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Investigation of uranium plasma emission from 1050-6000 Ã

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Investigation of uranium plasma emission from 1050-6000 Ã
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Mack, Joseph Michael, 1944-
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Absorptivity ( jstor )
Calibration ( jstor )
Electrons ( jstor )
Line spectra ( jstor )
Oscillator strengths ( jstor )
Plasma temperature ( jstor )
Plasmas ( jstor )
Uranium ( jstor )
Uranium plasmas ( jstor )
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INVESTIGATION OF URANIUM PLASMA EMISSION
FROM 1050 TO 6000 A







BY

JOSEPH MICHAEL MACK, JR.
















A THESIS PRESENTED TO THE GRADUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA 1977













A CKNO WLEDGEMENTS

This work describes research performed within the Department of Nuclear Engineering Sciences at the University of Florida and also at the Los Alamos Scientific Laboratory in New Mexico. The effort was financially supported by the National Aeronautics and Space Administration (Contract NGR 10-0050089) and directed by a committee composed of Dr. Richard T. Schneider, Chairman, Dr. Hugh D. Campbell, Dr. Edward E. Carroll, Dr. Dennis R. Keefer, Dr. John W. Flowers, and Dr. Leon J. Radziemski.

The author is grateful to Dr. Schneider for his constant encouragement and suggestions throughout the duration of this investigation. Dr. Campbell was of valuable assistance in maintaining a realistic perspective as to the theoretical and practical limitations.. Special thanks is given to Dr. Radziemski for his persistence in encouraging the author to complete this work and also for the many timely discussions regarding dissertation content.

The author wishes to show exceptional appreciation to

Dr. Robert D. Cowan for his willingness to allow the use of his atomic structure code and the sharing of his insight related to these computations. It was indeed a great honor to have worked with Dr. Cowan in this reQard.

Because of the extensive nature of the effort required for the successful completion of this research, many people became involved, both students and faculty alike. The author wishes to convey his ii








recognition of the assistance given by the following: Dr. Chester D. Kylstra, Arthur G. Randol, Noval A. Smith, John L. Usher, Bruce G. Schnitzler, George R. Shipman, Jeff Dixon, George Fogel, Kenneth Fawcett, Peter Schmidt, Ralph Nelson, and Willie B. Nelson.

The author is further indebted to his secretaries at the

Los Alamos Scientific Laboratory, Ofelia M. Diaz and Delores M. Mottaz, for their persistence in the painstaking labor which went into the typing of the manuscript.

Financial support through the University of Florida Assistantship Program and the Atomic Energy Commission Traineeship plan is acknowledged.































iii










TABLE OF CONTENTS

Page

ACKNOWLEDgMENTS ....................................... ii

ABSTRACT ..............................................

I. TNTRODUCTION.................................... 1

IT. PLASMA THEORY AND DIAGNOSTICS................... 5

Il-i. Equilibrium Considerations............... 5

11-2. Plasma Radiation......................... 8

11-3. Emission Coefficient Determination....... 12 1 -4, Plasma Temrrperature....................... 16

II-5. Density Measurements..................... 25

III. URA N TiM PLASMA EXPERIMENT HARDWARE.............. 29

III-1. Uranium Plasma Generation................ 29

11I-2. Uranium Plasma Stability ................. 35

II -3. Data Acquisition......................... 39

IV. LOW PRESSURE URANIUM ARC DATA REDUCTION......... 54 TV-1. Spectral analysis........................ 54

IV- 2. Temperature Measurement.................. 55

IV-3. Density Measurement...................... 63

IV-4. Emission Coefficient Determination....... 66

V. HELIUM-URANIUM ARC DATA REDUCTION............... 73

V- i. Spectral Analysis........................ 74

V-2. Temperature Measurement.................. 75

V-3. Density Measurement...................... 75

V-4. Emission Coefficient Determination....... 76

iv









Page

VI. THEORETICAL CALCULATIONS .......................... 91

VI- 1. ntroduction............................... 91

VT- 2. Termitnolo ................................ 91

VT- 3. Configuration Selection .................... 93

VI-4. CalcuZation of OsciZlator Strengths ........ 94 VI-5. Comparison of Results ...................... 100

VII. CLOSING REMARKS ................................... 104

APPEND [CES

A: SAHA NUMBER DENSITIES AND NORMAL
TEMPERA TURES................................... 107

B: COMPU'R SCHEMATIC FOR THE COWAN RCG CODE..... 116

C: CENTRAL LINE AND OSCILLATOR STRENGTH
D STRIBU'IONS FOR SELECTED UTII CONFIGURATION
PA/I TRS............................................ 118

D: REPRESENTATIVEE ENERGIES OF SELECTED UI AND
UlT CONFIGUA14TIONS ............................ 128

E: UF6 PHOTOABSORPTION EFFECTS OF THE
MIARTENEY AND FLORIDA EMISSION COEFFICIENT
iATA............................................ 133

REFERENCES................................................ 143

BIOGRAPHICAL SKETCH........................................ 151

















V












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



INVESTIGATION OF URANIUM PLASMA EMISSION FROM 1050 TO 6000 A

By

Joseph Michael Mack, Jr.

December 1977

Chairman: Dr. Richard T. Schneider
Major, Department: Nuclear Engineering Sciences
Absolute emission coefficient measurements on arc-generated

uranium plasmas in local thermodynamic equilibrium are described for

wavelength bandwidth of 1050 to 6000 A. Low- and high-pressure arcs

were investigated for their emission properties, characteristic temperatures and uranium partial pressures. Temperatures from 5500 to

8000 K and uranium partial pressures from 0.001 to 0.01 atm were found

at the arc centerline. The new emission data are compared with other similar experimental results and to existing theoretical calculations.

The effects of cold-layer UF 6 photoabsorption on uranium plasma emnission characteristics are established for UF molecular densities

ranging f rom 1 .0 x 10 16 to 1.0 X 10 17 cmnf3 and layer thickness from

1 .0 to 5. 0 cm.







vi








,,4b TnitLi? atomic structure calculations were made using relativistic Hartree exchange wavefunctions, from which oscillator strength distributions were computed for transition arrays of interest. These calculations give supporting evidence as to the credibility of the measured emission at various wavelengths, particularly in the vacuum ultraviolet. It is suggested that a consistent picture as to the nature of uranium plasma emission, at these plasma conditions, emerges and the capability now exists to successfully compute major emission features of uranium and other complex atomic systems.

































vii












1. INTRODUCTION

With the advent of the nuclear age and the subsequent strong trend toward development of uranium-based technology, research priorities concerning the nature of the uranium atom have acquired substantially increased importance. Initial involvement in metallurgical and nucleonic properties was largely due to the apparent need for weapon fabrication and later some aspects of reactor technology. By 1947 a new area of interest was the study of uranium plasmas at high temperature (6 keV), for a physical understanding of energy release caused by nuclear detonations. This was the first significant attempt to model the uranium atom using a.quantum and statistical mechanical basis from which was extracted thermodynamic and optical information. Eventually, interest was generated in lower temperature (0.5 5 eV) uranium plasmas because of the potential usefulness of plasma core reactors as a means for space propulsion and possibly as an energy source for MHD power generation. 2-4 More recently, worldwide need for uranium isotope enrichment using laser processes 5-12 has opened a new and significant area which is stimulating much basic research of the uranium atom. Uranium plasma research is also influencing the development of nuclear-pumped laser systems. This particular program has had some recent breakthroughs 13,14 which will likely increase the research momentum on the study of neutral and onceionized uranium.

An accurate theoretical model of the uranium atom would represent a monumental step in understanding complex atomic systems. Tile mathematical description of many-electron atoms has been attempted using several






2

methods imbedded with various approximations.151 In many situations,
experimental results are available to substantiate theory or at least to raise questions about the validity of certain aspects of theoretical treatment. Currently, there is little conclusive theoretical-experimental validation of the atomic properties of uranium and uranium plasmas. However, there is a significant effort under way by Steinhaus et al. 18'19

-to establish experimentally the energy levels of neutral and onceionized (UI and [HI) uranium. This effort evolved from work by Schuurmans 20 and Kiess et al. 21in 1946. With subsequent improvement in optics,spectroscopic techniques, and atomic structure calculations, confidence is increasing in energy-level definition but progress is slow.

The specific emission coefficient c (T,P) characterizes the light emission from a volume element of plasma. It is defined as the amount of energy emitted per unit time, from a given volume, into a specified solid angle and wavelength interval. It can be composed of continuous and/or discrete components, both of which are strong functions of plasma temperature and density (pressure) of the radiating species. The formulation of an adequate theoretical model of the uranium atom can be strongly assisted (perhaps out of necessity) by obtaining from experiment detailed knowledge of the uranium emission coefficient. Because calculation of such a property (for uranium) is impossible without a model that suffers from several approximations, experimental verfication through emission coefficient measurement is needed. This thesis reports on an experiment designed to measure the specific emission coefficient of a uranium plasma and to relate these data to state-of-the-art theoretical predictions.






3

Miller 22 and Marteney et al. 23 have acquired emission coefficient data from UF 6 shock-tube and radio-frequency induction-heated Ar-UF 6 plasmas, respectively. Uranium plasma emission coefficients obtained from UF 6 discharges present distinct impurity problems, potentially resulting in distorted emission coefficient wavelength dependence.

A dc uranium arc was chosen as the light source for the present experiment to reduce plasma impurities and provide a steady-state, less contaminated plasma to determine its emission properties. The wave0
length bandwidth considered is from 1050 A to an upper limit of 6000 A. The emission data are then compared to similar data generated by other research groups. Also included is a comparison to theoretical emission coefficient predictions. In summary, this effort was conceived to establish a unified picture of the progress made over the past few years concerning the experimental and theoretical investigations characterizing

uranium plasma emission.

Chapter II describes the plasma diagnostics necessary for the

determination of basic plasma properties such as temperature, particle densities, and radiation. Particular attention is given to the application of such diagnostics to uranium plasmas. Uranium arc plasma generation and arc stability are discussed in Chapter 111. Also examined are the various methods of data acquisition and intensity calibration applied in the course of this investigation. Chapters IV and V indicate the emission measurements for uranium plasmas at two distinct arc conditions. Brief descriptions and comparisons of other similar experiments are given among these, the present effort, and theoretical predictions. In Chapter VI theoretical models of the uranium atom are critically considered. A comparison is made between emission peak locations of the








present results to theoretically predicted locations for the higher temperature arc plasma. A discussion of the major points of this overall effort then concludes this study.














IT. PiIlSMA 271P ORY ANO ) T[A( N()STTCS

Plasma temperature and density diagnostics are based on the

assumption that relevant information can be extracted from theoretical descriptions of microscopic plasma processes. Generally, plasma constituents exhibit balance between the population and depopulation of neutral and/or ionic energy levels. This implies that for every excitation event (to use an example) there is a corresponding deexcitation, not necessarily brought about by the inverse excitation process. Plasma particles that are excited and de-excited by the same mechanism demonstrate detailed balancing. Arc plasmas are usually considered to be collision-dominated in the sense that e -atom collisions cause most of the excitations and de-excitations. However,

radiative de-excitation can also be important as indicated by strong photon output. Therefore, arc plasmas are rarely characterized by detailed balancing, and various approximations such as local thermodynamic equilibrium (LTE) and partical LTE24 must be used.

I1-1. Equ iibriums2 Considerations

Griem25 has developed criteria that indicate which equilibrium state applies to a given plasma. Most of these tests set limits on the dominance (or lack thereof) of collisional rates over radiative rates. Griem developed the following criterion for complete LTE in

a hydrogen-like system:


n -9 x 1017Te 1 Z7I


5






6

Where n e =electron density (cm- 3
Z = net plasma charge (Z=l for neutral; Z=2 for singly ionized),

O = energy (eV) of 1st excited state with respect to the ground state,

J e = thermal energy of plasma electrons (e0), and

E H = ionization potential of hydrogen (eV).

This criterion estimates the lower limit of electron density required to maintain a hydrogenic system in complete LTE. A hydrogenic system is usually characterized by a large energy gap between the ground state and first excited level, and successively smaller energy separations between levels as continuum is approached. Hydrogen (and helium) is also one of the more difficult elements to bring into LTE because of its relatively high-lying first excitation level. Thus, hydrogen can usually serve as an upper-limit estimation for the validity of LTE for more complex systems. However, the electron density criterion offered by Eq. (11-1) is not directly applicable to the uranium system because the known energy-level description of the uranium atom (or ion) simply does not fit the hydrogenic picture. In fact, the first excitation levels of UI and UII are 0.077 eV (UI) and 0.03 eV (U11), which, for singly ionized Uranium at 8500 K, implies n e > 3.9 x 10~ cm This is well below any reasonable values for n e basically because of the strong dependence on AE O1 which has a very small value for neutral and once-ionized uranium. Applied to hydrogen at 8500 Kne 88x116cm -3, this limiiting value for n e is probably too restrictive for the uranium system. Griem, 26McWhirter, 27and






7


Wilson 28have developed a test which depends on the energy level structure of a specific atomic system, thus reducing the necessity of assuming hydrogen-like characteristics. This criterion (hereafter called the ladder criterion) is more applicable to complex systems.

The ladder criterion presumes that the most difficult level to populate will form the largest energy gap ascending the energy level diagram. Existence of LTE in an optically thin collision-dominated plasma is tested by


ne C T 112 (E E [) 3 (11-2)
e e k 1

where C = 1.3 x 10 12 (Mc~hirter 27)

The electron temperature T e has units of K; the largest energy gap in eV for the atom under Study is (E k- E ) Equation (11-2) is not sufficient for LTE because e relaxation time, e -atom relaxation time, and atom relaxation time must dominate whatever other transient phenomena occur in the plasma. Most stable steady-state arcs satisfy these relaxation requirements.

To apply Eq. (11-2) to a uranium plasma it is necessary to define the largest energy-level gap found in its level diagram. Complete tabulation of this information is unavailable, but a representative gap width may be defined by examination of the work by Steinhaus et al. 18'19 and Blaise and Radziemski. 29Considering neutral uranium NOl, the 620.323 cm- -~ 3800.829 cm- levels provide the largest gap

(3180 cm-I). This implies an electron density of 7.2 x 10 12cmat 5500 K. Similarly for singly ionized uranium (UTI), the largest gap is about 2126 cm-1 (2294.70 -, 4420.87). 30 Assuming an electron temperature of 10 000 K (UII), the corresponding electron density






8

limit is then 2.93 x lO12 cm3. If partial LTE is assumed, the largest energy gap need only be defined above the thermal energy limit.

In conclusion, although there is no feasible way to determine accurately the LTE limits on electron density for atomic and onceionized uranium, reasonable estimates can be obtained using Eqs. (11-1) and (II-2).

IT-2. Plasma Radiation

Many factors affect the net photon output from a plasma. Optical depth and absorption are the most important. In many laboratory plasmas, photons emitted from the plasma central region may be absorbed en route to the outer boundary. The degree of trapping implies an optical depth, T (x), which is simply the effective absorption coefficient integral K'(x) over a given homogeneous plasma depth X. The relation between the intensity I V(x) and energy emitted as a function of the line-of-sight depth into the plasma is governed by Eq. (11-3), the equation of radiative transfer.

dl (x) vx
dI V(x) I ( (X (11-3)

V V


The specific emission coefficient, c"(x), (energy/volume-wavelengthtime-solid angle) and LV(x)/ .V(x) is the source function of radiation (energy/area-wavelength-time-solid angle). The source function for an LTE plasma is equivalent to the Planck function.




In this sense X connotes a homogeneous plasma depth, and the subscript implies that there is a spectral dependence to T and :.






9

The general solution to the equation of radiative transfer is

x
x= I( (o) e-"v(x) + B(T) K'(x) e-v(x') dx (11-4)
0

where I (x) observed intensity at X, v (energy/area-time-solid

angle-wavelength,

I V(o) = intensity of background source (if there is one) at v,

BK(T) = Planck function at T, v (energy/area-time-solid

angle-wavelength),

K'(x') effective absorption coefficient (length-) at x-, V,
and

SV(x') = specific emission coefficient at x-, v (energy/volumetime-solid angle-wavelength).

In Eq. (11-4), a situation is possible where all emitted photons transport beyond the outer plasma boundary, that is, if c (x) o. Then the observed intensity is simply the emission coefficient integral over the line-of-sight depth, provided the plasma is homogeneous. This plasma is designated optically thin. The other extreme would be V Wx -; here all emitted photons are trapped within the outer plasma boundary, and then the plasma radiates as a surface where I V B This plasma is designated optically thick and exhibits a blackbody spectral distribution of radiation.

Generally, in relating the concept of optical depth to arc plasmas, the line-of-sight depth and the effective absorption coefficient must be determined. Usually the line-of-sight depth will be quite small (for arcs), making the effective absorption coefficient the important quantity. Unless the plasma pressure is 50 atmospheres or







10

greater (dense arc plasmas), the only significant absorption will be located (on the wavelength scale) at some of the spectral line centers, usually formed in the lower energy levels. In many cases for low- and intermediate-density plasmas, the effective absorption coefficient will be small for most wavelengths.

Line, recombination, and continuum radiation are three basic

radiation types occurring in an arc plasma. Line radiation is usually associated with relatively low temperatures, i.e., 4000 K-15 000 K; recombination and continuum radiation can be substantial when the characteristic plasma temperature is > 15 000 K. Detailed treatments of recombination and continuum radiation are given by Cooper.)1

Spontaneous emission and stimulated emission result in line radiation. Stimulated emission (often thought of as negative absorption) is a difficult item to isolate and therefore, is usually defined as an effective absorption coefficient for any plasma as shown by: K'(X) = KC (X) + KC (X) (II-5a)
V V

KL (X) = K L (X) K SE (x) ,(11-5b) V V V)

where K' = total (measured) effective absorption coefficient at


V



KL (x) = line absorption coefficient at x, -v,


K (x W total continuum absorption coefficient at x, j, and






11

KSE (x) = negative absorption coefficient caused by stimulated

emission at x, v.

Thus, KSE (x) represents an effective decrease in K'(x). If an energy
V
absorption transition by a bound electron of an atom is considered, where u :-> upper level and k => lower level, the description of line absorption at a given frequency is given by



KK (x) n Bu N(v) (11-6)


where vk.u the frequency of the transition (s-l

n. =population density of the lower state (cm- 3),

B = Einstein's probability for absorption (cm/g),

= absorption line-shape function with Jiine4(V) dv = 1, and


X = line-of-sight distance into plasma.

Similarly, the line emission coefficient for a homogeneous plasma at frequency v is described by hvu A (v) (11-7)
L (x) 47T nu Au C


where cL (x) is the specific line emission coefficient at v and plasma
V
depth x. Actually, a continuum emission coefficient should also be considered for completeness, but this is not included here because of its small (or inextractable) contribution. The population density (cm- 3) of the spontaneous upper level transition and Einstein probability for such a transition are given by nu and Au+>(s-l) respectively. The normalized line-shape function is indicated by 4jv), such that








12

fine pcj)dv = 1. The line intensity I (x) from such a transition
would simply be determined by multiplying the line emission coefficient by the appropriate LOS plasma depth through a constant emission zone.

Arc plasmas are inherently inhomogeneous to varying degrees. Freeburning arcs usually exist with significant temperature gradients along the major part of an approximately cylindrical arc column radius, which results in radially varying intensities. Therefore, the emission coefficient will also have a radial dependence that must be extracted by unfolding methods applied to observed intensities. Many wall-stabilized arcs have less severe temperature gradients, with the exception of that region approaching the wall. 32-37 This implies the possibility of an approximately homogeneous nature in temperature and density in the major part of the cylindrical arc plasma in the radial direction. Although a relatively constant temperature profile does not assure homogeneous density and emission profiles, it can be a strong indicator. 11-3. LP,issior Coe iLcient _Determination

The geometry of inhomogeneous optically thin arc plasmas is approximated by a number of concentric zones about the vertical axis, as shown in Fig. I1-1. Each zone is assumed to display constant emission which is a function of a single temperature and density for that zone. The intensity at a given location along the arc chord is the sum of emission contributions for each zone intercepted by a LOS ray passing through the geometry. The emission coefficient must then be unfolded from the measured integrated intensities by the familiarAbel transform. The analytical -form of the transform equations is






13
xr

I(y)= 2 C(r)dx = 2 E(r)rdr and (II-8a)
o y -y



c(r) = 2y)dy (II-8b)
r y 2yr



The geometrical relations are developed using Fig. II-l.

There are two common approaches used in solving Eqs. (TI-8a) and (II-8b) for c(r). The first is by fitting an appropriate polynomial to the experimental intensities, differentiating, and using Eq. (II-8b) to obtain c(r). The details of such a method are given in Ref. 39. The second method approximates the integrals with sums and extracts the desired information numerically. The numerical form of Eq. (II-8a) is given by

T (y) = 2 Erj(r) 9ij (11-9)
J

In Fig. II-1, the ith LOS in the j th concentric ring is defined by the length coefficients, Zii, and cj(r) represents the average emission coefficient for the jth ring. Equation (11-9) results in a system of simultaneous linear equations for each cj(r), IT(y), which can be solved by matrix inversion to obtain the j(r) vector.

When the plasma under investigation has significant intensity gradients, a number of rings (as many as 40) may be necessary to approximate adequately the intensity profile and allow computation of emission coefficients within acceptable error. Each ring requires a corresponding intensity determination, which may be too difficult to obtain, depending on plasma stability. However, too many subdivisions may cause








14






"",







.ILI
\ \\

i}"-..-. i \ :J ?
N: "-.,,: ;'",9- \ : I 1 "
r N ',..N....; o...
t \ -<:I \,,2
N .. i








-'2.











Fig. I -I. Zonal division of a cylindrically symmetric plasma.







15

oscillations in the unfolding process if an exceptionally smooth intensity profile is not available. Substantial error (20 30%') on the intensity profile measurement (especially for the outermost ring) will be propagated to the central zone and will yield a poor estimate of its emission value. For this situation, too many rings will introduce large oscillations and an unacceptable error propagation. Obviously, there is an optimum number of rings depending upon the overall intensity profile shape and the experimental error value, particularly at the outermost ring.

Many studies have dealt with various techniques to implement the inversion 40-43 but these primarily address algorithmic problems (interpolation, smoothing, etc). Kock, 44 Nestor, 42 and Bockasten 43 address error propagation by using numerical methods for inversion. These analyses imply that the correct number of subdivisions is a direct function of the experimental error in the outermost zone as well as the shape of the intensity profile. 44 When error in the outer zones approaches 20% or more, four or five zones may define the limiting accuracy.

To relate these considerations to the inversion of the wallstabilized uranium arc intensity data, a four-ring numerical unfolding scheme was chosen because of time limitations involved in acquiring zonal intensity data for more than four zones, and the experimental error associated with the outermost zonal intensity was ,, +25%. When this error is considered with a 10% calibration error and an estimate of error for using only four rings, the total error estimate of central zone emission coefficients ranges from 28 -- 36%.








II-4. Plasma Temperature 16

Many techniques used for temperature diagnostics were developed by
.23 45 46
Griem,23 Hefferlin,45 and Lochte-Holtgreven.46 The following discussion considers only those temperature diagnostics applied to a uranium arc plasma, including the Boltzmann plot, norm temperature, relative norm temperature, and the modified brightness-emissivity methods.

A. Boltztomann PZot Method

The integrated line intensity for a homogeneous, optically thin plasma into a depth x is

hv
I- u+ A n X (II-10)
47- >k

If the plasma is in complete LTE and inhomogeneous, n (T) is determined
U
by the Boltzmann factor yielding


I hvu gu A n (T) e-(Eu/kT)Z (II-ll)
v 41 Z(T) u+1 o

where T = excitation temperature (K) ,

A = transition propability (seconds-) ,
qu+* = transition frequency ,

gu= statistical weight of the upper level ,
n (T) = ground state population density of a particular ionization

state (#/cm3)

Z(T) = partition function ,

Eu = energy of upper level (eV), and
R,. = ring depth of zone of assumed constant emission (Fig. II-1).



Integrated in this sense means integration over the line-shape function line (u)dv has already been performed.







17

Taking the natural log of both sides of Eq. (II-11) and rearranging terms yield an equation analogous to that of a straight line:


Iln {V u Z v In fh no(T)ki i __ E (11-12)



If for two or more spectral lines, In (constant I V) is plotted against Eunm ("in' refers to a particular transition), the resultant slope of the curve will approximate -l/kT. If I. is measured in absolute units, the ordinate intercept also determines the LTE ground state number density for that species.

Equation (11-12) was developed considering complete LTE and can be modified for use with less restrictive equilibrium concepts. When partial LTE is assumed, the Boltzmann plot method for complete LTE is modified to yield


ln I V n {h E) (11-13)
jgu Au__, kT(E


where: E. energy level of lower energy, and

9= lower level statistical weight.

The essential difference between Eq. (11-12) and Eq. (11-13) is that the intercept term no longer defines the true ground-state density in partial LTE.

Application of the Boltzmann plot technique for relative or absolute temperature determination requires the following conditions:

(1) at least partial LTE must exist in an optically thin plasma,

(2) many transitions should be used,







18

(3) these spectral lines should have a correspondingly significant

energy-level separation, and

(4) this technique can be used for inhomogeneous plasmas, but the

intensity data ideally should first be spatially resolved to

express the emission coefficient as a function of plasma radius

(in cylindrical geometry). If there is no spatial resolution the computed temperature will be an approximate value, bot in

many instances it will yield a good estimate of an average arc

temperature. The accuracy of these temperatures is governed by intensity measurement and uncertainty in atomic constants. The

largest source of error for uranium plasmas is usually caused

by the uncertainty of gA values which can be as much as 50%.

Only in extreme cases will the average centerline temperature deviate by more than 20% from the true centerline temperature.

To apply this method to uranium plasmas (or any method dependent on gA values), availability of well-defined spectral lines is severely limited. These lines must meet the previously mentioned requirements and be locatable with the instrumentation to be used. Application of the Boltzmann plot method to uranium plasmas is straightforward in principle; but practically speaking, a very tedious task strongly dependent on spectrograph resolution, line identification, and availability of relevant constants.

B. Ncnm-Te2LeYLa uLe Method

If the equilibrium emission c V (T) of a transition in a specified ionic state is plotted against temperature, and if the temperature is high enough, the resultant curve will be peaked at the norm-temperature T n defined on an emission-vs-temperature plot as the temperature







19

at which dc(T)/dT = c'(T) = 0. The norm temperature can then be used to estimate the characteristic plasma temperature. First, it is necessary to determine which ionization state corresponds to identified emission lines generated by the plasma. Then c V(T) is computed for a spectral line known to be from the dominant ionic stage by using appropriate equilibrium relations. Then ce(T) = 0 is determined, thus defining T n' The maximum temperature of an equilibrium plasma emitting a line in a particular dominant ionic state can be on the order of Tn5 which is indicative of the energy necessary to ionize the plasma to that state.

Obvious disadvantages of such a method are that Tn is only an

estimate of the characteristic plasma temperature, and while transition probabilities need not be known, the Saha equation must be solved to obtain the neutral and ionic number densities, thereby requiring LTE. The primary advantages are that only spectral line is necessary and that this method can easily be adapted to the relative norm-temperature method.

C'. Rh lative Temperature Mlethod

The relative temperature method is an extension (in many cases) of the norm-temperature method in that the norm-temperature can be used as a reference plasma temperature and temperatures at other spatial locations related to it. It can be used for plasmas which have cylindrical geometry with radial temperature profiles T(r) and at least one defined temperature such as T n. If this is the case, the resultant emission profile c. (r) pertaining to a specific transition can be similar to that shown in Fig. 11-2; one point on the desired temperature profile T(r) is defined by c,(r 0) and T n' From equilibrium relations, ratios of C (r 0 VC/V (r i) may be computed and the corresponding T(ri ) determined.








20









CL '2
0






j- Vv4SV






i n-LV l 3 d N -1 cl




4
0 ui S0
<
4





0



ro
F Ul < ro







21

exp _u] l 1 (11-14)
S(r0) Z[T(ri)] nT(r0) T(ri T(ro)


Any temperature on T(r), determined by other independent methods, will suffice for T(r0).

The relative temperature method is particularly straightforward

when dealing with the norm-temperature situation. Transition probabilities are not needed, but the temperature dependence of partition function should be considered. Only one transition need be used, thus eliminating any calibration procedures. This method is very attractive for use with spectroscopically complex plasmas because it is independent of gA values.

D. MA.!ijiecl Bvightness-Emissi vit/ method

Temperature measurement methods previously discussed require the assumption of negligible absorption or an optically thin plasma. If certain spectral lines emitted by a thin plasma have measurable absorption (say at the spectral-line centers), temperature may be determined using spectral-line absorption as a basis.

The brightness-emissivity method (BEM) adapts the radiativetransfer equation (Eq. (11-3)] solution to a homogeneous LTE absorbing plasma.46'47 The following equations form the basis for this method.


I T(x) I (x) e-v(X) + IP(x)


IT(x) S(o) ePTvx) + B (T) 1 e W (11-15)


T S -E(x) BP
I(x) = I )(o) e + B (T)



Emissivity, as considered in this instance, is the ratio of the plasma intensity to the Planck intensity at a specified temperature and wavelength.







22

where tv =emissivity,

x = LOS plasma depth,

I T (x) =total observed intensity at (N, x),

I 5(x) = total external source intensity without absorption

at (v, x),

S ()= total external source intensity without absorption

at v, x = o (the plasma boundary), and

B P(T) =Planck function indicative of the brightness temperature

of the plasma.

The known quantities Ij TxW, I (xW, T (x), and allow determination of the plasma brightness temperature using the Planck function for the plasma.

The primary disadvantage of the BEM is lack of applicability to inhomogeneous plasmas such as those formed with arcs. Usher and Campbell 48 have adapted the BEM to the homogeneous case. The modified BEM differs from the BEM in that an unfolding scheme resolves the absorption coefficient and temperature profiles spatially.

The absorption coefficient of a spectral line is determined by a constant intensity background source and measurement of the wavelength attenuation as the line passes through the plasma. If the inhomogeneous plasma is composed of homogeneous rings (similar to Fig. 11-1), an unfolding technique 47can be used to calculate the average line-center absorption coefficient, KC(X), for each ring from



i~7(I V T1 Sn- -ii~~i (11-16)






23

Voltage signals Vs, VT, and V P are from a photomultiplier tube for the ith LOS position. The voltages indicate background source intensity, total attenuated intensity, and plasma intensity, in that order. The k iiin Eq. (11-16) represents the length segments in the ith ring along the i th LOS position as shown in Fig. II-l. Figure 11-3 shows a typical oscillogram of the photomultiplier output related to Eq. (11-16). The background source of known characteristics (Xenon flashtube) is flashed on the line-center of interest as shown on the upper trace. The lower trace shows the flashtube signal spread in time to facilitate intensity voltage measurement. The oscillograms are recorded at different chordal positions of the plasma and Eq. (11-16) is used to determine the linecenter absorption profile across the radial dimension of an assumed cylindrically symmetrical arc.

