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TITLE START BROADENED PROFI1,ES WITH SE1.F-CONSIS’I’ENT RADIATION TKANSFERAND ATOMIC KINKTICS IN PLASMAS PRODUCED BY tllG1l lNTENSITY [,ASERS

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Stark Broadened Profiles with Self-Consistent Radiation Transfer

and Atomic Kinetics in Plasmas Produced by High Intensity Lasers

Gordon L. Olson, Jack C. Cornly, J. Kenneth La Gattuta, David P. Kilcrease

Los Alamos National Laboratory

Los Alamos, NM 87545

5th International Workshop on Radiative Properties of Hot Dense Matter

2-6 November 1992, Santa Barbara, CA

to appear in a special issue of

Journal for Quantitative Spectroscopy and Radiative Transfer

STARK BROADENED PROFILES WITH SELF-CONSISTENT

RADIATION TRANSFER AND ATOMIC KINETICS IN

PIJNW.AS PRODUCED BY HIGH INTENSITY LASERS

GORDONL. 01.soN, JACK C. COMLY,~J.KENNETHLA Gxrrwi, DAVID P. KILCREASE

Los Alamos National Laboratory, Los Alamos, NM 87545, U, S. A.

Abstract+ pectral line shapes and line strengths have long been used todiagnose plasma temperatures and densities. In dense plasmas, the additionalbroadening due to Stark effects ~jve additional information about the pla?madensity. We present calculations that are self-consistent in that the radiationfields of the line transitions and the atomic kinetics are iterated to convergence.Examples are given for simple plasmas with temperature gradients, densitygradients, and velocity fields. Then a more complex example of a laser producedplasma is presented.

1. INTRODUCTION

The proceedings of the previous conference in this seriesl contains excellent

presentations dealing with the importance of spectroscopy in understanding

plasmas. Parallel to advances in experimental spectroscopy, numerical techniques

for the solution of the radiation tra~~sfer equation have improved significantly over

the last fcw years:) ~ Comhin~d with recent improvements in personal computers

and scientific wor!istations, it is now easily affordable to do steady-state one-

dimcnsional raiiativ~ transfer coupled to atomic kinetics, The need for escape

probabilities and other approximations should diminish in the future.

Whiie experiments can be carefully designed to have uniform densities and

t(’1])~)(’r:~tur(’s,~;they are the exception r[~ther th:m the rule. Most experiments have

d(’r~slty :~nd tcrnpcrature gradients nnd velocity fields. Many times, they arc nlso

stron~:]y t,illle d(’p(’ncient, This paper will deal with denso plasmas which have all of

thcs(~ corl)])lic:lt,ions,” In the following section, the m(~t.hods W(Juse in cnlcxllnting Iinu

})rofil(’s in dl’nsc pl:~srnns are prcsontcd. Then i!l See, 3, line profiles nrc !{howrl

which nriso in simple, but non-( ]niform pl:ismns. ~Section 4 discuswls the radint, ion-

}Iy(iro(ivll:ltl)i(’s co(l(” Ilsv(i in th~’ !)r(’s(?nt c:llclllntions. ~S(’ct,ion ,5 shows n l:isrr -

plasma interaction calculation that comes from modeling an actual high intensity

laser experiment.

2, STARK PROFILE-CODE MODIFICATIONS

Since the general formulation and assumptions used in calculating density-

broadened line profiles are well documented,T and the specific approximations used

in the profiles presented here are published,s we will concentrate on the changes we

have made rather than the over-all theory.

Lees made a significant contribution to line theory applications by using the

APEX theoryg! 10 and several well chosen approximations. The resulting code for

calculating line shapes is dramatically faster than those previously available and

makes line shape calculations practical on a perso~~al computer. On a

supercomputer, one can now do complex radiation-hydrodynamic simulations that

include Stark. broadened line profiles.

