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Modeling of absorption spectra in dense argon plasmas
Pergamon
kopynght c 1994 Eli&w Sxnce Lid Pnnted m Great Bntam All nghb reserved
00224073(93)EOO25-N
MODELING
OF ABSORPTION SPECTRA ARGON PLASMAS
R C MANCMI,~ C F Department of Physics
00224073:94
Unrverslty
HOOPER
of Flonda,
S6 00 + 0 00
IN DENSE
JR, and R L COLDWELL
215 Wdhamson
Hall.
GameswIle
FL 3261 I, U S A
Abstract-We have modeled the optical depth of hot, dense Ar plasmas due to lme absorpuon m n = I to n = 2 Inner-shell tranatlons m L-shell Ar Ions by performmg Stark broadened absorption hne profile and tomzatlon balance calculations Our results have built-m the temperature and density dependence charactenstlc of the level populations as well as the density sensmvlty Inherent m the Stark broadening of these transItIons Results are presented that Illustrate the temperature and density dependence of the optical depth As an apphcatlon. we use these results to analyse absorption spectra recorded dunng the collapse of laser dnven lmploslons of Ar-filled plastic mlcroballoons
I
INTRODUCTION
Lme absorption spectroscopy has been used m the past m the analysis of laser-dnven lmploslon expenments to study regions of the pusher where self-emlsslon was not useful for dlagnostlc apphcatlons I ’ More recently, laser-produced plasma expenments usmg layered planar targets have been diagnosed by absorption spectroscopy Analysis of these expenments rehed on detalled atomic structure and level population calculations m order to model complex absorption spectra m multlelectron Ions In turn, these models were used to make quantltatlve estimates of the temperature dlstnbutlon and lomzatlon balance m the absorbing medium ‘-9 Also, expenments usmg x-rays to heat the absorbmg medium have been performed m connection with detalled opacity measurements ‘&I3In the aforementioned work, Stark broadened absorption lme profiles were not used m the spectroscopic analysis either because they were not available at the moment or the absorbmg media were not dense enough for Stark broadenmg to be Important The widths of the absorption features were density independent and due pnmanly to Doppler and mstrumental effects Hence, analysis of the absorption spectra ylelded mformatlon about the temperature and lomzatlon balance condltlons m the absorbmg media while density estimates came from other conslderatlons Laser dnben lmploslons of Ar-filled plastic mlcroballoons performed at the Laboratory for Laser Energetlcs of the Umverslty of Rochester produced condmons during the collapse of the implosion such that contmuum radlatlon emltted from the central hot spot was absorbed by regions of Ar close to the core gas-pusher interface These outer, cooler layers of Ar were dense enough (N, 3 10”cm-3) for the absorption features to display slgmficant Stark broadenmg which could be used to estimate the electron density N, m the absorbmg region I”’ In this paper we model the opacity of a dense Ar plasma In the photon energy range 2900-3200 eV due to n = I to n = 2 Inner-shell transltlons m the L-shell Ions of Ar usmg Stark broadened absorption hne profile and romzatlon balance calculations. and we apply these results to analyse expenmental absorption spectra Our results have built-m the temperature and density dependence charactenstlc of the level populations as well as the density sensltlvlt] Inherent In the Stark broadening of the absorbing transltlons In Set 2 we present the model to compute the optical depth, m Set 3 we descnbe the analysis of the absorption spectra, and m Set 4 we present our conclusions 2
MODELING OF THE OPTICAL DEPTH OF A UNIFORM ABSORBING MEDIUM We begin by consldermg the formula for the photoexcltatlon cross sectlon m the dipole
tPresent address Department of Physics Umversity of Nevada. Reno NV 89557. U S A QSRT3, I-I--lu
201
202
R C MAN~INI et al
approxlmatton
for an Isolated
Ion m state I to absorb
a photon
of energy hv and end up m state
1
a,,(e) =
where hi,, IS the energy
of the transmon,
E/;,d(\,-
\I,,),
f;, IS the absorptton
e and m are the electron charge and mass, the absorbing Ion If we multiply a,,(v) probablhty that an ton IS In state I, p,, and range, we obtam the frequency dependent
osctllator
strength,
c IS the speed of hght, and d IS the dipole moment of by the denstty matnx element assoctated wtth the sum over all transmons that he m a given frequency photoexcttatlon cross sectton for the Ion, (3)
To render this expresston mto a form amenable for Stark broadenmg calculattons, we note that the primary frequency dependence of thts cross sectlon IS due to the delta functions, provided that the frequency range IS sufficiently narrow In that case. we can approximate the cross sectlon as follows.