The temperature is determined by an extension of the brightnessemissivity method to the inhomogeneous case. The technique uses measured voltages and calculated line-absorption values. The temperature method requires that the background source temperature (or equivalently, the intensity) be known. The average temperature in the jth ring of the

plasma is determined from
T. = ( 21-l(Tb
ln [1 + e b- (e (1-17)


The Planck functions BS and B. represent intensities of the background source and the j th plasma ring at wavelength X, and Tb is the brightness temperature of the background source. The B.'s are calculated using the measured voltages and the computed plasma absorption profile. The complicated expression for B. is found in Ref. 47.







24
















____ BASELIN f


SPECTRAL LINE1 _____OF INTEREST ________ BAS ELI NE



ST F LASHTIUBE




EXPANDED VIEW,, OF UPPER TRACE











Fig. 11-3. Oscillogram of photoniultiplier output.







25

There is very little available information about atomic properties of uranium. This information would be useful when performiing plasma temperature diagnostics on spectroscopically complex elements; however, the modified BEM is particularly effective for use with uranium plasmas because it is independent of these constants. Because this technique deals adequately with plasma inhomogeneities, it is suitable for application to arc plasmas. Implementation of the method is cumbersome because it means a long-duration (,-, minutes) steady-state plasma, a well-defined standard background source and its associated circuitry to provide a rather elaborate data acquisition sequence. 11- 5. Denisi t Aeaiiremw'its

To define plasma pressure, total or partial, it is necessary to determine ground-state population densities for all ionization stages in the plasma. The equation of state (in conjunction with Dalton's law of partial pressure) for each plasma component is then used to define a total pressure. A substantial effort is involved in establishing population densities. The determinations must rely on an accurate atomic description of the plasma constituents and precise intensity calibration. Griem 25 states that even in an optimum situation, it is often impossible .to reduce density error below 30%. Therefore, most plasma density determinations are order-of-magnitude estimates.

Two density diagnostics, which were applied to the uranium arc

plasma, are described in the following sections: absolute line intensity and pressure-temperature correlation (PTC).

A. Abso lute Li ne Intensity Method

The integrated line intensity for a transition from level u to level k. is given by Eq. (I1-10). Equation (11-10) applies to a line






26

emitted from a homogeneous optically thin LTE plasma. Modification to

an absorbing plasma requires compensation (build-up) along the entire line-shape profile. Obtaining absorption build-up factors at many points along the line profile may not be possible because of line-wing overlap, especially in plasmas displaying complex spectra where isolated lines may not exist. Fortunately, absorption in many arc plasmas tends to be concentrated at spectral-line centers (on the wavelength scale). Therefore, an absorption coefficient determined at the spectral-line center approximates, to a Usually acceptable degree, the maximum absorption coefficient taken over the entire line profile. This remains a good approximation as long as the spectral line exhibits a sharp profile. Using the above as a basis, absorption build-up may be incorporated into the line-intensity equation by the following:



a h\) u G u A n e- E u /kT e Pij Y (11-18)
V total 4,fi T u o


where y represents a dimensionless absorption build-up factor.

The variables in Eq. (11-18) are the intensity, the excitation

temperature, and the ground-state number density. Clearly, to find n 0 for a homogeneous plasma, absolute intensity units must be known and excitation temperature must be determined by an independent method. For an inhomogeneous plasma, unfolding should be performed, or the calculated number density would indicate an approximate value. The absorption build-up is determined experimentally, but this factor will be insignificant where the plasma is optically thin.

It is difficult to apply this method to plasmas emitting complex spectra to obtain precise values of n 0' In addition to uncertainties







27

associated with inadequately defined atomic constants, there are problems in defining the integrated-line intensity I a in absolute units for a
Vtotal
specific transition. Many practical considerations in the measurement of I a are discussed in Ref. 36, but procedures for spectral-line-wing

overlap in complex spectra are especially interesting.

Uranium spectra show no isolated line structure; therefore, we must find the peak magnitude and FWHM that can be used to define a corresponding Voigt profile, 49a theoretical representation of the actual line profile including wings. This area can be calculated analytically to yield a good estimate of the integrated spectral-line intensity.

B. Pr'&ssre -Terffperazture Correlation (PTC) Technigac

Partial pressure estimates of plasma constituents can be based a

pseudoanalytic approach such as the PTC technique. '05 This method uses a temperature profile correlation between experimentally determined and calculated tem-,perature profiles. The experimental profile is typically established by the Boltzmann plot method, whereas the calculated profiles are computed using the relative (norm) temperature method. Calculations of radiation specie number densities and, hence, partial pressures are inherent to the computed profiles. A family of calculated temperature profiles is generated to be parametric in the plasma total pressure. Because the experimental profile is an independent measurement, intersection of this curve with that of the calculated profiles implies (with the aid of the Saha equation) a plasma number density and partial pressure.

This method has the uncertainties found in applying the relative

(norm) temperature method (Sec. II.4C) as well as experimental inaccuracies inherent in the Boltzmann plot technique (Sec. II.4A). Full-width at half maximum of peak intensity value.







28

Uranium plasma number densities, as determined by the absolute-line method, are often uncertain. Pressure-temperature correlation removes some of this uncertainty and furnishes supporting evidence to experimentally determined densities.














I1T. UPArNICAl PLASMA EXPERIMENT HARDWARE III-7. Urnar~iwr Plasma Generation

For this investigation uranium plasma was generated by a direct51
current uranium arc constructed by Randol at the University of Florida. Many original features were retained; system details are in Ref. 51. There have been some important changes to the original system which will be described in this report.

A. Uranium PZasma Containment CelZ

Figure III-1 shows the uranium plasma containment vessel. The

stainless steel vessel is designed to withstand safely cover-gas pressure to 100 atmospheres. It can also be operated in the vacuum mode down to at least 300 torr. Contact is made between the tungsten cathode and uranium anode by remote movement of the cathode with a pneumatic electrode-drive cylinder. Both electrodes are water-cooled. The gas distribution head can give directional flow to the incoming cover-gas near the arc electrodes. The viewport windows are sealed from both sides for pressure or vacuum operation. The gas inlets also serve as the pumping ports when an evacuated chamber is desired.

B. S mented AssembZz

Within the containment vessel, fastened to the headplate, are several annular water-cooled copper segments (disks). The disks are arranged concentrically around the anode-cathode configuration for arc wall-stabilization. Figure 111-2 shows the segmented assembly with its orientation to the electrode configuration. The arc column length is

29







30








CATHODE TERMINAL CATHODE COOLANT INLET .... CATHODE COOLANT OUTLET

_PNEUMATIC ELECTRODE ~DRIVE CYLINDER PNEUMATIC PORTS DI
PRESSURIZING GAS COPPER SEGMENT
INLET COOLANT INLET





URANIUM PELLET
GAS DISTRIBUTION HEAD LIZVACUUM FLANGE
VIEW PORT




TUNGSTEN
CA4THODE PiN on- LWv
Q,"-(UAR]' } W DO

COPPER INSERT IN ANODE ........TEFLON ANODE
COPPER ANODE I 1 INSULATOR
PEDESTAL -L-PRESSURIZING GAS OUTLET

-ANODE COOLANT OUTLET ---ANODE COOLANT INLET ANO'DE TERMINALFig. III-1 Uraniuri plasma containment cell.








3]







ISUPF-ORT CATHODE

(S TAI NLESS (BASS)~BL

STEEL)



WATER ---I L E T GAS OUT LET
- INLETS



CCPPER RING__IN S U LATO'R R I N3-~ ~


1 PORT




VIAT ER OUTLET
I NLET.
S INSULATOR ORDER (ONSIDE-OLJT)
ARC BURNS BETWEEN 1.BRNNIRD
TUNGSTEN CATJHODE 6JN0. OONMTP
URANIUM ANODE ) 2. 0- RING
3. PHENOLIC (G-10) 4, COOLANT
5. PHENOLIC
ANODE 6. 0- RING
(CORPPE 13) 7. PHENOLIC





Fig. 111-2. UraniUm arc device segmented assembly.






32

shown undersized, and the plasma column was actually in contact with several of the water-cooled disks. The segmented assembly also acts as thermal shield for the pressure seals and as an effective particle shield to lessen deposition on the viewport window.

C. Systern

A schematic representation of the pressure system, designed for flexibility of regulation from 0-2000 psi, is shown in Fig. 111-3. Adequate cell exhaust filtering removes uranium which might escape to the atmosphere. The vent on the downstream side of the cell or the roughing pump on the upstream side provides particulate venting. The high-pressure gas supply is isolated for safety in case of electrical power failure. A high-pressure solenoid valve, normally closed, prohibits gas flow unless the solenoid is energized.

D. coolctnt silster!

Enough coolant must be supplied to the segmented assembly, anode, and ballast resistor. The cathode is primarily convection-cooled by the surrounding segmented assembly. The 60-psi water-line pressure provides adequate cooling for an arc power input of at least 100 watts; however, a centrifugal pump provides more flow if necessary. These features are shown in Fig. 111-4.

E. Poz'dc"Y' "'uppZY Cl'ystem

Two 650 A, 120 V dc, diesel motor generators arranged in a series are used as the primary source of electrical power for arc operation. They can be operated remotely or at the generator controls as a continuously adjustable voltage supply. Current through the arc circuit is limited by air- and water-cooled ballast resistors. The fuse limit is 300 A, 250 V. Current is adjusted for a given set of electrodes









33
.................

c.
):Iddns svo w
C) X 5 o<
Z
E
uj
ui LL) >
cc x
u


C)
Of
D IAJ
ui I-j
C) LJ
001, >

Q
T > DZ



CLI
C)
L
j w
;
0-' cl:

_j




to
CL a
C)
_j
LLJ
u
0 C.


C) z
0
Ld ui
W 17 L)
D
LJ
Ld U)
z

Ld cc u
0: LLJ
CL w

w LL>i CL: Zi
< u
> J 0 (A
3 ui

U J
>)


u
0- 0
V)
z z
0
<
Lo LJ
> L9 <
m Co
D LLi D 0 0 >-' co
<
< < D. > > > u Lli LO u LL V)


LL-









34
















cr

o <








C 3GONV :EI (YE


11-INI









LIJ




Z) Cf
Lo
0-


LIJ
4-1
-i LLJ F< CL U)
C-3
D cl
U- CIL Ll
CL E
"Wi Qj
I I >
Ln
Lk >)

4--)


z r 0

uj


CL


0 Or L-2
C l







35

during arc operation by parallel switching of air-cooled resistors into or out of the circuit. Typically, this operating point was 50 A, 20 V. The uranium arc circuitry is shown in Fig. 111-5. Current-voltage monitoring is accomplished on a continuous basis by Honeywell stripchart recorders (not shown on Fig. 111-5). III-L Urctniz 7 Pamzwncz St ability~

Construction of a dc uranium arc was not difficult; however, development of a stable dc uranium arc which would allow photoelectric diagnostics demanded extensive effort. For spectroscopic measurements, this particular uranium plasma was required to be very stable for density-temperature measurements and marginally stable for emission measurements. Arc current, i c', was used as a stability yardstick. Marginally stable implied average i c changes -10% over the entire length of data collecting time with a maximum of 5% for instantaneous i c* changes. Temperature-density stability is indicated by similar average i c limits and by instantaneous variation of i c 2%. The University of Florida uranium arc evolved from a free-burning arc to a rather sophisticated wall-stabilized arc (Fig. 111-6). A brief account of the development toward increased arc stability follows.

A. PRzee-Burnin(,j Arc

For simplicity, a free-burning arc under a static helium cover gas was used (Fig. TII-6A). Unfortunately, motion of the anode and cathode spots was inherent in its operation, and this caused unacceptable movement of the arc column as wel] as current-voltage fluctuations. There is no agreement among arc physicists as to the reasons for these spot

movements; however, bibliographical information can be obtained from Ref. 46. Maniy techniques were applied to reduce these instabilities,










36 CC













cr ui

Id cc
<

> <(

u QLLJ Li -i o--jv Ircl:
-) Fa
F
LIJ Of UJ
LE
LJ







0 D
0 C\J

< 4-)

rr G
0 ui ri

Ld V)

j
ci
u (10 S4-3




S
(D


Lu C\j


Lj Lj

ui UJ < 1,0
M
U

z LO LL-










37












C) C-I Ld <

1.0












C) ...............
03 7 U FLl












ZD

Ld l: C)
^r


Ld IJ
(r U-







38

such as sharply pointed and polished electrodes, changes in arc gap, changes in electrode diameter, and different cooling rates, but all were inadequate.



Next, a gas distribution head was used to localize large-scale movement of the arc column (Fig. I11-6B), and cover gas (helium) was directed downward from the gas head the length of the arc column. The flow contact with the anode caused a divergence of the cover gas at the uraniuni pellet and a bell-shaped cover-gas flow pattern formed.

The cover-gas flow boundary formed the 'wall" needed for arc-col umn local ization.

C. Tibe-StabiZized Arc

Stabilization was enhanced by forced containment of helium gas flow along the arc column (Fig. III-6C). A quartz tube was placed concentrically with the electrode vertical axis and helium was forced the length of the quartz tube. The restricted flow greatly reduced the helium turbulence and its effect on the outer and inner arc column. However, within five munutes of run time significant particle deposition coated the quartz tube causing unpredictable intensity attenuation and prohibiting long-duration (photoelectric) measurements.

D3. Secqmen ted-St ab Z~i zed Arc

The segmented assembly (Figs. 111-2 and III-6D) replaced the quartz tube from the previous case and reduced the deposit problem at the viewport. The vacuum (low-pressure) segmented arc provided stability for photo-electric intensity, temperature, and density measurements, while the high-pressure segmented arc exhibited marginal stability acceptable only for photo-electric intensity measurements. The







39

segmented-arc configuration was the final step attempted in the quest for superior arc stability. Even with marginal stability at higher pressures, this system was employed for most of the experiments reported here.

[I-113. _Da t-a AC is.

Spectroscopic diagnostics required detection and analysis of radiation emitted by the uranium arc plasma. The experimental effort of this research was composed of two broadly defined categories.

(1) the measurement of intensity (emission), and

(2) diagnostics for temperature-density determination.

Figure 111-7 illustrates necessary components for simultaneous measurements of intensity (to 2500 A), temperature, and low-pressure arc density. Intensity measurements which extended into the vacuum uv were performed using a third spectrograph (McPherson Model 218, not shown) designed specifically for use at low wavelengths. Temperature and density for a high-pressure arc were inferred from photographic spectral analysis completed by Rno51and Mack 52using a free-burning arc at similar I-V conditions. Details are in Chapter V.

A. SlprctraZ Line Pr ofile and Absorption Data for the Low-Pr essure

Arc

The modified BEN (Sec. II-4D) was used to determine the line-center absorption coefficient and characteristic plasma temperature for the low-pressure arc. The background source was a xenon flashtube (EGG FX-12-25). The firing and delay schematic is in Fig. 111-8. Flashtube calibration information follows in Sec. 111-30.

Figure 111-7 shows the sequence which established line absorption, temperature, and density: the beam splitter passed part of the arc radiation to S. A rotating refractor plate (quartz) in conjunction







40

xF LEGFNrI

XF XENON FLASHTUDE L RP REFRACTOR PLATE
Li LENS 1 ~j AK AC ARC CELL
L2: LENS 2 L, LENS 3
X Yk TUNGSTEN REFERENCE
BS5 BEAM SPUiTTER

S, SPECTROGRAPH 1 S2 SPECTROGRAPHA 2
-r~01 OSCILLOSCOPE 2
02 SIL)CPFT :FABRi-TEK SIGNAL
L2 ()AVERAGER
X :ARC POSrTIO



L 3
1





,BS
S2 Fr SI



2T 0









00




Fig. 111-7. Simultaneous data acquisition system.







41

with spectrograph (SI) used as monochrometer, swept a particular line of interest across the exit slit plane of SI. An RCA IP28 phototube placed behind the S exit slit responded to the spectral line as it moved past. That line profile was recorded by oscilloscopes by 01 and 02. At the instant the sweep reached the central wavelength of the line profile, the xenon flashtube triggered. This enabled the flashlamp radiation to be superimposed on a specific spectral line center (Fig. 11-3). Flashtube timing was accomplished by electronic delay circuitry shown in Fig. 111-8. The ground-state particle density was determined from the line profile of oscillograms 02 with the absolute line method; line center absorption and the plasma temperature were determined from oscillograms 01.

B. Photoe lect ic Intensity Data

Photoelectric intensity measurements were made from 2000 A
0 0 0
5500 A for the low-pressure uranium arc and from 1050 A 6000 A for the helium-uranium (high-pressure) arc. Intensity of the low-pressure uranium arc as a function of wavelength in the visible and near uv were recorded by using part of the data acquisition system shown in Fig. 111-2. A scanning spectrograph S2 received arc radiation reflected from the front surface of a beam-splitter. The phototube response was monitored and stored digitally by a signal-averager [a time-averaging digitizer that integrates (smooths) small random input voltage (arc) fluctuations] which resulted in very reproducible arc intensity traces as a function of wavelength. Four memory areas within the signalaverager were used for storage of the spectral intensity I(x), Where x is a particular LOS position in an arc traverse. A four-point Abel unfolding for spatial resolution of the arc intensities was performed










42











> Ld .-J

0 0
110









0

U) (YLd

0
0 C\j


co
ZL


LLJ
( -1)
2




cu 10
if)






Lj
0 uj cxl U- CL




z C) ----i
0

LIJ L.
(D

ct







43

to obtain the spectral emission coefficient ex(r), where r is the radial distance from the arc center. The limited arc stability duration prevented more than four acceptable LOS intensity measurements. Oscilloscope 02 was used to trigger the signal-averager sweep at the desired wavelength. Ultraviolet transmission through the optical system was carefully investigated to be certain that no glass was present and to
0
study the system attenuation properties. The 2537 A Hg spectral line generated by a very stable mercury discharge was chosen for these purposes. The line was transmitted with negligible attenuation and contamination signals produced by internal reflections within the spectrograph S2 were removed with baffles.

The photomultiplier used with S2 was an EMI-9514 with a sodium

salicylate window which acted as wavelength shifter from the ultraviolet to the visible. The phototube-sodium salicylate combination greatly improved the system wavelength sensitivity to ultraviolet and vacuum ultraviolet radiation. Sodium salicylate was ideal for use in the uv and vacuum uv because it possesses a nearly constant quantum efficiency from 500 A to ', 3300 A. :Fhe fluorescent radiation spectral
0 0
distribution maximum is 4300 A and 10% of the maximum at 3800 A and 5300 A,46,35 which conforms to the maximum wavelength response of many photomultipliers.

For vacuum uv intensity detection the McPherson (Model 218) spectrograph designed to be responsive at wavelengths in the vacuum uv was used in conjunction with the photomultiplier signal-averager system previously described. This particular spectrograph contained magnesium fluoride-coated (Al + MgF2) optics, a 2400-groove/mm grating blased for
0
1500 A, and a vacuum capability of at least 0.001 pj. The vacuum uv






44


region is reported only for the helium-uranium arc plasma because of its relatively higher temperature and correspondingly stronger emission in this wavelength region. The low-pressure arc did not have noticeable emission in this wavelength region.

In sonme instances, it was physically impossible to interchange the source with a reference standard at the same location; therefore, we

*used a symmetric arrangement of the calibration and uranium sources in which the light-path attenuation for either source was identical. We eliminated unwanted stray radiation from within the spectrograph, which is particularly critical in the vacuum uv where the signal detection is difficult. Many intensity-wavelength scans were taken below 2000 A with a deuterium lamp (Oriel C-42-72-12) in several orientations after each helium-uranium arc run to insure optimal signal transmission. These signals were carefully checked to minimize higher order contamination and internal reflections.

C. -Tte'nsity CaZibration

For radiation calibration in the visible and near-uv wavelength regions, the tungsten lamp and the positive crater of a carbon arc as standards are adequate; however, these sources are unacceptable for o55
lower wavelengths because of the weak intensities below 2500 A. In

fact, below 2500 A there are few commercially available standard calibration sources. LTE hydrogen discharges (fill gas is either hydrogen or deuterium) are the best potential sources, but they require extensive investigation for their own respective properties. The theoretical description of the hydrogen atom is essentially complete, and once the electron densities are known, the intensities are coniputed and cross-checked by experiment to provide calibration information for







45

such a discharge. Therefore, two calibration sources were used: a tungsten lamp for the visible and near uv, and a deuterium discharge for the uv and vacuum uv.

Two tungsten filament lamps made by the Eppley Company were used for intensity calibration in the visible and near uv. One was calibrated by the NBS and designated the "standard lamp"; the second served as a "reference lamp." The reference lamp was used as the experiment standard but periodically cross-calibrated to the standard lamp. The calibration curve for the standard lamp is given in Fig. 111-9. The associated accuracy of the values was stated to be 10%. 56

A deuterium discharge was used to calibrate intensities below

2500 A. The lamp had a suprasil fused-silica window with a 50% trans0 0
mission point at about 1750 A, and a calibration point at 1662 A was the apparent lower wavelength limit. Figures III-10 and III-11 show the wavelength dependence of the spectral radiance at two current modes. The absolute intensities as calibrated from this lamp carry a 10% uncertainty, 57 verified by cross-cheCk of the deuterium lamp intensity against the tungsten filament standard at four different wavelengths above 2500 A. The percentage difference between the quoted deuterium intensities and the cross-checked intensities was always within the uncertainty limits. The percentage difference tended to increase toward the lower wavelengths and the calibration points below 2000 A are associated with an unknown maximum uncertainty less than 10% up to 1750 A. The last deuterium calibration point resides at 1662 A as dictated by the fUsed-silica window cutoff of the discharge lamp. The 1662 A calibration point is below the fused-silica 50% transmission wavelength of
0 57
1750 A and is quite uncertain. Calibration for intensity data to the






46










10






00
LiB
(5 ~ 10
B (XT61 X5





S10 ~~

5 11.0 50 5 5



W AV- E kl0.45n m







Fig. 111-9. NBS tungsten standard lamp calibration,
(EPUV-1148)--35 amperes.







47
























o2









(25O2)= 1.56 X IO0 ergs cm2- Ar' s~1 L


I ,G IGG 2062 2.2G2 2462 26
10
WAVELENGTH (A)




Fig. II1-10. Deuterium lamp calibration curve,
Kern lamp at 300 ma.







48

4




10 --- ---I







00
I
L.





L J




2000 2500 3000 3500
O
WAVELENGTH (A)





Fig. III-11. NBS deuterium lamp calibration curve,
Oriel lamp at 315 ma.






49

LiF cutoff ,(1050 A) called for an approach which did not require explicit standard calibration points at the lower wavelengths.

The branching-ratio technique was considered for absolute intensity calibration in the vacuum uv and it is based on the intensity partition of at least two spontaneous optically thin transitions with a common upper level.58'59 The intensity ratios of these two lines is a strict function of the transition-probability ratio and independent of plasma inhomogeneities and LTE. To apply this technique in the vaccum uv, one transition must appear in the visible and the other in the vacuum uv. This method is sound provided isolated spectral lines exist and welldefined transition probabilities are used. The application of branchingratio calibration to uranium spectra fails in both respects.

Back-extrapolation calibration (BEC), an approximate technique, was used. Helium-uranium arc intensity data were collected in bandwidths
0 0 0 0
900 A -1750 A 4300 A. Intensities above 1750 A were calibrated against the deuterium discharge and tungsten standard; whereas arc intensities at wavelengths below 1750 A were assigned absolute units by BEC. (Intensity signals from the low-pressure uranium arc required calibration down to 2500 A which was done with the tungsten standard.)

Intensity calibration using a standard source is essentially a system response comparison of (in this case a spectrograph-photomultiplier combination) a known photon flux to a photon flux of an unknown source. The absolute intensity of the unknown is then related to that of the standard by:


IARC() = ISTD(X) SmD(') VARC(X)

ARC- VSTD-)







5O
2_ 0
where IARC(X) = arc intensity [ergs/cm sec-A-str] at X, 2
ISTD(X) = standard source intensity [ergs/cm sec-A-str] at ,

STD( ) = optical path reduction factor (%) for the standard
source at ,

ARC(X) = optical path reduction factor (%) for the uncalibrated

source at X,

VSTD(A) = response signal (volts) of optical system to standard

photon flux at X, and

VARC() = response signal (volts of optical system to uncalibrated photon flux at X.

If the standard and uncalibrated sources are in identical orientations, the optical path reduction ratio 4)STD(X)/ ARC(X) will cancel. The system response will inherently be accounted for in the VARC(X) and VSTD(X) signals. Equation (Ill-1) is valid as long as ISTD(X) is known,
0
in this case to the 1750 A cutoff of the deuterium lamp fused-silica
0
window. To apply Eq. (Ill-1) to wavelengths less than 1750 A, a system
0
response below 1750 A for the standard source intensity as a function of wavelength must be assumed.
0
The wavelength dependence of system response below 1750 A was

assumed flat and equal to 1.0, which implies that the combined effect of the incident (to the optical system) photon flux on transmittance caused by losses in all of the intercepted optical elements is negligible. This is categorically not the case. However, such a tactic provides a straightforward approach to a conservative estimate of the correct absolute intensities. Relating this idea to Eq. (III-]), a unique intensity implies a unique system voltage with no wavelength dependence. Knowing the absolute intensity of the standard and its







51

corresponding voltage at 1750 A in addition to the arc intensity system response voltage for all wavelengths of interest below 1750 A, the absolute arc intensity may be estimated by solving:


IR( =I STD (1750 A) V ARCMX (111-2)
IACV VSTD (1750 A)



VARC(X retains the system response to the arc intensity, but the wavelength dependence of the system response to the standard intensity cannot be recorded because of the window cutoff. Therefore, assuming the negligible optical loss, the arc intensities-are underestimated by

the composite optical loss factors and whatever molecular absorption is present.

Whenever an approximation is applied, as was thie case with the intensity calibration in the vacuum uv, an indication of uncertainty is valuable. In this investigation the uncertainty was a function of the

attenuation of photon flux incident on the optical elements of the system composed of a 10-mm LiP window, two spectrograph mirrors, the sodium-salicylate phototube window, and the grating. (The spectrograph mirrors and grating were Al-MgF2 coated). A composite wavelengthdependent transmission curve can be constructed if transmission/reflectance data for each optical component are available. This total curve can then weight the appropriate system response voltage, thereby recovering (to a first approximation) the photon losses as the field passes through the optical system.

Reflectance-wavelength information is available in the literature 6,1for coated and uncoated optics as is transmission data for

LiF. 62,63 The grating efficiencies for the McPherson 2400-groove/mm






52

grating blazed at 1500 A (Al-MgF 2 coated) were furnished by Quartz et al. 64Table III-] is a compilation of the relevant information which allows construction of a composite system transmission curve. These data provide an approximation of intensity calibration error (using back-extrapolation) based on system optical losses. The quantum efficiency of the sodium salicylate phototube window was assumed to be approximately unity 6 with a constant wavelength dependence. 53,65,66

The composite efficiencies of Table III-] indicate that backcalibration intensity values can be in error at the longer wavelengths (1750 A) by a factor of 6 and more toward shorter wavelengths. A calibrated "signal' detected below 1200 A is suspect because of the sharp LiF cutoff near 1200 A as shown by Table 111-1.

Use of the xenon flashtube for temperature-absorption diagnostics required a calibration for dependence of brightness temperature on wavelength. This was accomplished by comparison (at a desired wavelength) of the system response to the xenon discharge and to an NBScalibrated tungsten-filament lamp. 67A xenon lamp brightness temperature of 6745 K 1 100 K was established in a wavelength range of
0 0
3600 A -~ 5400 A.











53






M r- LO '-Zt'
0 -0 C-li r-I cli r- Lo L Lx
0- Lo -zt
E=- CO M
0





C:
0

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LO CD C) Ln CD CD CD CD CD CD CD CD 0) 0) Q) m
CD ,P Ln Q0 r W M CD














TV!. LOW-P RT'[SSURE UIRANIUM ARC DATA RETIwON IV-1. SpecotraZ anaZ)Isi8.

Spectra emitted by the low-pressure uranium arc plasma (u300 torr) were identified manually and by computer. 68They exhibited a mixture of atomic (Ut) and singly ionized (UII) uranium line structure, but dominated by atomic uranium emission lines. For diagnostic purposes
0' 0 0
the 3653.21 A and 3659.16 A Ut emission lines were used. The 3653.21 A line is reported 69to have upper and lower levels at 31 166 cm- and 3801 cm-1, respectively. It was selected primarily because of its relatively high-lying lower and upper levels, which enhanced the possibility of evaluating energy states populated above the thermal limit if partial LTE existed. The 3659.16 A line was chosen for the same diagnostic purposes (temperature and density measurements) as the 3653.16 A line. Its transition is between levels 27 941 cm1 and 620 cm1.9 The first excited level of atomic uranium is 620 cm- and it would be less likely to meet LTE criteria. A comparison of temperature-density diagnostics using the lines with two distinctly different lower levels

served as one useful indicator of the validity of LTE assumptions. While energy -level was a prime line-choice factor, the spectral lines were also selected on a basis of wavelength, relative isolation (from the other nearby lines), identification certainty, and availability of transition probabilities for transitions considered.


54







55

IV- 2. Tempeiratzae Measur ement

The electron temperature was measured by the modified brightnessemissivity method (Sec. II.4). First, it was necessary to obtain linecenter absorption coefficients as a function of arc radius by applying flashtube absorption diagnostics (Sec. III.3A). Line-center absorption profiles using the 3653.21 A and 3659.16 A UI transitions are shown in Fig. IV-l and represent absorption measurements taken during the best conditions of arc stability and flashtube firing. The two reported profiles indicate maximum absorption at the arc center which is usually the region of maximum temperature.

Uncertainty in absorption coefficient values was both numerical
)47
and experimental. The unfolding scheme converting K (x) K 0o(r) was responsible for the numerical uncertainty, and the accuracy of the oscillogram voltages defined the primary experimental error (K0 indicates the line-center absorption coefficient). The oscillograms contained recorded voltages representing the flashlamp intensity attenuated by the plasma as well as the true plasma intensity. The plasma voltage uncertainty was mainly caused by arc intensity change which fell within +2% during data collection. Flashlamp attenuation uncertainty resulted from arc intensity fluctuation, flashlamp intensity variation, and arc cell viewport attenuation.

Since the flashlamp was located behind the arc cell, its light output passed through two viewport windows in the segmented assembly (Figs. III-] and 111-2); whereas the arc photon field passed through only one on its path to the detector. During arc operation, deposits occurred on both viewports; line-center absorption of the light emitted by the flashlamp was recorded photoelectrically at four points from the arc









56
















Ln


0



0
10
(D LO 0 C, t-- o') 7) N a) C) 4C\j (D m Ln 0
C\j ro rn C'i
0 o (--) F C) C) c) o d d d C; (3 C3 (3
+ I jr I + I + Le) 4-)

Z)
0 d
t ly) C) u
0 o LCI o cr) rl) <
Q) pe) Cr) 0 U) r1r) CQ
C\j (\, I
0 r) FD I C 0 4F6 (D (D
Ln 6 cs C; 0 0 c 0
Qo + I +
I + u


C) 0
Ld
rn

0
Ln

-D
o
UA Cj
Of 4-3
0

It)
oi
rr

LO



10





C)







57

cente r outward, thus the values at further distance from the arc center were more uncertain. Usher 47 has considered all of these possible contributions to absorption profile uncertainty. Using an argon arc with the same experimental apparatus as this uranium arc, Usher 47 found a fairly constant absorption profile uncertainty across the arc. This was not true of the uranium arc because the viewport deposition problems resulted in a larger absorption coefficient uncertainty as outer regions of the arc were approached. The flashlamp intensity was degraded because its radiation field passed through two viewpoints (as opposed to one for the arc plasma emission), resulting in overestimates of the true absorption coefficient values at all points along the arc radius. Error analysis showed that these estimated uncertainties were

10'0' at the centerline to r, 62% at the outer point.

