroscopic diagnostic such as a line ratio. The more common way to use
the codes is to diagnose the temperature and/or density of plasmas. In the following
analysis, the codes were used to determine temperatures and densities.
Figure 5-1 shows the spectrum of aluminum in the 20 to 50 Á region for two
different temperatures. The dotted line is the spectrum at 200 eV. It is dominated by Li-
like emission. The character of the spectrum drastically changes as the temperature
increases because the Balmer lines of H-like aluminum become dominant.

81
Line Shapes
Line shapes are affected by the plasma environment and the resolution of the
spectrometer. They can be used to determine ion density or temperature. At high
densities, Stark broadening causes the energy levels which are essentially degenerate to
become shifted in response to the strong plasma fields. For hydrogenic species, the
electron density can be schematically represented by
3/2
ne= C(ne,T) AX
where C is a slowly varying function of density and temperature. This measurement is
not dependent directly on the atomic cross sections, and therefore, is a good complement
to measurements of the density by line ratios. In this thesis, the line shape codes of Lee
are used to estimate electron density.118 However, Stark broadening was not a
significant factor because the densities were not high enough.
At lower densities, the line width is usually dominated by Doppler broadening,
in which case it provides a measure of the ion temperature, Tj.
where M is the mass of the ions, X is the wavelength of the line, c is the speed of light,
and k is the Boltzmann constant.
Figure 5-2 shows the 200 eV spectrum including Stark broadening which is
convolved with an instrument FWHM width of 3 eV. This synthetic spectrum shows
how drastically the line spectrum can be affected by instrument resolution as well as line
broadening mechanisms.

Figure 5-1. Synthetic spectra at 200 and 1000 eV.


Figure 5-2. A spectrum including Stark broadening convolved with an instrument width of
3 eV.


86
Absolute Flux
This measurement depends on the collection efficiency of the detector. In
principle, the equation for line intensities can be used to calculate the number density of
the upper level. However, the line shape is not always well known, and the plasma
length is not usually well characterized. Only optically thin lines can be used for
calculating number densities by this method. Measurements of the absolute intensity of
the continuum can be used to calculate density; although in practice, it is very hard to
determine the absolute efficiencies of detectors.
In this thesis, the absolute flux was used to calculate the number of photons per
steradian emitted by the plasma source. It is a measurement of the conversion efficiency
from laser energy to x-rays. No attempt is made to determine the plasma conditions
from these numbers. The reduction of the recorded flux to the source flux is dependent
on the detector geometry and the crystal efficiency and therefore, will be discussed
below.
Experimental Results
Experiment I
Time integrated line ratio measurements in the preliminary experiment for the
pump plasma determined the temperature range, density range, and the absolute photon
number of the pump. An example of the spectrum is shown in figure 5-3 in which the
lines have been identified. The analysis of experiment I consisted of the following:
l.)line intensity ratios of the He-like dielectronic satellites to the Li-like dielectronic
satellites, and [Al XIII l^Sj/2 - 2“P¡/2 / Al XII 1 ^Sq - 2^Pj] for temperature, 2.) the
line intensity ratios of the [Al XII 11 Sq - 2^P\ / Al XII 1 ^Sq - 2*Pi] and the width of

87
the He USq - 5^Pj line due to Stark broadening for density, and 3.) the absolute flux
calculation. To determine the source size, the width of the 1 ^Sq - 23p^ Une on the
minispectrometer were used.
Line ratios from time-integrated data
Figure 5-4 shows all the temperature sensitive line intensity ratios. Since bare
aluminum was irradiated, large temperature and density gradients would be expected in
the plasma. The line ratios for the [ 12S j/2 _ 22P3/2/ ^Sq - 2^] and the [He-like
satellites / Li-like satellites] decrease slightly with increasing energy. Within the error of
these measurements, this variation is not significant.
The ratio involving only the satellites is probably the most reliable diagnostic
since these lines are optically thin. The value for the ratio is 0.4 + 0.2. From the
RATION graphs given in figure 5-5, we find that this ratio implies a temperature range
of 400 to 600 eV.
The ratio of the Al XIII l2S1/2 - 22P3/2 to the Al XII USq - 2^ is a
temperature diagnostic because the lines are from different ionization stages.
Unfortunately, these lines are vulnerable to opacity effects. Therefore, line ratios
involving these lines are difficult to interpret. The value of this ratio is 0.5 + 0.2 which
indicates a temperature of 200 to 600 eV for densities 1.0 x 1022 or less.
The two ratios involving the satellites to the resonance lines do not give as
conclusive a measure of temperature. As discussed in the introduction, satellite lines are
formed by discrete states above the first ionization limit. The intensity ratio of the
satellite line to its parent resonance line is generally a good temperature diagnostic
because the ratio can be expressed as a function of temperature multiplied by a term
depending on the decay rate (an atomic parameter) of the satellite line which is generally

88
a function of Z. The review paper by Dubau and Volonte,6 shows that the temperature
dependence of the ratio can be expressed by
rep ,«P((E0_Es)/kT)
where E0 is the energy of the parent line and Es is the energy of the satellite line. The
exponential factor is usually a slowly varying function of T because in this case, the
energy (E0 - Es) « kT. Therefore, the ratio is proportional to the inverse of T.
The value of the [Li-like satellites / 1 - 2!Pj] ratio is approximately
0.27 + 0.04. This regime on the RATION plots shown in figure 5-6 tend to imply an
electron temperature of 200 to 400 eV for the same density range. However, the
observed intensity of the resonance line is depressed by radiative trapping. Hence, tt is
conceivable that the ratio could be too high by a factor of 4. The range of temperatures
indicated by a ratio that is 0.25 smaller, is again 500 to 600 eV which agrees with the
previous ratios. The ratio of the [He-like satellites / 12S1/2 - 22P3/2] is ~ 0.2 + 0.04.
Again radiative trapping probably inflates this ratio. In fact, if the same multiplicative
factor is used for both of these ratios, the temperature range indicated by both track each
other. Although the ratios are not conclusive, they are in the approximate range
expected.
Density was deduced from the ratio of the Li-like satellites to the Al XII
l^o - 23Pj, which is called the intercombination line, and from the intercombination
line to the resonance line. The figure 5-7 gives the density sensitive ratios as a function
of laser energy. The [Li-like satellites / 11 Sq - 23P¡ ] ratio has a value of 1.4 + 0.4 .
The plots in figure 5-8 show that this ratio implies the density should be in a range of
1021 to 1022 cm '3.
The [1 *So - 23Pj / 1 *So - 2!Pj] ratio is a better diagnostic because both of the
lines are emitted from the same region of the plasma. The intercombination line is

89
density sensitive because the population of this level is collisionally mixed with that of
the 1 Pi resonance level which can decay much more quickly. The value of the ratio is
from 0.05 to 0.2 . However, the resonance line persists about three times as long as the
intercombination line. Hence, it is reasonable to assume that the ratio could be wrong
by a factor of 3. From figure 5-8 we find that the upper limit of the ratio gives a density
is 5.0 x 1019 . The lower limit implies densities near 1021 cm '3 which implies that the
lines are emitted over a density equal or less than the critical density at which the laser
energy is deposited.
A consistent determination of the temperature and density must take into account
measurements from all the ratios. Since gradients affect the individual line intensities
differently, the diagnostics that are presented bracket the plasma parameter regime
possible in the experiment. With this in mind, these ratios indicate that the plasma has a
temperature in the range of 400 to 600 eV and an electron density in the range of
5 x 1019 to 5 x 1021 cm_3.
Line widths
To determine the line broadening resulting from the Stark broadening
mechanism, an optically thin line was first used to determine the line width contributions
due to the source size and instrument. Next, the line width at full-width-half-maximum
was taken of the highest order resolvable line. The spectra were considered
unresolvable at principal quantum number n = 6, so the 11 So - 5 *Pi transition was
used. This measurement also assumes that the emission region of the optically thin
satellite is about the same as the region emitting the n=5 line. Although both lines are
probably emitted in the dense, hot region in the center, there was no independent method
used to confirm this fact. The electron density determined by this method was
~ 5.0 x 1021 cm‘3 .

Intensity (arb. units)
Figure 5-3. Sample spectra recorded on the minispectrometer.

Ratio
91
Laser energy (J )
Figure 5-4. Time-integrated temperature intensity ratios for aluminum.
0 He-like satellites/ Ly a
A Li-like satellites/ He a
X Li-like satellites/ He-like satellites
-f Ly a / He a
Lya = 12S
3 1 1/2
He a = l S -
0
2 P
1 3/2
2 P
1

Figure 5-5.
RATION plots for temperature ratios,
a) [He-like satellites / Li-like satellites];
b)[l2S1/2-22p3/2/llSo-2lP1].

93
Z = 13; oopfiie is alO ot 15:32:45 on 07/07/89
Tr = 0.000 Opacity is On Calculation is NlTE
Size = '• 000e-06. impurity Zbar = 0 0000
N: hea2 -he2st hea3 -he2pt hea4 -he2ps
0: jkl -Cp aPca -iCp
Density
= 1000e+18
- l.OOOe+19
=* l OOOe-t-20
* 1COO**21
= iOOOe+22
(a)
Z = 13: pooriie is oi13x at 10:03:23 on 07/07/89
Tr = 0.000 Opacity is On Calculation is NLTE
Size = 1 350e—02. impurity Zbar = 0 0000
N; hv2 — hyl
D: he2ps -neis
Density
a = l 000e+18
t> - 1 COOe+19
c = 1000e+20
d = 1000e+21
e * iOOOe+22
(b)

Figure 5-6. RATION plots for temperature ratios.
a) [Li-like satellites/ LSq - 21Pi];
b) [He-like satellites / 12Sj/2 - 22P3/2].

95
Z = 13; popfile is oil3b at 17:23.58 on 09/26/89
Tr = 0.000 Opacity is On Calculation is NlTE
Sice = 1 350e—02; impurity Zbar = 0.0000
N: jkl -Ii2p aDcd -Ii2p
D: he2ps -neis
Density
= 1 G00e+18
l.000e+19
= 1000e+20
= i000e+21
= I000e+22
Te (ev)
(a)
Z = 13; popfile is ai13b at 17 23.53 on 09/26/39
Tr = 0.000 Opacity is On Calculation is NlTE
Sice = l 350e-02. impurity Zbar = 0 0000
N: heo2 — he2st heap -helpt hea4 —ne2ps
l: hv2 — hvl
Density
a = i 000e+18
o - 1.000e+19
c = 1000e+20
j a = 1GOOe+21
j e = I OOOe+22
Te (ev)
(b)

Ratio
96
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
6 7 8 9 10 11 12
Laser energy ( J )
Figure 5-7. Time-integrated intensity ratios for density.
X Li-like satellites / IC
â–¡ IC/ He a
He a = l1 s - 2!P
0 l
IC = l1S - 23P
0 1

Figure 5-8. RATION plots for density ratios.
a)[llS0-23p1/llS0-2lP1];
b) [Li-like satellites / ^Sq - 2^ ].

98
Z = 13: ooprue is oilox at 10:03:23 on 07/07/89
Tr = 0.000 Opacity is On Calculation is NlTE
Size = 1 550e-02: Impurity Zbar = 0.0000
N: he2pt -heIs
D: he2ps —he is
Temperatures
a = 100.00
b “ 200.00
c = 300.00
a =
400-00
500.00
600 00
700.00
i
â– I
I
(a)
Z = 13; poprile is ail3b at 17:16:46 on 09/26/89
Tr = 0.000 Opacity is On Calculation is NLTE
Size = I 350e-02; Impurity Zbar = 0.0000
N: jkl —Ii2p abed
D: he2Dt -hete
-lizp
b -
Temperotures
3 * 100 00
200.00
300.00
400 00
500.00
600.00
700.00
Log Ne
(b)

99
Absolute flux
By using the source to film distance, filter transmission, the crystal reflection
coefficient, and the solid angle subtended by the detector, the equivalent photons/sr from
the source were derived from the photons/|im2 that were measured on the film.
The size of the source (~ 100 qm) is negligible compared to the distance from
the detector to the source (~ 3 cm). Hence, the quantity that is measured can be
expressed in ergs steradian _1 hz -1, which is defined as the fluence, d E / d (hv). The
energy emitted in a line, E, is the fluence integrated over the energy
r
d ^ d(hv)
ergs'
3(hv)
sr
where 3E is the energy transported by the radiation per steradian, in an energy interval
hv + 8(hv). The energy recorded on the film, integrated over an element dy in the
dispersing direction, at a position x on the film, is equal to the energy emitted by the
source into the solid angle subtended by the detector. The total energy on the film is the
exposure integrated over the area; it is equal to the energy from the source integrated
over v and solid angle, Q.
J (Exposure) dx dy =
3 E
3(hv)
d(hv) dQ
where the (Exposure) is measured in photons/qm2 of the film. The solid angle equals
dxdy / r 2, where r is the distance from the source to the film. The element dy on the
film can be related to the angle © of the source by dy = r R(hv,0) d(@), where
R(hv,@) is the crystal reflectivity. Therefore, per unit dx in the non-dispersing
direction, the energy recorded on the film, assuming isotropic radiation, is

100
r
I (Exposure) dy
3E Rc
8(hv) r
d(hv)
where the integral over @ on the right hand side has been absorbed into the definition of
the crystal rocking curve, Rc. (See appendix B for a discussion of the crystal rocking
curve.) After the integration over the energy interval is done, the equation can be solved
for the total energy in the line
â– line
(Exposure) dy
where Ei;ne is in ergs per steradian. The absolute flux of photons is found by dividing
the energy in the line by the photon energy of the transition.
For laser energies in the range of 5 to 12 J, the absolute number of photons
derived from the time-integrating spectrometer, which directly measured the pump
plasma only, were on the order of 1.0 x 1013 to 3.0 x 1013 W/cm2 . The photons/sr
actually incident on the front plasma were measured to be = 2.0 x 1012.
Figure 5-9 shows that with increasing laser energy, the conversion efficiency
generally increases. However, the highest energy shot, 12.0 J, shows a lower number
of photons than the 9.7 J shot. This decrease could be due to the breakup of the beam
by either spatial filamentation of the beam or a non-Gaussian temporal laser pulse. If
filamentation of the beam occurs, the spatial beam profile is not uniform. The hot spots
that are developed, reduce the conversion efficiency of frequency-doubling crystal. The
energy that is actually measured is the energy in the 1(0 beam, not the energy in the
frequency-doubled beam. One the other hand, if the beam breaks up in time, then a dip
can occur at the peak of the pulse.119 This problem typically occurs if the laser system
is driven at energies that the optics cannot handle. The calorimeters that measure the
energy are not sensitive to the pulse shape, but again, the conversion efficiency of the
doubling crystal is significantly reduced if a double-peaked pulse occurs.