In October of 1991, we obtained the then current version of Lee’s line shape

code. Although it had been optimized by using fast approximations for complicated

physics, we found several places where we rewrote details so that calculations

wculd vectmiize on a Cray YMP. The largest single algorithmic change was to throw

out the Doppler convolution routines which were based on fast Fourier transform

(FFT) techniques. Because the frequency grid on which the profile is calculated is

not uniform, it was necessary ta interpolate the profile on to an equally-spaced grid,

do thr IWT, and then interpolate back on to the variable grid. We found that

directly evaluating the convolution as a double intigral on the original grid was fo~ir

to fivu times faster than the F~ plus interpolation,

In the line code there ore various integrals over probability distributions. If

onu is int.rrcstcd only in frcquoncics near line center, it is nccemary only to do these

intcgrills out to 15 normalized cncr~y units, However, to reliably calculate ~nr into

thu witlgs, w(’ Ilii(i to incrcnsd these intcg-mls out to 35 units.

‘1’h[l liir~(~st physics ~hiil~~(!We mucic W[~S to include th{! twl] t~n~~~ll’iit~lr(~

A1’IH tllw)ry prwwnted by Kilcrcnsc 1I rlscwhcro in tl~is confircnm. In sin~uliltiorls

of’iIltcllso I:ls(*rs, tt)(: ion :~nd (’lectron tvmperu~uros i~r(~ ofl.cn signi~ic:int,ly dif~crc’nt.

~roIn (IiiclI othvr, AddiI)l! th(’ nbility to huvc two tvn~pcr:itur(’s Viit+tly bromivns thr

11])])1i(”ill)ilit.oyof”;1linr ])rorll~t c()(]c.

Working wi tll MI~gc(I1~ w{’ l]~ii(ll~ vnrious CIIIIIlgtIS th:it IIIIILIQ tl~(~ pt-ofil(* c()(l(~

Illot’(” 1“01)!st iit l~igl]cr (1(’tlsitios. M:Ig(’I’ ill S() (’l(t(’1)(1(’(1 tll(’ ti~! I(’S 01” :Ilolllic

2

parameters down to hydrogen. NOM-the calculations can be done for hydrogen

through iron,

Rather than show isolat,ed, idealized profile shapes which canbe found in

other references, Figs. 1 and 2 show self-consistent calculations of :he radiation

emitted from a 10 micron thick slab of aluminum at a temperature of 600 eV with

five different ion densities. These calculations are self-consistent in the that

radiation field is solved iteratively until converged with the atomic kinetics

equations. More details about the code used for this calculation are given in Sec. 4.

Note that at low densities the lines are narrow and have essentially Doppler shapes.

With increasing density the traditional Stark shapes appear. At the highest density

shown, the line wings are dominated by the continuum intensity. The line from the

upper quantum levels (n = 4 and above) disappear as their optical depths become

less than the neighboring continuum optical depth.

3. EFFECTS OF PHYSICAL GRADIENTS

In most laboratory or astrophysical plasmas, there are density gradients,

temperature gradients, and velocity fields. Figure 3 shows four dll~’erent emitted

shapes for the Lyman ~ line cf aluminum, All four are from a 10 micron-thick sl.ib

with a baseline ion number density of 3x10~l cm-;] and temperature of 600 PV. The

uniform case, labeled U, has no gradients or velocities and is the basic line shape

produced by I.ec’s code.B The CL-ve labeled with a T has a linear temperature drop

of 100 cV from one side of the slab to the other. The curve labeled with a N, has a

linc:~r ion density decreasing from 3X 10~1 to 2x10z~ cm-s from one edge to the other.

The curve l:ibc’led with a V has a parabolic velocity distribution ranging from zero

on one surfncc to 6“10’7 ctrds on the other surface, Note that the density (Ind

tcmperatur-c [~ri~dirnts produce nearly the same exuission line shape,

I“igure 4 shows IJyman a. nnd some of its satellites for the same conditions [1S

in F’ig. 3, }Icrc ttlc’ density a~)(l t~’mp(.’ruturcs produce results that nrc not ns Sirllililr

:1~, tt](,y \Y(I).~1 f~)r [,v1]):]ll ~j ‘1’h(>v(}lo~it,y fi(~][~:lll(lws p}loto[l$i”to CSC:lp(> th[lt Wolll(i

tl:lv(’ 1)(’(’rlf I“ii])p(’(1 by s(’lf[lt)sor[)tiO1l;” thcr(’for~?, th(’ pc’nk (’mission of I,ymnn (I is

l:IrKII~ \vit 1~:1 \I(’locity fi(’ld, us w~’11:1s 1)(’ing displiic(~(l in f“r(~qu(~ncy.‘1’1~(’s:~t(’llit(’s