The apparent uncertainties of radial absorption coefficients influenced the temperature computation uncertainty. Again, the error analysis of Usher 47 was used to obtain temperature uncertainties. Figure IV-2 illustrates the radial temperature dependence for the lowpressure arc plasma. The uncertainty limits generally increase as the arc center is approached. If we consider that the uncertainty calculated for the outer radial location is propagated to the central locations, it is possible that the innermost temperature will have an

associated uncertainty greater than that of the outermost temperature value. Therefore, while the outermost temperature had the largest experimental error, the central temperature had the largest total error. Several temperature profiles were determined using both tran0 0
sitions (3653.21 A, 3659.19 A), and Fig. IV-2 shows results for each transition. The 3653 A diagnosis typically showed a very reproducible









58























CO




0 40

cu
s
u I
<
cc r 10
0 L
to C) (n o 0 0 qQ, 0 1-1
U ) 0 (J) Ln 0) Ln 00 Lo
.1 1 U)
U +
+

0 u
in <
d


1-i co
Ln LO 0
0 o 0
(1) 0 Ln r- un Lo 1,C) zr tr) ro
+ + + +


LLJ E SC) 0
Lo cf Ul)
z N C) (A
0 co
0 F (:3 z S0
Q) C\j
C-)

o :3



C\j




10

N LL-







59

temperature profile; whereas the 3659 A transition indicated less reproducibility. The profiles from both transitions compared rather well and offered supporting evidence for the existence of LTE conditions within the bulk of the arc column down to fairly low-lying levels.

Of particular interest is the rather flat radial temperature dependence. There have been numerous flat temperature profiles reported for various wall-stabilized arc plasmas. 32-38 Plasma confinement using a cooler material wall generally results in a reduction of the temperature gradient from the arc center toward the wall. In many cases, conduction loss is not the only contributor to the profile curvature. Conductive heat transfer along the arc temperature gradient to the wall and radiative transfer losses, which are strongly dependent on the plasma conditions and type of radiating species, account for most of the energy loss from an arc. That a flat temperature profile in wallstabilized arcs can be realized is substantiated in the literature and not in controversy; at issue is the rationalization of such a temperature.profile for a wall-stabilized uranium arc which is measured by this investigation.

The temperature profile for wall-stabilized arcs must be consistent with the energy-balance equation given by


2
a E F c + v F R (IV-I)


where cy = electrical conductivity,

E = electric field,

Fc = conduction flux density, and

F R = radiation flux density.






60

The implication is that the electrical energy input to a steady-state arc plasma balances the radiation and conduction losses (convection being neglected). Conduction loss is governed by the temperature profile gradient; whereas, radiative losses are defined by the equation of radiative transfer, Eq. (11-3).

Temperature profile curvature will be a function of the relative magnitude of the conduction or radiation loss terms. If radiation effects are negligible, conduction becomes the dominant loss mechanism, resulting in an approximately parabolic temperature profile with a comparatively high central temperature as shown in Fig. IV-3. 34 When radiation losses become important, the central temperature generally lowered and the profile shape flattened. Also included in Fig. IV-3 are the effects of self-absorption on the temperature profile. In general, having zero absorption implies a smaller central temperature caused by the larger radiation loss term. A flatter profile also results because most of the curvature is caused by conduction near the wall. When absorption is included, the result is an increase in central temperature and more radial curvature. The curvature of the profile at the arc center is typically controlled by radiation losses, while at the arc boundary such curvature is usually controlled by conduction losses.

Several parameters affect the magnitude of conduction and radiation loss terms. Generally, wall-stabilized arcs exhibit high radiation losses at higher pressures, greater temperatures, smaller radii, and at greater emission density of the dominant radiating plasma constituent. 34,35,70,71 The current and pressure of the low-pressure uranium arc would indicate that the temperature profile shape would







61




















IV) I
fRADIATIOIN OMITTED








uI


I.


H ABSORPTION AND 03 RADIATION'




~ABSOFPT!ON
C.M 1 IT E D






0 -1~ 0.2 0.3 0.4 0.5 0-(-- 07 0,S 0.9 1.0
ARC RAMUS (IOF RkAV-hZ 0)



Fig. IV-3. Effect of radiation on arc profile.







62

not be highly flattened except for the significant radiation flux loss produced by such a dense emitter as uranium. The striking lack of temperature profile curvature (till the arc boundary is approached) can be reasonably attributed to the dense core radiation characteristic of excited uranium in a wall-stabilized configuration. 72Shumaker 73has shown that nitrogen and argon wall-stabilized arcs operating at similar current, voltage, and pressure conditions produced temperature profile shapes of different degrees of curvature. The radiating species with the denser characteristic radiation (argon) produced the flatter temperature profile.

From LTE considerations the normal temperature (Sec. II.4B) for several UI transitions was calculated to be about 5000 K at 0.001 atm uranium pressure. The 5500 K measured temperature indicated a mixture of UI and UII radiating species with UI dominating, which was consistent with the spectral analysis. (See Appendix A for Saha equation number density and normal temperature curves). The probability that partial LTE exists also implies that the gas temperature differs from the electron temperature--magnitude of difference is questionable. This problem has been studied by Gurevich 74 who used mercury and argon discharges at total pressures from 0.1 to 1 atm. Their technique essentially monitors the distinct cooling of the electrons to the gas temperature and subsequent general cooling of the plasma. The intensity output tracks the cooling and can be followed with a scope-phototube combination. The method is sensitive to electron-gas temperature differentials as smi~all as 0.5%. The conclusions are that the temperature differential is a strong function of total (and electron) pressure and weak function of arc current. The extrapolated temperature differential







63

for the present arc could be as much as 100 K to 200 K because of the partial LTE state arc plasma.

117-3. _)ensLt Meaurement

The ground-state particle density (UI) for the low-pressure uranium arc was determined by the absolute line method (Sec. II.5A). This method involved the shape definition of the desired spectral line, its absolute intensity calibration, an independent temperature measurement, and uncertainty estimation. The exact line profile could not be defined because of the large line-overlap characteristic of uranium spectra. A Voigt analysis 49was used to approximate the line area of the same lines (3653 A, 3659 A) used for the temperature measurements. Because these data were taken simultaneously with the intensitywavelength information, significant temporal fluctuation should be common to'all and treatment of fluctuation was unnecessary. Line intensity calibration was performed with a tungsten-filament NBS-calibrated lamp. No attempt was made to establish a radial density profile because associated errors negated the effort. Line-center absorption was also accounted for by appropriate build-up factors. The calibrated UI ground14 3
state density for the low-pressure uranium arc was r\ 7 x 10 cm

This val-ue is an order-of-niagnitude estimate of an approximate density radially through the arc column. Assuming uncertainties in spectral line area, gA, and temperatures of 15, 50, and 20%, respectively, 14 15 3
resulted in a density range of 1.28 x 101 7.89 x 10 cm This indicated, from Saha analysis, that a nominal value for the uranium total pressure, rounded to the nearest integral logarithmic pressure, would be -0.001 atm (1.3 x 10 15 cm-3)







64
The electron density, ne, for the low-pressure uranium arc will generally follow the curve for singly ionized uranium. Saha equation calculations of n e for a plasma with a total uranium pressure of 14 3
0.001 atm, T = 5500 K, predicts n e = 6 x 10 cm This is we'll within the LTE -ladder criterion of 3.8 x 10 11 cm- 3 established in Sec. 11.1. Measurement of the electron density by an independent technique such as a line broadening analysis was too uncertain, primarily because uranium lines lacked isolation and definition. Therefore, this effort was abandoned and no direct experimental evidence of the magnitude of the electron density was obtained. However, similar work of Voigt 75 on a 5500 K uranium arc reported n e to be
13 3
5 x 10 C111 This substantiated the assumption of ne large enough for the present arc to be characterized by at least partial LTE nearly

at the ground level .

One of the more subtle aspects of this density determination was the implicit assumption of complete LTE. Strictly speaking, this is very difficult to realize, and one usually resorts to a commitment of partial LTE. If partial LTE is valid, an exact density measurement (using a diagnostic method which relies upon complete LTE, such as the absolute line method) is not possible, and any attempt will be in error because of this apparent conflict. The magnitude of this error can be calculated for hydrogen and estimated for helium. Unfortunately, for the case of uranium only a qualitative description of error direction is valid. 76,77

The effect of the complete LTE assumption when there is only partial LTE can be understood by considering the population densities of a simple energy level diagram as illustrated in Fig. IV-4.







65




--- -- -- -----------thermal limit
Cross-sections for Cross-sections for
Collisional processes > Radiative processes




ni I ._ _ _ _ _ _ _ _

n ___ 0___ ______ ground state


Fig. IV-4. Energy-level diagram with thermal
1 i mi i t.


When complete LTE exists, the population density of each level is defined by the Boltzmann Factor, n u/n 0 a exp [-E U/kT]. However, if partial LTE prevails, the population of levels below a thermal limit are influenced by radiative de-excitation from upper levels and selfabsorption, particularly with transitions terminating at the ground level. Detailed definition of level population for uranium is virtually impossible, but in most cases one can argue that if partial LTE holds, the levels below the thermal limit will be over-populated. Thus, by assuming partial LTE and using complete LTE relations to determine the ground-state density, an underestimate results, probably proportional to some function of the thermal limit height above the ground level. The thermal limit in the uranium system cannot be well established; but from LTE criteria applied to the low-pressure uranium arc (Sec. 11.1), it is likely to be close to ground level. If the thermal limit is close to ground level, the error incurred by using complete LT[ relations to determine the ground-state population is "small." Because this is an order-of-magnitude measurement, such error is most likely to be insignificant at these temperatures and pressures.






66

if V-4. Ernission Coefficient Determination

Spectral analysis of radiation structure emitted by the lowpressure uranium arc plasma indicated a preponderance of known UI line spectra mixed with some identifiable U1I structure. The species-mix ratio is not available because of uncertainties involved in line identification on uranium spectra. However, at the maximum temperature of 5500 K a Saha ratio of n UN/nUl can approach 1.0, and cooler arc regions will be weighted toward larger values of nUl.

Intensity from the low-pressure arc was observed at four equally spaced arc positions. Details of data acquisition are in Sec. III.3B. The spectrograph used for this study was a Hilger-Ingis (Model S05-10000) modified to a rapid-scan capability (1.28 s from 2000 to
0
6000 A). A 1200-grooves/mm grating was used with a blaze angle of
0
17.20 corresponding to a wavelength of 5490 A in the first order. Intensity calibration was performed using a tungsten-filament NBScalibrated standard.

Preliminary experiments indicated a rapid decrease of arc intensi0 0
ty below 3500 A and very little signal at wavelengths less than 2500 A. Steinhaus et al. 18,19 also indicates little structure between 2000 and 2500 A for UI. We decided that emission from this particular arc plasma below 2000 A would be relatively insignificant, and the effort required to detect potential vacuum uv emission was not justified for this plasma.

The calibrated arc intensity-wavelength data is plotted in

Fig. IV-5. Four similar sets of intensity data were generated for each arc burn; the data plotted in Fig. IV-5 corresponds to the central arc region only. The data acquisition method (signal averaging) produced









67


















0

C5 If If
D
a
ul

4--3

b
00

4-J
ra



Ld ro
-j u
LLJ
> < ro




0 ro
0 So ff) (1)

















X) is 0 3 s W,),/ s r I a
Li-







68

very reproducible intensity-wavelength data sets; only major arc intensity fluctuations Could not be removed. When these major fluctuations occurred the data were discarded, thus, the data plotted in Fig. IV-5 is in error by the intensity uncertainty of the standard tungsten lamp calibration source, which is approximately 10%. 55 The calibration of uranium plasma intensity was done using the "Plasma Source Calibration Program." 78 However, intensity data sets taken in the outer arc regions are -in error by as much as +12 to 20% because deposition on the viewport interfered with the optical path from the plasma source to the spectrograph entrance slit.

The four intensity-wavelength data sets were spatially resolved by a four-point numerical Abel unfolding after averaging over 100 A bandwidths. The results for this emission coefficient calculation in the central arc location are shown in Fig. IV-6. Error sources in these data are attributed to the absolute intensity calibration, viewport deposition, and four-point spatial resolution. The calibration and deposition errors have already been mentioned and are carried over to the emission coefficient determination. Spatial resolution error is much more difficult to address. It is composed of error caused by propagation of experimental uncertainties and the high probability of using a non-optimal zone number for the unfolding (statistical error).

Experimental error propagation through the inversion process was estimated by unfolding the data with and without such error included. The statistical error was estimated by relying on the analysis of Kock and Richter, 44 based on the form of the intensity profile, number of rings chosen, smoothness of profile, and maximum outer-zone experimental error. An exact match did not exist and extrapolation was











69




















S
C-1 C)
>








>




W



4
4














u












(D FS.- 0
m Scl i: CD 0 CD








c

iS,







70

applied. Following the above approach, the error for the central zone emission coefficient shown in Fig. JV-6 should fall within -14% to +23%.

Credibility of the shape and location of the important features on the wavelength scale is questionable; unfortunately, there are no other data recorded at the same conditions for comparison. However, comparison data exist 181'79 for qualitative assessment of credibility.
Krascella 79 tried to approximate the intensity-wavelength distribution of an Argon-UF 6 system at temperatures varying from 5000 to 9000 K. Level populations were calculated through equilibrium relations, whereas partition functions, atomic constants, and observed line location were extracted primarily from Corliss and Bozman. 69Using this information the possible integrated line intensities were computed and averaged over 100-A bandwidths. This semiempirical technique lacks

information about important quantities such as statistical weights, accurate transition probabilities, uncertain UF 6 decomposition schemes, and offers very incomplete uranium line structure tables. However, this work was valuable in establishing observable spectral distribution

of electromagnetic radiation from uranium plasmas at various conditions and was useful for comparison to our results even though Krascella estimates had gaps. The comparison at least substantiated a trend in the emission coefficient shape. N\o comparison was made between absolute values because of the diversity in systems.

A comparison is shown in Fig. IV-7 where the Krascella data were shifted in magnitude to be superimposed upon our results which follow the shape trend shown by Krascella. The irregularities in the Krascella data (caused by the lack of experimental line data in the gap regions) are expected and do not detract from the conclusion that the







71





T---T- ~ ~~~~~~T ~~~ ---T-6 cm- FOR PLANK FUNCTION

00
cm FOR PLASMA EMISSION T (PLANCK) = 5500* K T (PLASMA) 55000 K








I
<10 5U

(KPASCE. A, A- T = 50000 K, UI)
I,
I



E
4;

\I 1
10



(PRESENT RESULTS, T = 5500 K, UI)

3
Iu _____L_ ._I __J
2000 3000 4000 5000 6000 70:0
O
0
WAVELENGTH (A) Fig. IV-7. Low-pressure uranium plasma emission coefficient
comparison to Planck intensity.







72

two data sets are supportive. Thus, we have established corroborative evidence of the shape credibility of the low-pressure arc emission coefficient.

The work of Steinhaus et al. 18,19 also lends support to the major peak location around 4000 A (for UT) and to the validity of the rapid emission decrease below 3500 A. The range of experimentally observed UT levels extends to 40 000 cm-1 on the energy-level diagram (% 5 eV). This implies there are no known UI transitions below approximately 2500 A. Also, the bulk of known lines established by Steinhaus for UT falls within 3300 to 6000 A, which also supports our information.

The Planck function for a blackbody temperature of 21, 5500 K is also plotted in Fig. IV-7 along with the emission data (different units). Since the magnitudes of the arc emission and Planck intensity

are plotted logarithmically, the difference of these values at a specific wavelength is an indication of the absorption coefficient, KX The value Of K X is actually an average (over 100 A) because the emission coefficient is also averaged over 100 A. At all wavelengths K 0.034, thus implying an optically thin plasma. Line-center absorption coefficients can be significantly greater for some lines as
0 0
illustrated by the line-center K X for the 3653 A and 3659 A UT lines.















1/. RPIJ,iI- UI Al/10,11 AR~C D9ATA QTDUCT fON

The objective of this phase of research was the investigation of uranium plasma emission at higher temperature (than that of the lowpressure uranium arc) from the visible through portions of the vacuum ultraviolet wavelength region. The experimentally observed levels of U11 (singly ionized uranium) extend up to 50 000 cm- ,1 and the ionization energy is about 100 000 cm 1. Hence, U11 line structure is likely to appear in the visible, uv, and vacuum uv wavelength regions. For this reason a uraniuni arc which produced strong UII radiation and operated under conditions simiilar to those observed by Rno51and [lack 52was used.

The uranium plasma for the present study was generated with the identical configuration as the low-pressure arc (Figs. I11-1 to 5). Helium cover-gas at 3 atm was added; the arc current and voltage were maintained at 30 A and 35V, respectively. Current-voltage and arc emission characteristics were controlled to duplicate those determined by Randol 51 toinfer temperature and density from his photographic diagnostics. This was an important consideration because our uranium arc was too unstable for accurate photoelectric temperature and density diagnostics such as those performed on the low-pressure arc. This inference seemed reasonable, if spectral similarity (line location, half-width, and peak values) for arc plasmas generated by cascade and free burning systems at the same pressure-current-voltage conditions could be established within the error limits of Randol 's temperature and density measurements.

73









V-1. Spectral Analysis 74

The line spectrum emitted from the helium-uranium arc was identified manually arid cross-checked with the line identification computer analysis of Kyi stra. 68Identified lines were highly correlated with the known U11 spectrum. Only a few helium line possibilities were observed, which indicated a relatively pure uranium plasma. This spectrum, as a whole, was significantly different in comparison with the lowpressure arc plasma, and provided some evidence that operation from a low- to a high-pressure arc was accompanied by a corresponding shift of radiation dominance to UII in addition to a shift from lower to higher temperature.

Comparison of hel ium-uranium arc spectra sets (ours and Randol s51 was first done on a wavelength basis. When superimposed, the two sets of spectra were virtually indistinguishable. Both line sets were composed of line spectra at the same wavelength locations and emitted by the same plasma constituent; namely, singly ionized uranium. This was necessary but not enough to justify the assumption of similar temperature and pressure (T-P uii). The other necessary factor (provided most of the lines were sharp) to insure similar T-P Uii conditions was consistency between the two sets of peak and half-width values. Detailed study showed little discrepancy for the lines examined at the arc centerline used in Randol's 51 diagnostic analysis. Further, peak and half-width values of these lines compared with those recorded at different current, voltage, and pressure conditions showed discernible differences which indicates the sensitivity of the comparison. Therefore, the centerline temperature and pressure of the constricted helium-uranium arc plasma was approximately characterized by Randol 51







75

to be between 8000 and 9000 K and 0.01 atm UTI partial pressure rounded to the nearest integral logarithmic pressure. Because of the inferred temperature and pressure, only a brief overview will be given (Sec. V.2 and V.3) of the methodology used by Randol 51 to determine these parameters.

V- 2. TmeutrAe~zrm~

The central temperature of the helium-uranium arc plasma operated

at 30 A, 36 V, and 3-atm total pressure was estimated by the Fowler-Milne method and measured by the relative Boltzmann plot method. The normal temperature for this plasma was estimated to range between 7000 and 9000 K for a corresponding pressure range of 0.001 to 0.1 atm total uranium pressure, using the 4171 A UII transition. Slight off-axis maximums in the emission profile indicated the probability of close proximity to the normal temperature. To define temperature, the corresponding pressure must be known because temperature and pressure must be consistent. Because the spectrum taken from this plasma showed a clear majority of UII structure, and Saha analysis indicated (at 0.01 atm) a dominance of UII particles in the 7000 to 9000 K temperature range, the probability of close proximity to the normal temperature was increased. The centerline temperature was then measured for the above conditions using the Boltzmiann plot method and found to be 8113 K t 8%. 51 The centerline temperature of our helium-uranium arc plasma operated at similar conditions was therefore inferred to be %t 8000 K.



The central UII partial pressure for the helium-uranium arc was

measured by -the absolute line method and cross-checked by the pressuretemperature correlation (PTC) technique (Sec. II.5B). This diagnostic was






76

similar to that applied to the low-pressure arc. Order-of-magnitude disagreement occurred between the absolute line values and those determined by vaporization and PTC studies. In fact, the absolute line values were always lower than the others. These discrepancies were explained (to some degree) by assuming an inhomogeneous pressure profile radially across the arc and, as well, the characteristic uncertainties associated with most density measurements. In any event, the centerline UII density reported51 for a 3-atm helium-uranium arc was '- 3.8 x 1016 cril-3 (0.042 atm) at a central temperature of 1_ 8100 K. By Saha analysis this pressure and temperature imply a total uranium pressure of -] 0.055 atm and an electron density of 4.3 x 1016 cm-3

The temperature measurement assumed partial LTE; however, the spectroscopic density determination required complete LTE. As described in Sec. IV.3, assuming complete LTE where only partial LTE was assured caused an underestimation of the ground-state densities; the magnitude of error was a function of the thermal limit. For the hel ium-uranium arc a rather high electron density was achieved, which easily satisfied the ladder, and possibly the hydrogenic LTE criterion as well. Based on these considerations, the ground-state underpopulation factor (if it could be calculated) would be small compared to the other uncertainties found in the density measurement. The collective error applied to this density measurement implied slightly better than an order-of-magnitude estimate.

V-. ". E" m n _.~eqcent Determination

Radiation from a helium-uranium arc operated at a total pressure of 3 atm and % 1000 W arc power was detected without any collimating lenses. The arc chamber was continually purged with helium and the vacuum







77

spectrograph (McPherson M~odel 218) was maintained at 1, I t Separating the pressure-vacuum (arc cell-spectrograph) interface was a 3/8-in. Lif (lithium fluoride) window. The spectrograph grating contained 2400 grooves/mi and was blazed for 1500 A in the first order. The sodium salicylate-phototube combination (described in Sec. III.3B) was used to detect photons transmitted by the spectrograph.

After initial detection of a vacuum uv signal, we tried to eliminate possible undesirable signals caused by internal reflections, stray light, etc. The McPherson spectrograph had a history of reflection problems, so optical blockouts (baffles) were used on the two spectrograph mirrors and the grating. The geometry of the baffles allowed only the central image of a light source to pass through the spectrograph to the exit slit, and the spectrographic internal reflections were eliminated.

Arc intensity data were collected in two wavelength segnients, from 1050 A to 1750 A and from 1750 A to 4300 A. These bandwidths were used because the deuterium calibration standard had no valid calibration
0 0
values lower than 1750 A. Intensities at wavelengths above 1750 A were calibrated as described by Eq. (111.1). The calibration standard used
0
at wavelength > 1750 A was the Oriel deuterium discharge. This region was cross-checked at several wavelengths using the tungsten filament standard as a reference, and most of the uncertainty associated with the deuterium calibration values was removed.

Accurate calibration of intensity data found in the vacuum uv region below 1750 A by ordinary methods was impossible. Many of the difficulties encountered are discussed in Sec. III.3C; application of backextrapolation calibration (BEC) was necessary (see Sec. IIII.3C).






78

Because the intensity data were collected without a collimating lens, no detailed spatial resolution was performed on the observed intensities. However, a homogeneous plasma of 1-cm depth (the actual arc plasma diameter) was assumed. The intensity was converted to an approximation of the arc-centerline emission coefficient by simply weighting each intensity value by the inverse of the arc plasma depth (in this case 1/1). In general, this procedure yielded a conservative estimate of emission coefficient and a slight distortion of the true shape.

The calibrated and converted intensity values are shown in the

approximate form of emission coefficient values in Fig. V-1. There is moderate emission in the 1000 to 2000 A bandwidth mostly caused by overlapping line structure. This bandwidth has been recalled in Fig. V-2 to expose more spectral detail. Figure V-2 indicates notable line structure and one distinct emission peak at % 1550 A, partly caused by grating response at the nominal blaze angle.

Grating scan uncertainty of +10 A and rather large slit widths made precise wavelength location of the line structure unobtainable for comparison. Kelly, 80 however, lists a rather intense cluster of lines at

0 0 0
1575 A, 1579 A, and 1585 A--consistent with our results. The emission data shown in Fig. V-2 are one of many sets taken (at similar arc conditions) which were cross-referenced to eliminate noise and insure that most of the residue be the desired signal.

Figure V-1 shows the remainder of the spectrum to 4300 A. Many of the known U11 and some of the stronger UI lines were potentially identified. Many unidentifiable lines could be of UII origin. There are









79







0


u S
ro

E









uj




LIJ M 0 Ld 0 0
cr_ 0
0- 00



0
0
_0 0








Ln U)





Ln














ton [f)
L)


(V










80





LO







r1r)









4-3 Qj






4-)








in

ro ..........
Li 4-)





cr) >)

Lr)
31





ro
F-
UI








M





C) CII
C)
LO cr)
C\j N 3 1 N I







81

0 0
distinct peaks at approximately 2300 A and 2900 A. The theoretical predictability of these peaks and the one at 1500 A will be addressed in Chapter VI.

Vacuum uv signal authenticity and order contamination caused by

overlapping orders were investigated. Light emitted by the uranium arc

was passed through the vacuum spectrograph system and detected as usual with one exception--a test material composed of either Lif, quartz, or glass was placed just behind the entrance slit. Arc intensity data collected indicated that the system was detecting a true vacuum uv signal, and that contamination from other orders of the grating was negligible.

Uncertainty in the absolute value of the emission coefficient is a function of several sources, such as calibration of the standard radiation source, minimal spatial resolution, standard source positioning, digital processing, grating scan error, and arc fluctuation. For higher wavelength (>1750 A) the emission coefficient value error is probably within 30%. However, it is much more difficult to identify value error to wavelengths less than 1750 A. Back-extrapolation calibration in this region assumed negligible system (optical) losses which is not the case. A good indicator of value uncertainty at these wavelengths is the system efficiency data in Table III-I. The dashes in Fig. V-1 represent the uncertainty limits on data at selected wavelengths in the vacuum uv. Clearly, as lower wavelengths are approached, the losses begin to dominate and are really indicative that all photons emitted below 1200 A are unlikely to be detected. The error in emission coefficient values at wavelength > 1750 A does not have this loss component because the calibration is more precise.







82


An extension of these data to 6000 A was accomplished by comparison to uranium plasma emission coefficient data 81 taken using this arc system and is shown in Fig. V-3. The line structure in this figure refers to the latest measurements at 3-atm total pressure; the dashed-line curves represent previous results. The deviation it) magnitude can be explained by our more sophisticated and accurate data-acquisition system. Even so, the comparative magnitudes remain within reason. Comparative shapes (along the wavelength scale) offer a high degree of correlation, as expected if past and present measurements were made properly. These
0
factors validate the extrapolation of the present data to 6000 A with substantial credibility. Thus, a spectral emission coefficient is now defined for a uranium plasma (8000 K, 0.01-atm uranium pressure, and 1-cm plasma depth) from 1200 to 6000 A.

Figure V-4 shows the present results with the corresponding Planck function and other comparable measurements reported in the literature, 222,2along with theoretical predictions made by Parks et al.83 For the moment Parks' results will be accepted and their validity examined in Chapter VI. Because the graph is semilogarithmic, Kirchoff's Law provides a ready means to estimate directly the absorption coefficient by merely subtracting the value difference between plasma emission and the Planck function at a given wavelength.

For comparison it is necessary to remember that the Miller 22and

Marteney et al. 23 experiments used UF 6as the discharge gas; the Florida experiment vaporized metallic uranium. Figure V-4 clearly indicates the differences in emission coefficient wavelength dependencies among experiments. At similar plasmia conditions and compositions, differences in shape should be minimal. A distinct fall-off in emission coefficient is










83
















E E E -0
4- C) 4--)
(D U)

U')
n
4-)



l 0 u u
0 .- S0 4- (0
-4 V)
4
(1) E

U





01-0,
Ln


7


lo
Ln 71


Li i D >

LA

ij

ro



+_3 U) CD (1) Ln >







ro 4-) 4
Ln ro c











V-ls --)as -wzy'sbia)









84

10


cr
1 0 0



Ni
c;

<
0


0 Uj

0










Ln
10




o U) Lli


c
if) Q)
Lij I J
_j u
U) 4
2 4(3)




Li ci









X 0
E
CL Ld C\j



_j o ro
co C) 0
-.J 0
0







I-00 IT 0
C)
LL-






85

apparent between 2500 and 4000 A in both the Miller and Marteney results that is not evident in the Florida values. This discrepancy may be caused by strong UF 6 absorption in this wavelength region. This can be supported by Fig. V-5 which is a reproduction of some of the latest UF 6 photo absorption 848 and electron impact cross-section data86'87'88 indicating significant UF 6 absorption at these wavelengths. It is unlikely that other candidates such as UF5, UF2, and F play a major role in light absorption within UF6 discharges because their mean free paths are typically on the order of centimeters.A9'90

Recent and fairly conclusive evidence shows that Mliller's measurements may exhibit a substantial absorption effect from cold layers ofUF6,priual nte20-t 82 pr
of priulryi he20-t 4000-A bandwidth. Spector pr
formed a low-temperature (700 to 1400 K) ballistic piston UF6 absorption experiment with results remarkably similar in magnitude and shape to those of Miller whose temperature was a reported 10 000 K. The implication of this similarity is that while the uranium plasma in the Miller experiment nay have been at 10 000 K, its emission/absorption characteristics were masked by such properties of UF 6'

Unfortunately, the Miller data do not extend below 2500 A; however, the Marteney and Florida results do extend into the vacuum uv. Both indicate a small emission peak between 1400 and 1800 A. The Florida
0 0
peak appears at 1500 A, while the Marteney peak is located at 1650 A. The wavelength displacement between the two peaks cannot be explained by experimental error and, therefore, is attributed to the nature of each plasma and its associated emission/absorption mechanisms. The small peak shown by the Marteney curve at -, 1650 A is inconsistent with the relatively large UF 6 absorption cross section in the 2000 to 4000 A






86








10: 17 L. De POORTE9 AND
C.K. ROFER -De POORTERU




10 2




U-2




IT22
20030040
WAELNGH A

Fi .V 5 h to b o p i n s ec r m o F6






87

bandwidth. However, work by Srivastava et al.,86 McDiarmid,87 and
88
Trajimar has substantiated significant variation in the UF6 absorption
0
cross section in the 1500 to 2000 A bandwidth as illustrated in Fig. V-6. (For absolute units the common point between Figs. V-5 and V-6 is at the peak value near 2255 A.) In fact, there appears to be an absorption window at 1650 A which may account for the emission peak at that wavelength from the Marteney measurement. This may also explain the vacuum uv peak shift between the Florida and Marteney results.

