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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xi, 207 leaves : ill. ; 28 cm.
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Back, Christina Allyssa, 1961-
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Laser plasmas   ( lcsh )
Plasma spectroscopy   ( lcsh )
Radiative transfer   ( lcsh )
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non-fiction   ( marcgt )

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

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Full Text










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.




























































a
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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