101
Laser energy ( J )
Figure 5-9. Absolute photon flux vs. laser energy.
—■— data from MA spectrometer
—□— data from MB spectrometer
The minispectrometer MB measured a lower absolute flux than the front
minispectrometer, MA. This result is expected since the photon flux incident on MB is
attenuated by the plastic of the target substrate. The transmission coefficient of a solid
filter, T, is given by
T = exp ( -M-P x)
where (I is the mass attenuation coefficient, p is the density, and x is the thickness of the
filter. Measurements of the x-ray transmission through the CH were within 3% of the
transmission predicted from the CH attenuation of the simultaneously measured pump
plasma flux. This result is very important because it allows us to extend the

102
understanding of x-ray backlight efficiencies to radiative pumps. Essentially, a radiative
pump is the same as a backlight except that it will perturb the plasma. During the
photopumping experiment, the flux incident on the plasma could not be directly
measured. Therefore, based on these results, the direct flux of the pump plasma was
measured and then used to determine the flux incident on the front plasma by correcting
for the attenuation of radiation due to the CH substrate.
Target parameters
For providing the maximal photon flux for photopumping, it is not desirable to
bum through the aluminum. The total x-ray conversion efficiency would also be lower
if the laser pulse began ablating the CH substrate. Shots on both the 3000 Á and
4000 Á coatings of aluminum showed that the laser did not bum through in either case.
The aluminum ablation rate is roughly 1900 A/ns. Hence, the thinner 3000 A A1
coating was chosen for the final experiment to minimize the attenuation of the helium¬
like aluminum x-rays by the cold, unablated aluminum.
The thickness of the CH substrate did not affect the edge of the plasma emission
as witnessed by the film pack. Therefore, to minimize attenuation by the plastic, the
20 (im thickess was chosen for the final experiments.
Source size
The source size was determined from the width of the intercombination line on
the film. This line is spectrally isolated, so the contributions of overlapping, unresolved
lines do not cause artificial broadening. By knowing the geometry of the spectrometer,

103
and the rocking curve, the size of the emitting source can be calculated. The
measurement indicated a source sizes of 250 to 300 |im.
Experiment II
This experiment used the two streak cameras. The data were analyzed for line
ratios as well as time-resolved features. The shots in this series determined: 1.) the
temperature and density of the plasma; line ratios of the Al XI and Al XII lines from the
Harada grating streak camera bracketed the ranges, while the [ 12S j/2 - / 1 1Sq -
2^1] ratio from carbon gave a lower limit on the temperature, 2.) the minimal laser
energy to create a He-like A1 plasma, and 3.) the temporal behavior of the resonance
lines.
Identification of control shots
Figure 5-10 shows the He-like and H-like spectra. The intercombination line of
Al XII is not well resolved from the resonance line. Another feature in this spectrum is
that the peak intensity of the Al XII 1 JSo - 3 !Pi satellite at 6.81 Á is the same order of
magnitude as the 1 *So - 3 !P| parent line at 6.64 Á at the time this lineout is taken.
This effect is probably due to radiative trapping. Since the doubly excited state in the Li-
like ion is efficiently coupled to the 31Pj level by collisions and autoionization, the
decay of the 3]Pi level can proceed via the doubly excited state. Thus, if the parent line
becomes optically thick, the satellite line becomes more intense because the radiative
decay rate of the doubly excited level becomes the preferred mechanism for
depopulation.
Figure 5-11 shows the predominantly Li-like spectra of aluminum taken during
an alignment shot on a solid aluminum target. A carbon only spectra from the Harada

104
Figure 5-10. Line identification for a time-resolved spectrum of helium-like aluminum.

105
Figure 5-11. Line identification for a time-resolved spectrum of lithium-like aluminum

106
1
- 2
Figure 5-12. Line identification for a time-resolved spectrum of K-shell carbon.

107
c~
o\
Al XII
Figure 5-13. Line identification for a time-resolved spectrum from a microdot.

108
grating streak camera was recorded during a low energy shot in which the laser only
caused ablation of the plastic substrate of the target. Figure 5-12 shows this reference
spectra with the hydrogen-like and helium-like carbon series identified. Finally, figure
5-13 is a typical spectra of a microdot showing the Li-like aluminum, H-like carbon and
He-like carbon lines.
The overlap of the carbon and aluminum lines was a problem for obtaining good
resolution. The strongest lines in the Li-like aluminum are the P to D transitions. The
structure of the A1 lines having principal quantum number n = 3 to n = 2, can be
identified most readily because of the absence of carbon lines in this wavelength region.
Notice that the principal Al XI 4 2D- 2 2P line does not exactly coincide with the C V
iSo - ]Pi line. It was fortunate that the the carbon line occurred later in time because it
allowed use of the aluminum line for diagnostics. This late time behavior has been
noted by Key, Lewis, and Lamb in time-resolved spectra of carbon 120
Line ratios of time-resolved data
The lines from the crystal streak camera were not intense enough to use for line
ratios. Indeed the point of this experiment was to determine when the He-like aluminum
emission was minimal. The absence of the H-like lines does indicate that the
temperature was not high enough to create a significant H-like ion population.
Figure 5-14 presents the results of the line intensity ratios taken from the Harada
streak camera data. The following figures, 5-15 and 5-16, show the relevant line ratio
plots from RATION. The best diagnostics are the He-like to the Li-like aluminum lines
because the microdot insures that they are emitted from the same plasma volume and the
lines are from different ionization stages. The ratio using the He-like 3 !P- 2 *S lines to
the Li-like n=3 to n=2 lines gives a ratio of 0.4 + 0.2 . We can see from the RATION
plot that this ratio does not satisfactorily limit the temperature range, but indicates that

109
the density is ~ 1021. The ratio of He-like 3 'P- 2 lines to the Li-like 4 2D- 2 2P lines
gives a ratio of 0.8 + 0.2 which implies a temperature of 200 to 400 eV for electron
densities consistent with the previous ratio.
The ratio of the Li-like 4 2D- 2 2P lines to the Li-like 3 *P- 2 lines is not a
very good temperature diagnostic because the upper levels of the transitions are only
150 eV apart. However, the value of the ratio, 0.35 to 0.65, falls within the
temperature and density range determined from the other two line ratios.
The carbon line ratio, [ 12S j/2 - 22P3/2/ 1jSq - 2^], gives a lower limit of the
temperature. The ratio is taken at a later time because the He-like carbon lines form after
the peak of the Li-like A1 line emission. Also, the carbon lines originate from the
tamping material, so the density would be expected to be lower than that of the
microdot. The value of the ratio is 0.25 ± 0.1 which implies a temperature of 125 eV
or less for densities less than 1020 cm'3. Notice that the RATION plot provides the
inverse of the experimental ratio.
Line intensities from the Al XII and Al XI stages were used for the following
front plasma line ratios: [3^ - 21S0] /[42D1/2 - 22P1/2], [31?! - 21S0] /[32D1/2 -
22Pj/2Í, and [42Dj/2 - 22P1^2]/[32D1/2.22Pj^]. These line intensity ratios, which arise
from the critical ion stages in this experiment, are a function of temperature and density,
thus, the plasma conditions were bracketed. In conclusion, the temperature is in a
range of 200 to 400 eV, and the electron density is approximately 5 x 1020 to
1 x 1021cm'3.
Determination of laser energy needed to create the front plasma
To create a plasma that has a substantial ground state population and also
minimize the self-emission, we needed to determine threshold laser energy at which the
emission is detectable. As the data in figure 5-17 indicate, there is a distinct increase in

Ratio
110
1.0 -
a
ffl
0.8 -
m
a
E
0.6-
a
A
o
0.4-
XJ
A
A
o
A
0.2 -
o
o
0.0-
i i i i 1 r
2.0 2.2 2.4 2.6 2.8 3.0
Laser energy ( J )
Figure 5-14. Line intensity ratios taken from the 20 - 50 Á
time-resolved spectra.
O C: He a / Ly a
EB Al: He 3P-2S / Li 4D-2P
M Al: He 3P-2S / Li 3D-2P
^ Al: Li 4D-2P / Li 3D-2P

Figure 5-15. RATION plots.
a) [31P1 - 21S0] /[4^D1/2 - 22p1/2];
b) [31?! - 2lS0] /[32D1/2.22p1/2].

Te (ev)
100.0 200.0 300.0 400.0 ,00 0 600 O 700
Te (ev)
N)
2 = 13; popfiie is oil3x at 22:04:28 on 07/09/89
Tr = 0.000 Opacity is On Calculation is NlTE
Size = i 350e—02. 'mpurity Zbar = 0.0000

Figure 5-16. RATION plots.
a) [42D1/2 - 22p1/2]/[32D1/2.22p1/2];
b) [l2S1/2-22p3/2]/[llSo-2lP1] for carbon.

114
I Z = 13; oopme is oil3x ot 10.03.23 on 07/07/89
! Tr = 0.000 Opacity is On Calculation is NtTE
I Sice = ¡ 350e-02. impurity Zbar = 0 0000
N; Ii4d -h2d
D: Ii3d -ii2p
Censity
= l OOOe+18
- 1000e+19
* l000e+20
= lOOOa+21
= iOOOe+22
Te (ev)
(a)
Z = 6; popfile is oi6 at 12:06:32 on 09/29/89
Tr = 0.000 Opacity is On Calculation is NUE
Size = 1 350e—02. impurity Zbar = 0.0000
'
(b)

Figure 5-17. He-like Al spectra 5-8Á for different laser energies. A
distinct increase in emission is visible for laser energies
greater that 2.5 J. The target was an embedded A1 microdot
1500 Á thick that was overcoated with 1000Á of parylene-
N. The energy in the laser is given. Please see figure 5.10
for line identification.
a) 2.0 J;
b) 2.5 J;
c) 2.7 J;
d) 3.0 J.

116
(a)
(b)
-A.
V,

Figure 5-18. The corresponding spectra in the 20-50 Á region from the
Harada grating streak camera spectra for the same shots
shown in figure 5-17. Please see figure 5-13 for line
identification.

118

119
emission between 2 and 3 Joules of laser energy. These lineouts were taken at the peak
of the resonance line emission. They show a factor of 7 to 25 increase in the emission
of the resonance line.
The apparent decrease in resonance line emission shown in figure 5-17 (d) is due
to a combination of focus and laser conditions. The data in (a), (b), and (d) were taken
on the same day and have poor resolution. These shots are "fuzzy" because the film
was not pressed uniformly against the back of the microchannel plate phosphor. The
lineout (c) was taken two days earlier and did not suffer from this film problem. Based
on these results, the optimal laser conditions were determined to be a laser pulse at
1.06 pm with less than ~ 2.5 J of energy.
Figure 5-18 shows the corresponding spectra recorded on the Harada streak
camera. In general, the Li-like aluminum emission is increasing relative to the H-like
carbon emission. This result is consistent with a higher temperature plasma since more
carbon atoms will be fully stripped.
Time behavior
Although the streak speed and therefore the time axis was not calibrated, we
approximated the speed of the sweep in the following way. Typically, the continuum
emission is only present when the laser irradiates the target. For the sweep speed
estimate, the amount of time that the continuum emission was present was taken to be
~ 1 ns, the length of the laser pulse. The data from high energy shots indicated a sweep
speed of -250 ps / mm. According to this estimate, the resonance line persisted for at
least 2 ns. Hence, we deduced that the if the x-ray pump was "turned on" - 1 ns after
the peak of the laser pulse, then there would exist a significant He-like ground state
population that could be photopumped.