Now we examine UF6 photoabsorption effects on the present arc data and the Marteney data because it may explain some of the discrepancies in shape. The Florida arc-emission coefficient data shown in Fig. V-l were folded with several UF6 photoabsorption strengths defined by layer thickness (as in the Marteney experiment) and molecular density. The concentrations correspond to UF6 to approximately 0.01 to 0.1 atm at room temperature. (The details of the folding are found in Appendix E.) The results are shown in Fig. E-l through E-4. They indicate a rather severe emission reduction in the 2100 to 2900 A bandwidth, a possible
0 0
peak emerging at 1750 A, and the original peak at 1500 A reduced and shifted toward the lower wavelengths. Attenuation is a function of the number of mean-free-paths traversed in all cases. This approximately agrees with the main features of the UF6 Marteney emission data and strongly suggests that UF6 photoabsorption is the common denominator between the Florida and Marteney results. Also included in Appendix E (Figs. E-5 through E-8) are results showing the original Marteney data with the same UF6 photoabsorption strengths unfolded. These unfolded data exhibit characteristics in the unaltered arc emission data. However,







88
















1000-UF6 ELECTRO14 IMPACT

EXPERIMENT, E 0 2o ev i800
z

> 600r200



4313 3100O2480 2067 1770 1550 138 10


WAVELENGTH (A)




Fig. V-6. Photoabsortpion cross-section approximation
into the vacuu-ultraviolet.






89

this analysis does not resolve the disparity in emission coefficient magnitudes as illustrated in Fig. V-4.

Shown in Fig. V-4 are differences in the absolute values of the emission coefficient measured at given wavelengths. This question has been addressed by Schneider, Campbell, and Mack, 91 where an optically thin plasma and an emission coefficient that is a direct function of particle density was assumed. It was then possible to use the perfect gas law to normalize the existing data to a common temperature and density. (The exponential temperature dependence of the emission coefficient was neglected.) The details of this comparison are an extension of this study and will only be summarized. The Marteney and Florida

0 0
results agreed in the 1500 to 2200 A bandwidth. Beyond 2200 A the Marteney and Miller results agreed in shape and magnitude but differed from the Florida results by I to 3 orders of magnitude at 5000 A. However, if the exponential temperature dependence were considered in the Miller (10 000 K) and Narteney (8500 K) data, their magnitudes would differ as well. These disparities among the three sets of measurements may, to some extent, be attributed to UF 6 masking processes. Substantial correlation in shape and magnitude resulted between Parks' theoretical data and the Florida experimental results when the two were normalized as previously described. The shape correlation can clearly be seen in Fig. V-4.

In summary, the emission coefficient of a uranium arc plasma

(T -- 8000 K, P = 0.01 atm) has been measured and compared with theory and other similar experimental data. The Florida emission data were measured from a relatively uncontaminated uranium plasma; the experimental comparison data were generated using UF 6 discharges exhibiting







90

UF 6 photoabsorption features that probably disguise the true emission picture. The emission coefficient curves taken from the UF 6 discharge experiments have been, to some extent, justified by relating their shape to that of the UF 6 photoabsorption cross sections. The predictability of emission coefficient shape and magnitude was addressed by a comparison between the Florida results and Parks' calculations. Favorable agreement exists in the 2000 to 4000 A bandwidth. Since no calculations were made by Parks in the vacuum uv, this region will be investigated specifically in the next chapter by independent calculations.














VI_. TI NEOSLXTA I- CA LOILA TITONS



Theoretical justification for computing quantitatively accurate

uranium plasma emission coefficients from first principles is nearly impossible because complete quantum-m-echanical description of the uranium atom does not exist. There must also be theory (statistical mechanics) which determiines the level population densities and ultimately, emission/ absorption coefficients. However, it is possible to obtain useful information about relatively strong emission/absorption features as a function of wavelength without the approach described above. This -information is in the oscillator strength calculations for those transitions in probable and strong transition arrays located in the wavelength region(s) of interest. Oscillator strength distribution can be a reasonable indicator to the emission characteristics of the system at those wavelengths.

For singly ionized uranium the task of calculating transition array oscillator strengths is still formidable--but possible. The procedure used to acquire this information for correlation to the UII experimental emission coefficients will be discussed. VI- 2. &7ermizooz.l

Consistent terminology regarding atomic energy levels is necessary for unambiguous discussions about atomic structure calculations. The state of an atom is the condition caused by the collective motion of all the atomic electrons. The state is specified by four quantum numbers for each electron or a set of coupled quantum numbers for the entire atomic 91







92

system. The ground state is the lowest energy state. A -level is represented by the total angular momentum, 3. The lowest energy level is defined as the ground level. Several states can correspond to a given

energy level. Terms are collections of levels tagged by multiplicity S and orbital angular momentum L. The statistical weight (distinct states) in a level is 2J + 1; in a term (2S + 1)(2J + 1). Definition of the n and k quantum numbers for each electron orbital specifies a configuration. Electrons in equivalent orbitals are designated equivalent electrons. A transition of an electron between two levels generates a spectral line, whereas a multpe is a group of transitions between two terms. Finally, a -transition array is composed of transitions allowed between two configurations.

Coupling is the process whereby two or more electron angular momenta are combined into resultant angular momenta. Regarding LS, 33, and intermediate coupling, the dominance of 33 over LS is expressed by the relative magnitudes of spin-orbit and electrostatic contributions to energy separation. Relative importance of spin-orbit interaction generally increases with increasing Z and n (principal quantum number); thus, for high-Z elements and large-electron orbits, 33 coupling would seem a logical choice. Conversely, for low-Z and small electron orbits, LS coupling would appear valid. However, at low- and high-Z there are many exceptions to these rules of thumb; intermediate coupling 92is required for many atomic systems. A good example of the rule-of-thumb breakdown is in the highest energy level (J = 2) in the 2p 54f configuration of neutral neon. The electron eigenfunction given in a pure LS basis representation is composed of 93

0.6811 3 F2 > + 0.4631 3 D2 > + 0.567 1D2 >






93

whereas, if pure LS coupling really existed (as expected of neon with Z = 10) there would be no contribution from two of the three components and 100% contribution from the third. 'VI- 3. Conl 7ijtrc2tion Se Zection2

The credibility of the observed UII emission wavelength can be established (to some degree) by calculating transition arrays and their associated oscillator strength distribution of particular configuration pairs. Valuable information can be computed from first principles relating to the location, and in some cases, the strength of emission for a given transition array. Generating specific transition arrays is directly related to selection of configuration pairs that are likely to produce spectra at relevant wavelengths. The selection of particular configuration pairs requires knowledge of configuration average energies Eav* The difference AEa between configurations is indicative of the average transition array wavelength between two specified configurations. Average energies are tabulated frequently in the literature for less complex atomic system but not for uranium; trial and error tactics were necessary.

We considered probable configurations where singly ionized uranium could find itself, beginning with the ground-state configuration 5f 37s 2 and exciting an electron to another likely orbit. Table VI-I summarizes configuration pairs which were ultimately considered.

Table VI-l
UII CONFIGURATION PAIRS
5f 37s 2 5f7~ a 5f 26d7s 2 5f 26d 2 7s
5f72_5f37s8p a5f 26d7s 2- 5f2 6d7s 2
5f37s 2 5f2 2 5f6d7s 00 5f 36d7p a
5f3 7s2 5f 2 7s27 5f37s7p 5f37s8d a
5f2 Gdls 2 5f2 6d7s7 5*f 36d7s-5 3 7spa
a Configuration pairs which were very strong and/or lead to oscillator
strength distribution at the desired wavelengths.




Full Text
VII. CLOSING REMARKS
Emission coefficients of uranium plasma at two distinct tempera
tures and pressures over an unusually broad wavelength region have been
measured. These new data represent an extension of previous information
published by Krascella,^ Miller,^ Marteney et al.,^ Randol,^ and
68
Kylstra. The results are significant additions to available informa
tion, and the major points are summarized below.
Specific emission coefficients for a low-pressure uranium arc at
o
5500 K, 0.001-atm uranium pressure were measured from 2500 to 5500 A.
These data were in reasonable agreement with the semi-empirical work
79
of Krascella and the spectral line catalogue of the first spectrum
of uranium reported by Steinhaus et al.^^ For this arc there was no
o
emission detected below 2500 A, probably because of the relatively low
temperature and the importance of radiation from neutral uranium. Plasma
temperature, pressure, and emission coefficient were obtained simultan
eously, thus reducing fluctuation problems usually associated with
photoelectric diagnostics. The temperature and pressure diagnostics
depended upon assuming LTE, and although not proven, LTE was reasonably
75
substantiated with cross-checks and comparison to NBS work by Voigt.
Specific emission coefficients of a high-pressure helium-uranium
arc at approximately 8000 K, 0.01-atm uranium pressure were measured
o
from 1050 to 6000 A. These results represent a rare successful attempt
to obtain emission coefficient data for singly ionized uranium in the
vacuum ultraviolet. Intensity calibration in the visible and vacuum
104


76
similar to that applied to the low-pressure arc. Order-of-magnitude dis
agreement occurred between the absolute line values and those determined
51
by vaporization and PTC studies. In fact, the absolute line values
were always lower than the others. These discrepancies were explained
(to some degree) by assuming an inhomogeneous pressure profile radially
across the arc and, as well, the characteristic uncertainties asso
ciated with most density measurements. In any event, the centerline UII
51 16 3
density reported0 for a 3~atm helium-uranium arc vas 3.8 x 10 D cm
(0.042 atm) at a central temperature of 'y 8100 K. By Saha analysis this
pressure and temperature imply a total uranium pressure of IV 0.055 atm
16 3
and an electron density of 4.3 x 10 cm .
The temperature measurement assumed partial LTE; however, the spec
troscopic density determination required complete LTE. As described in
Sec. IV.3, assuming complete LTE where only partial LTE was assured
caused an underestimation of the ground-state densities; the magnitude
of error was a function of the thermal limit. For the helium-uranium
arc a rather high electron density was achieved, which easily satisfied
the ladder, and possibly the hydrogenic LTE criterion as well. Based on
these considerations, the ground-state underpopulation factor (if it
could be calculated) would be small compared to the other uncertainties
found in the density measurement. The collective error applied to this
density measurement implied slightly better than an order-of-magnitude
estimate.
V-4. Emission Coefficient Determination
Radiation from a helium-uranium arc operated at a total pressure of
3 atm and % 1000 W arc power was detected without any collimating lenses
The arc chamber was continually purged with helium and the vacuum


FRACTIONAL OSCILLATOR STRENGTH (GF)
WAVENUMBER (IOOO err,'1)
Fig. C-9. RHX transition array oscillator strength
distribution for LUI 5f3 7s2-.-5f3 7s7p.


Fig. V- 3. Past and. present uranium plasma emission coefficients established
with the University of Florida D. C. uranium arc.
CO
CO


95
In this case the columns of the diagonalization matrix, D, form the
eigenvectors and the diagonal elements are the energy eigenvalues. The
standard "bra" and "ket" notation used in many quantum mechanics
92 95
texts serves as shorthand for operator matrix elements H in this
case. The proper definition of the energy matrix elements H^- is the
crucial step in obtaining the correct eigenvalues and eigenvectors.
The complete Hamiltonian can be written as
H -
h_
2 m
i=I i 1 j>l 1J i
Si) +
:vi-3)
Kinetic
energy of
electron
Nuclear Electrostatic
electro- potential
static energy
potential between
energy of electrons
electron i i and j
Magnetic Other
spin-orbit terms
energy of of
electron i lesser
importance
For uranium, Eq. (VI-1) cannot be solved in closed form with this
Hamiltonian. Therefore, approximations are usually made which force a
given electron to move in a central field of the nucleus and the N-l
other electrons. If spherical symmetry is assumed, the angular portions
of the one-electron wavefunctions are hydrogenic and can be calculated.
A self-consistent field (SCF) Hartree-Fock calculation with a spheri
cally symmetric potential is used for the radial wavefunctions. In many
cases the Hartree-Fock approach is too complex for solution, and further
approximation is necessary. These approximations are apparent as the
form of radial potential that will account for the system's exchange
properties. It is hoped that the potential used will have the important
properties of the Hartree-Fock potential, will yield "correct" energy
eigenvalues, and will establish properly orthogonal determinantal radial
wavefunctions.


49
LiF cutoff '(1 050 A) called for an approach which did not require expli
cit standard calibration points at the lower wavelengths.
The branching-ratio technique was considered for absolute intensity
calibration in the vacuum uv and it is based on the intensity partition
of at least two spontaneous optically thin transitions with a common
58 59
upper level. 5 The intensity ratios of these two lines is a strict
function of the transition-probability ratio and independent of plasma
inhomogeneities and LTE. To apply this technique in the vaccum uv, one
transition must appear in the visible and the other in the vacuum uv.
This method is sound provided isolated spectral lines exist and well-
defined transition probabilities are used. The application of branching-
ratio calibration to uranium spectra fails in both respects.
Back-extrapolation calibration (BEC), an approximate technique, was
used. Helium-uranium arc intensity data were collected in bandwidths
900 A +1750 A -> 4300 A. Intensities above 1750 A were calibrated
against the deuterium discharge and tungsten standard; whereas arc in-
o
tensities at wavelengths below 1750 A were assigned absolute units by
BEC. (Intensity signals from the low-pressure uranium arc required
o
calibration down to 2500 A which was done with the tungsten standard.)
Intensity calibration using a standard source is essentially a sys
tem response comparison of (in this case a spectrograph-photomultiplier
combination) a known photon flux to a photon flux of an unknown source.
The absolute intensity of the unknown is then related to that of the
standard by:
T /, \ T ^STD(X) VARC^
arc x istd(A) cj)AR^rxy vSTD[xy
(III-l )


40
30
ro
E
o
'o
20
>-
o
O'
UJ
a
UJ
10
0
EVEN PARITY
f3 dsp
,2,2
f d s
f^dsSp
,3,2
f d p
f4ds
,3 2
f S p
,4 2
f s
ODD PARITY
f3d 7s 8 s
f 4 sp
,3 j2
f d s
f3 ds2
Fig. D-l. Energy of lowest levels of known
UI configurations.


SUPPORT
CATHODE
BOLT
l
ASSEMBLY
(STAINLESS
(BRASS)
STEEL)
WATER
1
!

INLET
GAS
OUTLET r-
JTT
COPPER RING ;
INLETS
f
i I
zrr
j.\
'n-^rrz
rr:7,r:~
INSULATOR RING
fe2
~ET
lH
M cr;
~iT~r
>XI
,S;ZK\
if
-/
WATER
INLET
ARC BURNS BETWEEN
TUNGSTEN CATHODE AND
URANIUM ANODE
ANODE
(COPPER)
-viewing
port
V i
OUTLET
INSULATOR ORDER
(INSIDE-OUT)
L BORON NITRIDE
2. 0 RING
3. PHENOLIC (G-IO)
A COQL ANT
5- PHENOLIC
6. 0- RING
7. PHENOLIC
Fig. III--2. Uranium arc device segmented assembly.


III. URANIUM PLASMA EXPERIMENT HARDWARE
III-l. Uranium Plasma Generation
For this investigation uranium plasma was generated by a direct-
51
current uranium arc constructed by Randol at the University of
Florida. Many original features were retained; system details are in
Ref. 51. There have been some important changes to the original system
which will be described in this report.
A. Uranium Plasma Containment Cell
Figure 111-1 shows the uranium plasma containment vessel. The
stainless steel vessel is designed to withstand safely cover-gas pres
sure to 100 atmospheres. It can also be operated in the vacuum mode
down to at least 300 torr. Contact is made between the tungsten cathode
and uranium anode by remote movement of the cathode with a pneumatic
electrode-drive cylinder. Both electrodes are water-cooled. The gas
distribution head can give directional flow to the incoming cover-gas
near the arc electrodes. The viewport windows are sealed from both
sides for pressure or vacuum operation. The gas inlets also serve as
the pumping ports when an evacuated chamber is desired.
B. Segmented Assembly
Within the containment vessel, fastened to the headplate, are
several annular water-cooled copper segments (disks). The disks are
arranged concentrically around the anode-cathode configuration for arc
wall-stabilization. Figure 111-2 shows the segmented assembly with its
orientation to the electrode configuration. The arc column length is
29


14
Fig. II-l
Zonal division of a cylindrical ly symmetric plasma


NUMBER DENSITY (cmw
113
IS
TEMPERATURE (K)
Fig. A-5. Uranium plasma Saha number densities,
P = 0.0 01 atm.


62
not be highly flattened except for the significant radiation flux loss
produced by such a dense emitter as uranium. The striking lack of
temperature profile curvature (till the arc boundary is approached) can
be reasonably attributed to the dense core radiation characteristic of
72 73
excited uranium in a wall-stabilized configuration. Shumaker has
shown that nitrogen and argon wal1-stabilized arcs operating at similar
current, voltage, and pressure conditions produced temperature profile
shapes of different degrees of curvature. The radiating species with
the denser characteristic radiation (argon) produced the flatter tem
perature profile.
From LTE considerations the normal temperature (Sec. 11.4B) for
several UI transitions was calculated to be about 5000 K at 0.001 atm
uranium pressure. The 5500 K measured temperature indicated a mixture
of UI and UII radiating species with UI dominating, which was consistent
with the spectral analysis. (See Appendix A for Saha equation number
density and normal temperature curves). The probability that partial
LTE exists also implies that the gas temperature differs from the
electron ternperature--magnitude of difference is questionable. This
problem has been studied by Gurevich^ who used mercury and argon
discharges at total pressures from 0.1 to 1 atm. Their technique
essentially monitors the distinct cooling of the electrons to the gas
temperature and subsequent general cooling of the plasma. The intensi
ty output tracks the cooling and can be followed with a scope-phototube
combination. The method is sensitive to electron-gas temperature dif
ferentials as small as 0.5%. The conclusions are that the temperature
differential is a strong function of total (and electron) pressure and
weak function of arc current. The extrapolated temperature differential


II-4. Plasma Temperature
16
Many techniques used for temperature diagnostics were developed by
23 45 46
Griem, Hefferlin, and Lochte-Holtgreven. The following discussion
considers only those temperature diagnostics applied to a uranium arc
plasma, including the Boltzmann plot, norm temperature, relative norm
temperature, and the modified brightness-emissivity methods.
.4. Boltzmann Plot Method
~k
The integrated line intensity for a homogeneous, optically thin
plasma into a depth x is
I
v
hv
u->£
4'rr
A n X
u-^£ u
(11 -10)
If the plasma is in complete LTE and inhomogeneous, n (T) is determined
by the Boltzmann factor yielding
I
v
hv
u->£
4tt ziry
A 0 n (T)
U-Hl 0x
- E /kTl
e u' 'i. .
U
(11-11)
where T
A o
u-*Jl
Vu-H
9u
%
Z(T)
excitation temperature (K) ,
transition propability (seconds ^ ) ,
transition frequency ,
statistical weight of the upper level ,
ground state population density of a particular ionization
state (#/cm^) ,
partition function ,
energy of upper level (eV), and
ring depth of zone of assumed constant emission (Fig. 11-1).
Integrated in this sense means integration over the line-shape function
y¡
. d> (v)dv has already been performed,
line £


22
where v = emissivity,
x = LOS plasma depth,
I (x) = total observed intensity at (v, x),
C
I (x) = total external source intensity without absorption
at (v, x),
Q
1(0) = total external source intensity without absorption
at v, x = o (the plasma boundary), and
p
B^T) = Planck function indicative of the brightness temperature
of the plasma.
T S
The known quantities I (x), I (x), x (x), and t allow determina-
^ v v v v
tion of the plasma brightness temperature using the Planck function
for the plasma.
The primary disadvantage of the BEM is lack of applicability to
inhomogeneous plasmas such as those formed with arcs. Usher and
Campbell^ have adapted the BEM to the homogeneous case. The modified
BEM differs from the BEM in that an unfolding scheme resolves the absorp
tion coefficient and temperature profiles spatially.
The absorption coefficient of a spectral line is determined by a
constant intensity background source and measurement of the wavelength
attenuation as the line passes through the plasma. If the inhomogeneous
plasma is composed of homogeneous rings (similar to Fig. II-l), an un
folding technique^ can be used to calculate the average line-center
absorption coefficient, for each ring from
1
V
. 1
2
In
i-1
E
(11-16)


6
_3
Where ng = electron density (cm ),
Z = net plasma charge (Z=l for neutral; Z=2
for singly ionized),
AEq i = energy (eV) of 1st excited state with respect
to the ground state,
kTe = thermal energy of plasma electrons (eV), and
E,, = ionization potential of hydrogen (eV).
ri
This criterion estimates the lower limit of electron density re
quired to maintain a hydrogenic system in complete LTE. A hydrogenic
system is usually characterized by a large energy gap between the
ground state and first excited level, and successively smaller energy
separations between levels as continuum is approached. Hydrogen (and
helium) is also one of the more difficult elements to bring into LTE
because of its relatively high-lying first excitation level. Thus,
hydrogen can usually serve as an upper-1imit estimation for the validity
of LTE for more complex systems. However, the electron density
criterion offered by Eq. (11-1) is not directly applicable to the
uranium system because the known energy-level description of the
uranium atom (or ion) simply does not fit the hydrogenic picture. In
fact, the first excitation levels of UI and UII are 0.077 eV (UI)
and 0.03 eV (UII), which, for singly ionized uranium at 8500 K, implies
> 9-3
n 3.9 x 10 cm This is well below any reasonable values for n
e e
basically because of the strong dependence on AEq ^ which has a very
small value for neutral and once-ionized uranium. Applied to hydrogen
at 8500 K, n 8.8 x 1016 cm-3, this limiting value for n is probably
0 c
26 27
too restrictive for the uranium system. Griem, McWhirter, and


K, ABSORPTION COEFFICIENT (cm
Fig. IV-1. Line-center absorption coefficient profile.
en
or


88
Fig. V-6. Photoabsortpion cross-section approximation
into the vacuum-ultraviolet.


90
UFg photoabsorption features that probably disguise the true emission
picture. The emission coefficient curves taken from the UFg discharge
experiments have been, to some extent, justified by relating their
shape to that of the UFg photoabsorption cross sections. The predic
tability of emission coefficient shape and magnitude was addressed by
a comparison between the Florida results and Parks' calculations.
o
Favorable agreement exists in the 2000 to 4000 A bandwidth. Since no
calculations were made by Parks in the vacuum uv, this region will be
investigated specifically in the next chapter by independent calcula
tions.


139
icr
l.t.j
o
¡T
lu
i.U
o
o
o
to
CO
' f 1
1X1
L.J
L'.J
O
UJ
CL*
ir
o
O
F-
id
¡0
n
10
i ^
i n
'T
T
r
r
UFg DEPTH 1.5 cm
UE. CONCENTRATION [vlVcm3]
b
.0 x 01
2= 2.0 xIO1
3= 4.0x10'
4s 8.0 xIQ16
17
-i
5; 1.0 x 10
i...
[000
2200
L
2600
*7 4'. /\
oUOu
o
WAVELENGTH (A)
Fig. E-5. Marteney Ar-UFg emission coefficient data as altered
by photoabsorption unfolding for 1.5 cm of UFg.


45
such a discharge. Therefore, two calibration sources were used: a
tungsten lamp for the visible and near uv, and a deuterium discharge
for the uv and vacuum uv.
Two tungsten filament lamps made by the Eppley Company were used
for intensity calibration in the visible and near uv. One was cali
brated by the NBS and designated the "standard lamp"; the second served
as a "reference lamp." The reference lamp was used as the experiment
standard but periodically cross-calibrated to the standard lamp. The
calibration curve for the standard lamp is given in Fig. 111 9. The
56
associated accuracy of the values was stated to be 10%.
A deuterium discharge was used to calibrate intensities below
O
2500 A. The lamp had a suprasil fused-silica window with a 50% trans-
o o
mission point at about 1750 A, and a calibration point at 1662 A was
the apparent lower wavelength limit. Figures 111-10 and 111 -11 show
the wavelength dependence of the spectral radiance at two current modes.
The absolute intensities as calibrated from this lamp carry a 10% un-
57
certainty, verified by cross-check of the deuterium lamp intensity
against the tungsten filament standard at four different wavelengths
O
above 2500 A. The percentage difference between the quoted deuterium
intensities and the cross-checked intensities was always within the un
certainty limits. The percentage difference tended to increase toward
o
the lower wavelengths and the calibration points below 2000 A are asso-
O
dated with an unknown maximum uncertainty less than 10% up to 1750 A.
O
The last deuterium calibration point resides at 1662 A as dictated by
O
the fused-silica window cutoff of the discharge lamp. The 1662 A cali
bration point is below the fused-silica 50% transmission wavelength of
57
1750 A and is quite uncertain. Calibration for intensity data to the


68
very reproducible intensity-wavelength data sets; only major arc inten
sity fluctuations could not be removed. When these major fluctuations
occurred the data were discarded, thus, the data plotted in Fig. IV-5
is in error by the intensity uncertainty of the standard tungsten lamp
55
calibration source, which is approximately 10%. The calibration of
uranium plasma intensity was done using the "Plasma Source Calibration
78
Program." J However, intensity data sets taken in the outer arc re
gions are in error by as much as +12 to 20% because deposition on the
viewport interfered with the optical path from the plasma source to the
spectrograph entrance slit.
The four intensity-wavelength data sets were spatially resolved by
Q
a four-point numerical Abel unfolding after averaging over 100 A band-
widths. The results for this emission coefficient calculation in the
central arc location are shown in Fig. IV-6. Error sources in these
data are attributed to the absolute intensity calibration, viewport
deposition, and four-point spatial resolution. The calibration and
deposition errors have already been mentioned and are carried over to
the emission coefficient determination. Spatial resolution error is
much more difficult to address. It is composed of error caused by
propagation of experimental uncertainties and the high probability of
using a non-optimal zone number for the unfolding (statistical error).
Experimental error propagation through the inversion process was
estimated by unfolding the data with and without such error included.
The statistical error was estimated by relying on the analysis of Kock
44
and Richter, based on the form of the intensity profile, number of
rings chosen, smoothness of profile, and maximum outer-zone experi
mental error. An exact match did not exist and extrapolation was


141
.
WAVELENGTH
o
(A)
Fig. E-7. Marteney Ar-UFr emission coefficient data as altered
by photoabsorption unfolding for 3.0 cm of UFg.


WAVELENGTH (A)
Fig. V-4. Uranium plasma emission coefficient survey.
CO
-E*


APPENDIX A
SAHA NUMBER DENSITIES AND NORMAL TEMPERATURES
Saha analysis was used to calculate LIE number densities of
uranium for two stages of ionization at several total pressures of
interest. The Saha equations are given by
Si(T) = -
i+1
2UH1(T) (2^ m0k)2/3 _E /KT
T e 1
Ui(T)
h
3
(A-l)
where
i = the ionization stage,
_3
n^ = number density (cm ) for all i-fold ionized particles,
ng = electron number density (cm ),
U.(T) = partition function of i-fold ionized atom,
_ pQ
mQ = electron rest mass (= 9.108 x 10" gm),
-27
h = Planck's constant (= 6.626 x 10 ergs-seconds),
k = Boltzmann's Constant ( = 1.381 x 10~^ ergs/K),
E.j = ionization energy for ionization from i -* i+1,
T = absolute temperature (K).
The number density solutions were obtained using Eq. (A-l) coupled with
the equation of charge neutrality:
n = E in, (A-2)
e i=0 1
and the equation of state:
i
P=kT{n + E n.}
e i=0 1
(A-3)
107


98
Table VI-2
UII ATOMIC STRUCTURE CALCULATIONS --
A COMPARISON OF THE PARKS (STF) AND RHX APPROACH
SUBSTANTIAL ASPECTS OF CALCULATION PARKS(STF) RHX
Sealed-Thomas-Fermi (STF) X
Hartree-Exchange (HX) X
Relativistic (Dirac) X X
Magnetic Spin-Orbit Interaction X
Correlation Effects X
Configuration Interaction
Self-Consistent Field (SCF) X X
Scaled Thomas-Fermi Potential X
Hartree-Exchange Potential X
Coupling Schemes
1. None X (Statistica
treatment)
2. Intermediate
X


12
~nne = ^ The line intensity I^(x) from such a transition
would simply be determined by multiplying the line emission coefficient
by the appropriate LOS plasma depth through a constant emission zone.
Arc plasmas are inherently inhomogeneous to varying degrees. Free-
burning arcs usually exist with significant temperature gradients along
the major part of an approximately cylindrical arc column radius, which
results in radially varying intensities. Therefore, the emission coef
ficient will also have a radial dependence that must be extracted by
unfolding methods applied to observed intensities. Many wall-stabilized
arcs have less severe temperature gradients, with the exception of that
32-37
region approaching the wall. This implies the possibility of an
approximately homogeneous nature in temperature and density in the major
part of the cylindrical arc plasma in the radial direction. Although
a relatively constant temperature profile does not assure homogeneous
density and emission profiles, it can be a strong indicator.
II-3. EYnission Coefficient Detei'mination
The geometry of inhomogeneous optically thin arc plasmas is approxi
mated by a number of concentric zones about the vertical axis, as shown
in Fig. IT-1. Each zone is assumed to display constant emission which
is a function of a single temperature and density for that zone. The
intensity at a given location along the arc chord is the sum of emission
contributions for each zone intercepted by a LOS ray passing through the
geometry. The emission coefficient must then be unfolded from the
measured integrated intensities by the familiar Abel transform. The
38
analytical form of the transform equations is


41
with spectrograph (S-|) used as monochrometer, swept a particular line
of interest across the exit slit plane of Sy An RCA 1P28 phototube
placed behind the S-| exit slit responded to the spectral line as it
moved past. That line profile was recorded by oscilloscopes by 0-| and
tiy At the instant the sweep reached the central wavelength of the
line profile, the xenon flashtube triggered. This enabled the flash-
lamp radiation to be superimposed on a specific spectral line center
(Fig. I1-3). Flashtube timing was accomplished by electronic delay
circuitry shown in Fig. 111-8. The ground-state particle density was
determined from the line profile of oscillograms O2 with the absolute
line method; line center absorption and the plasma temperature were de
termined from oscillograms Oj.
B. Photoelectvio Intensity Data
O
Photoelectric intensity measurements were made from 2000 A -
o 00
5500 A for the low-pressure uranium arc and from 1050 A 6000 A for
the helium-uranium (high-pressure) arc. Intensity of the low-pressure
uranium arc as a function of wavelength in the visible and near uv were
recorded by using part of the data acquisition system shown in
Fig. III-2. A scanning spectrograph Sg received arc radiation reflected
from the front surface of a beam-splitter. The phototube response was
monitored and stored digitally by a signal-averager [a time-averaging
digitizer that integrates (smooths) small random input voltage (arc)
fluctuations] which resulted in very reproducible arc intensity traces
as a function of wavelength. Four memory areas within the signal-
averager were used for storage of the spectral intensity I^(x), where
x is a particular LOS position in an arc traverse. A four-point Abel
unfolding for spatial resolution of the arc intensities was performed