We now relate this to the hne shape function
which 1s defined
as,‘”
notmg that this same expression IS used for both emlsston and absorption lme profiles. the only difference being whtch set of states IS averaged over (mltlal states) and whtch IS summed over (final states) Using this defimtlon of cp(v) we wrote uT(v) as.
Multlplymg and dlvldrng normahzed hne profile as.
the
r h s
of this equation
by 5 q(v) dv, and
denotmg
V(V)
ij(v) =
the area
(7)
cp(v) dv s we obtain.
and. agam usmg the approxlmatlon the hv mslde the Integral. perform
that hv varies neghgtbly m the v range of Interest, we can brmg the Integration. and wrote (recalhng the defimtton ofJ;,),
Finally. we define an average or efTecttve oscillator set of lruttal states to the set of final states 7 as,
dnd wnte
strength
for the set of transitions
from the
for Ok, (11)
Absorption
703
spectra m dense argon plasmas
The mteractlon between the absorbrng ron and the plasma mrcrofields perturbs the he profile mtrodunn_e Stark hroabemng e?iects, these eflects are mc’mdeb m the caIcula’l)on o’i she Imes’nape function $j( v) A recently developed multi-electron radiator hne profile formahsm and code.” I5was used to calculate Stark-broadened absorption hne profiles for Inner-shell n = I to n = 2 transmons m Ar L-shell Ions The electron temperature T, range of Interest was IOCMOOeVand the electron number density N, ranged from 5 x IO” cm-’ to 5 x Iti cm-’ Doppler broadenmg IS Included by convolvmg the Stark profile with a Gaussian profile Ion broadening 1s treated m the static-ron approxlmatlon and the effects of dynamic electrons are Included using a second order relaxation theory Ion- and electron-radiator mteractlons are computed m the dipole approxlmatlon All the necessalr) alomrc ph_vsIcs data {eflergv let& and reduced rnalrrh demenrs’r were ca\cu’taIed usrng Cowan’s multlconfiguratlon atomic structure codes mcludlng relatlvlstlc correctlons ” A detailed descrlptlon of the results obtamed for the Stark broadened absorption lme profiles was presented elsewhere ” For IV, larger than z 5 x 102’cm-’ Stark broadenmg becomes the dominant broddenmg mec+r3trrsn, -.imi *fl *fmi-&uc~~ ^a 3iAfla “&13fSj pS?3fSfUVfij lfh “Cdl~ +.R v.f& 5%i T3qgmmi apphcatlons, the temperalure dependence of lhe hne profifes 1s weak for the plasma condmons consldered here The !!&‘r~& &o&en& a?rs~~f~~ r’cnc~RZ&& &II,-&e L-s&=8 ~7~s & rlr cczrz USed (‘~7 L-&XY&Y the frequency dependem opllca’, beprh o!i a ~mn~‘iormabsorbing layer 03 _g)v~n Bensn_v &, temperature T,,and thickness I Using Eq (I 1) the optical depth due to absorption by tons m a particular lomzatlon stage, e g Be-like Ar, Tag. IS given by. TB~(\‘)= r~e(l’..IV,. T,.I)=oTdv.N,.T,)N,B,eI = ~f:&(v.N,)N,,(N,. T,)I
(12)
where N, BcIS the number density of Ions In the mltlal states of the Inner-shell transltlons In Be-like Ar, and 9ne lemperalure anb &-nwly bepenr5enres &J jhe 1meshapp anb IMP ~~slr>~ul>M 05 populations are explicitly dlsplayed We Ignore the weak temperature sensltlvity of the lmeshape For specr4 ra~gcs 5~ W+Y&&XQ~OQ~ de. ‘ro ‘rr~-i~~,~~~~ KI ‘rw~ DT more. ~5’Tr12’at~l~~ s$agE K important, the optical depths due to all relevant lomzatlon stages are added to yeld the total optlcal depth
a[ the layer
Hence. T(V) = TF(V) + To(V) +
+ 7L,(Y) + q-k(l')
where F refers to F-(rke Ar, 0 to O-hke Ar, etc The total r\pwal depth of the contnburrons from Wansrrlons m a3 rhe relevant IonJzarJon sfages ar rhe given baturs N, Effwwe br>soqxlon osc3Ialor slreqj2ins~7 3~ IBPSP Tra_nwrms haw JXY~Jralrtiatfd L-shell Ions I5 The distnbutlon of population among the mltlal states of the absorption
(13)
layer has nl^ 7, and
J~J aJ .4r transltlons
4
3 5 % G
3 % 0
2
He
1
0 3040 Energy
3060
3120
3160
WI