120
Another observation concerning the time-resolved data was the onset of the
H-like emission. In high energy shots (not shown) the onset of the H-like A1 emission
coincided with the He-like emission. Kauffman, Lee, and Estabrook have analyzed the
spectra from a sulfur seeded microdot for similar irradiance conditions. A time lag of
several 100 ps between the onset of the H-like emission and the onset the emission of
the He-like lines has been predicted by hydrodynamic calculations. The predicted lag is
due to the finite amount of time necessary to ionize the He-like ions.88 Likewise, the
time lag should exist in aluminum since the rate coefficients determining the ionization
will scale similarly. However, no time lag was detected in their experiments or in these
experiments.
Target overcoat
The difference between the two thicknesses of overcoatings, 1000 Á and 2000 Á
was not significant. The ablation rate of parylene-N is ~ 4500 Á/ns, so for a laser pulse
length of 1 ns, the onset of the aluminum emission would have been delayed by
approximately 0.2 ns. However, we did not have an absolute timing fiducial from the
laser, so delays of this magnitude could not be distinguished from the jitter of the streak
camera trigger.
There was no measurable difference in the emission due to the presence of an
extra 1000 Á of overcoating. Therefore, the for final experiment, a total of 1000 Á of
parylene-N was used to overcoat the aluminum microdot.
Experiment III
To insure consistency, the results of the first two experiments were confirmed.
Next, preliminary shots were taken to test the alignment procedures and tantalum block.

121
Finally, the two-beam photopumping shots were performed and the fluorescence signal
was observed! The analysis consisted of the following: 1.) the ratio of the self-emission
to the fluorescence signal was determined from rime-resolved streak camera data, and
2.) the fluorescence signal was quantified for the absolute number of photons per
steradian.
Confirmation of experiment I
Line ratios. One-beam shots were done using the same configuration as in the
first experiment. One of the minispectrometers was replaced by a space-resolved
spectrometer that used a curved crystal. Unfortunately, this spectrometer proved to be a
poor diagnostic. The detected emission was too weak to make a decisive measurement
of the absolute flux. The signal to noise ratio was low and the space-resolving slit
drastically reduced the intensity. Figure 5-19 shows a sample spectra of the data. The
variations in the spectrum from shot to shot were quite pronounced. The following
figures, 5-20 and 5-21, give the same line ratios that were taken in experiment I. Due to
the space-resolving slit, the satellite lines were weak. Only the [Li-like satellites / He-
like satellites] and [Al XIII 1 2S - 2 2P / Al XII 1 'So - 2 'Pj ] resonance line ratios
were used. The value of the resonance line ratio presented here range from 0.3 to 1.7 as
compared to a value of 0.5 from experiment I. The ratio of the satellites is
approximately 0.5 to 1.0 as compared to 0.4. These higher values would imply a hotter
temperature, a range of 500 to 700 eV.
The density sensitive ratios were measured. The ratio of the intercombination
line to the resonance line, 0.3, is generally a factor of two larger than the ratio from the
first experiment. This value agrees better with the determination of the electron density
at 1.0 x 1020 cm-3. The ratio of the He-like satellites to the intercombination line is

Intensity (arb. units)
122
Figure 5-19. Sample spectrum from the curved crystal spectrometer (CCS).

Ratio
123
2.0
1.5
1.0
0.5
0.0
5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8
Laser energy ( J )
Figure 5-20. Time-integrated CCS intensity ratios for temperature.
X Li-like satellites/ He-like satellites
+ Ly a / He a
2
Lya = 1 S -
J i 1/2
He a = l s -
0
22P
1 3/2
2 P
1

Ratio
124
2.0
1.5
1.0
0.5
0.0
5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8
Laser energy ( J )
Figure 5-21. Time-integrated CCS intensity ratios for density.
X Li-like satellites / IC
â–¡ IC/ He a
Hea = i !s - 2*P
0 1
IC = 1!S - 23P
0 1

125
0.5 to 2.0. The large spread in data can be attributed to the poor resolution of the He-
like A1 intercombination line and satellites.
These ratios are based on the the integration of the data so that it corresponds to
space-integrated data. The spread in the line ratios suggests that the plasma may have
been formed by a lower quality beam in which hot spots have developed. This
possibility was supported by the observation of obvious imperfections in the frequency¬
doubling crystal that was used during this experiment.
Absolute flux. The MB minispectrometer was placed in the same position as in
experiment I to monitor the x-rays transmitted through the CH substrate of the target.
But, the flux on the same side of the laser was monitored with the curved crystal
spectrometer (CCS). The data recorded through the CH is within the range expected
from the first experiment. The absolute flux recorded by the curved crystal spectrograph
was lower than that recorded in the first experiment by a factor of two.
The lower values were due to a combination of difficulties. The curved
geometry of the crystal reduces the crystal reflectivity. After the shots, the crystal itself
was found to have been damaged. The stress due to the curvature had created small
fractures in the crystal. It is not clear when these fractures appeared. In addition,
because of the geometry of the spectrometer, the baffel which blocks direct x-rays from
the film may have also blocked the signal. Because of these problems, a straight line
was fit to the data and is shown in figure 5-22. The absolute flux from the shot at 5.7 J
was excluded from the fit because it was anomalously low due to alignment problems.
The data from MB was considered more reliable, since the same detector and
crystal was used as in the experiment I. Since the data from MB did not indicate a factor
of 2 drop in the absolute flux, the CCS data was "normalized" to the average of the data
taken from the first experiment. The value of the flux for the 5.7 J was interpolated
from this fit. The error in this fitting process could be as large as 50%.

126
Figure 5-22. Absolute photon flux vs. laser energy from the CCS and the
fit to the data. The data from experiment I is shown for
comparison.
x data from CCS
data from MB (exp III)
fit to CCS data
—■— data from MB (exp I)
—o— data from MA (exp I)
Confirmarion of experiment II
Although defocussing problems of the crystal streak camera during the second
experiment were eliminated here, the intensity of the self-emission of the He-like A1
resonance line is much lower than that of the preliminary experiment. This decrease was
due primarily to the faster sweep speed used for the streak camera. The presence of the
Ta block also may have contributed to the decrease by blocking part of the front plasma
from the streak camera.

127
Laser energy. The laser energy needed to reach the threshold of detectable self¬
emission was ~ 2 J as found in experiment II. This result indicates that the loss of
resolution in experiment II was not significant for determining the appropriate laser
energy.
Line ratios. The same A1 line ratios used in experiment II were used. The
Harada streak camera was also used at a faster sweep speed. In this data, the He-like
carbon resonance line generally began at the end of the streak camera sweep. The sweep
speed was measured to be 81 ps / mm.
Figure 5-23 shows several intensity plots at different times during the sweep.
The profiles have some variation, but the overall shape is roughly the same. The carbon
series was artificially cut-off because a defect in the photocathode limited the useable
wavelength range. The profile at the top of the page is integrated over 0.98 ns. It is
compared to one from experiment II which covers roughly the same time period.
Although the camera was not timed in experiment H, the appearance of the He-like
carbon resonance line in recombination is a distinct feature in the time evolution of the
plasma. The onset of this line was used to estimate the time of the sweep as
-250 ps /mm. The important point is that the spectrum from experiment II has the
same features as the spectrum from experiment III. The line ratios, averaged over
approximately the same amount of time as from the preliminary experiment, are
consistent with the results from experiment II. They are shown in figure 5-24.
Time dependence of the pump plasma
Figure 5-25 shows time lineouts of the backlight from one shot to check the
absolute flux. The time resolution was 65 ps per mm. The satellite lines tend to be only
in emission when the laser irradiates the target. This is because the doubly excited states
only appear in emission when the plasma can collisionally populate the states. The

Figure 5-23. Li-like Al intensity vs. wavelength for different times.
These spectra show that the ionization balance is not
significantly changing for the time period over which the
photopumping occurs. All times are relative to plot (d).
a) 0.8 ns;
b) 0.5 ns;
c) 0.2 ns;
d) 0.0 ns.

129

Ratio
130
Figure 5-24. Intensity ratios from the 20 - 50 Á wavelength range.
O C: He a / Ly a
EE Al: He 3P-2S / Li 4D-2P
[Xj Al: He 3P-2S / Li 3D-2P
^ Al: Li 4D-2P / Li 3D-2P

00
ca.
Figure 5-25. Intensity vs. time for the pump plasma. The duration of the He-like A1 resonance line is -250 ps
at full-width-half-maximum.

132
resonance lines, on the other hand, persist for times longer than the sweep, ~ 2.4 ns.
The time behavior of the resonance line and satellites has been reported before by Key et
al.36 They suggest that the behavior is due to the rapid adiabatic cooling of the plasma
after the pulse.
Source size
The source size was determined by examining the images of the source from the
pinhole cameras. The pinholes were sizes 12 to 15 (im in diameter and had a filtering of
25|im of Be and 50 (im of Mylar. X-rays at 1598 eV, the energy of the He-like Al
resonance line, had a transmission of 1%. The size of the source was approximately
300 pm.
In this experiment, the line width of an optically thin line may have a
contribution from each of the two plasmas. In this case, the width is a check of whether
the two plasmas were aligned back to back. The source size determined by this method
was ~ 300 (im, which is not significantly larger than the focal spot size. This result
indicates that the alignment was not skewed.
The photopumping shots-preliminarv tests
Initally, a two-beam shot was done on solid Al to get the timing between the
beams correct. Figure 5-26 shows data from a timing shot on a full target with no Ta
shield in place. It clearly shows the line coincidence and proved that the Doppler shifts
were not large enough to macroscopically shift the wavelength of the pump. The
Doppler shifts are not significant because the most intensely emitting region for both
plasmas is localized on the front and back surfaces of the full target. In this particular
two-beam shot, the pump plasma laser energy was decreased and the front plasma laser

133
energy was increased so that both front and pump plasma emission would show up on
the streak camera.
A shot of only the backlight was done with the Ta block. This shot was a critical
to proving that Ta block shielded the crystal streak camera from the pump emission.
The data, a shot on Polaroid, showed no He-like A1 or H-like A1 emission. The
spectrometers that were not blocked, verified that the emission was present. This shot
did indicate that stray light amplified by the streak camera might be a problem. Due to
time constraints, the background emission could not be studied in more detail.
Another test was a pump-plasma-only shot for the Harada streak camera. The
result was a null spectrum. This shot proved that the Li-like A1 emission on the Harada
camera was only due to the front plasma. The Li-like A1 emission from the pump
plasma is not detected by the Harada camera because it is entirely absorbed by the CH.
Identification of photopumping
Figures 5-27 and 5-28 show data of the front plasma emission that were
recorded simultaneously by the crystal and Harada streak cameras. The raw data
appears in figure 5-27; the corresponding intensity lineouts as a function of wavelength
are shown in figure 5-28.
To identify the photpumping, we will examine more closely the time-resolved
crystal streak camera data shown in figure 5-27 (c). Figure 5-29 shows a lineout of the
data centered on a line at B which corresponds to the 1 1Sq-21Pi intensity as a function
of time. The first peak is the self-emission created by the first laser pulse. The second
peak occurs during the photpumping. At these low emission levels, the total signal
includes background due to stray light and continuum emission. To establish the
baseline intensity, a region near the resonance line (indicated by A on figure 5-27) was
sampled. The corrected fluorescence signal is found by subtracting lineout A from B.

134
Figure 5-30 shows all the lineouts of the intensity as a function of time, in which
photopumping was observed. The data have been corrected for the background by the
method described in figure 5-29. The first peak is due to the self-emission; the second
peak is the fluorescence emission.
The lineout in figure 5-30 (a) is the best example of the fluorescence signal. It is
well-resolved in time from the self-emission. The self-emission peaks at roughly the
same time as the laser pulse, then dies out before the pump plasma is created. In lineout
(b) the energy in the front plasma was 30% higher creating a higher temperature plasma.
In this case, the self-emission does not end before the fluorescence signal appears. The
maximum intensity of this shot relative to the others shown is a factor of 10 higher, the
fluorescence appears as a bump on the tail. In lineout (c), the laser parameters are the
same as those for lineout (a). The fluorescence signal is weaker, but is still significantly
higher than the noise. The last lineout, (d), was done for a shot with virtually the same
laser energies, but the focal spot of the pump laser 200 pm, smaller by a factor of 26 %
in diameter. In this shot, the photopumping did not appear to be as efficient because the
radiative pump did not entirely cover the microdot.
Other possible interpretations of the second peak are not very probable. The
most obvious one is that the second peak could be due to the pump plasma radiation.
But, the H-like aluminum lines do not appear in all the shots. The absence of these
lines, which are strongly emitting lines of the pump plasma during the fluorescence, is
strong proof that the pump plasma is not observed directly.
Another mechanism that could cause the second peak could be heating due to a
shock produced by the pump laser beam. The shock would travel at about the speed of
sound through the CH substrate, 10 6 cm/sec. Therefore, for the target used in these
experiments, the shock transit time would be ~ 2.5 ns. The fluorescence signal appears
after ~ 1 ns, too early to attribute the signal to the heating of the front plasma by a shock
front.