66
IV-4. Emission Coefficient Determination
Spectral analysis of radiation structure emitted by the low-
pressure uranium arc plasma indicated a preponderance of known UI line
spectra mixed with some identifiable UII structure. The species-mix
ratio is not available because of uncertainties involved in line
identification on uranium spectra. However, at the maximum tempera
ture of 5500 K a Saha ratio of nuj¡/nyj can approach 1.0, and cooler
arc regions will be weighted toward larger values of n^j.
Intensity from the low-pressure arc was observed at four equally
spaced arc positions. Details of data acquisition are in Sec. III.3B.
The spectrograph used for this study was a Hilger-Ingis (Model
S05-10000) modified to a rapid-scan capability (1.28 s from 2000 to
o
6000 A). A 1200-grooves/mm grating was used with a blaze angle of
o
17.2 corresponding to a wavelength of 5490 A in the first order. In
tensity calibration was performed using a tungsten-filament NBS-
calibrated standard.
Preliminary experiments indicated a rapid decrease of arc intensi-
o o
ty below 3500 A and very little signal at wavelengths less than 2500 A.
Steinhaus et al."'^ also indicates little structure between 2000 and
o
2500 A for UI. We decided that emission from this particular arc
o
plasma below 2000 A would be relatively insignificant, and the effort
required to detect potential vacuum uv emission was not justified for
this plasma.
The calibrated arc intensity-wavelength data is plotted in
Fig. IV-5. Four similar sets of intensity data were generated for each
arc burn; the data plotted in Fig. IV-5 corresponds to the central arc
region only. The data acquisition method (signal averaging) produced


87
86 87
bandwidth. However, work by Srivastava et al., McDiarmid, and
88
Trajinar has substantiated significant variation in the UFg absorption
o
cross section in the 1500 to 2000 A bandwidth as illustrated in
Fig. V-6. (For absolute units the cominon point between Figs. V-5 and
o
V-6 is at the peak value near 2255 A.) In fact, there appears to be an
o
absorption window at 1650 A which may account for the emission peak at
that wavelength from the Marteney measurement. This may also explain
the vacuum uv peak shift between the Florida and Marteney results.
Now we examine UFg photoabsorption effects on the present arc data
and the Marteney data because it may explain some of the discrepancies
in shape. The Florida arc-emission coefficient data shown in Fig. V-l
were folded with several UFg photoabsorption strengths defined by layer
thickness (as in the Marteney experiment) and molecular density. The
concentrations correspond to UFg to approximately 0.01 to 0.1 atm at
room temperature. (The details of the folding are found in Appendix E.)
The results are shown in Fig. E-l through E-4. They indicate a rather
o
severe emission reduction in the 2100 to 2900 A bandwidth, a possible
o o
peak emerging at 1750 A, and the original peak at 1500 A reduced and
shifted toward the lower wavelengths. Attenuation is a function of the
number of mean-free-paths traversed in all cases. This approximately
agrees with the main features of the UFg Marteney emission data and
strongly suggests that UFg photoabsorption is the common denominator be
tween the Florida and Marteney results. Also included in Appendix E
(Figs. E-5 through E-8) are results showing the original Marteney data
with the same UFg photoabsorption strengths unfolded. These unfolded
data exhibit characteristics in the unaltered arc emission data. However,


APPENDIX C
SPECTRAL LINE AND OSCILLATOR STRENGTH DISTRIBUTIONS
FOR SELECTED UII CONFIGURATION PAIRS
The following figures illustrate UII spectral line and oscillator
strength distributions as a function of wavenumber. They compose the
majority of graphical output from the RCG calculation. Figures C-l,
C-3, C-5, C-7, and C-9 are the oscillator strength distributions for a
specified UII configuration pair and have already been presented in
Fig. VI-2. Figures C-2, C-4, C-6, C-8, and C-l0 illustrate the calculated
fractional spectral line distributions for corresponding configuration
pairs. The number of spectral lines calculated for the five configura
tion pairs reported approached 203 000. Only those lines which had
strengths above a user-set cutoff were plotted.
118


75
to be between 8000 and 9000 K and 0.01 atm UII partial pressure rounded
to the nearest integral logarithmic pressure. Because of the inferred
temperature and pressure, only a brief overview will be given (Sec. V.2
51
and V.3) of the methodology used by Randol to determine these param
eters.
V-2. Temperature Measurement
The central temperature of the helium-uranium arc plasma operated
at 30 A, 36 V, and 3-atm total pressure was estimated by the Fowler-Milne
method and measured by the relative Boltzmann plot method. The normal
temperature for this plasma was estimated to range between 7000 and
9000 K for a corresponding pressure range of 0.001 to 0.1 atm total
o
uranium pressure, using the 4171 A UII transition. Slight off-axis
mximums in the emission profile indicated the probability of close
proximity to the normal temperature. To define temperature, the corres
ponding pressure must be known because temperature and pressure must be
consistent. Because the spectrum taken from this plasma showed a clear
majority of UII structure, and Saha analysis indicated (at 0.01 atm) a
dominance of UII particles in the 7000 to 9000 K temperature range, the
probability of close proximity to the normal temperature was increased.
The centerline temperature was then measured for the above conditions
51
using the Boltzmann plot method and found to be 8113 K 8%. The
centerline temperature of our helium-uranium arc plasma operated at
similar conditions was therefore inferred to be ^ 8000 K.
V-3. Density Measurement
The central UII partial pressure for the helium-uranium arc was
measured by the absolute line method and cross-checked by the pressure-
temperature correlation (PTC) technique (Sec. II.5B). This diagnostic was


147
54. Fowler, M., Marion, J. B., Fast Neutron Physics (Interscience
Publishers, Inc., New York, Part I, I960) 705.
o
55. Pitz, E., "Spectral Radiance of the Carbon Arc Between 2500 A and
1900 A," Appl. Opt. 10, 813 (April 1971).
56. Ott, W. R., National Bureau of Standards, Washington, DC, personal
communication (September 1975).
57. Ott, W. R., Plasma Spectroscopy Section, Optical Physics Division,
National Bureau of Standards, personal communication,
(July 1972).
58. Griffen, W. G., McWhirter, R. W. P., "An Absolute Intensity
Calibration in the Vacuum Ultra-Violet," in
Proceedings of the Conference on Optical Instruments
and Technology, K. J. Habell, EdTT (John Wiley & Sons,
Inc., New York, 1963) 14-21.
59. Hinniov, E., Hopmann, F. W., "Measurement of Intensities in the
Vacuum Ultraviolet," J. Opt. Soc. Am. 53^ 1259-1265
(1 963).
60. Berning, P. H., Hass, G., Madden, R. P., "Reflectance-Increasing
Coatings for the Vacuum Ultraviolet and Their Applica
tion," J. Opt. Soc. Am. 5_0, No. 6, 586-597 (June 1 960).
61. Hunter, W. R., "High Reflectance Coatings for the Extreme Ultra
violet," Optica Acta 9^, 255-268 (January 1 962).
62. "Harshaw Chemical Company Catalogue," Harshaw Chemical Co.,
Ohio (1967).
63. Hass, G., Tousey, R., "Reflective Coatings for the Extreme
Ultraviolet," J. Opt. Soc. Am. 4_9, No. 6, 593-602
(June 1959).
64. Quartz, J., Bausch & Lomb Optical Company, personal communication,
(November 1975).
65. Allison, R., Burns, J., Tuzzolino, A. J, "Absolute Fluorescent
Quantum Efficiency of Sodium Salicylate," J. Opt. Soc. Am.
54, 747-751 (1964).
66. Watanbe, K., Inn, E. C. Y., "Intensity Measurements in the Vacuum
Ultraviolet," J. Opt. Soc. Am. 43_, 32-35 (1953).
67. Smith, N. A., Jr., "Xenon Flashtube Brightness Temperature
Calibration," Special Report, University of Florida,
Department of Nuclear Engineering Sciences (January
1970),


150
94. Radziemski, L. J., Jr., Blaise, J., "Current Status of the Spectrum
of Uranium UI and UII," Atomic Spectroscopy Symposium,
U.S. Dept, of Commerce, Ed., Proceedings of Atomic
Spectroscopy Symposium, National Bureau of Standards,
Gaithersburg, MD, September 23-26, 1975, 124-125.
95. Slater, J. C., The Quantum Theory of Matter, (McGraw-Hill, Inc.,
New York, 1963), 326-349.
96. Shortley, G. H., "The Energy Levels of Rare-Gas Configurations,"
Phys. Rev. 44, 666 (October 1933).
97. Cowan, R. D., "Theoretical Calculation of Atomic Spectra Using
Digital Computers," J. Opt. Soc. Am. 58, No. 6, 808
(1968).
98. Cowan, R. D., "Atomic Self-Consistent-Field Calculations Using
Statistical Approximations for Exchange and Correlation,"
Phys. Rev. 163, No. 1, 163 (November 1967).
99.Stewart, J. C., Rotenberg, M., "Wavefunctions and Transaction
Probabilities in Scaled Thomas-Fermi Ion Potentials,"
Phys. Rev. 140, A!508 (November 1965).
100.Cowan, R. D., "Theoretical Study of pm p111-"' i Spectra." J. Opt.
Soc. Am. 58, No. 7, 924 (July 1968).


PLASMA THEORY AND DIAGNOSTICS
Plasma temperature and density diagnostics are based on the
assumption that relevant information can be extracted from theoretical
descriptions of microscopic plasma processes. Generally, plasma
constituents exhibit balance between the population and depopulation
of neutral and/or ionic energy levels. This implies that for every
excitation event (to use an example) there is a corresponding de
excitation, not necessarily brought about by the inverse excitation
process. Plasma particles that are excited and de-excited by the
same mechanism demonstrate detailed balancing. Arc plasmas are usually
considered to be collision-dominated in the sense that e -atom colli
sions cause most of the excitations and de-excitations. However,
radiative de-excitation can also be important as indicated by strong
photon output. Therefore, arc plasmas are rarely characterized by de
tailed balancing, and various approximations such as local thermo-
24
dynamic equilibrium (LTE) and parti cal LTE must be used.
II-l. Equilibriwn Considerations
25
Griem has developed criteria that indicate which equilibrium
state applies to a given plasma. Most of these tests set limits on
the dominance (or lack thereof) of collisional rates over radiative
rates. Griem developed the following criterion for complete LTE in
a hydrogen-1ike system:
(II-l)
5


99
83
calculations0 and the RHX calculations. Results are discussed in
Sec. VI-5. A flow diagram for RCG is given in Appendix B.
Parks used a relativistic Hartree-Fock-Slater self-consistent
99
field treatment to calibrate the scaled Thomas-Fermi potential. With
this potential, he computes one-electron wavefunctions for the opacity
calculations. The Thomas-Fermi model for heavy elements is adequate
until encountering electrons in overlapping levels and when matching
large and small radii boundary conditions. The scaled Thomas-Fermi
potential does not account for the exchange contribution to the electron
potential energy. The Hartree-exchange potential resembles the charac
teristics of the Hartree-Fock potential, and accounts for the exchange
terms in the central-field approximation. This implies that wavefunc
tions developed with the Thomas-Fermi potential often will exhibit a
greater uncertainty than those calculated with the Hartree-exchange po
tential. Even the energy eigenvalue calculations can be poor, as shown
for the 5f uranium binding energy in Fig. 1 of Ref. 83. The exclusion
of correlation effects in the Parks model is not a serious drawback and
98
may be inconsequential; however, omission of a detailed treatment of
actual coupling could be its most serious shortcoming. Large inaccura
cies are possible in line-pattern calculations and oscillator strengths,
particularly if one configuration in the transition array is not well
characterized by a pure coupling scheme. This situation arises often
in the case of uranium.


Fig. 111-5. Uranium arc electrical schematic.
co
CTi


FRACTIONAL NUMBER OF LINES
122
WAVENUMBER (iOOO cm1)
Fig. C-4. Fractional spectral line distribution in
Awavenumber interval for the f3 6d7s f3 7s7p
UII transition array.


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
ABSTRACT Vi
I. INTRODUCTION 1
II. PLASMA THEORY AND DIAGNOSTICS 5
11-1. Equilibrium Considerations 5
II-2. Plasma Radiation 8
11-3. Emission Coefficient Determination 12
II-4. Plasma Temperature 16
II-S. Density Measurements 25
III. URANIUM PLASMA EXPERIMENT HARDWARE 29
III-l. Uvani'um Plasma Generation 29
III-2. Uranium Plasma Stability 35
III-3. Data Acquisition 39
IV. LOW PRESSURE URANIUM ARC DATA REDUCTION 54
IV-1. Spectral analysis 54
IV-2. Temperature Measurement 55
IV-3. Density Measurement 63
IV-4. Emission Coefficient Determination 66
V. HELIUM-URANIUM ARC DATA REDUCTION 73
V-l. Spectral Analysis 74
V-2. Temperature Measurement 75
V-3. Density Measurement 75
V-4. Emission Coefficient Determination 76
i v


I. INTRODUCTION
With the advent of the nuclear age and the subsequent strong trend
toward development of uranium-based technology, research priorities con
cerning the nature of the uranium atom have acquired substantially in
creased importance. Initial involvement in metallurgical and nucleonic
properties was largely due to the apparent need for weapon fabrication
and later some aspects of reactor technology. By 1947 a new area of
interest was the study of uranium plasmas at high temperature (6 keV),^
for a physical understanding of energy release caused by nuclear detona
tions. This was the first significant attempt to model the uranium atom
using a quantum and statistical mechanical basis from which was extracted
thermodynamic and optical information. Eventually, interest was
generated in lower temperature (0.5 5 eV) uranium plasmas because of
the potential usefulness of plasma core reactors as a means for space
2-4
propulsion and possibly as an energy source for MHD power generation.
More recently, worldwide need for uranium isotope enrichment using laser
5-12
processes has opened a new and significant area which is stimulating
much basic research of the uranium atom. Uranium plasma research is also
influencing the development of nuclear-pumped laser systems. This
13 14
particular program has had some recent breakthroughs 5 which will
likely increase the research momentum on the study of neutral and once-
ionized uranium.
An accurate theoretical model of the uranium atom would represent
a monumental step in understanding complex atomic systems. The mathema
tical description of many-electron atoms has been attempted using several
1


Page
VI. THEORETICAL CALCULATIONS 91
VI-1. Introduction 91
VI-2. Terminology 91
VI-3. Configuration Selection 93
VI-4. Calculation of Oscillator Strengths 94
VI-5. Comparison of Results 100
VII. CLOSING REMARKS 104
APPENDICES
A: SAHA NUMBER DENSITIES AND NORMAL
TEMPERATURES 107
B: COMPUTER SCHEMATIC FOR THE COWAN RCG CODE 116
C: CENTRAL LINE AND OSCILLATOR STRENGTH
, DISTRIBUTIONS FOR SELECTED UII CONFIGURATION
PAIRS 118
D: REPRESENTATIVE ENERGIES OF SELECTED UI AND
UII CONFIGURATIONS 128
E: IJFb PHOTOABSORPTION EFFECTS OF THE
MARTENEY AND FLORIDA EMISSION COEFFICIENT
DATA 133
REFERENCES 143
BIOGRAPHICAL SKETCH 151
V


I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
- 1
/'
i
21-
Dr. Leon J/ Radziemski
Staff Member, Group AP-4
Los Alamos Scientific Laboratory
This dissertation was submitted to the Graduate Faculty of the
College of Engineering and to the Graduate Council, and was accepted
as partial fulfillment of the requirements for the degree of Doctor
of Philosophy.
Dean, Graduate School


85
apparent between 2500 and 4000 A in both the Miller and Marteney results
that is not evident in the Florida values. This discrepancy may be
caused by strong UFg absorption in this wavelength region. This can be
supported by Fig. V-5 which is a reproduction of some of the latest UFg
photo absorption and electron impact cross-section data
indicating significant UFg absorption at these wavelengths. It is un
likely that other candidates such as UFg, UF£, and F play a major role
in light absorption within UFg discharges because their mean free paths
89 90
are typically on the order of centimeters.
Recent and fairly conclusive evidence shows that Miller's meas
urements may exhibit a substantial absorption effect from cold layers
Q?
of UFg, particularly in the 2000- to 4000-A bandwidth. Spector per
formed a low-ternperature (700 to 1400 K) ballistic piston UFg absorption
experiment with results remarkably similar in magnitude and shape to
those of Miller whose temperature was a reported 10 000 K. The implica
tion of this similarity is that while the uranium plasma in the Miller
experiment may have been at 10 000 K, its emission/absorption charac
teristics were masked by such properties of UFg.
o
Unfortunately, the Miller data do not extend below 2500 A; however,
the Marteney and Florida results do extend into the vacuum uv. Both
o
indicate a small emission peak between 1400 and 1800 A. The Florida
o o
peak appears at 1500 A, while the Marteney peak is located at 1650 A.
The wavelength displacement between the two peaks cannot be explained by
experimental error and, therefore, is attributed to the nature of each
plasma and its associated emission/absorption mechanisms. The small
O
peak shown by the Marteney curve at ^ 1650 A is inconsistent with the
o
relatively large UFg absorption cross section in the 2000 to 4000 A


.4 CKNOWLEDGEMENTS
This work describes research performed within the Department
of Nuclear Engineering Sciences at the University of Florida and
also at the Los Alamos Scientific Laboratory in New Mexico. The
effort was financially supported by the National Aeronautics and
Space Administration (Contract NGR 10-0050089) and directed by a
committee composed of Dr. Richard T. Schneider, Chairman,
Dr. Hugh D. Campbell, Dr. Edward E. Carroll, Dr. Dennis R. Keefer,
Dr. John W. Flowers, and Dr. Leon J. Radziemski.
The author is grateful to Dr. Schneider for his constant en
couragement and suggestions throughout the duration of this inves
tigation. Dr. Campbell was of valuable assistance in maintaining
a realistic perspective as to the theoretical and practical limita
tions. Special thanks is given to Dr. Radziemski for his persistence
in encouraging the author to complete this work and also for the many
timely discussions regarding dissertation content.
The author wishes to show exceptional appreciation to
Dr. Robert D. Cowan for his willingness to allow the use of his
atomic structure code and the sharing of his insight related to these
computations. It was indeed a great honor to have worked with
Dr. Cowan in this regard.
Because of the extensive nature of the effort required for the
successful completion of this research, many people became involved,
both students and faculty alike. The author wishes to convey his



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142
WAVELENGTH (A)
Fig. E-8. Marteney Ar-UF6 emission coefficient data as altered
by photoabsorption unfolding for 5.0 cm of UFg.


PRESSURE (atm)
115
Fig. A 7. Pressure vs normal temperature of
neutral and singly-ionized uranium in LTE.


8
12 -3
limit is then 2.93 x 10 cm If partial LTE is assumed, the larg
est energy gap need only be defined above the thermal energy limit.
In conclusion, although there is no feasible way to determine
accurately the LTE limits on electron density for atomic and once-
ionized uranium, reasonable estimates can be obtained using Eqs. (11 -1)
and (11-2).
IT-2. Plasma Radiation
Many factors affect the net photon output from a plasma. Optical
depth and absorption are the most important. In many laboratory
plasmas, photons emitted from the plasma central region may be absorbed
en route to the outer boundary. The degree of trapping implies an
optical depth, x (x), which is simply the effective absorption coeffi-
~k
cient integral k"(x) over a given homogeneous plasma depth X. The
relation between the intensity I^(x) and energy emitted as a function
of the 1ine-of-sight depth into the plasma is governed by Eq. (11-3),
the equation of radiative transfer.
dl(x) e (x)
-t-V-t = I (x) r
dx (x) vv k^Tx)
(I1-3)
The specific emission coefficient, e (x), (energy/volume-wavelength-
time-solid angle) and e (x)/k^(x) is the source function of radiation
(energy/atea-wavelength-time-solid angle). The source function for an
LTE plasma is equivalent to the Planck function.
In this sense X connotes a homogeneous plasma depth, and the
subscript o implies that there is a spectral dependence to
T and k.


138
Fig. E- 4. Florida uranium emission coefficient data as altered
by photoabsorption through 5.0 centimeters of UFg.


CROSS SECTION
86
WAVELENGTH (A)
Fig. V-5. Photoabsorption spectrum of U F ^.


15
oscillations in the unfolding process if an exceptionally smooth in
tensity profile is not available. Substantial error (20 30%) on the
intensity profile measurement (especially for the outermost ring) will
be propagated to the central zone and will yield a poor estimate of its
emission value. For this situation, too many rings will introduce large
oscillations and an unacceptable error propagation. Obviously, there is
an optimum number of rings depending upon the overall intensity profile
shape and the experimental error value, particularly at the outermost
ring.
Many studies have dealt with various techniques to implement the
40-43
inversion but these primarily address algorithmic problems (inter-
44 42 43
polation, smoothings, etc). Kock, Nestor, and Bockasten
address error propagation by using numerical methods for inversion.
These analyses imply that the correct number of subdivisions is a direct
function of the experimental error in the outermost zone as well as
44
the shape of the intensity profile. When error in the outer zones
approaches 20% or more, four or five zones may define the limiting
accuracy.
To relate these considerations to the inversion of the wall-
stabilized uranium arc intensity data, a four-ring numerical unfolding
scheme was chosen because of time limitations involved in acquiring
zonal intensity data for more than four zones, and the experimental er
ror associated with the outermost zonal intensity was 'v +25%. When this
error is considered with a 10% calibration error and an estimate of
error for using only four rings, the total error estimate of central
zone emission coefficients ranges from 28 + 36%.


V-l. Spectral Analysis
74
The line spectrum emitted from the helium-uranium arc was identi
fied manually and cross-checked with the line identification computer
analysis of Kylstra.^0 Identified lines were highly correlated with
the known U11 spectrum. Only a few helium line possibilities were ob
served, which indicated a relatively pure uranium plasma. This spectrum,
as a whole, was significantly different in comparison with the low-
pressure arc plasma, and provided some evidence that operation from a
low- to a high-pressure arc was accompanied by a corresponding shift of
radiation dominance to UII in addition to a shift from lower to higher
temperature.
51
Comparison of helium-uranium arc spectra sets (ours and Randol's )
was first done on a wavelength basis. When superimposed, the two sets
of spectra were virtually indistinguishable. Both line sets were com
posed of line spectra at the same wavelength locations and emitted by
the same plasma constituent; namely, singly ionized uranium. This was
necessary but not enough to justify the assumption of similar tempera
ture and pressure (T-Pyjj)- The other necessary factor (provided most
of the lines were sharp) to insure similar T-Pyjj conditions was
consistency between the two sets of peak and half-width values. De
tailed study showed little discrepancy for the lines examined at the
arc centerline used in Randol's diagnostic analysis. Further, peak
and half-width values of these lines compared with those recorded at
different current, voltage, and pressure conditions showed discernible
differences which indicates the sensitivity of the comparison. There
fore, the centerline temperature and pressure of the constricted
51
helium-uranium arc plasma was approximately characterized by Randol


135
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// / i
'//! t
/y?\
/ y v\ \
3
f
¡¡r*
¡/¡¡\ !
/;//¡rw a
/ \ \ / /
///! I \ A i
/// / f
i% ¡¡Z / !
0A3 //
, A /f V
r/, A / ,00
a // V
\ /
r / o.y
o
"1
JLW //
A /-'x'
/ ¡
f \\ V /
\\
' w
7
v
uf6
o
UFe, DEPTH 1.5 cm
CO\!CENTRAT10L! [LVcs 11
6
16
¡6
:
i .0 L
2.0 xIO
4.0 x ¡0
, ,. 16
8.0 >,
LO x¡0
_L_.
¡ V.-' v.A-'
i A 00
I \W | Ci0 6\A\
I 0 6M.J OO
260
. >*\
5000
y s c\
wavelength (A)
Fig. E-l. Florida uranium emission coefficient data as altered
by photoabsorption through 1.5 centimeters of UFg.


89
this analysis does not resolve the disparity in emission coefficient
magnitudes as illustrated in Fig. V-4.
Shown in Fig. V-4 are differences in the absolute values of the
emission coefficient measured at given wavelengths. This question has
91
been addressed by Schneider, Campbell, and Mack, where an optically
thin plasma and an emission coefficient that is a direct function of
particle density was assumed. It was then possible to use the perfect
gas law to normalize the existing data to a common temperature and den
sity. (The exponential temperature dependence of the emission coeffi
cient was neglected.) The details of this comparison are an extension
of this study and will only be summarized. The Marteney and Florida
results agreed in the 1500 to 2200 A bandwidth. Beyond 2200 A the
Marteney and Miller results agreed in shape and magnitude but differed
o
from the Florida results by 1 to 3 orders of magnitude at 5000 A.
Flowever, if the exponential temperature dependence were considered in
the Miller (10 000 K) and Marteney (8500 K) data, their magnitudes
would differ as well. These disparities among the three sets of meas
urements may, to some extent, be attributed to UFg masking processes.
Substantial correlation in shape and magnitude resulted between Parks'
theoretical data and the Florida experimental results when the two were
normalized as previously described. The shape correlation can clearly
be seen in Fig. V-4.
In summary, the emission coefficient of a uranium arc plasma
(T 8000 K, P 0.01 atm) has been measured and compared with theory
and other similar experimental data. The Florida emission data were
measured from a relatively uncontaminated uranium plasma; the experi
mental comparison data were generated using UFg discharges exhibiting


1
i-
LO
I
C.I
i
k-
V
o
I
LO
u>
O
(i
4
10
10
WAVELENGTH (A)
F i g 111 -11 .
NBS deuterium lamp calibration curve,
Oriel lamp at 315 ma.


IV. LOW-PRESSURE URANIUM ARC DATA REDUCTION
IV-1. Spectral analysis
Spectra emitted by the low-pressure uranium arc plasma (r^ 300 torr)
were identified manually and by computer.^ They exhibited a mixture
of atomic (UI) and singly ionized (U11) uranium line structure, but
dominated by atomic uranium emission lines. For diagnostic purposes
the 3653.21 A and 3659.16 A UI emission lines were used. The 3653.21
69 -1
line is reported to have upper and lower levels at 31 166 cm and
3801 cm respectively. It was selected primarily because of its
relatively high-lying lower and upper levels, which enhanced the possi
bility of evaluating energy states populated above the thermal limit if
o
partial LTE existed. The 3659.16 A line was chosen for the same diag-
O
nostic purposes (temperature and density measurements) as the 3653.16 A
line. Its transition is between levels 27 941 cm-"' and 620 cm
The first excited level of atomic uranium is 620 cm and it would be
less likely to meet LTE criteria. A comparison of temperature-density
diagnostics using the lines with two distinctly different lower levels
served as one useful indicator of the validity of LTE assumptions.
While energy level was a prime line-choice factor, the spectral lines
were also selected on a basis of wavelength, relative isolation (from
the other nearby lines), identification certainty, and availability of
transition probabilities for transitions considered.
54
O

17
Taking the natural log of both sides of Eq. (11-11) and rearrang
ing terms yield an equation analogous to that of a straight line:
1 n
( vu-h )
k v*)
(h n (T)£.. )
1n I- o 1_LL(
W¡T j
(11-12)
If for tv;o or more spectral lines, In (constant I )m is plotted
against E ("in" refers to a particular transition), the resultant
slope of the curve will approximate -1/kT. If I is measured in abso
lute units, the ordinate intercept also determines the LTE ground state
number density for that species.
Equation (11-12) was developed considering complete LTE and can be
modified for use with less restrictive equilibrium concepts. When
partial LTE is assumed, the Boltzmann plot method for complete LTE is
modified to yield
where: E^ = energy level of lower energy, and
g£ = lower level statistical weight.
The essential difference between Eq. (11-12) and Eq. (11-13) is that
the intercept term no longer defines the true ground-state density in
partial LTE.
Application of the Boltzmann plot technique for relative or abso
lute temperature determination requires the following conditions:
(1) at least partial LTE must exist in an optically thin plasma,
(2) many transitions should be used,


accepted a staff position within the Diagnostic Design Radiation-
Hydrodynamics Group (J-15) at the Los Alamos Scientific Laboratory
in New Mexico where he is presently located.
Joseph Michael Mack, Jr., is married to the former Hazel Luci
Robinson and is the father of Mark David, age ten.


146
41. Barr, W. L., "Method for Computing the Radial Distribution of
Emitters in a Cylindrical Source," J. Opt. Soc. Am. 52_,
No. 8, 885-888 (August 1962).
42. Nestor, 0. H., Olsen, H. N., "Numerical Methods for Reducing
Line and Surface Probe Data," Sci. Am. Rev. 2, No. 3,
200-206 (July 1960).
43. Bockasten, K., "Transformation of Observed Radiances into Radial
Distribution of the Emission of a Plasma," J. Opt. Soc.
Am. 51, No. 9, 943-947 (September 1961).
44. Kock, M., Richter, J., "The Influence of Statistical Errors on the
Abel Inversion," Wright-Patterson Air Force Base, Office
of Aerospace Research, AF61(052)-797 (November 1967).
45. Hefferlin, R., "Diagnostics in Field-Free Plasmas with Medium-
Dispersion Optical-Spectrographic and Source Monitoring
Equipment," Pergamon Press, Oxford and New York, re
printed from Progress in High Temperature Physics and
Chemistry, C. W. Rouse, Eds. (Pergamon Press, Oxford and
New York, 1969) 149-229.
46. Lochte-Holtgreven, W., Plasma Diagnostics (North-Holiand-Amsterdam,
Inc., New York 1964T)
47. Usher, J. L., "Temperature Profile Determination in an Absorbing
Plasma," M.S. Thesis, University of Florida, Gainesville
(August 1971).
48. Usher, J. L., Campbell, H. D., "Temperature Profile Determination
in an Absorbing Plasma," J. Quant. Spectrosc. Radiat.
Transfer 12, 1157-1160 (1972).
49. Van De Hulst, H. C., Reesinck, J. J. M., "Line Breadths and Voigt
Profiles," Astrosphy. J. 106, 121-127 (April 1947).
50. Randol, A. G., III, Schneider, R. T., Shipman, G. R. "Measurement
of the Temperature and Partial Pressure of a Uranium
Plasma," J. Appl. Spectrosc. 24_, No. 2, 253-258
(March/April 1970).
51. Randol, A. G., Ill, "A Determination of High Pressure, High
Temperature Uranium Plasma Properties," Ph.D. Disserta
tion, University of Florida, Gainesville (August 1969).
52. Mack, J. M., Jr., "Temperature Profile Determination of a Uranium
Plasma in a Helium Atmosphere," M.S. Thesis, University
of Florida, Gainesville (June 1969).
53. Dejardin, G., Herman, L. "Remarques sur la Fluorescence du
Salicglate de Sodium," Seance 2A_, 651 -654 (1 936).