[lr~)v(’rv tt)i r]; tl)(’rl’forx’, v(~lo(’ity (’lli’(’ts jllst spr(’lld ollt (h(’ir (’mission i]) froqi]l’rl(’.v,

cil~lsing t}lc (’lnission p(’:li<s to (lrv)~), Ilv m(I:isur-in~ thv irlt(’nsitios nnd sl~:ip(~s of”

s(’v(Ir:ll Iirl(’s, or](” C;III II)()(J,J I :ln(i (1(’(llr(’(’ tll(’ (’ollll)itl(’(1 (Jfli’(’(s of t(’[]1])(’r:it{ll.(’ illl({

(I($tlsi!y ~:r:~(li(’r)ls.

In standard treatments of line radiation transferals one can usually assurn(? a

line profile is symmetric. Most astrophysical plasmas have low enough densities

that Stark effects are negligible so this is a reasonable assumption. This symmetry

property allows significant savings in computer time and programming effort, even

with non-zero velocities. Unfortunately, Stark profiles are in general non-

syrnmetric, so none of these savings are available.

4. ZAP

ZAP is the name of the code that has been used to calculate the examples

presented here. Although the above examples are steady-state solutions, ZAP 1s a

general-purpose radiation-hydrodynamics code. The primary uses of ZAP are to

model detailed atomic processes in x-ray lasersl A and to model plasmas for

spectroscopic diagnostics.

ZAP solves the one-dimensional Lagrangian hydrodynamics equations for

slab, cylindrical, or spherical geometry. The numerical method uses a half-step-full-

step algorithm with a staggered spatial mesh and a even time discretization. Either

w)e or t WOenergy balance equations are solved for one or two temperatures (ion and

electron). Thermal conduction can be included for just electrons or both electrons

and ions.

The radiation transfer in ZAP uses deterministic one-dimensional slab

geometry methods. The non-LTE line transfer uses approximate operator

itcration$tjq and the equivtilen t-two-level-atom technique to solve the transf’er

(’quation consist~~ntly with the atomic kinetics rate equations. The line transf(er

il)cludcs the velocity and non-symmetrical profile comt)lications mcntiol)~’d in the

previous section, Imscr energy is d(’posited using a simple ray trncin~ scheme,

SOIII(’of the utomic data is gvnerat(’d with a fnnlily of I,os Aliil~~os co(!(~sl~,1(;

h~~sed on l-{i~l.tr(~~~-1~’()~kwavo f’ux)ctions. 1*’rom these codes, we get energy 1(’v(IIs,

oscill:lt~)r s.tr(’ngt 11s,:lnd (’lr(’troll imp:l(l (’xrit:]tion riit(’S. ‘1’() pt-odLIc;CI (:orlfig(lr:ltioll-”

:Irl(i lJ,y(ll )(\r}~- ;lv(~r{l/;(’(i aton]ic 1[’VPIS W(’ hil Vf.’ written our Own il(lt,O1llOtf(?d [’[)({ (’S (()

])10(1(1 (’(” t}l(’ :kt,orllic (Iiltil bilS(’S. W(’ llS() SCill L’d hydrogrnic (’lectron illlpilCt (’xcibltion

;IIl(i iot)iz:ltiol)” r:ltos, l’; 2 1 I)llotl )iollixiltiorl crms s(~ctions ilro 7J-SCill(’(1 fits l“or (’:1(’11

(()]~fiL~~lr:lt,i()r~.~~ AlltoioI)iz:ltioi~ ii]~~] di(’1(’r[ro~lic r(’coi~)l)ir]:ltioll” c~~nh(~ in(’l(](i(’d hy

The atomic model used in the aluminum calculations presented here contains

309 energy levels from the once ionized through the totally stripped atom.

Configuration-averaged levels are used for principle quantum numbers of 1, 2, and

3. In the highly stripped ions, the n = 4 levels are also configuration-averaged. In

the near neutral ions, the n = 4 levels are Rydberg-averaged. In all ions, the n = 5,

6, and 7 energy levels are Rydberg-averaged. In order b include the autoionization

and dielectronic recombination processes, doubly-excited levels are added to the Be-,

Li-, and He-like ions. This also causes some satellite lines to appear in calculated

spectra.