135
Since the laser beam that creates the pump plasma irradiates the back side of the
target, one could suppose that the time-delayed laser beam heats the front plasma. For
these experiments, the laser did not bum through all the aluminum in the bare microdot
on the target. Moreover, the CH substrate was 24 p.m thick. Hence, the possibility of
direct heating of the front plasma by the laser beam that created the pump plasma, was
eliminated by the target design.
Next, we will examine the sensitivity of the photopumping to the state of the
front plasma. Based on the behavior of the time-resolved He-like resonance line
intensity, these shots can be divided into three classes shown in figure 5-27 and 5-28:
1.) No appreciable self-emission and no photopumping (a), 2.) Self-emission from
front plasma which dies off before the pump radiation (c), and 3.) Strong self-emission
which does not die off before the fluorescence (e).
In the first class, there was not enough energy in the front plasma to create a
large enough population of He-like ground state ions. Therefore, the self-emission is
absent. This conclusion is confirmed by the absence of emission from the Li-like ions
which is shown in figure 5-27 (b) and 5-28 (b).
In the second class, only the Al XII resonance line is observed in emission. The
Al XIII lines and other Al XII lines are not detected even though they lie in the measured
spectral range. The lack of strong emission in the other He-like lines indicates that the
excited state population of He-like ions is small and the emission is not detectable.
However, the weak signal could also be due in part to the blocking effect of the Ta
shield. Because the alignment of the block was crucial to eliminating the spectra from
the pump, the shield may have also partially blocked the emission from the front plasma.
Since blocking the pump plasma was critical to the experiment, the tendency in
alignment was to over-compensate by obscuring part of the front plasma emission.

Figure 5-26. Data of front and pump plasma with no shielding of the pump plasma.
The wavelength overlap of the front and pump plasmas is not affected
by Doppler shifts.
a) Spectrum before the pump is turned on (1.9 J, 600 pm);
b) Spectrum at the peak of the pump (3.2 J, 270 pm);
c) Spectrum 0.27 ns after the peak of the pump;
d) Spectrum 0.53 ns after the peak of the pump.


Figure 5-27. Raw data recorded by the two streak cameras viewing the
front plasma only. This data illustrates the three classes of
photopumping two-beam shots. The photographs on the left
hand side are from the crystal streak camera (a,c,e) and the
photographs on the right hand side are from the Harada
grating streak camera (b,d,f). The laser energies are given
for the front and pump plasmas. The pairs of data were
recorded simultaneously.
a) and b) Class I: 2.0 J front plasma / 5.4 J pump plasma;
c) and d) Class II: 2.7 J front plasma / 6.8 J pump plasma;
e) and f) Class III: 3.7 J front plasma / 6.2 J pump plasma.

139

Figure 5-28. Intensity vs wavelength plots for the raw data shown in
figure 5-27. The crystal streak camera plots are taken at the
peak of the intensities of the self-emission and fluorescence.
The Harada streak camera intensites, taken ~ 0.4 ns apart,
do not significantly change.

141

Figure 5-29. The lineout of the time-resolved fluorescence signal and the
raw data. The lineout labelled B is the total intensity as a
function of time taken at the wavelength correponding to the
He-like A1 resonance line. Lineout A is the background
intensity. To find the fluorescence signal, lineout A is
subtracted from B.

MIX IV
(y) Y m.—
I¡X IV
1 ns i time

Figure 5-30. The lineouts of the He-like A1 resonance line vs time
showing the fluorescence signal. From the left, the first
peak is the self-emission; the second peak is the fluorescence
signal. Table 5-1 gives the laser focal spots.
a) 2.7 J front plasma / 5.4 J pump plasma;
b) 3.7 J front plasma / 6.8 J pump plasma;
c) 2.2 J front plasma / 6.2 J pump plasma;
d) 2.2 J front plasma / 5.8 J pump plasma.

(su) 31UI1
Z 1
O
q
S+lT

146
The probability for observing the fluorescence signal is greatest for plasmas
characteristic of this class. Indeed, the data shows a fluorescence signal that is well-
resolved in time from the self-emission.
In the third class, the He-like A1 resonance line is still observed in emission
when the photopumping begins. The fluorescence signal is more difficult to distinguish
because it appears on the tail of the self-emission. The Al XII 3 - 1 !So line is
present also. This transition in the front plasma is not expected to couple to the radiative
pump as strongly as the resonance line because its opacity is lower by a factor of 4
compared to the 2 1Pi - 1 opacity. A lineout of the Al XII 3 JP] - 1 !So line
does show some evidence of photopumping, but the signal is very noisy, and difficult to
quantify.
In summary, the second peak in this data can be unambiguously attributed to the
fluorescence effect. Five two-beam shots revealed that the photopumpinging is very
sensitive to the front plasma conditions. The optimal plasma to photpump was created
by a laser beam having a laser energy of 2 J. The fluorescence was observed in four
shots. It has a full-width-half-maximum of 200 ps and appears ~ 1 ns after the first
laser pulse.
Ratio t
The crystal streak camera data was used to determine a quantity, defined as
the ratio of the time-integrated recorded signal due to the self-emission to the recorded
signal due to the fluorescence. The ratio is a measure of the relative strength of the
fluorescence to the self-emission. If the ratio is less than one, then the predominant
emission of the resonance line that was pumped, occurs during the fluorescence.
Conversely, if the ratio is greater than one, then the self-emission dominates the

147
fluorescence. The data from this experiment that had the most pronounced fluorescence
signal, gave a value ~ 1 for the ratio.
The table below gives the focal spots and energies of the two beam
photopumping shots. The first three cases correspond to the raw data shown in figures
5-27 and 5-28. In cases in which the self-emission did not end before the fluorescence,
an extrapolation of the self-emission tail was used.
Table 5-1. The laser energy, focal spots, and ratio £ for the photopumping
shots.
Front focal spot
Energy 1.06 (im
Pump focal spot
Energy 0.53 |im
Ratio
600
1.0
600
5.4
600
2.7
270
6.8
1.00
600
3.7
270
6.2
3.34
600
2.2
200
6.5
1.12
600
2.2
270
5.8
0.92
Absolute flux of fluorescence
During the photopumping shots, the MB minispectrometer was used to record
the absolute flux of photons detected in the fluorescence signal. The absolute flux is
shown in figure 5-22. The reduction of the absolute photon number due to the
fluorescence signal is based on the absolute photon number from the radiative pump and
the ratio of the integrated fluorescence signal to the self-emission signal from the streak
camera.
First, we consider the radiation that reaches the spectrometer. The aspect ratio of
the target is such that the diameter of the spots are a factor of 100 times the distance
between them (see the figure 4-6 for the geometry), so the radiation reaching the
minispectrometer, which is positioned at an angle of 54 degrees from the laser axis,

148
must be passing through the front micrdot plasma. The lateral spreading of the emission
region is assumed to be minimal and will be justified in the final section of this chapter.
The total emission recorded on the minispectrometer is the sum of the attenuated
emission from the back-plasma pump, IpumpTcHTAl. the self-emission from the front
plasma, Ifr0nt. and the fluorescence signal, Ifiuor- The pump radiation is attenuated by
the CH and front A1 microdot plasma.
I total — ^pump^CH ^Al ^ front ifiuor
where Tch and Tai are the transmission coefficients for CH and A1 respectively. Ipump
has already been corrected to represent the radiation that is incident on the microdot, that
is, the measured pump flux has already been attenuated by the CH of the substrate
This equation can be simplified. For the front plasma, the absorption coefficient
of the resonance transition is = 1.77 x 10^ cm‘l. Therefore, the pump photons are
absorbed within the first 0.2 (im of the front plasma. Since the transmission of the
pump flux predicted to pass through the A1 microdot is reduced to zero, the term
involving Ipump in hie total detected flux goes to zero.
An upper limit on the fluorescence emission is that all the radiation absorbed
from the back pump is emitted into 4ji. The amount absorbed then reemitted would be
i _ I pump
1 flúor- 4^
The measurement from the experimental data gives Iback ~ 2.0 x 1012 photons/sr.
In addition, the collisional deexcitation rate is on the order of 1011 crxvVsec for
the resonance transition. So the probability of photon destruction, i.e. that the photon is
absorbed into the thermal pool of energy, is 10'2. (A more complete analysis follows in

149
chapter 6). This value means that a photon absorbed near the center of the embedded
microdot will probably be lost to the thermal pool and not detected by the streak camera.
An independent measure of the front self-emission could not be obtained because
the quality of the CCS data was too poor. Hence, in order to solve for the number of
photons due to the fluorescence effect, we must find a relationship between the
integrated fluxes of the self-emission and the fluorescence. The streak camera gives the
ratio of integrated fluxes of the self-emission to the fluorescence. The equation,
rewritten in terms of the ratio, defined in the previous section, gives
Here, we assume that the emission is essentially isotropic so that the difference in the
angle of observation by the streak camera and minispectrometer is not critical. This
equation is used to determine the number of photons in the fluorescence signal. Thus,
the absolute flux of the fluorescence signal was estimated to be ~ 1.5 x 1011 photons per
steradian. This calculation is only an order of magnitude estimate.
The level of the fluorescence signal recorded by the minispectrometer is
significantly above the noise. The minimum intensity that the mini spectrometer can
record is about 1 pJ/sr. In terms of photons having the energy of the He-like resonance
transition, this amounts to ~ 1010 photons/sr. The background measurements for the
film, with the fog already subtracted are ~ 1.1 x 1010 photons/sr, so this confirms this
approximate number.
The streak camera, because of the microchannel plate intensifier, is much more
sensitive than the Bragg crystal and film. However, this fact does not necessarily mean
that the absolute fluorescence flux cannot be measured with the minispectrometer. G.
Glendenning of LLNL has done an informal analysis of the relative sensitivities by

150
comparing DEF film and the streak camera. When DEF film was placed at the position
of the photocathode, x-rays of 2 keV produced a film density reading of 6. This density
corresponded to 6 photons/pm2. With the streak camera on sweep speed 3 at the high
gain setting with a 750pm slit and a Csl photocathode with 2.5pm of mylar, the density
on TRIX film was 2. Therefore, she finds that the streak camera is only about twice as
sensitive as the DEF film when the two are exposed to a similar source and identical
geometrical conditions. This measurement is not definitive because the sweep speeds of
different cameras are not necessarily the same. A more sophisticated experimental set¬
up would be required to resolve this question.
A problem may be caused by the lateral spreading of the pump plasma. If the
pump plasma is directly recorded on the film and dominates the self-emission and
fluorescence signal, then this effect could skew the results of absolute photon flux on
the minispectrometer. If the ablation rate in the lateral direction is assumed to be the
same as the rate in the direction of the laser, then during the 100 ps pump laser beam,
the lateral ablation of the plasma would have less been than 40 pm. Even if this entire
volume is assumed to be emitting, the radiation will contribute much less than 5% of the
pump radiation.
Potential problems
The image on the pinholes show a deterioration of the back focal spot Since the
3 pinholes were imaged through the brass cutout, the elliptical nature of the image could
be due to the obscured line of sight of the 3 pinholes. However, given the fact that the
target was in a fixed position and that the pinholes were at a fixed height, even if the
brass was obscuring the emission, the back beam could not possibly be focussed at the
same place as the shots which do not have elliptical pinhole images. Further, if the
emission were not being cut off by the brass hole, then, the emission should not have a

151
sharp edge. Since the pinholes are sensitive to photons of greater than 1.6 keV, then the
sharp edge could imply that only part of the aluminum is being irradiated and that indeed
the focus did drift when it was defocussed. However, the brass hole did not appear
degraded.
Variations
One shot with different timing between the laser beams was tried. Changing the
timing of the photopumping would indicate the sensitivity of the photopumping to the
evolution of the plasma. Unfortunately, the pulses seem to occur simultaneously and,
therefore, the fluorescence could not be resolved from the self-emission. A different
pump plasma, Samarium (Z - 62), was also tried as a photopump. Samarium seems to
be a promising pump because the broad band M-shell emission has a very high x-ray
conversion efficiency and coincides in energy with the He-like A1 lines. But in this shot
the laser irradiance was probably not intense enough to sufficiently ionize the Samarium.