27
associated with inadequately defined atomic constants, there are problems
in defining the integrated-line intensity I in absolute units for a
vtotal
specific transition. Many practical considerations in the measurement of
1 are discussed in Ref. 36, but procedures for spectral-1ine-wing
total
overlap in complex spectra are especially interesting.
Uranium spectra show no isolated line structure; therefore, we must
find the peak magnitude and FWHM that can be used to define a corres-
49
ponding Voigt profile, a theoretical representation of the actual line
profile including wings. This area can be calculated analytically to
yield a good estimate of the integrated spectral-1ine intensity.
B. Pressure-Temperature Correlation (PTC) Technique
Partial pressure estimates of plasma constituents can be based a
50 51
pseudoanalytic approach such as the PTC technique. This method uses
a temperature profile correlation between experimentally determined and
calculated temperature profiles. The experimental profile is typically
established by the Boltzmann plot method, whereas the calculated profiles
are computed using the relative (norm) temperature method. Calculations
of radiation specie number densities and, hence, partial pressures are
inherent to the computed profiles. A family of calculated temperature
profiles is generated to be parametric in the plasma total pressure. Be
cause the experimental profile is an independent measurement, intersection
of this curve with that of the calculated profiles implies (with the aid
of the Saha equation) a plasma number density and partial pressure.
This method has the uncertainties found in applying the relative
(norm) temperature method (Sec. II.4C) as well as experimental inaccura
cies inherent in the Boltzmann plot technique (Sec. II.4A).
~k
Full-width at half maximum of peak intensity value.


REFERENCES
1. Jacobson, B. A., "The Opacity of Uranium at High Temperature,"
Ph.D. Dissertation, Univ. of Chicago, 1947.
2. Thom, K., "Introduction and Review of Research on Uranium Plasmas
and their Technical Applications," 1st Symposium on
Uranium Plasmas, University of Florida, Gainesville,
January 7-8, 1970.
3. Schneider, R. T., Thom, K., "Research on Uranium Plasmas and their
Technological Applications," Proceedings of 1st Uranium
Plasma Symposium, University of Florida, Gainesville,
January 7-8, 1970
4. Clement, J. D., Ragsdale, R. G., Williams, J. R., A Collection of
Technical Papers, Proceedings of 2nd Uranium Plasma
Symposium, Georgia Institute of Technology, Atlanta,
November 15-17, 1971.
5. Robinson, C. P., "Laser Isotope Separation," Annals New York Academy
of Science, 267, 81-92 (1976).
6. Dubrin, J. W., "Laser Isotope Separation," Lawrence Livermore
Laboratories report UCRL-75886 (November 1974).
7. Gillette, R., "Uranium Enrichment: Rumors of Israeli Progress with
Lagers," Science 183, 1172 (22 March 1974).
8. "The News in Focus," Laser Focus Magazine, Vol. 10, 10 (March 1974).
9. Moore, C. B., "Isotope Separation with Lasers," adapted from Moore's
article in Accounts of Chemical Research in Laser Focus
Magazine, Vol. 10, 65 (April 1974).
10.Metz. W. D., "Uranium Enrichment: Laser Methods Nearing Full Scale
Test," Science 1_85, 602 (16 August 1974).
11. "Highest Rate of Isotope Enrichment is Attained with Radiation
Pressure," in "News Update," Laser Focus Magazine, Vol. 10,
18 (October 1974).
12. Forsen, Harold EXXON Nuclear Company, personal communication,
July 1974.
13. Schneider, R. T., Thom, J., "Fissioning Uranium Plasmas and
Nuclear-Pumped Lasers," Nuclear Technology 27_, 34-50
(September 1975).
14. McArthur, D. A., Tollefsurd, P. B., "Observation of Laser Action in
CO as Excited Only by Fission Fragments," Sandia
Laboratories report SAND-74-01 (July 1974).
143


n
kSE ^ = negative absorption coefficient caused by stimulated
'v
emission at x, v.
Thus, i<2£ (x) represents an effective decrease in k'[x). If an energy
v
absorption transition by a bound electron of an atom is considered,
where u =-> upper level and £ => lower level, the description of line
absorption at a given frequency is given by
kk (x)
v
hv
£->u
n. B £ £->-U V' '
(11-6)
where = the frequency of the transition (s ^),
_3
n = population density of the lower state (cm ),
B = Einstein's probability for absorption (cm/g),
& >"U
cj) (v) = absorption line-shape function with
I <
^1 ine
j K
X = 1 ine-of-sight distance into plasma.
Similarly, the line emission coefficient for a homogeneous plasma
at frequency v is described by
hv
eL (x) T?
V
u->£
n A >£ (j) (v) ,
u u
(11-7)
where (x) is the specific line emission coefficient at v and plasma
v
depth x. Actually, a continuum emission coefficient should also be
considered for completeness, but this is not included here because of
its small (or inextractable) contribution. The population density
(cm ) of the spontaneous upper level transition and Einstein probabil
ity for such a transition are given by n^ and A ^(s ^), respectively.
The normalized line-shape function is indicated by <|> (v), such that


78
Because the intensity data were collected without a collimating lens,
no detailed spatial resolution was performed on the observed intensi
ties. However, a homogeneous plasma of 1-cm depth (the actual arc
plasma diameter) was assumed. The intensity was converted to an
approximation of the arc-centerline emission coefficient by simply
weighting each intensity value by the inverse of the arc plasma depth
(in this case 1/1). In general, this procedure yielded a conservative
estimate of emission coefficient and a slight distortion of the true
shape.
The calibrated and converted intensity values are shown in the
approximate form of emission coefficient values in Fig. V-l. There is
O
moderate emission in the 1000 to 2000 A bandwidth mostly caused by
overlapping line structure. This bandwidth has been rescaled in Fig. V-2
to expose more spectral detail. Figure V-2 indicates notable line
o
structure and one distinct emission peak at ^ 1550 A, partly caused by
grating response at the nominal blaze angle.
o
Grating scan uncertainty of +10 A and rather large slit widths made
precise wavelength location of the line structure unobtainable for com-
80
parison. Kelly, however, lists a rather intense cluster of lines at
0 0 o
1575 A, 1579 A, and 1585 A--consistent with our results. The emission
data shown in Fig. V-2 are one of many sets taken (at similar arc condi
tions) which were cross-referenced to eliminate noise and insure that
most of the residue be the desired signal.
o
Figure V-l shows the remainder of the spectrum to 4300 A. Many of
the known UII and some of the stronger UI lines were potentially iden
tified. Many unidentifiable lines could be of UII origin. There are


NUMBER DENSITY (cm
A 5. Uranium plasma Saha number densities,
P=0.0001 atm.
Fig.
LILLI


INVESTIGATION OF URANIUM PLASMA EMISSION
FROM 1050 TO 6000 A
BY
JOSEPH MICHAEL MACK, JR.
A THESIS PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1977


FRACTIONAL NUMBER OF LINES
126
Fig. C-8. Fractional spectral line distribution in
Awavenumber interval for the 5f3 7s2 5f3 7s8p
UII transition array.


FRACTIONAL OSCILLATOR STRENGTH (GF)
121
Fig. C-3. RHX transition array oscillator strength
distribution for UII f3 6d7s--f3 7s7p.


APPENDIX t
COMPUTER SCHEMATIC FOR THE COWAN RCG_ CODE
The information in Fig. B-l was taken from two sources9^and
represents the major steps in the RCG code for calculating oscillator
strength distributions used in this study. It is not meant to expose
the intricacies of the entire calculation but to present an overview of
the calculations reported in this study. Electrostatic interaction
95 k
parameters in the form of Slater radial integrals are denoted by F
and G1 for the direct and exchange contributions, respectively. The
ppin-orbit interaction term is indicated by £ and Eav is the average
energy of all states of a configuration.
116


50
where I^(A)
TSTD^
^STD^
^ARC^
VSTD^
varc^
2
arc intensity [ergs/cm -sec-A-str] at A,
2 0
standard source intensity [ergs/cm -sec-A-str] at A,
optical path reduction factor {%>) for the standard
source at A,
optical path reduction factor {%) for the uncalibrated
source at A,
response signal (volts) of optical system to standard
photon flux at A, and
response signal (volts of optical system to uncali
brated photon flux at A.
If the standard and uncalibrated sources are in identical orientations,
the optical path reduction ratio ^)/^ARC^^ cancel. The
system response will inherently be accounted for in the V^^(A) and
VstdU) signals. Equation (111 -1) is valid as long as is known,
o
in this case to the 1750 A cutoff of the deuterium lamp fused-silica
o
window. To apply Eq. (111-1) to wavelengths less than 1750 A, a system
o
response below 1750 A for the standard source intensity as a function
of wavelength must be assumed.
O
The wavelength dependence of system response below 1750 A was
assumed flat and equal to 1.0, which implies that the combined effect
of the incident (to the optical system) photon flux on transmittance
caused by losses in all of the intercepted optical elements is negli
gible. This is categorically not the case. However, such a tactic
provides a straightforward approach to a conservative estimate of the
correct absolute intensities. Relating this idea to Eq. (III-l), a
unique intensity implies a unique system voltage with no wavelength
dependence. Knowing the absolute intensity of the standard and its


2 8
Wilson have developed a test which depends on the energy level
structure of a specific atomic system, thus reducing the necessity
of assuming hydrogen-like character!'stics. This criterion (hereafter
called the ladder criterion) is more applicable to complex systems.
The ladder criterion presumes that the most difficult level to
populate will form the largest energy gap ascending the energy level
diagram. Existence of LTE in an optically thin collision-dominated
plasma is tested by
"e2cTe/23
where C = 1.6 x 10^ (McWhirter^).
The electron temperature Tg has units of K; the largest energy gap in
eV for the atom under study is (E^ E.). Equation (11-2) is not suf
ficient for LTE because e relaxation time, e -atom relaxation time,
and atom relaxation time must dominate whatever other transient phe
nomena occur in the plasma. Most stable steady-state arcs satisfy
these relaxation requirements.
To apply Eq. (11-2) to a uranium plasma it is necessary to define
the largest energy-level gap found in its level diagram. Complete
tabulation of this information is unavailable, but a representative
gap width may be defined by examination of the work by Steinhaus
18 19 29
et al. 5 and Blaise and Radziemski. Considering neutral uranium
(UI), the 620.323 cm-"* + 3800.829 cm-* levels provide the largest gap
-1 12 -3
3180 cm ). This implies an electron density of 7.2 x 10 cm
at 5500 K. Similarly for singly ionized uranium (U11), the largest
-1 30
gap is about 2126 cm (2294.70 -* 4420.87). Assuming an electron
temperature of 10 000 K (U11), the correspondng electron density


VI. THEORETICAL CALCULATIONS
VI-1. Introduction
Theoretical justification for computing quantitatively accurate
uranium plasma emission coefficients from first principles is nearly im
possible because complete quantum-mechanical description of the uranium
atom does not exist. There must also be theory (statistical mechanics)
which determines the level population densities and ultimately, emission/
absorption coefficients. However, it is possible to obtain useful infor
mation about relatively strong einission/absorption features as a function
of wavelength without the approach described above. This information is
in the oscillator strength calculations for those transitions in probable
and strong transition arrays located in the wavelength region(s) of
interest. Oscillator strength distribution can be a reasonable indicator
to the emission characteristies of the system at those wavelengths.
For singly ionized uranium the task of calculating transition array
oscillator strengths is still formidable--but possible. The procedure
used to acquire this information for correlation to the UII experimental
emission coefficients will be discussed.
VI-2, Terminology
Consistent terminology regarding atomic energy levels is necessary
for unambiguous discussions about atomic structure calculations. The
state of an atom is the condition caused by the collective motion of all
the atomic electrons. The state is specified by four quantum numbers for
each electron or a set of coupled quantum numbers for the entire atomic
91


105
ultraviolet was done with a tungsten standard and hydrogen discharge for
each respective wavelength region. Calibration below the wavelength
o
cutoff (1750 A) of the hydrogen standard was inferred by extrapolation.
23
Direct comparisons with similar experimental results by Marteney et al.
were understandably poor because of differing discharge systems and plasma
characteristics. The Marteney data were consistent in shape with our
results because of probable UFg photoabsorption in the Marteney experi
ment. The emission coefficient values of the Florida and Marteney efforts
agreed to within an order of magnitude if scaled to a common temperature
91
and density.
Comparison of our experimental results for singly ionized uranium
83
with Parks et al.u theoretical calculations using a relativistic scaled
Thomas-Fermi model, and those using the relativistic Hartree exchange
approach, provided insight into the origin of the vacuum uv emission and
strong emission at other wavelengths. The Parks calculation included a
statistical mechanical treatment of the calculated energy level popula
tion. The RHX computations defined only the oscillator strength distri
bution for selected transition arrays, which are useful for predicting
significant emission location as a function of wavelength. The Parks
and RHX calculations supported the experimental results to varying degrees.
o
The peak locations at 2100 and 2900 A were predicted by both approaches,
but for different reasons. The disagreement is explained by the
distinctions between the two models. Although the Parks calculations
did not extend through the vacuum uv, RHX calculations conclusively
O
predict the peak in UII emission coefficient observed at about 1540 A.
These theoretical-experimental comparisons indicate that substantial
success can be anticipated in predictions of qualitative features in the
wavelength dependence of emission from plasmas of very complex systems.


23
T P
Voltage signals V<~, V., and V.¡ are from a photomultiplier tube for the
ith LOS position. The voltages indicate background source intensity,
total attenuated intensity, and plasma intensity, in that order. The
il..j in Eq. (11-16) represents the length segments in the ring along
+* h
the i LOS position as shown in Fig. 11 -1. Figure 11-3 shows a typical
oscillogram of the photomultiplier output related to Eq. (11-16). The
background source of known characteristics (Xenon flashtube) is flashed
on the line-center of interest as shown on the upper trace. The lower
trace shows the flashtube signal spread in time to facilitate intensity
voltage measurement. The oscillograms are recorded at different chordal
positions of the plasma and Eq. (11-16) is used to determine the line-
center absorption profile across the radial dimension of an assumed
cylindrically symmetrical arc.
The temperature is determined by an extension of the brightness-
emissivity method to the inhomogeneous case. The technique uses measured
voltages and calculated line-absorption values. The temperature method
requires that the background source temperature (or equivalently, the
intensity) be known. The average temperature in the ring of the
plasma is determined from
The Planck functions and B- represent intensities of the background
t h
source and the j plasma ring at wavelength A, and T^ is the brightness
temperature of the background source. The B.'s.are calculated using the
J
measured voltages and the computed plasma absorption profile. The
complicated expression for B- is found in Ref. 47.
U
In
1 +
B.
J
eC2/^Tb -j
(II-17)


CENTRIFUGAL
WATER PUMP
Fig. Ill-4. Coolant system schematic.
GO
4^


21
ev(ri) Z[T(rQ)] nT(r.)
(11-14)
ev(ro} Z[T(r.)] nT(ro)
T(r.) T(r )
i v o'
Any temperature on T(r), determined by other independent methods,
will suffice for T(r ).
v o'
The relative temperature method is particularly straightforward
when dealing with the norm-temperature situation. Transition probabili
ties are not needed, but the temperature dependence of partition function
should be considered. Only one transition need be used, thus eliminating
any calibration procedures. This method is very attractive for use with
spectroscopically complex plasmas because it is independent of gA values.
D. Modified Bvightness-Emissivity Method
Temperature measurement methods previously discussed require the
assumption of negligible absorption or an optically thin plasma. If
certain spectral lines emitted by a thin plasma have measurable absorp
tion (say at the spectral-line centers), temperature may be determined
using spectral-1ine absorption as a basis.
ik
The brightness-emissivity method (BEM) adapts the radiative-
transfer equation (Eq. (11-3)] solution to a homogeneous LTE absorbing
46 47
plasma. The following equations form the basis for this method.
T
Iv(x) = Iv(o) e
Emissivity, as considered in this instance, is the ratio of the plasma
intensity to the Planck intensity at a specified temperature and wave
length.


144
15. Slater, J. C., Quantum Theory of Atomic Structure, Volumes I and II,
(McGraw-Hill, Inc., New York 1960).
16. Herman, F., Skillman, S., Atomic Structure Calculations (Prentice-
Hall, Inc., Englewood Cliffs, N.J. 1963).
17. Cowan, R. D., Los Alamos Scientific Laboratory, unpublished notes,
1971.
18. Steinhaus, D. W., Phillips, M. V., Moody, J. B., Radziemski, L. J.,
Fisher, J. J., Hahn, D. R., "The Emission Spectrum of
Uranium Between 19080 and 30261 crrH," Los Alamos
Scientific Laboratory report LA-4944 (August 1972).
19. Steinhaus, D. W., Radziemski, L. J., Cowan, R. D., Blaise, J.,
Guelachvili, G. Osman, F. B., Verges, J., "Present
Status of the Analyses of the First and Second Spectra
of Uranium (UI and U11) as Derived from Measurements of
Optical Spectra," Los Alamos Scientific Laboratory
report LA-4501 (October 1971).
20. Schuurmans, P. H., "On the Spectra of Neodymium and Uranium,"
Physica 1J_, 419 (February 1946).
21. Kiess, C. C., Curtis, J. H., Laun, D. D., "Preliminary Description
and Analysis of the First Spectrum of Uranium."
J. Res. Natl. Bur. Stand. 37, No. 57 (July 1946).
22. Miller, M. H., "Measured Emissivities of Uranium and Tungsten
Plasmas," Proceedings of 2nd Uranium Plasma Symposium:
Technology, Atlanta, Georgia (November 15-17, 1971).
23. Marteney, P., Mensing, A. E., and Krascella, N. L., "Experimental
Investigation of Spectral Emission Characteristics of
Argon-Tungsten and Argon-Uranium Induction Heated
Plasmas," United Aircraft Corporation NASA report
CR-1314 (1969).
24. Drawin, F., Felenbok, P., Data for Plasmas in Local Thermodynamic
Equilibrium (Gauthier-Viliars, Paris, 1965).
25. Griem, H. R., Plasma Spectroscopy (McGraw-Hill, Inc., New York
1 964TT
26. Griem, H. R., "Validity of Local Thermal Equilibrium in Plasma
Spectroscopy," Phys. Rev. 131, 1170 (1963).
27.McWhirter, R. W. P., "Spectral Intensities," in Plasma Diagnostic
Techniques, R. H. Huddlestone and S. L. Leonard, Eds.
(Academic Press, New York, 1965), Ch. 5, 206.


V. HELIUM-URANIUM ARC DATA REDUCTION
The objective of this phase of research was the investigation of
uranium plasma emission at higher temperature (than that of the low-
pressure uranium arc) from the visible through portions of the vacuum
ultraviolet wavelength region. The experimentally observed levels of
UII (singly ionized uranium) extend up to 50 000 cm 5 and the
ionization energy is about 100 000 cm-"'. Hence, UII line structure is
likely to appear in the visible, uv, and vacuum uv wavelength regions.
For this reason a uranium arc which produced strong UII radiation and
51
operated under conditions similar to those observed by Randol and
. 52
Mack was used.
The uranium plasma for the present study was generated with the
identical configuration as the low-pressure arc (Figs. 111-1 to 5).
Helium cover-gas at 3 atm was added; the arc current and voltage were
maintained at 30 A and 35V, respectively. Current-voltage and arc
emission characteristics were controlled to duplicate those determined
51
by Randol to infer temperature and density from his photographic
diagnostics. This was an important consideration because our uranium
arc was too unstable for accurate photoelectric temperature and density
diagnostics such as those performed on the low-pressure arc. This
inference seemed reasonable, if spectral similarity (line location,
half-width, and peak values) for arc plasmas generated by cascade and
free burning systems at the same pressure-current-voltage conditions
could be established within the error limits of Randol's temperature
and density measurements.
73


134
Presumably, the Marteney data have UFg photoabsorption contamina
tion at the strenghs defined by UFg layers of 1.5 to 5.0 cm and molecular
concentrations of 1 x 10^ to 1 x 10^ cm The reciprocal absorption
strength factors were also folded into the matreney data to remove the
potential UFg photoabsorption effects, thus yielding an uncontaminated
uranium emission coeffienent. These results are displayed in Figs. E-5
through E-8.


Fig. IV 3. Effect of radiation on arc profile.


NUMBER DENSITY (cm
112
Fig. A-4. Uranium plasma Saha number densities,
P = 0.01 atm.


NUMBER DENSITY (cm
109
19
TEMPERATURE (K)
Fig. A-l. Uranium plasma Saha number densities,
P=3 atm.


FREE-BURNING
ARC
CAR
STABILIZED
ARC
Fig. III-6. Uranium arc configurations.
TUBE-STABILIZED
ARC
SEGMENTED-STABILIZED
ARC
QUARTZ TUBE
-WATER-COOLED
COPPER SEGMENTS
rr
T1
I
H- -T-
-M
H
=zi
\
(D)
GO


120
5 10 i5 20 25 30 35 40 45
WAVENUMBER (1000 cm1)
Fig. C-2. Fractional spectral line distribution in
Awavenumber interval for the f3 6d7s--f3 6d7p
UII transition array.


FRACTIONAL OSCILLATOR STRENGTH (GF)
Fig. C-7. RHX transition array oscillator strength
distribution for UII 5f3 7s2--5f3 7s8p.


137
Fig. E-3. Florida uranium emission coefficient data as altered
by photoabsorption through 3.0 centimeters of U F g .


44
region is reported only for the helium-uranium arc plasma because of
its relatively higher temperature and correspondingly stronger emission
in this wavelength region. The low-pressure arc did not have noticeable
emission in this wavelength region.
In some instances, it was physically impossible to interchange the
source with a reference standard at the same location; therefore, we
used a symmetric arrangement of the calibration and uranium sources in
which the light-path attenuation for either source was identical. We
eliminated unwanted stray radiation from within the spectrograph, which
is particularly critical in the vacuum uv where the signal detection is
o
difficult. Many intensity-wavelength scans were taken below 2000 A
with a deuterium lamp (Oriel, C-42-72-12) in several orientations after
each helium-uranium arc run to insure optimal signal transmission.
These signals were carefully checked to minimize higher order contami
nation and internal reflections.
C. Intensity Calibration
For radiation calibration in the visible and near-uv wavelength
regions, the tungsten lamp and the positive crater of a carbon arc as
standards are adequate; however, these sources are unacceptable for
55
lower wavelengths because of the weak intensities below 2500 A. In
o
fact, below 2500 A there are few commercially available standard cali
bration sources. LTE hydrogen discharges (fill gas is either hydrogen
or deuterium) are the best potential sources, but they require exten
sive investigation for their own respective properties. The theoreti
cal description of the hydrogen atom is essentially complete, and once
the electron densities are known, the intensities are computed and
cross-checked by experiment to provide calibration information for


149
81. Kylstra, C. D., Schneider, R. T., Campbell, H. D., "Uranium Plasma
Emission Coefficients," AIAA 6th Propulsion Joint
Specialist Conference, San Diego, California, June 15-19,
1976, AIAA Paper 70-692.
82. Spector, J., "Absorption Coefficient of Uranium Hexafluoride
Measured by a Ballistic Piston Compressor," M.S. Thesis,
University of Florida, Gainesville (1973).
83. Parks, D. E., Lane, G., Stewart, J. C., Peyton, S., "Optical
Constants of a Uranium Plasma," Gulf General Atomic
Incorporated report GA-8244 (NASA-CR-72348),
(February 1967).
84. DePoortter, G. L., Rofer-DePoorter, C. K. "The0Absorption
Spectrum of UFg from 2000 A to 4200 A; Digitized Form,"
Internal Memorandum, Los Alamos Scientific Laboratory
(May 1976).
85. DePoorter, G. L., Rofer-DePoorter, C. K., "The Absorption
Spectrum of UFg from 2000 to 4200 A," Spectroscopy
Letters, 8, No. 8, 521-524 (1975).
86. Srivastava, S. K., Cartwright, D. C., Trajinar, S., Chutjian, A.,
Williams, W. H., "Photoabsorption Spectrum of UFg by
Electron Impact," J. Chern. Phys. 65^, 208 (1976).
87. McDiarmid, R., "Assignments in the Electronic Spectrum of UFg
J. Chem. Phys. 65, 168 (1976).
88. Trajinar, S., Jet Propulsion Laboratory, Pasadena, California,
unpublished research, 1976.
89. Hay, P. J., Cartwright, D. C., "Rydberg, Conic, and Valence
Instructions in the Excited States of F2," Los Alamos
Scientific Laboratory report LA-7639 (1976).
90. Steurenberg, K. K., Vogel, R. C., "The absorption Spectrum of
Fluorine," Journal of American Chemical Society 78,
901 (March 1956).
91. Schneider, R. T., Campbell, H. D., Mack, J. M., "On the Emission
Coefficient of Uranium Plasmas," Nuclear Technology
20, 25 (October 1973).
92. Shore, B. W., Menzel, D. H., Principles of Atomic Spectra,
(John Wiley and Sons, Inc., New York 1968), 370.
93. Cowan, R. D., Los Alamos Scientific Laboratory, personal communi
cation, October 1976.


Fig. III-8. Xenon flashtube firing and delay schematic.


43
to obtain the spectral emission coefficient c (r), where r is the radi-
A
al distance from the arc center. The limited arc stability duration
prevented more than four acceptable LOS intensity measurements. Oscil
loscope O2 was used to trigger the signal-averager sweep at the desired
wavelength. Ultraviolet transmission through the optical system was
carefully investigated to be certain that no glass was present and to
o
study the system attenuation properties. The 2537 A Hg spectral line
generated by a very stable mercury discharge was chosen for these pur
poses. The line was transmitted with negligible attenuation and con
tamination signals produced by internal reflections within the spectro
graph were removed with baffles.
The photomultiplier used with was an EMI-9514 with a sodium
salicylate window which acted as wavelength shifter from the ultraviolet
to the visible. The phototube-sodium salicylate combination greatly
improved the system wavelength sensitivity to ultraviolet and vacuum
ultraviolet radiation. Sodium salicylate was ideal for use in the uv
and vacuum uv because it possesses a nearly constant quantum effi-
0 0 53
ciency from 500 A to 3300 A. The fluorescent radiation spectral
o o
distribution maximum is 4300 A and 10% of the maximum at 3800 A and
0 46 53 54
5300 A, 5 which conforms to the maximum wavelength response of
many photomultipliers.
For vacuum uv intensity detection the McPherson (Model 218) spec
trograph designed to be responsive at wavelengths in the vacuum uv was
used in conjunction with the photomultiplier signal-averager system
previously described. This particular spectrograph contained magnesium
fluoride-coated (Al + MgF£) optics, a 2400-groove/mm grating biased for
0
1500 A, and a vacuum capability of at least 0.001 y. The vacuum uv


65
________ thermal limit
Cross-sections for Cross-sections for
Collisional processes > Radiative processes
Dq ground state
Fig. IV-4. Energy-level diagram with thermal
limit.
When complete LTE exists, the population density of each level is de
fined by the Boltzmann Factor, n /n a exp[-E /kTl. Flowever, if
partial LTE prevails, the population of levels below a thermal limit
are influenced by radiative de-excitation from upper levels and self
absorption, particularly with transitions terminating at the ground
level. Detailed definition of level population for uranium is
virtually impossible, but in most cases one can argue that if partial
LTE holds, the levels below the thermal limit will be over-populated.
Thus, by assuming partial LTE and using complete LTE relations to
determine the ground-state density, an underestimate results, probably
proportional to some function of the thermal limit height above the
ground level. The thermal limit in the uranium system cannot be well
established; but from LTE criteria applied to the low-pressure uranium
arc (Sec. II.1), it is likely to be close to ground level. If the
thermal limit is close to ground level, the error incurred by using
complete LTE relations to determine the ground-state population is
"small." Because this is an order-of-magnitude measurement, such error
is most likely to be insignificant at these temperatures and pressures.


OSCILLATOR STRENGTH
Fig. VI-1. Comparison of UII oscillator strength distribution to
UII emission coefficient measurements.


46
10
(\j
e
£*
c
I
t-
to
\
£
H
LiJ
(/>
<£
Q
<
CC
-J
<£
Cd
l~
o
LU
n_
W
10
¡0
10
&
&
T
o

o
o
O C
.&
B (X ,T)
L /
^ X5 Iexp [p(I)/X] -!
~e
= <5 =0.45
P(i) = 5.5946 X 10*
250
jl__J 1 I
50 4 50
__i i I 1
550 650 750
850
WAVELENGTH (nm)
Fig. 111 9. NB S tungsten standard lamp calibration,
(EPUV-1 1 48) 35 amperes.


FRACTIONAL NUMBER OF LINES
124
30 35 40 45 50 55 SO 65
WAVENUMBER (1000 cm'1)
Fig. C-6. Fractional spectral line distribution in
Awavenumber interval for the f3 7s7p--f3 7s8d
U11 transition array.


35
during arc operation by parallel switching of air-cooled resistors into
or out of the circuit. Typically, this operating point was 50 A, 20 V.
The uranium arc circuitry is shown in Fig. 111-5. Current-voltage mon
itoring is accomplished on a continuous basis by Honeywell stripchart
recorders (not shown on Fig. 111-5).
Ill-2. Uranium Plasma Stability
Construction of a dc uranium arc was not difficult; however, de
velopment of a stab!e dc uranium arc which would allow photoelectric
diagnostics demanded extensive effort. For spectroscopic measurements,
this particular uranium plasma was required to be very stable for
density-temperature measurements and marginally stable for emission
measurements. Arc current, i was used as a stability yardstick.
Marginally stable implied average i changes 5, -10% over the entire
length of data collecting time with a maximum of 5l for instantane
ous i changes. Temperature-density stability is indicated by similar
average ic limits and by instantaneous variation of i < 21. The
University of Florida uranium arc evolved from a free-burning arc to a
rather sophisticated wal1-stabi1ized arc (Fig. 111 6). A brief account
of the development toward increased arc stability follows.
A. Free-Biaming Arc
For simplicity, a free-burning arc under a static helium cover gas
was used (Fig. I1I-6A). Unfortunately, motion of the anode and cathode
spots was inherent in its operation, and this caused unacceptable move
ment of the arc column as well as current-voltage fluctuations. There
is no agreement among arc physicists as to the reasons for these spot
movements; however, bibliographical information can be obtained from
Ref. 46. Many techniques were applied to reduce these instabilities,


APPENDIX D
REPRESENTATIVE ENERGIES OF SELECTED
VI AND UII CONFIGURATIONS
When estimating probable wavelength locations of transitions
between configuration pairs, the difference in average configuration
94
energies is useful. Radziemski and Blaise have tabulated energies of
the lowest known levels of ten configurations of UI and UII and this
information is shown in Figs. D-l and D-2. While the lowest level energy
is not the true average configuration energy, it is usually a good approx
imation. Also in Fig. D-3 are the average configuration energies, cal
culated by the RHX method, of the UII configurations used in this study.
129


2000 2500 3000 3500 4000 4500 5000 5500
WAVELENGTH (A)
Fig. I V-5.
Low pressure uranium arc calibrated intensity.