5. HIGH INTENSITY LASER PRODUCED PLASMA

The I,os Alamos Bright Source Lasers (IABS) are KrF and Xefll lasers,zst~’1

Briefly, the LABS I system is Krl? at 248 nm wavelength, with an energy of 30 rnJ,

a pulse width of 700 fs, and a peak intensity of 3X101T W/cm-z. The same quantities

for LABS II are 308 nm, 0.25 J, 300 fs, and 10lg W/cm-a. Time integrated

spectroscopy of solid aluminum targetszs.26 shows strong emission lines from the

hydrogen- and helium-like ion stages with line widths of 4 to 6 eV, With the lower

intensity laser, the He-like lines dominate the spectrum, With LABS 11, the H-like

lines are stronger, comparable to the He-like line strengths,

A surprise in these spectra is that the lines from higher n levels are not

significantly broader than those from lower n. If the emission occurs from a dense

plasma, one would expect that the line widths would generally increase with

increasing n. This surprise was a major motivation for adding Stark broadened

profiles to the radiation transfer abilities in ZAP. Our goal was to simulate these

plasmas in order to understand where the line emission originates,

These lasers have a moderate intensity ( 109 to 1012 W/cm 21 prepulsc that

illuminates the target for 1 to 10 ns before the main pulse urrives. ‘1’his prepulse

produc(!s u pl:lsma blowoff with which the mainpulse will then interact. According

to XAi’ simulations, the main pulse heats the plnsmn to between 1 and 5 keV,

dcponding on assumptions uhout how much energy is absorbed nnd reflected at he

l:ls~’r’s critic:d surfnce,

1+’i~<ur(’s5 :Jnd 6 show time int(’grntcd thw)retical spectra calculi] ted with ZA1’

f’or t.~l)i~i~lli~s(~r pnr:imct,crs of 1,.411S 1 nt~d 1I, rcspcctivc’ly. The lines in Fig. 6 nrc

5

Unfortunately, the experimental data do not show this behavior. The experimental

line widths and shapes differ very little between LABS I and 11 spectra.

This discrepancy between theory and experiment suggests that something is

wrong in our assumptions in modeling the laser plasma interaction. One possibility

is that, at the higher intensities, plasma instabilities cause the laser photcns to be

absorbed at lower densities than the critical density. This suggestion and others will

be explored in future research and publications.

6. CONCLUSIONS

In summary, we have discussed improvements to an existing package for

calculating Stark broadened line profiles. We have presented simple example

calculations and more complicated examples with density gradients, temperature

gradients, and velocity fields, The ZAP code which has the ca~ability to deal with all

these complications has been outlined. Finally, a full radiation-hydrod-ynamic

simulation has been presented for comparison to actual experiments,

In conclusion, it appears that al{ the practical tools are available for doing

steady-state radiation transfer and atomic kinetics calculations on workstation

computers. FuI1 rad-hydro calculations still require mainframe computers, Our

LABS I calculations typically take 50 CPU hours on a Cray YMP, and the LABS 11

calculations take more than 100 CPU hours,

G

REFERENCES

1. Radiative Propetiies of Hot Dense Mctter(Edited by W. Goldstein, etal. )WorldScientific (1991).

2. Methods in Radiative Transfer (Edited by W. Kalkofen) Cambridge UniversityPress (1984).

3. Numzrical Radiatiue Transfer ((Edited by W, Kalkofen) Cambridge UniversityPress (1987).

4, G. L. Olson, L. H. Auer, and J. R. Buchler, JQSRT 35,431 (1986).5. G. L. Olson and P, B. Kunasz, JQSRT 38,325 (1987).6. P. T. Springer, et al., Phys. Rev. ht. 69,3735 (1992).7, H. R. Griem, Spectrcd Line Broadening by Plasmas, Academic Press, NY

(1974).8. R. W, Lee, JQSR7’ 40, 561(1988).9, J. W. Dufty, D, B. Boercker, and C. A. Iglesias, Phys. Iku. 31A, 1681 (1985).

10, C, A. Iglesias, H. DeWitt, J. Lebowitz, D. MacGowan, and W. Hubbard, Phys.Rev, 31A, 1698 (1985).