CHAPTER 6
RADIATIVE TRANSFER THEORY
The preceeding analysis of data has assumed that the radiative transfer equations
and the rate equations are not coupled. This chapter will formulate the problem of
radiative transfer. First, some basic quantities must be defined. Then, the radiative
transfer equation and some approaches to solving the equation are discussed. Finally, a
simple model of the plasma emission that takes into accout some of the concepts will be
presented.
Definitions
Specific Intensity. The specific intensity gives a complete macroscopic
definition of the radiation at a particular position, r, into direction n. The specific
intensity is a vector whose amplitude is associated with the energy carried. The specific
intensity is I(r, n, v, t) and will be written in shorthand notation as Iv. Physically, Iv
represents the energy transported by photons of frequencies (v +dv) across an area dS,
into a solid angle dii and in a time interval dt.
dE = I(r, n,\, t) dS cos(@) d£2 dv dt
where dS cos(@) = n • s dS and s is the unit vector normal to the surface dS.
Statistically, it represents a group of photons described by six parameters: the
frequency, three spatial dimensions, and two angular variables (the direction cosines).
The radiation field, Iv, and the photon distribution function, f, are related by
152

153
I(r,«,v,t) = hv f(r,«,v,t)
cm2 sr sec hz
The photon distribution fuction is defined such that f dQ dv is the mean number of
photons in a unit volume at a specified position r that is travelling in direction n at time t
and having freqencies in a range of v to dv.
The specific intensity has been defined so that in the absence of sources or sinks
of radiation along the line of sight, it is independent of the distance between the source
and the observer. For a pencil of rays passing through an area of the source, dS, and an
area of the observer, dS', the amount of energy passing through either is equal. If the
unprimed quantities represent the source and the primed quantities represent the
observer, then the solid angles and areas are related by
dS cos (0)
2
r
where r is the distance between the two sources. Since the energy absorbed is equal,
then Iv = I'v. In the limit as dii goes to zero, the radiation becomes just a ray, and the
magnitude of this ray does not diminish with distance. It is this property that enables
the energy collected by a detector to be related to the energy emitted by the source.
Also, it is evident that the energy per unit area is proportional to the inverse square of the
distance between the two.
Mean intensity and Energy density. The mean intensity, Jv, is defined as the
specific intensity integrated over all solid angles
cm2 sec hz
ergs
and therefore is a more physical quantity. It is also the zero-order moment of the
specific intensity.

154
A related quantity is the energy density. Since photons travel with the speed of
light, c, dt can be re-expressed as tl c where ( is the length that a photon travels in time
dt. In the limit of an infinitesimal volume, the specific intensity becomes independent of
position and a monochromatic energy density, 'Ey, can be expressed as
£
V
4 7t
c
Jv
and has dimensions ergs cm-3 hz_1.
In thermodynamic equilibrium, the photons have a Planck distribution, and the
mean intensity can be replaced by BV(T) where BV(T) is the Planck function. When this
expression is integrated over all frequencies, it gives the Stefan's law for the total energy
density
£total = °sb T
where Gsb is the Stefan-Boltzmann constant.
Flux. This quantity, F, is a vector that physically represents the quantity of
radiation moving in an arbitrary direction n. Therefore, the net rate of radiant energy
flow across a surface dS per unit time per unit frequency is represented by the quantity
F • s dS, where s is a unit vector in a direction normal to the surface of dS. It has
dimensions ergs cm '2 sec hz _1. For instance, in cartesian coordinates, Fx equals
the integral of the component of flux in the x-direction over dQ. In planar geometries
that are homogeneous and infinite in the x- and y- directions, only Fz is a non-zero
quantity.

155
Macroscopic Coefficients
As the radiation interacts with matter, photons are absorbed and emitted. The
interactions between matter and radiation can generally be grouped into two categories:
absorption and scattering. Here, we will define a photon as absorbed when all or part of
the energy of the photon becomes lost to the thermal energy of the plasma. When a
photon is absorbed, it is destroyed. As such, the absorption directly affects the local
properties of the plasma. The process of scattering can be thought of as the interaction
of a photon with a scattering center. It can also be considered the absorption and
instantaneous emission of a photon having nearly the same energy. During scattering,
the photon's direction is changed and its energy may be slightly altered. This process
critically depends on the radiation field and the medium, thus it is responsible for the
more global effects in the plasma.
The total absorption coefficient, %v, describes how the material can remove
energy from the radiation field by either scattering or absorption.
dEabsorbed = Xv (ri «, v, t) I (r, n, v, t) dS ds dQ dv dt
This coefficient, X\ is defined as the opacity and has units of cm-1. As discussed in
chapter 4, the inverse of the opacity can be thought of as the mean free path of the
photon. This quantity depends on the number of absorbers which in turn depends on
the radiation field.
The emissivity is the amount of energy "released" from an element of material of
cross section dS and length ds into a solid angle dil, within a frequency band dv in
direction n in a time interval dt.
dEemittcd = fiv (ri n, v, t) dS ds d£2 dv dt

156
where r\ is the emissivity, having dimensions ergs cm'3 sr1 hz_1 sec'1. This coefficient
includes thermal energy from the plasma that is converted into photon energy, and
photons scattered into the proper angle. Again, this quantity depends on the radiation
field. In thermal equilibrium, the emissivity is given by the Kirchoff relation q = k Iv
Transfer Equation
If we think of photons as particles, the transport can be described by a
Boltzmann equation, the kinetic theory of particle transport. In this formulation,
I ( r + Ar) = I (r) +
ipl).
C \0t)
\as)
ds
where ds is the path length and dt is the time interval. We can rewrite this equation in
terms of the emissivity and opacity coefficients. Then we have
1
c h v
5 Iv
“ar
+ cVlv
= — (fiv-XvM
h v
This equation describes the energy in a frequency interval dv, passing in a time dt
through a volume element of length ds and cross section dS oriented normal to a ray
traveling in a direction n into solid angle d£l
For the remainder of this thesis only the time-independent version will be
discussed. Although a steady state is not achieved in the evolution of the plasma, on
the time scale of the hydrodynamics, the radiation field instantaneously adjusts to the
change in the macroscopic matter. Given any temperature and density, the radiation
field can be solved for self-consistently. Therefore, the time-independent approach is
still valid.

157
Here it is convenient to introduce another useful concept, x, the optical depth
T.
V
where ds is the plasma length. It is a dimensionless quantity that represents distance
into the medium in units of the photon mean free path. The optical depth is roughly the
number of interactions the photon will have to undergo before escaping the plasma. A
x < 1 means that a photon has a high probability of escaping without being absorbed.
Tau can be expressed in terms of the atomic coefficients. For line spectra, x is
quoted for the line center frequency. It is then expressed in terms of the Einstein
coefficients, or, equivalently, in terms of the absorption oscillator strengths. The
oscillator strengths are tabulated in references like Bethe and Salpeter or Weise, Smith
and Glennon.121’i22
We can also define the source function, Sv,
where r|v and Xv are the atomic coefficients. The source function depends on the
radiation field. Incorporating these definitions, the transfer equation becomes
where |i is the cosine of the radiation angle, cos (0).
The problem is to solve this transfer equation for Iv. The equation appears
simpler than it is. In reality, both the absorption and emission coefficients depend on
the specific intensity. The transfer equation is non-linear integro-differential equation.
To better understand the problem, a discussion of the source function and the solutions
will be undertaken.

158
Source Function
The source function is a very powerful concept. In the case of complete
redistribution when the absorption and emission profiles are equal, the source function
is independent of angle and frequency. If the plasma is homogeneous in two
dimensions, xv(r) = Xv(z)> then the source function is only a function of the depth, or
the related quantity T. The source function is essentially an effective emissivity.
The source function can be expressed in two ways. One way is to write it as a
function of the populations.
In this way it has the same form as the Planck function. By analogy, this equation can
be used to define a radiation temperature. The solution of the statistical equations are
implicitly included in the populations
An equivalent way to express the source function is as a function of the radiative
flux J.
( K Bv+ oJv)
(K + O)
where K is the absorption coefficient, a is the scattering coefficient, and Bv is the Planck
function. Expressed in this way, the contributions to the source function from the
scattering and thermal processes are emphasized.
In strict TE, the specific intensity equals the Planck function, and therefore the
source function is equivalent to the mean intensity, Jv. In LTE, the source function is
defined to be equal to the local Planck function at all points in the plasma, but the
macroscopic radiation field is allowed to depart from its TE value.

159
Thg FQrmal Solution
The formal solution of the transfer equation is
I(x1,q,v) = I(T2,q,v) exp
where t is the dummy integration variable. Note that the intensity outside of the source,
the emergent intensity, can be found by integrating the formal solution from x equals
zero to infinity.
Analytic Approximations
The Eddington-Barbier approximation assumes Sv is a linear function of depth.
Then,
Ie(v) = S0(v) + S1(v)M.
where |i is the cosine of the angle between the radiation and the normal to the surface.
The physical meaning of this equation is that the emergent intensity is equal to the
characteristic value of the source function at optical depth unity along the line of sight.
Essentially, any photon that lies within one mean free path of the surface boundary will
escape.
Another simple approximation is to assume the Sv is constant. Then for planar
geometry, the emergent intensity of a finite slab having an optical thickness T will be
I = S ( 1 - exp (- T))

160
The limit for an optically thick slab,T » 1, is Iv = Sy In this case, the emergent
intensity appproaches a fixed value that is independent of the thickness of the medium.
The optically thin limit, T « 1, gives I = Sv T. Essentially, this case indicates that the
emergent intensity is sensitive to photons emitted throughout the entire medium.
The diffusion approximation takes advantage of the concept of radiative
equilibrium, Jv =SV. In thermal equilibrium, Sv approaches Bv at large depths.
Therefore, one method to find a solution is to assume the form of Sv is a power
expansion of Bv.
I(q, i) = B(h,t) + h|—'j
\dxj
In the limit of large optical depth, it can be shown that the flux is given by a
diffusion-like equation
F = -kd(VT)
where Kq is the diffusion coefficient, which is proportional to the photon mean free
path. This approximation is valid for semi-infinite plasmas in which the photons
undergo many interactions before escaping.
The Grev Atmosphere
Another good test case is that of a "grey" atmosphere. Here, we assume
X = constant, thus the radiative transfer problem is independent of the physical
medium. This assumption can be valid for astrophysical atmospheres in which line
transport is not significant. By the constraint of radiative equilibrium, the mean intensity
equals the source function. Then the transfer equation becomes

This equation is known as Milne's equation and has a formal solution given by
J(t)Ej t-T
dt
where Ei is the exponential integral. The solution is an equation linear in Jv. The form
of this solution appears so frequently in radiative transfer theory that the right hand side
of the equation has been defined as the lambda operator, A(f(t)), where f(t) = J(t) in this
case.
Some approximate solutions to this problem include the Eddington
approximation, lambda iteration, and the Unsold procedure. The Eddington
approximation consists of assuming that the diffusion approximation is valid
throughout the atmosphere. Then, the flux and the mean intensity can be related and a
solution for Iv can be found. This approximation holds if I is isotropic, and expandable
in odd powers of |i.
Lambda iteration is an improvement on the Eddington approximation. In this
scheme, corrections to the Eddington approximation are determined from an analytic
solution of J = A(J (°)) where J (°) is assumed to depend linearly on tau. The mean
intensity is found by iterating until J is arbitrarily close to J (°). Since the lambda
operator involves exp(-x), the corrections will be the greatest at the surface where the
Eddington approximation is the worst. Unfortunately, lambda iteration fails to be
effective at large depths because too many iterations are necessary.
In the Unsold procedure, the assumption Sv = Bv, is used to begin the iteration.
The flux is then used to derive a perturbation for the change dBv that satisfies the

162
requirements of radiative equilibrium. This method essentially corrects the temperature
structure.
Numerical Solutions
The solution to the radiative transfer problem is a formidable one. With the
advent of computers, it has become possible to numerically solve the transfer equation.
The transfer equation can be solved by either differential methods or integral methods.
It is instructive to examine the numerical studies of radiative transport because they
reveal underlying complexities that simple analytic models cannot address. Chapter 7
will examine a differential approach to solving the line transport in the experiment
discussed in this thesis.
The integral equations can be solved by numerical discretization. In this case,
some functional representation of Sv is introduced, then it is integrated analytically
against a kernel function to get a new Sv. The coefficients of the kernel only involve
optical depth x and the exponential functions Ej and E2. Hence, it is calculated once for
each depth scale. However, these methods are not easy to adapt to non-LTE problems
because one must solve for each frequency point in a line profile. This representation is
useful because it can give physical insight into the equations by the analytic study of the
kernel functions. An excellent reference for line transport is that of Ivanov.123
In practice, differential methods are usually used to find a solution to the transfer
equation. An analysis by Mihalas shows that if the probability that a photon is
thermalized is small, then even for an isothermal atmosphere the mean intensity at the
surface can be very different from the Planck black body value. He applies a
straighforward lambda iteration to solve the radiative tranfer equation and finds that the
number of iterations needed for convergence is proportional to the inverse of the square
root of the probability that a photon is thermalized. Laser plasmas may have transitions

163
in which the radiative decay rate is two orders of magnitude higher than the collisional
rate; therefore for these cases, the differential equation must be reformulated in order to
converge to a solution.
Two main differential methods have been found to be robust: the Feautrier
method and the Rybicki method. The discussion of techniques presented here mainly
follows that of chapter 6 in Mihalas.81 The Feautrier method depends on defining two
new quantities, a mean intensity-like quantity, U, and a flux-like quantity, V. With
some manipulation, the transport equation can then be expressed as a single second-
order equation involving U. Then the system can be solved by imposing the boundary
conditions at x = 0 and x = Xb , the value at the opposing boundary. The crux of the
resulting system of difference equations is that a fully frequency dependent source
function is solved for each depth.
In contrast to this method is the Rybicki Method. If complete redistribution
holds, then the depth information can be grouped together, and the source function is
solved for each frequency. Each vector describes the depth variation at a given
frequency. The advantage of this method lies in its vastly reduced time of computation.
Non-LTE Line Transfer
The formulation of the transfer equation for line transitions is called the
equivalent two-level atom (ETLA) formulation. It is an iteration scheme and is well-
suited for the study of multi-level non-LTE problems. The method can be generalized to
include continuum processes and multiple level systems. This discussion follows
chapter 11 of Mihalas.81 However, several good references address line
transport.124'130
To give a concrete example, we will consider the transfer equation for a two-
level atom.