140
10"
L
O
t:
Ll.
LfJ
O

o
co
co
J
O
f~
O
Id
nr
q:
O
o
2
¡0
10
.0
¡0
10
¡0
1000
1000 2200 2600
WAVELENGTH (A)
3000
Fig. E-6. Marteney AR-UFg emission coefficient data as
by photoabsorption unfolding for 2.0 cm of UF
3400
altered
6


39
segmented-arc configuration was the final step attempted in the quest for
superior arc stability. Even with marginal stability at higher pres
sures, this system was employed for most of the experiments reported here.
III-3. Data Acquisition
Spectroscopic diagnostics required detection and analysis of radia
tion emitted by the uranium arc plasma. The experimental effort of this
research was composed of two broadly defined categories.
(1) the measurement of intensity (emission), and
(2) diagnostics for temperature-density determination.
Figure 111-7 illustrates necessary components for simultaneous measure-
o
ments of intensity (to 2500 A), temperature, and low-pressure arc den
sity. Intensity measurements which extended into the vacuum uv were
performed using a third spectrograph (McPherson Model 218, not shown)
designed specifically for use at low wavelengths. Temperature and den
sity for a high-pressure arc were inferred from photographic spectral
51 52
analysis completed by Randol and Mack using a free-burning arc at
similar I-V conditions. Details are in Chapter V.
A. Spectral Line Profile and Absorption Data for the Low-Pressure
Arc
The modified BEM (Sec. II-4D) was used to determine the line-center
absorption coefficient and characteristic plasma temperature for the
low-pressure arc. The background source was a xenon flashtube
(EGG FX-12-25). The firing and delay schematic is in Fig. Ill-8. Flash-
tube calibration information follows in Sec. III-3C.
Figure 111-7 shows the sequence which established line absorption,
temperature, and density: the beam splitter passed part of the arc
radiation to S|. A rotating refractor plate (quartz) in conjunction


DISTANCE FROM PLASMA £
Fig. II-2. Plasma emission-temperature profile.
PLASMA TEMPERATURE
DISTANCE FROM PLASMA C£_
no
o


(ergs/crn
Fig. V-l. Uranium plasma emission coefficient from the helium-uranium arc.


18
(3) these spectral lines should have a correspondingly significant
energy-level separation, and
(4) this technique can be used for inhomogeneous plasmas, but the
intensity data ideally should first be spatially resolved to
express the emission coefficient as a function of plasma radius
(in cylindrical geometry). If there is no spatial resolution
the computed temperature will be an approximate value, but in
many instances it will yield a good estimate of an average arc
temperature. The accuracy of these temperatures is governed by
intensity measurement and uncertainty in atomic constants. The
largest source of error for uranium plasmas is usually caused
by the uncertainty of gA values which can be as much as 50%.
Only in extreme cases will the average centerline temperature
deviate by more than 20% from the true centerline temperature.
To apply this method to uranium plasmas (or any method dependent on
gA values), availability of well-defined spectral lines is severely
limited. These lines must meet the previously mentioned requirements
and be locatable with the instrumentation to be used. Application of
the Boltzmann plot method to uranium plasmas is straightforward in
principle; but practically speaking, a very tedious task strongly de
pendent on spectrograph resolution, line identification, and availa
bility of relevant constants.
B, Norm-Temperature Method
If the equilibrium emission e (T) of a transition in a specified
ionic state is plotted against temperature, and if the temperature is
high enough, the resultant curve will be peaked at the norm-temperature
T defined on an emission-vs-temperature plot as the temperature


51
corresponding voltage at 1750 A in addition to the arc intensity system
O
response voltage for all wavelengths of interest below 1750 A, the
absolute arc intensity may be estimated by solving:
I
W1750 A) V
LARC 1 VCTn( 1751
Vstd(1750 A)
;arc^
(III-2)
Varc^^ re,tai'ns the system response to the arc intensity, but the
wavelength dependence of the system response to the standard intensity
cannot be recorded because of the window cutoff. Therefore, assuming
the negligible optical loss, the arc intensities are underestimated by
the composite optical loss factors and whatever molecular absorption
is present.
Whenever an approximation is applied, as was the case with the in
tensity calibration in the vacuum uv, an indication of uncertainty is
valuable. In this investigation the uncertainty was a function of the
attenuation of photon flux incident on the optical elements of the
system composed of a 10-mm LiF window, two spectrograph mirrors, the
sodium-salicylate phototube window, and the grating. (The spectrograph
mirrors and grating were Al-MgF^ coated). A composite wavelength-
dependent transmission curve can be constructed if transmission/reflec
tance data for each optical component are available. This total curve
can then weight the appropriate system response voltage, thereby re
covering (to a first approximation) the photon losses as the field
passes through the optical system.
Reflectance-wavelength information is available in the litera
ture
60,61
for coated and uncoated optics as is transmission data for
r o r o
LiF. The grating efficiencies for the McPherson 2400-groove/mm


70
applied. Following the above approach, the error for the central zone
emission coefficient shown in Fig. IV-6 should fall within -14% to +23%
Credibility of the shape and location of the important features on
the wavelength scale is questionable; unfortunately, there are no other
data recorded at the same conditions for comparison. However, compari-
18 19 79
son data exist 5 for qualitative assessment of credibility.
79
Krascella tried to approximate the intensity-wavelength distri
bution of an Argon-UFg system at temperatures varying from 5000 to
9000 K. Level populations were calculated through equilibrium rela
tions, whereas partition functions, atomic constants, and observed line
69
location were extracted primarily from Corliss arid Bozman. Using
this information the possible integrated line intensities were computed
o
and averaged over 100-A bandwidths. This semiempirical technique lacks
information about important quantities such as statistical weights,
accurate transition probabilities, uncertain UFg decomposition schemes,
and offers very incomplete uranium line structure tables. However,
this work was valuable in establishing observable spectral distribution
of electromagnetic radiation from uranium plasmas at various conditions
and was useful for comparison to our results even though Krascella
estimates had gaps. The comparison at least substantiated a trend in
the emission coefficient shape. No comparison was made between abso
lute values because of the diversity in systems.
A comparison is shown in Fig. IV-7 where the Krascella data were
shifted in magnitude to be superimposed upon our results which follow
the shape trend shown by Krascella. The irregularities in the
Krascella data (caused by the lack of experimental line data in the gap
regions) are expected and do not detract from the conclusion that the


72
two data sets are supportive. Thus, we have established corroborative
evidence of the shape credibility of the low-pressure arc emission co-
efficient.
The work of Steinhaus et al. also lends support to the major
o
peak location around 4000 A (for UI) and to the validity of the rapid
O
emission decrease below 3500 A. The range of experimentally observed
UI levels extends to 40 000 cm ^ on the energy-level diagram 5 eV).
This implies there are no known UI transitions below approximately
o
2500 A. Also, the bulk of known lines established by Steinhaus for UI
O
falls within 3300 to 6000 A, which also supports our information.
The Planck function for a blackbody temperature of IT 5500 K is
also plotted in Fig. IV-7 along with the emission data (different
units). Since the magnitudes of the arc emission and Planck intensity
are plotted logarithmically, the difference of these values at a spe
cific wavelength is an indication of the absorption coefficient, k^.
O
The value of k, is actually an average (over 100 A) because the emis-
A
o
sion coefficient is also averaged over 100 A. At all wavelengths
k, 0.034, thus implying an optically thin plasma. Line-center ab-
sorption coefficients can be significantly greater for some lines as
o o
illustrated by the line-center for the 3653 A and 3659 A UI lines.


52
grating blazed at 1500 A (Al-MgF£ coated) were furnished by Quartz
64
et al. Table III-l is a compilation of the relevant information which
allows construction of a composite system transmission curve. These
data provide an approximation of intensity calibration error (using
back-extrapolation) based on system optical losses. The quantum effi
ciency of the sodium salicylate phototube window was assumed to be
approximately unity with a constant wavelength dependence.
The composite efficiencies of Table III-l indicate that back-
calibration intensity values can be in error at the longer wavelengths
o
(1750 A) by a factor of 6 and more toward shorter wavelengths. A cali-
o
brated "signal" detected below 1200 A is suspect because of the sharp
LiF cutoff near 1200 A as shown by Table III-l.
Use of the xenon flashtube for temperature-absorption diagnostics
required a calibration for dependence of brightness temperature on
wavelength. This was accomplished by comparison (at a desired wave
length) of the system response to the xenon discharge and to an NBS-
67
calibrated tungsten-filament lamp. A xenon lamp brightness tempera
ture of 6745 K 100 K was established in a wavelength range of
3600 A + 5400 A.


102
(3) The experimental emission coefficient "shelf" between 1900 and
1750 A can be supported by the fairly strong TAOSD from the 5f^8s7p -
3
5f 7s8d configuration pair.
o
(4) The emission coefficient decrease at ^ 2500 A is validated by
o
a corresponding sparcity of oscillator strength between 2200 and 2500 A.
(5) Similarly, an observed emission coefficient decrease in the
O
1600 to 1700 A bandwidth is supported by a lack of oscillator strength
with similar qualification as mentioned in point 4.
(6) The 5f^7s^ 5f^7s8p TAOSD indicates good potential for a small
+ 74 0
but significant emission peak at 1539 g^ A, and it represents a
theoretical-experimetnal verification of prominent UII emission in the
vacuum ultraviolet wavelength region.
The Parks calculation, as far as it was taken in wavelength, re
produces the experimental results at the major peaks. He attributes
O
the appearance of distinct emission/absorption peaks at 2800 and 2200 A
3 2 3
to the transition array formed between the 5f 7s 5f 7s7p configuration-
83
pair for J = 1/2, 3/2 of the 7p electron. One can hypothesize a
corresponding enhancement of the oscillator strength at these wavelengths
for this transition array. However, the RHX calculation for the same
transition array shows three clusters of lines (Appendix C, Fig. C-10)
at 5890 A, 4000 A, and 2700 A, but only one distinct oscillator strength
o
peak at 2700 A (Appendix C, Fig. C-9). It is evident that the distinct
peaks predicted by the Parks model for J = 1/2, 3/2 of the 7p electron
are not predicted by the more sophisticated model of Cowan. The experi-
o
mental peak at 2100 A is predicted by the RHX calculation of the transi-
3 3.
tion array formed from the 5f 7s7p 5f 7s8d configuration-pair.


FRACTIONAL NUMBER OF LINES
128
Fig. C-1 0. Fractional spectral line distribution in
Awavenumber interval for the 5f3 7s2 5f3 7s7p
UII transition array.


ergs/cm sec
71
10
0<
i_
cn

to
4
10
10
2000
*cm2 FOR PLANCK FUNCTION
cm3 FOR PLASMA EMISSION
T (PLANCK) ~ 5500 K
T (PLASMA) 5500 K


(KPASCELl A,
|| T 5000 K, UI)
\ / MtL
\ *1 ^¡>0
\ i i / i-
i / \
v
\
\

(PRESENT RESULTS,
T 5500 K, UI)
-I
I
3000
4000
SOCO
6000
WAVELENGTH (A)
Fig. IV-7. Low-pressure uraniurn plasma emission
comparison to Planck intensity.
7000
coefficient


77
spectrograph (McPherson Model 218) was maintained at ^ 1 p. Separating
the pressure-vacuum (arc cel 1-spectrograph) interface was a 3/8-in.
Lif (lithium fluoride) window. The spectrograph grating contained
O
2400 grooves/mm and was blazed for 1500 A in the first order. The
sodium salicylate-phototube combination (described in Sec. III.3B) was
used to detect photons transmitted by the spectrograph.
After initial detection of a vacuum uv signal, we tried to elimi
nate possible undesirable signals caused by internal reflections, stray
light, etc. The McPherson spectrograph had a history of reflection
problems, so optical blockouts (baffles) were used on the two spectro
graph mirrors and the grating. The geometry of the baffles allowed
only the central image of a light source to pass through the spectrograph
to the exit slit, and the spectrographic internal reflections were
eliminated.
Arc intensity data were collected in two wavelength segments, from
1050 A to 1750 A and from 1750 A to 4300 A. These bandwidths were used
because the deuterium calibration standard had no valid calibration
o o
values lower than 1750 A. Intensities at wavelengths above 1750 A were
calibrated as described by Eq. (111.1). The calibration standard used
o
at wavelength > 1750 A was the Oriel deuterium discharge. This region
was cross-checked at several wavelengths using the tungsten filament
standard as a reference, and most of the uncertainty associated with the
deuterium calibration values was removed.
Accurate calibration of intensity data found in the vacuum uv region
O
below 1750 A by ordinary methods was impossible. Many of the difficul
ties encountered are discussed in Sec. III.3C; application of back-
extrapolation calibration (BEC) was necessary (see Sec. III.3C).


103
The disparity in peak identification between the Parks and Cowan
models lies in the theoretical approach. Emission peak location is
determined by level splittings caused principally by spin-orbit and
electrostatic (direct and exchange) interactions. For U11 Parks ne
glects the exchange portion of the electrostatic interaction energy
altogether; he also neglects the higher-order direct contributions as
sociated with equivalent electrons in the 5f orbital. The RHX calcu
lation indicates that not only are these interaction energies impor
tant, they are dominant, particularly with regard to transition array
line-cluster location and oscillator strength distribution. The RHX
coupled wavefunctions are certainly more accurate than those uncoupled
wavefunctions used in the Parks treatment. Most quantities dependent
upon wavefunction description (including oscillator strengths) reflect
the accuracy (or inaccuracy) of the wavefunctions used. Further, Parks
includes level populations in his calculations, but the main effect
of ignoring this feature is to produce changes in relative peak magni
tude when calculating emission coefficients, but not in the locations
of such peaks. However, the Parks calculations indicate strong emission
o
trends between 2300 and 4000 A, and in that sense, are supported by ex
periment and RHX theory. In fact, it is remarkable that, for the most
part, the Parks calculations came out as well as they did considering
the approximations used and the complexity of the problem.


64
The electron density, n for the low-pressure uranium arc will
generally follow the curve for singly ionized uranium. Saha equation
calculations of ng for a plasma with a total uranium pressure of
0.001 atm, T = 5500 K, predicts ng 6 x 10 ^ cm This is well
11 -3
within the LTE ladder criterion of 3.8 x 10 cm established in
Sec. II.1. Measurement of the electron density by an independent
technique such as a line broadening analysis was too uncertain, pri
marily because uranium lines lacked isolation and definition. There
fore, this effort was abandoned and no direct experimental evidence of
the magnitude of the electron density was obtained. However, similar
75
work of Voigt on a 5500 K uranium arc reported ng to be
13 -3
'u 5 x 10 cm This substantiated the assumption of ng large enough
for the present arc to be characterized by at least partial LTE nearly
at the ground level.
One of the more subtle aspects of this density determination was
the implicit assumption of complete LTE. Strictly speaking, this is
very difficult to realize, and one usually resorts to a commitment of
partial LTE. If partial LTE is valid, an exact density measurement
(using a diagnostic method which relies upon complete LTE, such as the
absolute line method) is not possible, and any attempt will be in error
because of this apparent conflict. The magnitude of this error can be
calculated for hydrogen and estimated for helium. Unfortunately, for
the case of uranium only a qualitative description of error direction
is valid.7677
The effect of the complete LTE assumption when there is only par
tial LTE can be understood by considering the population densities of
a simple energy level diagram as illustrated in Fig. IV-4.


97
Clearly,
gf | < 0.9 ]Sn + 0.436 3P I rI 3P1 > 12
si o o 1 1 1 1
= | 0.9 < ]SQ |r| 3P1 > + 0.436 < 3PQ |r( 3P > |2
3 ,,3 ?
= 0.19 | < PQ |r[ P1 > | .
In an assumed LS or JJ coupling scheme, mixing would not be mam'-
3 1
test and the P. -> Sq would be disallowed, resulting in gf = 0.
Because the eigenfunction for the state is a linear combination of
basis wavefurictions, the transition between levels 1 and 2 is allowed
3 3
by the appearance of Pq and P^. Mixing frequently does occur and
can play a major role in determining oscillator strength distribution
and magnitude of transition arrays between two configurations. For a
given energy matrix, transformation to JJ, LS, or intermediate basis
representation will produce the same line pattern.
Oscillator strengths were calculated for the UII configuration
97
pairs labeled in Table VI-1 with a computer code RCG created by Cowan.
Briefly, the code implements the relativistic Hartree exchange (RHX)
98
approach to calculate angular and radial wavefunctions in a basis
representation defined by the appropriate coupling scheme. Established
wavefunctions and energy eigenvalues are used to compute wavelengths
and magnitudes of oscillator strength allowed between two configura-
83
tions. Parks et al. attempted a similar calculation using a statis
tical model for level distribution and the Thomas-Fermi approach for
the one-electron wavefunctions. Table VI-2 illustrates the major
considerations of the Parks relativistic scaled-Thomas-Fermi (RSTF)


145
28. Wilson, R., "The Spectroscopy of Non-Therman Plasmas," J. Quant.
Spectrosc. Radiat. Transfer, 2_, 447-490 (1 962).
29. Blaise, J., Radziemski, L. J., "Energy Levels of Neutral Atomic
Uranium (UI)," J. Opt. Soc. Am. 66, No. 7, 644 (July
1 976).
30. Radziemski, L. J., Los Alamos Scientific Laboratory, personal
communication, December 1976.
31. Cooper, J., "Plasma Spectroscopy," Reprint from Reports in Physics,
29, Part I, 35 (1966).
32. Emmons, H. W., "Arc Measurements of High-Temperature Gas Transport
Properties," Phys. Fluids 9, No. 6, 1125 (June 1967).
33. Bott, J. F., "Spectroscopic Measurement of Temperatures in an Argon
Plasma Arc," Phys. Fluids 9_, No. 8, 1540 (August 1 966).
34. Lowke, J. J., Capriotti, E. R., "Calculation of Temperature Pro
files of High Pressure Electric Arcs Using the Diffusion
Approximation for Radiative Transfer," J. Quant.
Spectrosc. Radiat. Transfer 9_, 207 (1 969).
35. Lowke, J. J., "Predictions of Arc Temperature Profiles Using
Approximate Emission Coefficients for Radiation Losses,"
J. Quant. Spectrosc. Radiat. Transfer]^, 111 (1964).
36. Lowke, J. J., "A Relaxation Method of Calculating Arc Temperature
Profiles Applied to Discharges in Sodium Vapor," J. Quant.
Spectrosc. Radiat. Transfer 9, 839-854 (1969).
37. Giannaris, R. J., Incropera, F. P. "Radiative and Collisional
Effects in a Cylindrically Confined Plasma I.
Optically Thin Considerations, II Absorption Effects,"
J. Quant. Spectrosc. Radiat. Transfer 1_3, 1 67-1 95 (1 973).
38. Horman, H., "Temperaturvertei1ung und Electronendichte in
Freibrennenden Lichtbogen," Z. Physik 97, 539 (1935).
39. Park, C., Moore, D., "A Polynomial Method for Determining Local
Emission Intensity by Abel Inversion," National Aero-
Nautics and Space Administration (Ames Research Center)
TN-A3444 (October 1969).
40. Berge, 0. E., Richter, J., "Measurement of Local Spectral
Intensities in Case of a Nonuniform Light Source of
Radial Symmetry," Wriqht-Patterson Air Force Base,
Ohio, AFML-TR-66-165 (October 1966).


92
system. The ground state is the lowest energy state. A 1 eve! is repre
sented by the total angular momentum, J. The lowest energy level is
defined as the ground level. Several states can correspond to a given
energy level. Terms are collections of levels tagged by multiplicity S
and orbital angular momentum L. The statistical weight (distinct states)
in a level is 2J + 1; in a term (2S + 1)(2J +1). Definition of the n and
quantum numbers for each electron orbital specifies a configuration.
Electrons in equivalent orbitals are designated equivalent electrons. A
transition of an electron between two levels generates a spectral line,
whereas a multiplet is a group of transitions between two terms. Finally,
a transition array is composed of transitions allowed between two con-
fi gurations.
Coupling is the process whereby two or more electron angular momenta
are combined into resultant angular momenta. Regarding LS, JJ, and
intermediate coupling, the dominance of JJ over LS is expressed by the
relative magnitudes of spin-orbit and electrostatic contributions to
energy separation. Relative importance of spin-orbit interaction gener
ally increases with increasing Z and n (principal quantum number); thus,
for high-Z elements and large-electron orbits, JJ coupling would seem a
logical choice. Conversely, for low-Z and small electron orbits, LS
coupling would appear valid. However, at low- and high-Z there are many
92
exceptions to these rules of thumb; intermediate coupling is required
for many atomic systems. A good example of the rule-of-thumb breakdown
5
is in the highest energy level (J = 2) in the 2p 4f configuration of
neutral neon. The electron eigenfunction given in a pure LS basis rep-
93
resentation is composed of
3D? > + 0.567|1D2 >
0.681
+ 0.463


NUMBER DENSITY (cm
4000 6000 8000 10000 ¡2000 14000 16000
TEMPERATURE (K)
Fig. A-2. Uranium plasma Saha number densities,
P = 0.3 atm.


BIOGRAPHICAL SKETCH
Joseph Mighael Mack, Jr., was born October 26, 1944, at Clarksburg,
West Virginia. In May, 1962, he was graduated from McCook Senior High
School, McCook, Nebraska. He attended the University of Wyoming the
next five years and received his Bachelor of Science in Mechanical Eng
ineering with a Nuclear Option in June, 1967. At this same time he was
also commissioned a Second Lieutenant in the United States Army Corps
of Engineers. He is a member of the National Society of Scabbard and
Blade, Sigma Tau, and Omicron Delta Kappa. During the summer of 1966
he worked in the Device Division, Mechanical Engineering Department, at
Lawrence Radiation Laboratory, Livermore, California. The following
summer he worked in the Mechanical Engineering Department of Pacific
Gas and Electric Company, San Francisco, California. In September of
1967 he enrolled in the Graduate School of the University of Florida
in the field of nuclear engineering and received his Master of Science
degree in June, 1969. He then accepted the challenge to work toward
the degree of Doctor of Philosophy in nuclear engineering sciences at
the same institution and worked under a teaching/research assistantship
and Atomic Energy Commission Traineeship during this period. In October
of 1972 he took a senior staff position at the Martin Marietta Corporation,
Aerospace Division, Orlando, Florida. In 1974 came retirement from the
Corps of Engineers with the rank of Captain. In February, 1975, he
151


PRESSURE REGULATION SYSTEM
Fig. Ill-3 Pressure system schematic.
CO
OJ


NUMBER DENSITY (crn
111
4000 0000 8000 !00O0 12000 14000 16000
TEMPERATURE (K)
Fig. A 3. Uranium plasma Saha number densities,
P=0.1 atm.


60
The implication is that the electrical energy input to a steady-state
arc plasma balances the radiation and conduction losses (convection
being neglected). Conduction loss is governed by the temperature pro
file gradient; whereas, radiative losses are defined by the equation
of radiative transfer, Eq. (11-3).
Temperature profile curvature will be a function of the relative
magnitude of the conduction or radiation loss terms. If radiation
effects are negligible, conduction becomes the dominant loss mechanism,
resulting in an approximately parabolic temperature profile with a
34
comparatively high central temperature as shown in Fig. IV-3. When
radiation losses become important, the central temperature is generally
lowered and the profile shape flattened. Also included in Fig. IV-3
are the effects of self-absorption on the temperature profile. In
general, having zero absorption implies a smaller central temperature
caused by the larger radiation loss term. A flatter profile also re
sults because most of the curvature is caused by conduction near the
wall. When absorption is included, the result is an increase in cen
tral temperature and more radial curvature. The curvature of the
profile at the arc center is typically controlled by radiation losses,
while at the arc boundary such curvature is usually controlled by con
duction losses.
Several parameters affect the magnitude of conduction and radia
tion loss terms. Generally, wall-stabilized arcs exhibit high radia
tion losses at higher pressures, greater temperatures, smaller radii,
and at greater emission density of the dominant radiating plasma
constituent.^^5^ The current and pressure of the low-pressure
uranium arc would indicate that the temperature profile shape would


96
When wavefunctions and energy levels are established, atomic
spectra information can be acquired. Several types of transitions are
possible, but only electric dipole transitions will be considered here.
Electric dipole transitions are allowed only when the matrix element
in the dipole matrix is nonzero. The dipole matrix elements E are given
by
E = < T|r|r > (VI-4)
where T and XV' represent the wavefunction for the upper and lower energy
state, and < f|r|T" > indicates the average radius of an electron in a
stationary state T for the entire radiation process. The gf values
(statistical weight times oscillator strength) are directly proportion
al to the square of the appropriate dipole matrix elements. The actual
coupling can affect significantly the strength and overall location of
a given transition array oscillator strength distribution. A simple
example will illustrate this point.
Consider the case where the oscillator strength between the
JPl -> Sq levels is desired, where -- gf |< 't|r|Â¥" >| Suppose that
eigenvector composition is
Level 1
Level 2
3P] >=1.0 |3P1 >
1$Q > = 0.9 |]S0 > + 0.439
* 3
Level 1 is a pure Pq state and level 2 is a mixture of the
3
Pq basis wavefunctions.
> .
and
For a development of the concept of purity, see G. H. Shortley's
article, Ref. 96.


3
22 23
Miller and Marteney et al. have acquired emission coefficient
data from UFg shock-tube and radio-frequency induction-heated Ar-UFg
plasmas, respectively. Uranium plasma emission coefficients obtained
from UFg discharges present distinct impurity problems, potentially
resulting in distorted emission coefficient wavelength dependence.
A dc uranium arc was chosen as the light source for the present ex
periment to reduce plasma impurities and provide a steady-state, less
contaminated plasma to determine its emission properties. The wave-
o O
length bandwidth considered is from 1050 A to an upper limit of 6000 A.
The emission data are then compared to similar data generated by other
research groups. Also included is a comparison to theoretical emission
coefficient predictions. In summary, this effort was conceived to estab
lish a unified picture of the progress made over the past few years
concerning the experimental and theoretical investigations characterizing
uranium plasma emission.
Chapter II describes the plasma diagnostics necessary for the
determination of basic plasma properties such as temperature, particle
densities, and radiation. Particular attention is given to the applica
tion of such diagnostics to uraniurn plasmas. Uranium arc plasma genera
tion and arc stability are discussed in Chapter III. Also examined are
the various methods of data acquisition and intensity calibration applied
in the course of this investigation. Chapters IV and V indicate the
emission measurements for uranium plasmas at two distinct arc conditions.
Brief descriptions and comparisons of other similar experiments are
given amoung these, the present effort, and theoretical predictions.
In Chapter VI theoretical models of the uranium atom are critically
considered. A comparison is made between emission peak locations of the


Abstract of Thesis Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
INVESTIGATION OF URANIUM PLASMA EMISSION
FROM 1050 TO 6000 A
By
Joseph Michael Mack, Jr.
December 1977
Chairman: Dr. Richard T. Schneider
Major Department: Nuclear Engineering Sciences
Absolute emission coefficient measurements on arc-generated
uranium plasmas in local thermodynamic equilibrium are described for
O
a wavelength bandwidth of 1050 to 6000 A. Low- and high-pressure arcs
were investigated for their emission properties, characteristic tem
peratures and uranium partial pressures. Temperatures from 5500 to
8000 K and uranium partial pressures from 0.001 to 0.01 atm were found
at the arc centerline. The new emission data are compared with other
similar experimental results and to existing theoretical calculations.
The effects of cold-layer UFg photoabsorption on uranium plasma emis
sion characteristics are established for UF^. molecular densities
o
16 17 3
ranging from 1.0 x 10 to 1.0 x 10 cm" and layer thickness from
1.0 to 5.0 cm.
VI


100
VI-5. Comparison of Results
Figure VI-1 is a collective plot of the RHX oscillator strength
distributions, the Parks theoretical emission coefficient STF calcula-
83
tion, and the experimentally determined UII emission coefficient, all
as a function of wavelength. Only the RHX oscillator strengths relate
to the absolute values found on the ordinate, whereas the Florida and
Parks emission coefficient curves are slightly distorted in the rela
tive magnitude but the major inflection points have been preserved.
This plot format shows only the significant features of the experimen
tal emission coefficient curves for comparison to theory; magnitude
was discussed in the previous chapter. For each transition array
oscillator strength distribution (TAOSD) shown in Fig. VI-1, the TAOSD
and the correspondng fractional number of spectral lines per wavelength
3 2 3
interval are plotted in Appendix C. Plots showing the 5f 7s 5f 7s8p
3 2 3
and 5f 7s 5f 7s7p transition arrays clearly show that many spectral
lines in a cluster do not insure strong oscillator strength and strong
emission.
In general, the Parks and RHX calculations support the variation in
shape in the Florida experimental emission coefficient. Several posi
tive points are made when comparing the RHX calculations with the
Florida measurements.
(1) For our configurations, the strongest emission is likely to
o
occur in the 2500 to 5000 A bandwidth.
, + OCfl 0
(2) An overall peak is likely in TAOSD at 2700 ^qq A, with a
relatively smaller peak at 2041 +_ ^ A.


I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
Dr. Richard T. Schneider, Chairman
Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
.,!/. L'' L L t- / <3 > fi () C'\
Dr. Hugh D. Campbell 1 *
Associate Professor of Nuclear Engineering
Sciences
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
?
/ (
i /
.i
/ /
L.
1.
-
Dr. Edward E.
Professor of
Carrol 1
Nuclear Engine
lering Sciences
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presentation and
is fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
//
S-Cl
/
Dr. Dennis R."Keefer /(
Associate Professor of Engineering Sciences


2
15-17
methods imbedded with various approximations. In many situations,
experimental results are available to substantiate theory or at least to
raise questions about the validity of certain aspects of theoretical
treatment. Currently, there is little conclusive theoretical-experimental
validation of the atomic properties of uranium and uranium plasmas. How
ever, there is a significant effort under way by Steinhaus et al
to establish experimentally the energy levels of neutral and once-
20
ionized (UI and U11) uranium. This effort evolved from work by Schuurrnans
21
and Kiess et al. in 1946. With subsequent improvement in opticsspectro
scopic techniques, and atomic structure calculations, confidence is increas
ing in energy-level definition but progress is slow.
The specific emission coefficient e. (T,P) characterizes the light
A
emission from a volume element of plasma. It is defined as the amount
of energy emitted per unit time, from a given volume, into a specified
solid angle and wavelength interval. It can be composed of continuous
and/or discrete components, both of which are strong functions of plasma
temperature and density (pressure) of the radiating species. The form
ulation of an adequate theoretical model of the uranium atom can be
strongly assisted (perhaps out of necessity) by obtaining from experi
ment detailed knowledge of the uranium emission coefficient. Because
calculation of such a property (for uranium) is impossible without a
model that suffers from several approximations, experimental verfication
through emission coefficient measurement is needed. This thesis reports
on an experiment designed to measure the specific emission coefficient
of a uranium plasma and to relate these data to state-of-the-art
theoretical predictions.