IF& I Oowal dqoth r{v\ tnr a unltarm laqw nT Irum rtwkwz~~ ~V.TJ y =L Y W’PK’ ,(---,\ 7, = i50et’, I---J I: = .Z.ZSeV In tnls figure. as well as the rest okhe tigures the peak structure IS labeled accordmg lo the dommant absorbmg Ar Ion
R C MANCINIet al
ii960
3000
3040 Energy
Fig 2 Optical T,=2OOeV,(---)
3060
3120
3160
WI
depth r(e) for a umform laqer of I pm thickness I-) A,=5 x I@‘cm-’ Ne= I x IO”cm-‘and T,=235eV ( ) N,=2 x 10?4cm-‘and T,=278eV ,I,=5 x 10z4cm~’ and T,=353eV
I-
and -b
IS calculated with the Saha equation For the temperatures and densltles consldered here the results of this LTE assumption have been compared to the correspondmg results from an NLTE model ‘O and agreement wlthm 5% was found between the two calculations Using these assumptions the total optlcal depth of d uniform absorbing layer due to tz = I to n = 2 Inner-shell transitions In the L-shell Ar Ions can be calculated as a function of the temperature T,. density N,, and thickness I of the layer We emphasize that the optical depth incorporates the electron temperature and density dependence of the dlstrlbutlon of population (through N,). and the density dependence of the Stark broadening effect [through q(v)] Figure I displays the optical depth for a layer of I pm thickness, N, of 5 x lO”cm-‘. and two temperatures I50 and 225 eV The change In r(\l) as the temperature rises reflects the shift m the lomzatlon balance. for T, = 150eV the absorption spectrum IS dominated by F-, 0-, N-. and C-like Ar. while for T, = 225 eV C-. B-. Be-. and LI-like Ar are prominent Note that. for the latter case the maxmium values of ~(19) for absorption by the dominant Ions are In general larger than m the former case because of an increase m absorption oscillator strength More Interesting from the point of view of Stark broadening IS the dependence of T(Y) on electron number density N, Changing NC affects both the lomzatlon balance and the Stark broadening of balance the absorption line profiles For a given T,. Increasing N< will shift the lonlzatlon downwards. as an Increase In three-body recomblnatlon will preferentially populate lower Ionization stages The Increase In V, will also Increase the Stark broadening of the absorption features To focus on the broadening effect. Fig 2 shows results for d layer thickness of I /urn and several combmatlons of N, and T, such that the lomzatlon balance remains approximately constant Hence. m each case ?(I#) IS dominated by the same Ions As the density rises from 5 x IO” cm-’ to 5 x lO”‘cm-’ the optical depth becomes less structured and the width of the absorption peaks become broader due to the density dependence of the lmeshapes Note that the values of the local maxima of the optical depth do not increase linearly alth density. ds might be expected For example. T(P) at the peak of the optical depth due to B-like Ar for the 5 x lO”cm~ cur\e IS 2 6 and when the density IS Increased by a factor of IO It IS 5 I The peaks of T(P) mcrease bj factors In the range of 24 This reflects the competition between tbo effects the Increase In the number of absorbing Ions which would tend to Increase the optical depth and the Increase m the strength of the plasma perturbation on the transitions which would tend to broaden the lmeshape and lower the peak optical depth In order to see the density dependence of the optical depth more clearly. note that the number density of Ions In the lower (mltlal) states of the absorption transltlons. for Ions m a particular lomzatlon stage, can be written as,
205
Absorption spectra m dense argon plasmas
where F,( T,, N,) IS the fractlonal Ion population, NT IS the total Ion number density and 2( T,. N,) IS the average lomzatlon stage Then we can write for the optlcal depth due to the Ions m this particular ionization stage, ne2 F,(T,. N,) T(V) = -_s G(l’, Ne)NJ mc z(T,, NC)