11, D. P. Kilcrease, JQSRT, this proceedings.1!2. N. H. Magee, private communication.13, Il. Mihalas, Stellar Atmosptires, 2nd Ed., W. H. Freeman and Co., SF ( 1978).14. G. L, Olson, J. K. La Gattuta, and J. C. Comly, Int. Colloquium on X-ray

Lasers, Inst. Phys. Conf. Ser. No. 116, IOP Publishing Ltd, 329 (1991).15, ,J. Abdallah, Jr., R, E, H. Clark, and R. D. Cowan, Theoretical Atomic Physics

Code Development I – CATS: Cowan Atomic Structure Code, LA- 11436-M, Vol.1, Los Alamos National Laboratory, (1988).

16. R. E. H. Clark, et al., Theoretical Atomic Physics Code Development II - ACE:Another Gllisional Excitation Cook, LA-11436-M, Vol. 2, Los Alamos NationalLaboratory, ( 1988).

17, 1.. B. Golden and D. H. Sampson, J. Phys. B 10, 2229 (1977).18, D. H. Sampson and L. B. Golden, J. Phys. B 11, 541 (1978)19, 1,, B, Golden, D. H, Sampson, and K. Omidvar, J. Phys. B 11,3235 (1978)20, D. L. Moores, L. B, Golden, and D. H. Sampson, J. Phys. B 13, 385 (1980)21, L. B. Golden and D. H. Sampson, J. Phys. B 13, 2645( 1980)22, R. K. H. Clark, private communication.23, J. l>. Robertst A. J. Taylor, P. H. Y, Lee, and R. B. Gibson, Opt. Lett. 13, 734

(1988).24, A. J. ‘1’:~ylor,~t al, Ultrafast Phcnomt?na VII, Springer Series in Chemicnl

Physics, 53, 104, Springer Vcrlnge, Berlin ( 1991)25, tJ, A. (hhble, C. T. Schappert, L, A. Jones, A. ,J. Tnyhn-, G. A. Kyrala, nnd R. D.

Fultxm, J. Appl. Phys. 69, 3369 ( 1991).26, (;, A. Kyrala, ct al, Appl. Ph.vs. Le/t., 00, 2195 (1992).

7

FIGURE CAPI’IONS

1. Theracliation emitted bya 10 micron-thick slab ofaluminurnat 600 eV and

five difierent ion densitws shows the n = 1 to 2 transitions of the helium- and

hydrogen-like ions.

2. Same as for Fig. 1, except this is for the higher energy transitions.

3. The Lyman ~ line of aluminum is shown for a uniform slab (U), one with a

temperature gradient (T), one with a density gradient (N), and one with a

velocity field (V). Details are given in the text.

4. The Lyman a line of aluminum and some of its satellites are shown for the

cases of Fig. 3.

5. A theoretical time-integrated spectrum for LABS I conditions. Each resonance

line is labeled. The weaker lines on the low energy sides of the strong lines are

satellite lines,

6. The same as Fig. 5 for LABS 11 conditions.

8

-m

@!

108

r i D I

~ ~23

R w

Is-zp

1 * I 1 I a I

1.5 1.6 1.7 1.8

Photon Energy - keV

LA

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1012

1010

108

1 I I I I I I 1 I I

(

*JI‘d\

1.8 1.9 2.0 2.1 2.2 2.3

Photon Energy – keV

-T-’

>

‘o

*9-

U)

0.8

0.6

0.4

0.2

0.0

.

.

eV~~-3

2.04 2.05 2.06

Photon Energy - keV

,>

1.6

1.2

0.8

0.4

0.0

.

.

1-

i

1

u, T

N

v

T’e= 600

hl~~= 3(?21

1 I r

u

eV~~-3

1

1-4

--—

1.71 1.72 1.73 1.74

Photon Energy - keV

,-

W.he

0.20

0.15

0.10

0.05

0.00

1sq3

LABS I conditions

on Aluminum

i

1.6 1.8 2.0 2.2

Photon Energy - keV

1 1 ! J 1 r 1 a 1 1 1 m 1 1 I I 1 I

[

0.6

1 1s~”l s2p

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0.2

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LABS H conditions

on Aluminum

is-2p

.

L.

1.6 1.8 2.0 2.2

Photon Enerqv – keVv-