136
WAVELENGTH (A)
Fig. E-2. Florida uranium emission coefficient data as altered
by photoabsorption through 2.0 centimeters of UFC.
b


32
shown undersized, and the plasma column was actually in contact with
several of the water-cooled disks. The segmented assembly also acts
as thermal shield for the pressure seals and as an effective particle
shield to lessen deposition on the viewport window.
C. Pressure System
A schematic representation of the pressure system, designed for
flexibility of regulation from 0-2000 psi, is shown in Fig. 111-3.
Adequate cell exhaust filtering removes uranium which might escape to
the atmosphere. The vent on the downstream side of the cell or the
roughing pump on the upstream side provides particulate venting. The
high-pressure gas supply is isolated for safety in case of electrical
power failure. A high-pressure solenoid valve, normally closed, pro
hibits gas flow unless the solenoid is energized.
D. Coolant System
Enough coolant must be supplied to the segmented assembly, anode,
and ballast resistor. The cathode is primarily convection-cooled by
the surrounding segmented assembly. The 60-psi water-line pressure pro
vides adequate cooling for an arc power input of at least 100 watts;
however, a centrifugal pump provides more flow if necessary. These
features are shown in Fig. 111-4.
E. Power Supply System
Two 650 A, 120 V dc, diesel motor generators arranged in a series
are used as the primary source of electrical power for arc operation.
They can be operated remotely or at the generator controls as a con
tinuously adjustable voltage supply. Current through the arc circuit
is limited by air- and water-cooled ballast resistors. The fuse limit
is 300 A, 250 V. Current is adjusted for a given set of electrodes


Fig. 11 3. Oscillogram of photomultiplier output.


recognition of the assistance given by the following:
Dr. Chester D. Kylstra, Arthur G. Randol, Nova! A. Smith, John L. Usher,
Bruce G. Schnitzler, George R. Shipman, Jeff Dixon, George Fogel,
Kenneth Fawcett, Peter Schmidt, Ralph Nelson, and Willie B. Nelson.
The author is further indebted to his secretaries at the
Los Alamos Scientific Laboratory, Ofelia M. Diaz and Delores M. Mottaz,
for their persistence in the painstaking labor which went into the
typing of the manuscript.
Financial support through the University of Florida Assistantship
Program and the Atomic Energy Commission Traineeship plan is acknowl
edged.


26
emitted from a homegeneous optically thin LTE plasma. Modification to
an absorbing plasma requires compensation (build-up) along the entire
line-shape profile. Obtaining absorption build-up factors at many
points along the line profile may not be possible because of line-wing
overlap, especially in plasmas displaying complex spectra where
isolated lines may not exist. Fortunately, absorption in many arc
plasmas tends to be concentrated at spectral-1ine centers (on the wave
length scale). Therefore, an absorption coefficient determined at the
spectral-1ine center approximates, to a usually acceptable degree, the
maximum absorption coefficient taken over the entire line profile. This
remains a good approximation as long as the spectral line exhibits a
sharp profile. Using the above as a basis, absorption build-up may be
incorporated into the line-intensity equation by the following:
^total
hv
u->£
4tt
JL A
Z A
u
-E /kT
n e u e £.. y
o ij '
(11-18)
where y represents a dimensionless absorption build-up factor.
The variables in Eq. (11-18) are the intensity, the excitation
temperature, and the ground-state number density. Clearly, to find nQ
for a homogeneous plasma, absolute intensity units must be known and
excitation temperature must be determined by an independent method. For
an inhomogeneous plasma, unfolding should be performed, or the calculated
number density would indicate an approximate value. The absorption
build-up is determined experimentally, but this factor will be insigni
ficant where the plasma is optically thin.
It is difficult to apply this method to plasmas emitting complex
spectra to obtain precise values of n In addition to uncertainties


40
LEGEND
XENON FLASHTUBE
REFRACTOR PLATE
LENS 1
ARC CELL
LENS 2
LENS 3
TUNGSTEN REFERENCE
BEAM SPLITTER
MIRROR
SPECTROGRAPH 1
SPECTROGRAPH 2
OSCILLOSCOPE 1
OSCILLOSCOPE 2
FABRi-TEK SIGNAL
AVERAGER
ARC POSITION
-tT
I
\-
M
,BS
Fig, 111 7. Simultaneous data acquisition system.


106
This effort has resulted in a credible definition of uranium plasma
emission properties over an extended wavelength range near the reported
temperature/pressure regimes. Presumably, the success of the theoretical
predictions will increase the confidence in atomic structure calculations
for heavy elements and will indicate possible areas for model improvement.
Although there were numerous difficulties in this research, and many
compromises were made, the overall result is clearly progressive in the
experimental and theoretical aspects of the problem.


TABLE III-l
VACUUM UV SYSTEM RESPONSE
Grating
A1+MgFg Mirror
Reflectance
Li F
Composite
Compos ite
A [A]
Effi ci enc.yG
Refl ectance"
Mirrors
Transmittance"
Transmission
Bui 1 dup1^
1050
0.06
0.30
0.09
0.10
0.00054
1852
1100
0.06
0.49
0.2401
0.20
0.00288
347
1200
0.32
0.78
0.6084
0.40
0.08709
12
1250
0.37
0.82
0.6724
0.55
0.1368
7.3
1300
0.40
0.82
0.6724
0.60
0.1614
6.2
1400
0.36
0.80
0.64
0.76
0.175
5.7
1500
0.43
0.78
0.6084
0.75
0.1962
5.1
1600
0.35
0.76
0.5776
0.80
0.1617
6.1
1700
0.32
0.76
0.5776
0.86
0.1589
6.3
1800
0.31
0.81
0.6561
0.87
0.1769
5.7
1900
0.30
0.83
0.6889
0.88
0.1818
5.5
2000
0.30
0.83
0.6889
0.89
0.1839
5.4
aRef. 64
bRef. 60, 61
cRef. 62
"Build-up factors indicate the multipliers necessary to account for losses at a specified
wavelength to increase the detected signal to its no-loss value.


Ah Initio atomic structure calculations were made using relativistic
Hartree exchange wavefunctions, from which oscillator strength distribu
tions were computed for transition arrays of interest. These calcula
tions give supporting evidence as to the credibility of the measured
emission at various wavelengths, part.icularly in the vacuum ultraviolet.
It is suggested that a consistent picture as to the nature of uranium
plasma emission, at these plasma conditions, emerges and the capability
now exists to successfully compute major emission features of uranium
and other complex atomic systems.
Vll


148
68. Kylstra, C. D., Schneider, R. T., "Computerized Spectrum Analysis,"
Appl. Spectrosc. 24, No. 1, 115-120 (Jan/Feb 1970).
69. Corliss, C. H., Bozman, W. K., Experimental Transition Probabili
ties for Spectral Lines of Seventy Elements, U. S.
Department of Commerce, National Bureau of Standards
Monograph 53 (1962).
70. Lowke, J. J., "Characteristics of Radiation Dominated Electric
Arcs," J. Appl. Phys. 41_, No. 6, 2588-2600 (May 1 970).
71. Shawyer, R. E., "Theoretical Prediction of Temperature Profiles in
a Wall-Stabilized Arc," European Conference on Tempera
ture Measurement, National Physical Laboratory,
Teddington, G. B., April 1975, 368-374.
72. Lowke, J. J., Westinghouse Research Laboratories, Pittsburg,
personal communications (November 1975).
73. Shumaker, J. B., Jr., "Arc Source for High Temperature Gas Studies,"
The Review of Scientific Instruments 32_, No. 1 65-67
(January 1960).
74. Gurevich, D. B., Podrnoshenski, I. V. "The Relationship Between the
Gas Temperature in the Positive Column of an Arc
Discharge," Opt. Spectrosc. 1J5, No. 5, 319-322 (November
1963).
75. Voigt, P. A., "Measurement of UI and UII Relative Oscillator
Strengths," Phys. Rev. A 1_1_, No. 6, 1845-1853 (June
1975).
76. Griem, H. R., Los Alamos Scientific Laboratory, personal communica
tion, June 1975.
77. Merts, A., Los Alamos Scientific Laboratory, personal communication
July 1976.
78. Mack, J. M., Jr., "Plasma Source Calibration Program," Special
Report, Dept, of Nuclear Engineering Sciences, University
of Florida, Gainesville (August 1972).
79. Krascella, N. L., "Theoretical Investigation of the Composition and
Line Emission Characteristics of Argon-Tungsten and
Argon-Uranium Plasmas," United Aircraft Research
Laboratories, NASA report CR-NASW-847, East Hartford,
Connecticut (September 1968).
80. Kelly, R. L., "A Table of Emission Lines in the Vacuum Ultraviolet
for all Elements," Lawrence Radiation Laboratory report
UCRL-5612 (1965).


INTENSITY
WAVELENGTH (A)
Fig. V-2.
Uranium plasma intensity in the vacuum-ultraviolet.


FRACTIONAL OSCILLATOR STRENGTH (GF)
119
Fig. C-1. RHX transition array oscillator strength
distribution for UII f3 6d7s--f3 6d7p.


present results to theoretically predicted locations for the higher
temperature arc plasma. A discussion of the major points of this over
all effort then concludes this study.


30
EVEN PARITY
0
3 dp
i3 sp
£ 20
o
o
>-
<3
¡r
uj 10
fV
f 2ds2
f 2d2s
f4 d
LU
f4s
ODD PARITY
fV
f 3 ds
fV-
Fig. D-2. Energy of lowest levels of known UII
configurations.


Fig. IV-6. Low-pressure uranium arc emission coefficient averaged over
100 angstrom intervals.
CT.
to


108
These number densities are plotted in Figs. A-l through A-6 as a func
tion of plasma temperature. Uranium ionization potentials used were
those reported by Williamson et alJ00 and partition function tempera
ture dependence was included by incorporating semiempirical curves
79
defined by Krascella et al. Lowering the ionization potentials was
not considered.
The Saha number densities at various total pressures were then
used to define normal temperatures for representative UI and UII transi
tions. The mathematical formalism is discussed in Secs. II-4B and 4C--
this information is in Fig. A-7.


Fig. B-1 Code schematic for RCG calculation of
oscillator strength distributions.


TEMPERATURE (K x 10 )
NORMALIZED ARC RADIUS (}'/R0)
Fig. IV-2. Low-pressure uranium arc temperature profile.


38
such as sharply pointed and polished electrodes, changes in arc gap,
changes in electrode diameter, and different cooling rates, but all
were inadequate.
B. Gais-Stabilized Ara
Next, a gas distribution head was used to localize large-scale
movement of the arc column (Fig. III-6B), and cover gas (helium) was
directed downward from the gas head the length of the arc column. The
flow contact with the anode caused a divergence of the cover gas at
the uranium pellet and a bell-shaped cover-gas flow pattern formed.
The cover-gas flow boundary formed the "wall" needed for arc-column
localization.
C. Tube-Stabilized Ara
Stabilization was enhanced by forced containment of helium gas
flow along the arc column (Fig. III-6C). A quartz tube was placed
concentrically with the electrode vertical axis and helium was forced
the length of the quartz tube. The restricted flow greatly reduced
the helium turbulence and its effect on the outer and inner arc column.
However, within five munutes of run time significant particle deposi
tion coated the quartz tube causing unpredictable intensity attenuation
and prohibiting long-duration (photoelectric) measurements.
D. Segmented-Stabilized Arc
The segmented assembly (Figs. 111-2 and III-6D) replaced the quartz
tube from the previous case and reduced the deposit problem at the
viewport. The vacuum (low-pressure) segmented arc provided stability
for photo-electric intensity, temperature, and density measurements,
while the high-pressure segmented arc exhibited marginal stability
acceptable only for photo-electric intensity measurements. The


13
i (y) 2
e(r)dx
r
2 / e(r)rdr and
J J 2 2
y \r "y
(II-8a)
e(r) = -
r(y)dy
I 2 2
-r
(11-8b)
The geometrical relations are developed using Fig. 11-1.
There are two common approaches used in solving Eqs. (II-8a) and
(11-8b) for e(r). The first is by fitting an appropriate polynomial
to the experimental intensities, differentiating, and using Eq. (II-8b)
to obtain e(r). The details of such a method are given in Ref. 39.
The second method approximates the integrals with sums and extracts the
desired information numerically. The numerical form of Eq. (II-8a) is
given by
IT(y) = 2 V e.(r) A. . (11-9)
i 7' L. J ij
U
In Fig. 11-1, the ith LOS in the concentric ring is defined by the
length coefficients, A.., and e.(r) represents the average emission
J J
4- T->
coefficient for the j ring. Equation (11-9) results in a system of
simultaneous linear equations for each e.(r), iT(y), which can be
J J
solved by matrix inversion to obtain the e.(r) vector.
When the plasma under investigation has significant intensity gra
dients, a number of rings (as many as 40) may be necessary to approximate
adequately the intensity profile and allow computation of emission
coefficients within acceptable error. Each ring requires a correspond
ing intensity determination, which may be too difficult to obtain,
depending on plasma stability. However, too many subdivisions may cause


FRACTIONAL OSCILLATOR STRENGTH IGF)
123
Fig.
0.20 p
Qi 8 -
0.16 -
0.14 -
QI2 -
OJO -
0.08
0-06
0,04 -
0.02 -
QOO __
7
WAVENUMBER (1000 cm1)
C 5 RHX transition array oscillator strength
distribution for UII f3 7s7p--f3 7s8d.
65


47
WAVELENGTH (A)
Fig. 111 -lo. Deuterium lamp calibration curve,
Kern lamp at 300 ma.


94
Once defined, likely configuration pairs were chosen (Table VI-1)
for a quantum mechanical calculation to establish the transition array
and oscillator strength distribution for a given pair. Appendix D
illustrates the average energies of these configurations as well as
average energies of some lower levels of UI and UII as reported by
94
Radziemski and Blaise.
171-4. Calculation of Oscillator Strengths
We calculated oscillator strengths and distribution by choosing a
coupling representation to determine the energy levels and wavefunctions
for an atom in a specified configuration. For precision, energy levels
and wavefunctions for all possible configurations must be found. These
wavefunctions are used to calculate the electric dipole matrix that leads
directly to oscillator strength for a given transition. The wavelength
for each transition is given by the energy-state differential between
levels of the transition.
To determine energy states and wavefunctions for the atom (ion) in
a given configuration the Schrodinger equation, Eq. (VI-1) must be solved
k k
for the total wavefunction T and energy eigenvalue E of each state k.
H Tk = Ek Tk (VI-1)
In this formalism H represents the complete Hamiltonian of the system.
This problem reduces to finding the eigenvalues (E ) and eigenvectors
of the Hamiltonian energy matrix in a given basis representation. This
is accomplished by the diagonalization of such a matrix into the follow
ing form:
< b IH | b" > = H,k. D
1 bb
(VI-2)


82
An extension of these data to 6000 A was accomplished by comparison
81
to uranium plasma emission coefficient data taken using this arc sys
tem and is shown in Fig. V-3. The line structure in this figure refers
to the latest measurements at 3-atm total pressure; the dashed-line
curves represent previous results. The deviation in magnitude can be
explained by our more sophisticated and accurate data-acquisition system.
Even so, the comparative magnitudes remain within reason. Comparative
shapes (along the wavelength scale) offer a high degree of correlation,
as expected if past and present measurements were made properly. These
o
factors validate the extrapolation of the present data to 6000 A with
substantial credibility. Thus, a spectral emission coefficient is now
defined for a uranium plasma (8000 K, 0.01-atm uranium pressure, and
1-cm plasma depth) from 1200 to 6000 A.
Figure V-4 shows the present results with the corresponding Planck
function and other comparable measurements reported in the litera-
22 23 82 83
ture, along with theoretical predictions made by Parks et al.
For the moment Parks' results will be accepted and their validity ex
amined .in Chapter VI. Because the graph is semi logarithmic, Kirchoff's
Law provides a ready means to estimate directly the absorption coeffi
cient by merely subtracting the value difference between plasma emission
and the Planck function at a given wavelength.
22
For comparison it is necessary to remember that the Miller and
23
Marteney et al. experiments used UFg as the discharge gas; the Florida
experiment vaporized metallic uranium. Figure V-4 clearly indicates the
differences in emission coefficient wavelength dependencies among experi
ments. At similar plasma conditions and compositions, differences in
shape should be minimal. A distinct fall-off in emission coefficient is


59
temperature profile; whereas the 3659 A transition indicated less re
producibility. The profiles from both transitions compared rather well
and offered supporting evidence for the existence of LTE conditions
within the bulk of the arc column down to fairly low-lying levels.
Of particular interest is the rather flat radial temperature de
pendence. There have been numerous flat temperature profiles reported
p p_ pO
for various wal1-stabi1ized arc plasmas. ~ Plasma confinement using
a cooler material wall generally results in a reduction of the tempera
ture gradient from the arc center toward the wall. In many cases,
conduction loss is not the only contributor to the profile curvature.
Conductive heat transfer along the arc temperature gradient to the wall
and radiative transfer losses, which are strongly dependent on the
plasma conditions and type of radiating species, account for most of
the energy loss from an arc. That a flat temperature profile in wall-
stabilized arcs can be realized is substantiated in the literature and
not in controversy; at issue is the rationalization of such a tempera
ture profile for a wall-stabilized uraniurn arc which is measured by
this investigation.
The temperature profile for wal1-stabi1ized arcs must be consis
tent with the energy-balance equation given by
a E2 = V Fc + V Fr (IV-1)
where a = electrical conductivity,
E = electric field,
F = conduction flux density, and
Fp = radiation flux density.


10
greater (dense arc plasmas), the only significant absorption will be
located (on the wavelength scale) at some of the spectral line cen
ters, usually formed in the lov/er energy levels. In many cases for
low- and intermediate-density plasmas, the effective absorption
coefficient will be small for most wavelengths.
Line, recombination, and continuum radiation are three basic
radiation types occurring in an arc plasma. Line radiation is usually
associated with relatively low temperatures, i.e., 4 000 K-15 000 K;
recombination and continuum radiation can be substantial when the
characteristic plasma temperature is > 15 000 K. Detailed treatments
31
of recombination and continuum radiation are given by Cooper.
Spontaneous emission and stimulated emission result in line radi
ation. Stimulated emission (often thought of as negative absorption)
is a difficult item to isolate and therefore, is usually defined as
an effective absorption coefficient for any plasma as shown by:
k'(x) = (x) + k (x)
V V
(II-5a)
(x) (x) (x) ,
(11-5b)
v
where k" = total (measured) effective absorption coefficient at
x, v cm
-1
(x) = total effective line absorption coefficient at x, v,
v
kl (x) = line absorption coefficient at x, v,
k (x) = total continuum absorption coefficient at x, v, and
v


APPENDIX E
UF,. PHOTOABSORPTION EFFECTS OF THE MARTENEY AND
b
FLORIDA EMISSION COEFFICIENT DATA
UFg photoabsorption strengths as a function of wavelength were
84 85
calculated using the cross-section data of DePoorter, 5
SrivastavaMcDiarmid,^ Trajinar,^ and Hay^ (Figs. V-5 and V-6).
The intensity of transmitted light 1^ that has passed through a de
fined depth of UFg of given molecular concentration is related to the
incident light IQ by the equation
where £ UFg cell or layer thickness in cm,
3
n = molecular concentration in UFt molecules/cm and
0
g(A) = wavelenght dependent UFg photoabsorption cross-
. 2
section in cm .
These absorption factors (I^/Iq) were used to illustrate the possible
effect of UFg photoabsorption on the arc emission coefficient data of the
present experiment. This was done by folding absorption strenghts
calculated using Eq. (E-l) with the arc emission coefficient values at
regularly defined wavelengths. The folding was preformed at UFg layer
thicknesses of 1.5, 2.0, 3.0, and 5.0 cm with molecular concentrations
ranging from 1 x 10^ + 1 x 10^ cnT^. The results of these calculations
are shown in Figs. E-l through E-8.
133


63
for the present arc could be as much as 100 K to 200 K because of the
partial LTE state arc plasma.
IV-3, Density Measurement
The ground-state particle density (UI) for the low-pressure urani
um arc was determined by the absolute line method (Sec. II.5A). This
method involved the shape definition of the desired spectral line, its
absolute intensity calibration, an independent temperature measurement,
and uncertainty estimation. The exact line profile could not be de
fined because of the large line-overlap characteristic of uranium spec-
49
tra. A Voigt analysis was used to approximate the line area of the
o o
same lines (3653 A, 3659 A) used for the temperature measurements. Be
cause these data were taken simultaneously with the intensity-
wavelength information, significant temporal fluctuation should be com
mon to all and treatment of fluctuation was unnecessary. Line intensity
calibration was performed with a tungsten-filament NBS-calibrated lamp.
No attempt was made to establish a radial density profile because asso
ciated errors negated the effort. Line-center absorption was also
accounted for by appropriate build-up factors. The calibrated UI ground-
14 -3
state density for the low-pressure uranium arc was ^ 7 x 10 cm .
This value is an order-of-magnitude estimate of an approximate density
radially through the arc column. Assuming uncertainties in spectral
line area, gA, and temperatures of 15, 50, and 20%, respectively,
resulted in a density range of 1.28 x 10^ -* 7.89 x 10^ cm This
indicated, from Saha analysis, that a nominal value for the uranium
total pressure, rounded to the nearest integral logarithmic pressure,
would be 0.001 atm (1.3 x 10^ cm ^).


80
70
60
50
40
30
20
10
0
3
EVEN PARITY
ODD PARITY
5f37s 8 d
5f3 7s8d
5f36d 7p
5f3 7s7p
5f 6d 7s
K. 3 2
5i 7s
-3. Relativistic Hartree exchange average
configuration energies for selected
UII configurations.


25
There is very little available information about atomic properties
of uranium. This information would be useful when performing plasma
temperature diagnostics on spectroscopically complex elements; however,
the modified BEM is particularly effective for use with uranium plasmas
because it is independent of these constants. Because this technique
deals adequately with plasma inhomogeneities, it is suitable for appli
cation to arc plasmas. Implementation of the method is cumbersome
because it means a long-duration minutes) steady-state plasma, a
well-defined standard background source and its associated circuitry to
provide a rather elaborate data acquisition sequence.
11-5. Density Measurements
To define plasma pressure, total or partial, it is necessary to
determine ground-state population densities for all ionization stages
in the plasma. The equation of state (in conjunction with Dalton's law
of partial pressure) for each plasma component is then used to define
a total pressure. A substantial effort is involved in establishing
population densities. The determinations must rely on an accurate atomic
description of the plasma constituents and precise intensity calibration.
25
Griem states that even in an optimum situation, it is often impossible
to reduce density error below 30%. Therefore, most plasma density
determinations are order-of-magnitude estimates.
Two density diagnostics, which were applied to the uranium arc
plasma, are described in the following sections: absolute line inten
sity and pressure-temperature correlation (PTC).
A. Absolute Line Intensity Method
The integrated line intensity for a transition from level u to
level i is given by Eq. (11-10). Equation (11-10) applies to a line


93
whereas, if pure LS coupling really existed (as expected of neon with
Z = 10) there would be no contribution from two of the three components
and 100% contribution from the third.
VI-3. Configuration Selection
The credibility of the observed U11 emission wavelength can be estab
lished (to some degree) by calculating transition arrays and their asso
ciated oscillator strength distribution of particular configuration pairs.
Valuable information can be computed from first principles relating to the
location, and in some cases, the strength of emission for a given transi
tion array. Generating specific transition arrays is directly related to
selection of configuration pairs that are likely to produce spectra at
relevant wavelengths. The selection of particular configuration pairs
requires knowledge of configuration average energies Egv- The difference
AEav between configurations is indicative of the average transition array
wavelength between two specified configurations. Average energies are
tabulated frequently in the literature for less complex atomic system but
not for uranium; trial and error tactics were necessary.
We considered probable configurations where singly ionized uranium
3 2
could find itself, beginning with the ground-state configuration 5f 7s
and exciting an electron to another likely orbit. Table VI-I summarizes
configuration pairs which were ultimately considered.
Table VI-1
UII CONFIGURATION PAIRS
3 2
5fJ7s
- 5f37s7p a
2 2
5r 6d7s£ -
2 2
5f 6d 7s
5f37s2
- 5f37s8p a
2 2
5r 6d7s -
2 2
5t 6d7s
5f37s2
- 5f26d7s2
5f36d7s -
5f36d7p
3 2
5f /s
2 2
- 5f /s /d
5f37s7p -
5f37s8d
2 2
5t 6d7s
- 5f26d7s7p
5f36d7s -
5f37s7p
Configuration pairs which were very strong and/or lead to oscillator
strength distribution at the desired wavelengths.


Fig. III-l. Uraniun plasma containment cell.


57
center outward, thus the values at further distance from the arc center
47
were more uncertain. Usher has considered all of these possible
contributions to absorption profile uncertainty. Using an argon arc
47
with the same experimental apparatus as this uranium arc, Usher found
a fairly constant absorption profile uncertainty across the arc. This
was not true of the uranium arc because the viewport deposition prob
lems resulted in a larger absorption coefficient uncertainty as outer
regions of the arc were approached. The flash!amp intensity was de
graded because its radiation field passed through two viewpoints (as
opposed to one for the arc plasma emission), resulting in overestimates
of the true absorption coefficient values at all points along the arc
radius. Error analysis showed that these estimated uncertainties were
^ 10% at the centerline to ^ 62% at the outer point.
The apparent uncertainties of radial absorption coefficients in
fluenced the temperature computation uncertainty. Again, the error
47
analysis of Usher was used to obtain temperature uncertainties.
Figure IV-2 illustrates the radial temperature dependence for the low-
pressure arc plasma. The uncertainty limits generally increase as the
arc center is approached. If we consider that the uncertainty calcu
lated for the outer radial location is propagated to the central
locations, it is possible that the innermost temperature will have an
associated uncertainty greater than that of the outermost temperature
value. Therefore, while the outermost temperature had the largest
experimental error, the central temperature had the largest total
error. Several temperature profiles were determined using both tran
sitions (3653.21 A, 3659.19 A), and Fig. IV-2 shows results for each
O
transition. The 3653 A diagnosis typically showed a very reproducible


55
IV-2. Temperature Measurement
The electron temperature was measured by the modified brightness-
emissivity method (Sec. II.4). First, it was necessary to obtain line-
center absorption coefficients as a function of arc radius by applying
flashtube absorption diagnostics (Sec. III.3A). Line-center absorption
O o
profiles using the 3653.21 A and 3659.16 A UI transitions are shown in
Fig. IV-1 and represent absorption measurements taken during the best
conditions of arc stability and flashtube firing. The two reported
profiles indicate maximum absorption at the arc center which is usually
the region of maximum temperature.
Uncertainty in absorption coefficient values was both numerical
and experimental. The unfolding scheme converting kq(x) k (r)^ was
responsible for the numerical uncertainty, and the accuracy of the
oscillogram voltages defined the primary experimental error (k indi
cates the line-center absorption coefficient). The oscillograms
contained recorded voltages representing the flashlamp intensity atten
uated by the plasma as well as the true plasma intensity. The plasma
voltage uncertainty was mainly caused by arc intensity change which fell
within +2% during data collection. Flashlamp attenuation uncertainty
resulted from arc intensity fluctuation, flashlamp intensity variation,
and arc cell viewport attenuation.
Since the flashlamp was located behind the arc cell, its light
output passed through two viewport windows in the segmented assembly
(Figs. 111-1 and 111-2); whereas the arc photon field passed through
only one on its path to the detector. During arc operation, deposits
occurred on both viewports; line-center absorption of the light emitted by
the flashlamp was recorded photoel ectrical ly at four points from the arc


81
O O
distinct peaks at approximately 2300 A and 2900 A. The theoretical
o
predictability of these peaks and the one at 1500 A will be addressed
in Chapter VI.
Vacuum uv signal authenticity and order contamination caused by
overlapping orders were investigated. Light emitted by the uranium arc
was passed through the vacuum spectrograph system and detected as usual
with one exception--a test material composed of either Lif, quartz, or
glass was placed just behind the entrance slit. Arc intensity data
collected indicated that the system was detecting a true vacuum uv
signal, and that contamination from other orders of the grating was
negligible.
Uncertainty in the absolute value of the emission coefficient is
a function of several sources, such as calibration of the standard
radiation source, minimal spatial resolution, standard source position
ing, digital processing, grating scan error, and arc fluctuation. For
o
higher wavelength (>1750 A) the emission coefficient value error is
probably within +30%. However, it is much more difficult to identify
O
value error to wavelengths less than 1750 A. Back-extrapolation
calibration in this region assumed negligible system (optical) losses
which is not the case. A good indicator of value uncertainty at these
wavelengths is the system efficiency data in Table III-l. The dashes
in Fig. V-l represent the uncertainty limits on data at selected wave
lengths in the vacuum uv. Clearly, as lower wavelengths are approached,
the losses begin to dominate and are really indicative that all photons
o
emitted below 1200 A are unlikely to be detected. The error in emis-
o
sion coefficient values at wavelength > 1750 A does not have this loss
component because the calibration is more precise.


19
at which de^(T)/dT = e^(T) = 0. The norm temperature can then be used
to estimate the characteristic plasma temperature. First, it is neces
sary to determine which ionization state corresponds to identified
emission lines generated by the plasma. Then e (T) is computed for a
spectral line known to be from the dominant ionic stage by using appro
priate equilibrium relations. Then e'(T) = 0 is determined, thus de
fining T The maximum temperature of an equilibrium plasma emitting
a line in a particular dominant ionic state can be on the order of T ,
which is indicative of the energy necessary to ionize the plasma to that
state.
Obvious disadvantages of such a method are that Tn is only an
estimate of the characteristic plasma temperature, and while transition
probabilities need not be known, the Saha equation must be solved to
obtain the neutral and ionic number densities, thereby requiring LTE.
The primary advantages are that only spectral line is necessary and that
this method can easily be adapted to the relative norm-temperature method.
C. Relative Temperature Method
The relative temperature method is an extension (in many cases) of
the norm-temperature method in that the norm-temperature can be used as
a reference plasma temperature and temperatures at other spatial loca
tions related to it. It can be used for plasmas which have cylindrical
geometry with radial temperature profiles T(r) and at least one defined
temperature such as Tn. If this is the case, the resultant emission
profile e (r) pertaining to a specific transition can be similar to that
shown in Fig. 11-2; one point on the desired temperature profile T(r)
is defined by e (r ) and T From equilibrium relations, ratios of
ev(ro)/cv(r.j) may be computed and the corresponding T(r^) determined.


Uranium plasma number densities, as determined by the absolute-line
method, are often uncertain. Pressure-temperature correlation removes
some of this uncertainty and furnishes supporting evidence to experi
mentally determined densities.


9
The general solution to the equation of radiative transfer is
x
Iv(x) = Iv(o) e~Tv(x) + f Bv(T) k'(x') e"Tv(x^ dx' (II-4)
o
where I (x) = observed intensity at X, v (energy/area-tiine-solid
angle-wavelength,
I (o) = intensity of background source (if there is one) at v,
Bv(T) = Planck function at T, v (energy/area-time-solid
angle-wavelength),
k'(x') = effective absorption coefficient (length ^) at x", v,
and
e (x-') = specific emission coefficient at x^, v (energy/volume-
time-so1 id angle-wavelength).
In Eq. (11-4), a situation is possible where all emitted photons
transport beyond the outer plasma boundary, that is, if t (x) -* o.
Then the observed intensity is simply the emission coefficient integral
over the 1ine-of-sight depth, provided the plasma is homogeneous.
This plasma is designated optically thin. The other extreme would be
t (x) here all emitted photons are trapped within the outer plasma
boundary, and then the plasma radiates as a surface where I + B .
This plasma is designated optically thick and exhibits a blackbody
spectral distribution of radiation.
Generally, in relating the concept of optical depth to arc plas
mas, the 1ine-of-sight depth and the effective absorption coefficient
must be determined. Usually the 1ine-of-sight depth will be quite
small (for arcs), making the effective absorption coefficient the
important quantity. Unless the plasma pressure is 50 atmospheres or