(15)
If we keep the lomzatlon balance approximately constant the mam density dependence of the optlcal depth IS m the product @(v. N,)N,, thus as N, Increases. peak values of r(\p) do not Increase at the same rate due to the drop m value at lme center of 4(\1. N,) However, values of T(V) m between peaks (dips, where the wmgs of the hneshapes overlap) Increase at a faster rate than does the density, Indeed, for Fig 2 values of ~0’) at the dips Increase by factors In the range between I2 and 30 while the density Increases by a factor of IO Here, at the dips, Instead of competmg, the two density dependent effects cooperate to Increase the value of the optlcal depth The Stark broadenmg effect on the absorption hne profiles removes the amblgulty of the lomzatlon balance alth respect to T, and N, As seen m Fig 2. several combmatlons of N, and T, can produce approximately the same lomzatlon dlstnbutlon but the corresponding optlcal depths are different because of the Stark broadenmg dependence on N,
3
4PPLICATION
TO THE
ANALYSIS
OF EXPERIMENTAL
SPECTRA
Laser driven lmploslon experiments of Ar-filled plastic mlcroballoons performed at the Laboratory for Laser Energetlcs of the Umverslty of Rochester produced core gas condltlons during the collapse of the lmploslon such that contmuum radlatlon emitted from the central hot spot was absorbed In the outermost layers of Ar near the pusher Interface ” In Fig 3 we shah a sequence of time-resolved spectra recorded on one of these expenments Early m time (spectrum a) we see the K-shell emlsslon from the He- and H-hke Ar Ions Later. this emlsslon gradually disappears and an absorption feature develops In the 305&3 I20 eV energy range These absorption features can be Interpreted as due to n = I to n = 2 Inner-shell transItIons m L-shell
2
3 5 @l
0 I 3000
I
3100
I
3200 Energy WI
I
3300
I 3400
Fig 3 Senes of time-resolved spectra Spectrum a IS earhest m time The spectra have been shifted vertically by arbitrary amounts for the purpose of display m the same picture
R C MANCINI
206
et al
absorbing Ions are B- ( 5 3060 eV), Be- ( z 3080 eV) and LI-hke ( z 3 IIOeV)
Ar Ions The dominant 4r
The temperature and density dependence of the optlcal depth dlscussed m the previous sectlon can be used to analyse these absorption spectra Preklous studies of absorptron spectroscopy In laser produced plasmas hdve mainly relied on the lntenslty of absorptton features to Infer plasma emlronmental condltlons ‘-’ Here. we combme mtenslty analIsIs with a study of the detailed shape of the absorption spectrum If we write for the experimental absorption spectrum I”p(11). IcXP(\’ ) = [;,‘P(\’ ) e - pr’p(y )
(16)
u here F”p(~v) IS the experimental
optical depth and I;;‘P(\q) IS the unattenuated (Incident) contmuum mtensitj. we can approximate J-erp(\l) / using our modeled T( \I) In order to Infer X”p( IV) from le’p( Y) tt IS necessary to know I,;“p(\v) In the case of the spectra of Fig 3 where parts of the Ar core gas are playing the role of the backlighting source while other parts are the absorbing media we did not have an independent characterization of the backlight source spectrum [I e. I;P(Y)] We overcame this problem bq using the spectral analysis code ROBFIT ROBFIT IS a general purpose spectral analysis code based on a least square mmlmlzatlon procedure ” The weights asslgned to each channel are determined from the fluctuations In the data The background fit IS robust m the sense that channels contalnmg peaks are weighted down relative to those free of peaks ROBFIT performed a fit to the data by slmultaneouslq and consistently karymg absorption and emlsslon peaks. and the contmuum background Figure 4 shows the details of the decon\olutton produced by ROBFIT for spectrum d of Fig 3 In thrs application we were Interested m the continuum determlnatlon done by ROBFIT which was used In Eq ( 16) to obtain Xe‘p(~~) To dpproxlmate ~‘P(Y) we mlmmlze the sum of squares. (17)