164
where A and B are the usual Einstein coefficients, u stands for the upper level, 1 stands
for the lower level, and (p is the line profile. Here we assume that the absorption
profile is equal to the emission profile, i.e. complete redistribution. If the relationships
between the Einstein A and B coefficients are used, then the source function can be
expressed in the Planckian form as discussed in the source function section. The
statistical equation for a two-level atom is
cpvJvdv + C1>u
cpvJvdv + CuJ
where C is the collision rate. The left-hand side represents the number of excitations per
unit time, while the right-hand side represents the number of de-excitations per unit
time. If this equation is solved for the ratio of upper and lower state populations, then
after some manipulation S can be written as
Sv=( 1 - e) Jv + E Bv
where Jv is the mean intensity integrated over the line shape, Bv is the Planck function,
and e represents the photon destruction probability, which is defined by
e =
Physically, this source function has a noncoherent scattering term , (1 - e)J, and a
thermal source term, eB. The photon destruction probability accounts for the photons
that are thermalized by collisionai de-excitation.

165
The photon escape probability is defined as
P
e
exp (-x cp(x)) d (i
where the line profile, cp, weighted by the escape factor, is integrated over a
dimensionless frequency variable, x, and angle, (i. The line profile cp allows for the
redistribution of photons. Allowing for frequency diffusion can fundamentally change
the nature of the solution because photons that diffuse out into the wings of the line
profile have a higher escape probability. If the angle integration is done first, the
solution is an exponential integral of (x cp) which must then be integrated over a line
profile, such as a Doppler, Lorentz, or Voigt. For a Doppler profile, the behavior of the
escape probability as a function of depth is found to be proportional to [x ln(x) ]_1. A
series of papers by Finn discusses the probability of photon escape from particular
optical depths within a medium.131'133
The thermalization depth that was mentioned above, can now be more
specifically defined. Following the work of Athay and Skumanich the thermalization
depth can be defined as the depth where the photon destruction probability equals the
photon escape probability.134 For a Doppler profile, it approximately equals the
inverse of the photon destruction probability. Thus, for small destruction probabilities,
the thermalization depth is very large. The escape of photons in the line wings causes
the source function to depan from the Planck function at very large depths, which
prevents the plasma from reaching LTE far from the surface of the plasma.
To estimate the effect of frequency diffusion at the surface, we can calculate the
value of the source function at the boundary of a semi-infinite medium. If e and T are
constant with depth, then the transfer equation can be solved by the method of discrete
ordinates. The source function at the boundary is found to be

166
S (0) = Ve B
This result is general since it does not depend on order of the quadrature of the sum or
the line profile. Notice that the boundary value of S is larger than the local creation rate,
eB. This effect is due to contributions to the source function from photons that originate
deep in the medium where S(x) » S(0). The source function at the surface, therefore,
is driven by non-local effects.
In summary, we will consider the effects of radiative transfer on the emergent
intensity of the line. In the line wings, where x < 1, the photons will escape the
medium. At the frequency corresponding to t ~ 1, the intensity will saturate at its local
black-body limit, while at frequencies closer to line center the intensity is depressed due
to scattering. We find the result that the emergent intensity shows a self-reversal at the
line core. Another way of interpreting a self-reversed line profile for media with
temperature gradients is the following: the emergent photons near the line core originate
from the cooler outer layers of the atmosphere, while the photons in the line wings
escape from deeper within the atmosphere and therefore sample a hotter medium.
Analytic Model of the Experiment
With this basic knowledge of radiative transfer, we will develop a simple model of
the fluorescence effect observed in these experiments. An analytic estimate of the
photopumping effect can be found if we use the following simple model of the plasma
emission. An equivalent two-level system is used to calculate the number of ions
excited to the 1P1 state during each period of interest. Then, the total number of emitted
photons is calculated by volume emission. Within the limits of this model we find that
the ratio, can be approximated by the ratio of the number of photons emitted during

167
the two periods, i.e. the initial formation of the plasma and the photopumping of the
plasma.
The experimental method used to produce the front plasma justifies the use of an
equivalent two level system for two reasons: 1.) the ground state population was the
dominant species during the experiment. The change in the ionization balance can
monitored by the Li-like A1 emission, which did not change significantly over the time
of interest, and 2.) the population into the upper level of the resonance line was
negligible. The absence of He-like A1 transitions from levels higher than n=2 supports
this claim.
The primary process in the front plasma, while the laser irradiates the embedded
microdot, is collisional excitation from the ground state, ^Sq. However, during the
radiative pumping, the stimulated absorption rate becomes stronger than the collisional
rate because the energy of the intense flux of photons from the pump plasma is matched
to the transition energy. In both cases, radiative decay is the dominant deexcitation
mechanism.
Due to the combined effect of the optical depth and collisional destruction of the
excited state, the detectable photons come preferentially from the plasma column edge.
We will approximate the number of observable photons by the emission from the plasma
region in which the optical depth, T, is <1. We define the active emitting volume by an
annular area times a plasma length. The area has an inner radius corresponding to x=l
for the frequency at the peak of the emergent intensity , and an outer radius
corresponding to T=0 (i.e. the radius of the microdot). For the ratio calculation, the
inner radius is not a critical parameter because the area will cancel out. The length of
the emitting region is different for the self-emission than for the fluorescence due to the
following reasons. When the plasma is heated by the laser, the self-emission will come
from the entire plasma column length, ~ 100 pm, which is determined by the ablation
rate of the material. But during the photopumping, the emitting region length extends

168
~ 5^m from the absorbing region. This length, -100 optical depths at line center, is
determined by the thermalization depth for the plasma conditions.
The number of excitations, Np, due to any rate, Rqj, from the ground state to any
level j is
where ng is the ground-state ion density, Tp is the laser pulse duration, and Vp is the
emitting volume. The rate is assumed to be constant over the laser pulse duration.
Since we assume that every photon originating in this restricted region escapes, the ratio
of the numbers excited during each phase approximately equals the ratio, The initial
plasma quantities are denoted by p=l and the fluorescing plasma quantities are denoted
by p=2.
where Cgj is the collisional rate (1/sec) and Pgj = BgjF (1/sec) is the photopumping rate.
Here Bgj is the Einstein stimulated absorption coefficient and F equals the measured flux
of the pump. Table I shows the results of three shots in which the laser energy creating
the front plasma varied <15% and the photon pump was virtually the same.
For an absorbing plasma near critical density, the ratio predicted by this analysis is
within a factor of 2 of the ratio from the crystal streak camera data. The agreement of
this simple model with the data indicates that the processes used to define the ratio are
the most important processes involved in generating the observed intensity.

169
Table I. A comparison of the calculated and experimental ratio, for comparable
plasma conditions. £ (calc) assumes an electron density of 5.0 x 10 21 cm-3.
The factor V j/V2 ~20.
Coj (109/sec)
PQj (lO^/sec)
^(calc)
£(exp)
1.18
2.53
0.93
0.91
4.05
2.60
3.11
3.33
1.18
2.71
0.87
1.00

CHAPTER 7
COMPUTER SIMULATION
The simple analytic model of the plasma emission presented in chapter 6 is
schematic. The object of the computational work was to gain insight into the important
parameters of the problem. The codes described in this chapter will be discussed from a
user's standpoint. The details of the physics and the computations are left to the
references.
Atomic Model
The foundation of any computer simulation of radiation transport in plasmas is
the atomic model. The atomic model provides the energy levels, atomic cross sections
or rates of the constituent particles of the plasma.
Atomic Physics Codes
For this thesis, a suite of codes, YODA, written by P. Hagelstein were used to
generate the atomic model. The code constructs a Hamiltonian and then solves for the
energy levels and wavefunctions. This is done by first forming the non-relativistic
Hamiltonian for the ion. Then, relativistic and spin-orbit terms are added. Finally, the
total Hamiltonian is solved as an eigenvalue problem. For the first approximation, the
one-electron Coulomb functions are used. The energy matrix is diagonalized to find the
relativistic, multi-configurational wavefunctions. Once the wavefunctions are known,
then other quantities such as the oscillator strengths, the collisional cross sections, and
170

171
the ionization cross sections, are calculated. The physics contained in the codes is
discussed in a neon-like application.135 A general reference on relativistic atomic
physics codes is presented by Grant.136
Since each ion has a different hamiltonian, the atomic codes must be run once for
each ionization stage present in the plasma. An additional computer program connects
the ionization stages by filling out the model with hydrogenic levels, and adding rates
for the ionization processes.
Aluminum Model
The aluminum model, generated using these codes, has 269 levels. In
particular, the He-like and Li-like ion stages include double excited states so that the
dielectronic recombination, which is often important for ionization balance, could be
included in the model. Since the autoionizing states connect two ion stages, it was
necessary to run the code twice to obtain consistent atomic data. First the code is run
without including the autoionizing process to calculate the energy levels for the ion and
the ground state that is involved in the auger process. In the second run, the energy
range for the auger electrons is entered by the user, based on the energy values
determined by the code in the previous run.
To decide on the number of ionization stages to include in the simulation, an
estimate was made by considering the ionization balance limits. In coronal equilibrium,
ions having an ionization potential roughly 1 to 3 times the temperature of the plasma
will be present; for Saha equilibrium the ionization potential of the ions is 3 to 10 times
the temperature. For the present case, a temperature of 200 eV implies that ions having
ionization potentials from 200 to 2000 eV are sufficient. For the model, fully-stripped
to carbon-like ions were included.

172
The choice of the number of hydrogenic levels to include was based on the
strength of the coupling between the excited levels and the ground state of the next
ionization stage. For the fluorescence problem, the He-like ion is not highly excited and
little cascading from upper levels is expected. In plasmas in partial LTE, levels with
large principal quantum numbers may be in LTE with the higher lying levels and with
the free electrons for densities.137-7
2x 1018Z6VT¡
ne> -
e 17/2
n
where n is the principal quantum number, Z is the charge of the ion, ne is the electron
density, and Te is the electron temperature in eV. Based on the above relation, the
hydrogenic levels above principal quantum number n = 6 were included in the model.
A few limitations of the code will now be discussed. The code was written
originally for high Z elements, so calculations of low Z elements are not "easy” to
perform. Inner shell processes are probably not well treated because the wavefunctions
are not as accurate. However, inner shell processes are not expected to be a significant
for the photopumping model.
The atomic rates are produced by fits to the calculated points. Unfortunately, the
user cannot easily control the fits. For instance, a special procedure had to be used in
order to fit the collisional rates to a suitable temperature range that matched the
experiment.
Creating a model is not an automated process. Each atomic model must be
treated separately. In the versions used here, some processes must be done by hand -
the user must modify and/or move files during several stages of the process. Due to this
and other "unfriendly" user aspects of the code suite the process is extremely time¬
consuming.

Radiative Transfer Simulation
altair Computer Code
ALTAIR is a code developed with the expertise of J. I. Castor by a team under
the direction of R.I. Klein.138 It solves the statistical rate equations and the radiative
transfer equation. The algorithms are based on the equivalent two-level atom scheme
described earlier. However, the scheme used in this code is in a much more generalized
form and also includes continuum processes. It is well-suited to solve non-LTE
problems because it was designed to treat the radiative transfer of multi-level system.
Thus, interlocking effects between the lines are included. The code used here is one¬
dimensional and presently treats only planar geometry.
An innovative feature of ALTAIR is an adaptable frequency mesh. Every
radiative transfer code is sensitive to the quality of the frequency mesh since it
determines the resolution of the lines. However, having too many frequency points is
prohibitive because the computing time can be proportional to the number of frequency
points cubed. In ALTAIR, the bound-free transitions are treated on the same formal
basis as the bound-bound transitions. This formulation allows a self-consistent
treatment of the overlap of the transitions. Moreover, the code detects the overlaps and
internally generates a frequency mesh at every time cycle. Thus, insuring that an
adequate resolution is achieved for a minimum number of frequency points. This
feature, in part, gives the code its speed.
Other parameters that the user can control are the time step and the zoning. The
time step can be chosen and modified by the user at any time during the computer run.
In general, the rate of change of the ionization balance should govern the length of the

174
time step. The gridding of the problem is determined by the optical thickness of the
lines that are being transported by the ETLA scheme.
For each time cycle, the ETLA iteration procedure consists of the following.
First, the radiative transfer is done for each frequency by using the formal solution.
This pass takes care of all the optically thin lines as well as providing the mean intensity,
J, necessary to begin the lambda and ETLA iterations. Then the kinetics equations are
solved using the radiative rates. Convergence is determined by comparing the source
function calculated by the form involving the populations to the form involving the
radiative quantity J. Also, the population convergence can be examined by monitoring
the change in population from one iteration to the next. The method is discussed by
Avrett.139
General considerations
The physical dimensions of the problems were based on the size of the ablated
microdot, a 270 qm wide diameter plasma, ablated to a length of ~ 100 |im. The
gridding for the problem was chosen so that the maximum optical thickness of any line
across any zone was ~ 0.1. The He-like and Al-like resonance lines determined the
thinnest zone. Any line that had an optical depth > 0.3 was assumed to have a Doppler
line shape and was transported by the ETLA scheme.
In figure 7-1, the ionization balance is shown for two calculations. Curves a and
b are for a calculation with radiation transfer calculated in detail for 66 lines while c and
d show results without radiative transfer, i. e. the plasma was optically thin. The curves
labelled a and c are for time = 0.1 ns and b and d are for time =1.2 ns. The x-axis is the
isoelectronic sequence number. Both problems were run for the same conditions, with
exactly the same gridding. The case with no detailed radiative transfer, cools more
quickly than the case with radiative transfer. The processes of radiative transfer causes

175
—■ CXI CXI CO CO zT“ zj~ 1_0 Li~> CO
Figure 7-1. A comparison of the ionization balance with and without detailed
radiative transfer. The atomic model used for both is the same. For
curves a and b, 66 lines are calculated by the ETLA scheme. For curves c
and d, none of the lines are done in detail. The x-axis is the isosequence
number, i.e. He-like equals 2.

176
the plasma to "hang up" in the K-shell ionization stages because of radiation trapping
effects.
Initial runs were performed to check the steady state ionization balance. The
code can either begin with LTE or coronal equilibrium. Then, for successive time steps,
the ionization balance is corrected to be consistent with the internal radiation field. The
simulations showed that the final steady state ionization balance was independent of the
initial condition. For the simulations that contained a photopump source, the initial
condition of coronal equilibrium was chosen, since this is the most physically realistic
case for the experiment.
The external radiative source used for these simulations was dictated by the
experimental results. The source was normalized to the experimentally determined
absolute number of photons incident on the plasma. The photopump was four Doppler
widths wide which reflects the emergent flux from a line pump. The plasma evolution
was performed with and without the pump. The precise temporal shape of the source
was not important because ALTAIR chooses the time step according to the demands of
the radiative transfer.
Constant density case
Since the simple model depended on the absorption of the photon flux in the first
0.2 (am of the plasma column and a thermalization length of ~5 fim, an important check
was to determine if the source function of the 1 - 2^1 He-like resonance line at the
far end of the slab had any dependence on the photon source. To check this, a slab of
constant density was irradiated with the external source. Figure 7-2 (a) shows the
ionization balance of a such a slab. The temperature for this case was chosen to be 200
eV. He-like ion ground state dominates the ionization balance and is over three orders
of magnitude larger than any other population. The photon destruction probability for

177
the resonance line is ~ 0.5 and the optical depth of the transition is on the order of 3000.
These parameters imply that the photons from the external photon source should be
quenched, or thermalized, very quickly.
However, to some degree, the source function throughout the slab is affected by
the photopumping. The contribution to the source function due to the external
photopump falls by three orders of magnitude in the first 2.0 (im of the of the slab.
However, an internal source of radiation keeps the source function above its initial
value. This result can be seen in figure 7-2 (b).
The rate matrix for a zone in the middle of the slab was examined for a time step
when the external photon flux was irradiating the plasma. By examining the rates into
the upper level of the transition, it was determined that recombination from the H-like
ions was populating the upper level. The population of the H-like ions is three orders of
magnitude lower than that of the He-like ions before the pump is turned on.
The external photon flux will pump any initial level that has an appreciable
population to a final level matching the energy of the photons in the radiative pump.
Hence, some doubly excited Li-like levels are observed to be pumped, and the upper
level of the He-like resonance line iPj can be pumped. However, these processes are
not very efficient, and do not significantly increase the H-like ion population.
On the other hand, once the photopump creates an increased population in the
2 !Pi level of the He-like ion, the collisional ionizations from 2 JPi to the H-like
ground state becomes effective. That this scenario is consistent with the processes
existing in the plasmas can be understood by the following analogy. The energy
difference between the 2 *Pi level and the H-like ground state, A E2,h is approximately
equal to the ionization potential of Li-like ions from the ls22s ground state, A El¡.
Moreover, since the collisional ionization rate is dependent on the energy gap, A E2,h or
A Elí, the almost complete ionization of the Li-like ions implies complete ionization of
the 2 iPj level.

ae2d
ae2d
(a) (b)
Figure 7-2. The constant density case. The x-axis corresponds to the distance, z, measured in units of cm.
a) The ionization balance as a function of distance. The curves a through f correspond to the C-like through
H-like ionization fractions of aluminum. He-like ions are predominant throughout the slab;
b) The source function as a function of distance shows that if the source is incident at z=0, the bulk of the
absorption occurs within 2 pm.

179
Linear temperature gradient and logarithmically decreasing density gradient
Other cases were done with a more realistic temperature and density gradient.
Since the code iterates to find the radiation field, the final temperature gradient was not
sensitive to the initial temperature gradient. Figure 7-3 shows the temperature and
density gradient used in one of the simulations. The corresponding ionization balance
before the photopumping and during the photopumping are given in figures 7-4 (a) and
7-4 (b). The ionization front has shifted from ~20 pm to ~60 pm due to cooling of the
plasma. Since radiative recombination is proportional to the electron density and 3-body
recombination is proportional to the square of the density, the distance that the front
moves is highly dependent on the how steep the density gradient is. The source
function before, during, and after, the external photon flux irradiates the slab are given
in figure 7-5. At the far end of the slab, the source function for the He-like aluminum
resonance line is a factor of three higher during the photopumping when compared to its
initial value. The source function does not drop as quickly as in the constant density
case because photon destruction probability is decreasing in this range due to the
logarithmically decreasing density.
Summary of results
In conclusion, the computer simulations have shown that the photopumping may
affect the entire plasma to some degree. The bulk of the external flux is absorbed within
2.0 pm of the slab, but the internal radiation field is sufficiently coupled to the
photopump to keep the source function up at the far end of the slab.
The computational work provides a general corroboration of the simple analysis,
but it illustrates the need for further experimental data. Further modeling of the

180
IS) C3 S3 C3
Figure 7-3. The temperature and density gradients versus z (cm) before the
photopumping in the second simulation. Curve a is the temperature in
units of 106K. Curve b is the electron density in units of 1021 cm"3.

CNI =T* CO CO S3 OJ
C2 S3 S3 S3 —. .—i
(a)
Figure 7-4. The ionization balance as a function of distance (cm) for the case with temperature and densitiy gradients shown
in figure 7-3. The curves a through e correspond to the C-like through fully stripped ions.
a) The ionization balance before the photopumping;
b) The ionization balance during the photopumping..

182
a9zd - source function
Figure 7-5. The source function versus z (cm) for the second simulation.
a) The curve a corresponds to the source function before the photopump;
b) Curve b is during the photopump;
c) Curve c is 100 ps after the photopump is turned off.

183
photopumping using the simulations would require running several cases to try to best
match the data. But, simply matching the experimental data will not give more
confidence in the validity of either the experimental data or the simulation. More
experimental work is needed explore the effects described here.
Limitations
This code does not include mechanisms for laser deposition, which is the source
for heating the plasma. The laser energy is deposited in the plasma in a very non-
uniform way and at this time there is no way to simulate a source internally in the
plasma.
The gridding is not dynamic so that convergence is a problem, since different
lines become optically thick in different zones. This ionization front may move in space
as the temperature and density changes, so the gridding must accommodate the smallest
zone. Since the computational time is proportional to the number of zones, the time
needed to create a simulation can become prohibitive.
The most outstanding limitation of the model created here is that hydrodynamic
cooling is not included. Hydrodynamic expansion of laser irradiated targets is often
responsible for a large fraction of the cooling in laser-produced plasmas, and is
important to determine the correct ionization balance of the plasma. To mitigate these
effects, the tamping of the aluminum microdot by the plastic overcoat was employed.
The relatively short duration of the photopump will further ease the importance of the
hydrodynamics. However, as stated previously, further detailed experiments are
required to study the system in sufficient detail to warrent further simulations.

CHAPTER 8
CONCLUSIONS
In this thesis, the phenomenon of resonance fluorescence has been investigated.
It had long been thought that this process would not be efficient enough to study without
using large-scale lasers to generate an intense photon flux. However, the results
contained in this thesis were obtained using a more modest-sized laser capable of
delivering 100 J of energy at 1.06 (im in 1 ns.
The first section of this thesis describes an experiment designed to observe
fluorescence. A line coincidence scheme involving the ^o^Pi transition in He-like
aluminum was used. The two-fold advantage of this scheme is that the large ionization
potential provides a large temperature range in which the ground state ions can exist
without significant emission of the He-like and H-like lines, and, the He-like resonance
line has a large absorption coefficient. Together, these factors create a scheme in which
it is possible to isolate the fluorescence.
Although the concept of the fluorescence experiment was straightforward, the
excecution required preliminary experiments that characterized the individual plasmas.
The primary importance of the first experiment was to show that a plasma could serve as
an x-ray pump and perturb another plasma. The previous development of backlight
sources for use in studying laser-produced plasmas was essential to this work. The
second experiment determined the optimal combination of laser irradiance conditions and
target necessary to achieve an ionized plasma that could be photopumped. A delicate
balance between creating a system that was ionized to the proper state and yet had a
minimum of self-emission in the fluorescing line had to be found. This work involved
184

185
the use of embedded microdots to minimize the temperature and density gradients in the
plasma.
The final fluorescence experiment involved a combination of the methods
described above. The front plasma, the one to be pumped, was created first in time.
The radiative pump plasma was created 1 ns later. Time-integrated and time-resolved
diagnostics recorded the spectra. The keys to observing the fluorescence were an x-ray
streak camera to time-resolve the emission and the use of a Ta block to shield the streak
camera from the direct pump flux.
The pump plasma was created by irradiating the target with a 0.53 pm
wavelength laser beam having 5 to 12 J of energy in 100 ps. The analysis showed that
the pump plasma had a temperature in the range of 400 to 600 eV and an electron density
in the range of 5 x 1019 to 5 x 1021 cm '3. The front plasma was created with a laser
beam having < 4 J of energy at 1.06 pm in 1 ns. The temperature was found to be 200
to 400 eV and the electron density was in the range of 5 x 10 20 to 1 x 1021 cm _3.
The fluorescence signal distinctly appeared on the time-resolved data. The
emission of the transition that was photopumped peaks twice in the data. The first peak
occurs at the peak of the laser pulse that initially created the plasma. The second peak is
due to the fluorescence. In some cases, the fluorescence intensity was the same order of
magnitude as the self-emission. Conclusive tests were done to show that the second
peak could not be attributed to the direct observation of the radiative pump. Other
sources of heating were considered, but were not sufficient to cause the second emission
peak.
The absolute photon flux of the fluorescence was measured to be on the order of
1.5 x 1011 photons per steradian. This calculation depended on the measurement of the
absolute photon flux delivered by the radiative pump and on the ratio of the self¬
emission to the fluorescence measured by the streak camera. This quantitative
measurement of the fluorescence is an upper limit on the fluorescence. More research is

186
necessary to resolve questions concerning the volume of plasma that is actually
fluorescing.
The second section of this thesis begins to analyze in detail the radiative transfer
occurring within the plasma. A simple analytic model based on a two-level atom is
presented to support the observation from a physical standpoint. However, the
agreement of simple model with the experimental data is better than can be expected
from such an order of magnitude estimate. This model should only be used as a guide.
In addition, computer simulations of the detailed radiative transfer were
generated. The simulation indicates that the internal radiation field is indirectly fed by
the photon flux. The result is that the external photon flux from the pump plasma was
found to affect the entire column of plasma. The experiments could not provide enough
data to discriminate between possible explanations of the discrepancies. The results of
the modeling are not conclusive and await more experimental data.
This thesis presents a direction for future spectroscopy on laser-produced
plasmas. Clearly, the optical depth effects that limit the established methods of studying
emission and absorption spectroscopy cannot be resolved without addressing the
question of radiative transfer. This work seems to indicate that photopumping and
fluorescence can be successfully used as a tool to study the interactions between
radiation and matter in laser-produced plasmas. The further development of this
technique will require a close interaction between computer simulations, such as the one
used here, and specific experiments designed to test radiative transfer theory.

APPENDIX A
DIAGNOSTICS
In this appendix, a brief description of each of the diagnostics used during the
experiments is given.
Dispersion Elements
Crystals. The x-ray spectrographs take advantage of the Bragg relationship for
diffraction of x-rays. Crystal provide a periodic structure that disperses the incident x-
rays at different planes, creating separate beams. When the beams recombine after
reflecting off the crystal planes, they interfere, thus producing a spectrum of the incident
light. The equation defining the relationship between the angle and the wavelength at
which constructive interference occurs is
n X = 2dsin(@)
Here 2d is the crystal lattice spacing, X is the wavelength of the incident radiation, and n
is the order of the diffraction.
Pentaerythritol (PET) crystals and potassium hydrogen phthalate(KAP) crystals
were used in these experiments. These crystals must be treated delicately because they
are prone to damage. Stress can cause the crystal planes to separate, thus changing the
diffraction properties. Sometimes a thin layer of aluminum (1000Á) is coated over the
crystal to protect the surface. The sensitivity of the crystals is given in appendix B.
187

188
PET crystals, C(CH20H)4, are commonly used because they produce a low
background. PET is hygroscopic so they should be stored in a dessicator and its
exposure to air should be minimized They also degrade with exposures to x-rays which
cause displacement of the atoms from the crystal lattice. The 2d spacing is 8.742Á, so
the useful wavelength region is 8.34Á to 0.762Á.
KAP has a 2d spacing of 26.632Á. Its chemical formula is KHC8H4O4 and is
useful in a range of 2.32 to 25.41Á. A KAP crystal was mounted on the front of the
sneak camera, perpendicular to the photocathode. Because of its larger 2d spacing, the
specna has a poorer resolving power, however, it has a wider wavelength range. This
crystal was used for the sneak camera in order to cover the whole wavelength region of
the He-like Al, and H-like A1 emission. A KAP crystal was also used in the curved
crystal specnometer. This crystal was used because of availability.
Harada grating The crystals are limited by the availability of natural materials
with a large crystal lattice spacing. So, for the 20-50Á wavelength region, a Harada
grating was used. It is a mechanically-ruled aberration-corrected grating that has a flat
focal field The grating has a periodic structure on the surface that creates a coherent
superposition of reflected light at wavlengths, X , that satisfy
7
where n is the diffraction order, N is the number lines per mm at the grating center, [3 is
the angle of diffraction at the wavelength, and a is the angle of incidence. The grating
was produced by Hitachi Ltd. was designed to be used at a grazing incidence angle of
1.36 °. It was 50 mm wide and had a nominal spacing of 2400 lines/mm. In general
gratings have a higher photon collection efficiency than crystals, the reflectivity of a

189
similar 1200 lines/mm grating is 7-12 %.140 Due to the design, the grating efficiency
and focussing properties are extremely dependent on the position of the source with
respect to the grating. The imaging properties of the Harada grating are given by Kita et
al.141
Spectrographs
Minispectrometers The minispectrometer used a PET crystal and film. The
window is covered with a light-tight filter like beryllium. Before a shot, the
spectrometer is loaded with film. Usually, there is also a filter placed between the
crystal and the film to attenuate the fluorescence from the crystal. It is then placed in the
vacuum chamber before the shot. After the shot, it is taken out to remove and develop
the film. These spectrographs are dependable and the alignment is fairly simple. Figure
A-l shows the geometry of the minispectrometer.
Figure A-1. Geometry of the minispectrometer. Three rays
corresponding to x-rays of three different wavelengths are
shown.

190
The curved crystal spectrometer is in principle the same as the minispectrometer,
but now the curvature of the crystal must be taken into account. The curvature can
increase the resolution of the spectra, however, it also reduces the crystal rocking curve
and the fragility of the crystal.
Pinhole cameras The pinhole cameras image the plasma. Using filters, the x-ray
emitting region imaged can be controlled. For these experiments, the pinholes were
filtered for 1.5keV x-rays or higher. The pinhole sizes were 12 and 15|im in diameter.
Streak cameras The streak cameras are much more sophisticated than the
minispectrometers. Figure A-2 shows the components of the streak camera. Kentech
low magnification re-entrant x-ray streak cameras were used in these experiments. It
has an entrance slit that is 25mm by 1mm. The x-rays are incident on a 25mm long
photocathode, such as Csl, that converts the x-rays into photoelectrons. These electrons
are then accelerated through focussing electrodes, pass through a hole in the anode and
are incident on a phosphor. As the electrons pass through the streak tube of the camera,
a ramp voltage is applied so that the electrons are swept over the face of a 40 mm
phosphor. The phosphor light then passes into a microchannel plate which provides the
signal gain. These electrons are then incident on another phosphor and the photons are
detected by film pressed up against the phosophor. The resulting image is time-resolved
in the direction of the sweep, and has a nominal magnification of 1.2 in the direction
perpendicular to the time axis (25 mm x 1.2 = 30 mm).
The variation in the ramp voltage controls the time resolution of the sweep. Six
sweeps speeds ranging from 10 to 805 ps/mm are available. The sweep is timed to
coincide with the x-ray signal by the trigger provided by the laser pulse. The
microchannel plate is gated on for 1 microsecond during which time the photoelectrons
are swept across the phosphor.

Figure A-2. Diagram of the x-ray streak camera. The dispersion direction
is perpendicular to the plane of the page, the sweep of the
electrons in time is shown.

192
The photocathode is the most delicate part of the spectrograph. The quality of
the data depends on the quality of the photocathode because this is the first step in the
conversion of the x-ray signal. The rest of the spectrograph enhances this signal.
Imperfections can lead to arcs that destroy the entire photocathode. The Csl
photocathodes were made by LUXEL. The composition was 0.1 pm of CH, 250 Á of
Al, and 1500 Á of Csl. The photocathodes used in the Harada grating were made of
250 Á Au deposited on a fine copper mesh. These photocathodes were more sensitive
to the soft x-ray region because they do not have a CH substrate. They were supplied
by EXITECH.
The P-20 phosphor is the final component of the streak camera. It has a yellow-
green appearance and fluoresces in a wavelength rage of 4950 to 6725 Á at a peak
wavelength of 5600 Á. The decay time of the P-20 is ~ 1 msec.
Determining the absolute gain of the streak camera depends critically on the
photoelectron conversion efficiency of the photocathode , but its efficiency degrades
with time and use. Also, the response of the entire system to photons (i.e. film and
streak camera) is not necessarily linear. So absolute numbers are not meaningful unless
the exact components and their configuration are calibrated.
Throughout this thesis, the streak camera that was used with a KAP crystal is
referred to the crystal streak camera. The other one, used with a Harada grating, is
called the Harada streak camera.
Other Elements
Filters. Filters are chosen according to the transmission of x-rays in a particular
regime. The tables compiled by Henke give the mass attenuation coefficients for most
of the common filters used for x-rays. The transmission can be calculated from the
following equation
T = exp (- p p x )

193
The filters used in the experiments were beryllium, Mylar, parylene, and aluminum.
A small computer program was written to compute the dispersion relations of all
the spectrographs. The program was used to convert the x-position to wavelength for
the spectra shown throughout the thesis.
Film. There are three main types of x-ray film. SB392 for energies greater than
1 keV, Direct Exposure Film for lower energies, and Industrex M which is 10 times
less sensitive than DEF.
In the minispectrometers, DEF or Industrex M film was used. DEF is a double
emulsion film, whose characteristics are extensively modeled by Henke. It is very
sensitive film and thus has a high fog level. Industrex M film was used only in the first
experiment in measuring the radiative pump data. DEF was used for the photopumping
experiment.
For any film, the density depends on the developing process: the chemical
concentrations, temperature of the chemicals, and the amount of time the film is in each
chemical. Therefore, for the absolute flux data, the technical photography department
developed the film.
The films used for the streak cameras were instant Polaroid 667 (ASA 3000) and
Polaroid 612 (ASA 20000) film for set-up shots. For taking data, "hard" film was used
so that it could be digitized. When using the "hard" film, the instant Polaroid was
placed behind the film so that we could gauge the results and prepare for the next shot
without waiting for the film to be developed.
For the second experiment, Kodak Royal X-Pan (RXP) film was used. The
RXP film had an ASA rating of 1200, but the film was grainy and led to a loss of
resolution. For the photopumping experiment, TMAX 400 film was used. Although
TMAX film has an ASA rating of 400, it recorded the green light of the phosophor with
intensities comparable to RXP and was much less grainy.

194
This film was developed by LLNL technical photograph department by a HOPE
500 machine. It would have been very impractical to develop them at JANUS because
the film had to be handled in complete darkness.

APPENDIX B
CRYSTAL CALIBRATION
The method for the crystal calibration follows the work of Henke.142 A
stationary x-ray anode source is used to provide a continuous flux of x-rays at the
characteristic K lines of the anode. The anode is kept under a vacuum on the order of
10 '7 torr in an effort to keep the anode pure, free of contaminants like carbon that
would form on the surface of the anode. The x-rays produced then pass through a
"window" into a chamber that has a millitorr range vacuum. The "window" is a slit
covered with a filter such as kimfoil which can withstand the pressure differential. The
x-rays then travel a distance of 120 cm to the crystal where they are Bragg diffracted to
a proportional counter detector 10 cm away.
The slit collimates the source and defines its size in the z direction. The x-rays
then are incident on a crystal-razor blade arrangement. The crystal is held in a mount
that is attatched to a shaft which is rotated by a stepping motor. The axis of rotation
should be at the crystal surface otherwise the x-rays will not sample the proper area.
Above the crystal, a razor blade can be vertically adjusted to make a slit. The purpose
of the razor blade is to enable discrimination of the zero degree angle.
The proportional counter is also attached to the shaft, but with a differential cog
that allows it to rotate at twice the rate of the crystal. In this way the Bragg angle
condition is always satisfied as the crystal is rotated. This counter has a detection
efficiency of about 90%.
A small electronic rack was set up to operate the proportional counter and anode
source. The high voltage to the anode was supplied by a "homemade" set-up and a
range from 1 to 20 kilovolts could be used.
195

196
Figure B-l. Schematic diagram of crystal calibration set-up. The center
of rotation for the crystal and proportional counter was the
center of the crystal.
The stepping motor rotates the crystal and proportional counter in units of 0.01
degrees every 2 seconds. At each angle, the detector measures the number of x-rays
and this number is registered by a multichannel analyzer. Each bin, or channel, of the
analyzer corresponds to the angle increment. The discriminator was set at 2 volts to
eliminate noise.
The crystal rocking curve is defined as
Rc= [ R (hv, 0) d@
Jo
where R(hv, 0) is the reflectivity of the crystal. Rc represents the efficiency of the
crystal. It is also called the Bragg reflection integral.
The crystal reflectivity depends on two measurements. The first measurement
determines how many x-rays are incident on the crystal. The second determines how
many are diffracted at the Bragg angle. These measurements are the used in the
equation for the reflectivity

197
coNr
R =
N0cos (0)
where co is the angular rate of scanning, Nb is the number of counts collected under the
Bragg peak, N0 is the number of counts at zero degrees, and 0 is the Bragg angle.143
The first measurement is done in the following way. When the crystal is at zero
degrees, the proportional counter sees some fraction of the direct beam. Then, as the
crystal rotates to positive degrees, the direct beam is detected as well as the specularly
reflected beam, so actually, the signal is enhanced by the reflections. The signal will
then peak at some value determined by the reflectivity of the surface, and then
dramatically drop. The experimental curves actually show a plateau at the zero degree
angle. Because of the razor blade, the number of counts at zero degrees, then, is 0.5
N0, since geometrically no matter what fraction of the entire beam is detected, the razor
blade will admit 50% of the direct beam that will be incident on the crystal when it is at
the Bragg angle. The measurement of x-rays diffracted is done by scanning over the
Bragg angle. The number of counts collected in the Bragg peak is the area under the
curve.
The crystal reflectivity is really a measurement of the efficiency of the crystal in
diffracting the x-rays at the Bragg angle. A crystal can be best represented by two
models, the perfect crystal and the mosaic. In the perfect crystal, the Bragg relationship
will only be satisfied by a small number of crystal planes that are correctly oriented.
This leads to a sharp Bragg peak.
In the mosaic crystal, the planes are not perfect, but are better described by a
"patchwork" of planes. The x-rays, therefore, can penetrate more deeply, and
moreover, because of the irregularities, they have a higher probability of Bragg
diffracting off more planes. The Bragg peak in this case broadens, and counter¬
intuitively, the absolute reflectivity can increase. As the crystal becomes more

198
deformed and degraded, the reflectivity will decrease because the integrity of the planes
will be compromised.
In general, the measured crystal reflectivity will fall between that predicted by
the mosaic model, and that predicted by the perfect crystal. Below is a table of the
values predicted by the two models, and values measured for the crystals used in the
experiments.144 The measurements indicate that the PET crystals were not of high
quality. KAP(curved) is the crystal used in the curved crystal spectrometer. MA and
MB stand for the minispectrometers used in experiment I and III.
Table A-1. Table of crystal rocking curve measurements. All values have
units of mrad.
Crystal
R(perfect)
R(mosaic)
R(measured)
KAP (curved)
0.0856
0.111
0.08 ± .02
PET (MA)
0.4647
1.304
0.29 ± .04
PET (MB)
0.4647
1.304
0.30 ± .03

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BIOGRAPHICAL SKETCH
Christina Back was bom in Vancouver, Washington, in 1961. She received her
Bachelor of Science in physics from Yale University in 1984.
207

standards of scholarly presentation and is fully ad(
dissertation for the degree of Doctor of Philosopi
Charles F. Hoópérydr.,
Professor of Physics
I certify that I have read this study and that in my opinion it conforms unacceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
J$nes W. Dufty
Professor of Physics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Neil S. Sullivan
Professor of Physics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
rVKA~t Ja©es N. Fry
Associate Professor of Physics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
1/v ^¡y{^uv A
Kwan Chenf
Professor of Physics and Astronomy
This dissertation was submitted to the Graduate Faculty of the Department of
Physics in the College of Liberal Arts and Sciences and to the Graduate School and was
accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy.
December 1989
Dean, Graduate School

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