,= I
with respect to the layer thickness I for given T,and ,Y, Since r(v) depends linearly on I this can he reddily done analytically We emphasize that while the values of T,and N, WIII determine the details of the shdpe of s(r). the value of 1~111 merely adJuSt the overall lekel of absorption to best reproduce the observed one Fits can be obtained for several comblnatlons of T,and ;Ve In order to see \thlch one best approximates the experimental spectrum Figure 5 displays two fits for N, s of I x IO” and 5 x lO”‘cm ml The photon energy range for the mlmmlzatlon IS 3045-31’5 eV which IS relevant for the leading absorbing Ions (B-. Be- and Ll-like Ar) Note that the fits do not reproduce effectlvelq the relative mtensltles of the absorption dips characterlstlc of each lonlzatlon state This suggests that the absorption feature was formed while the continuum radiation Has passing through a gradient of temperatures
To test this Idea we performed
fits using two absorbing
0 75 07 0 65 ;
06 0 55
I 3075 Fig 4 Detads of the deconvolwon spectrum
I 3175 Energy (ev)
I 3275
of spectrum d produced by the ROBFIT ) mdl~ldual peaks and background
(
I 3375 code
I-)
expernnental
207
Absorption spectra m dense argon plasmas
3050
3100 Energy WI
3150
3200
Fig 5 Modehng fits fo the absorption fealure of spectrum d, i-layer model (---_) expenmental ) T,=525eV and NC=5 x l@‘cn~’ spectrum, (---) T, = 325 eV and NC= I x lO”cm-‘, (
layers, and allowlng the radlatlon commg out of the first layer to be further transmltted through the second one Here, layers are characterized by the same N, but they can have different T,‘s, the mmmuzatlon IS done with respect to both layers thicknesses Figure 6 shows the result obtamed for N, = 1 x IO”cn-) It IS apparent that the two temperature model allows a better matching of the relative absorption mtensltles but the details of the broadenmg are not well reproduced At this pomt, we tned to Improve the fit by usmg also different densltles m the two layers. the new result IS shown m Fig 7 Now the Improvement IS even more significant since relative absorption dips as well as the broadening of each absorption feature can be better approximated. suggestmg that the absorption spectrum was produced whde the contmuum radlatlon was going through gradients of both temperature and density A study was done using a 34ayers model and the result IS also dlsplayed m Fig 7 The 34ayers result shows a small Improvement with respect to the 24ayers case To better understand the 24ayers model result, Fig 8 shows the contnbutlons to T(Y) from each layer The absorption m Be- and LI-hke Ar IS dommated by contnbuuons at higher density as compared to B-hke Ar This picture 1s consistent with radiation-hydrodynamics slmulatlon results which Indicate that the absorption features were produced when contmuum radlatlon emltted from the central hot spot behmd the reflected shock IS absorbed by cooler layers of Ar m front of the shock where density and temperature gradients are present 2z
145
139 3050
3150 3200 3100 Energy (W Fig 6 Modehng fits to the absorption feature of spectrum d, I- and 2-layers models (-) expenmenlal spectrum, (---) l-layer, same as (---) m Rg 5, ( ) 2-layers, 7, = 400 eV and N, = I x 10z”cm-‘. and T,= 25OeV and N,= I x IW’cm-
208
R C MANCINI et al
I 3000
LI
I
3050
3100 Energy
I 3150
3200
WI
Fig 7 Modehng fits to the absorption feature of spectrum d 2- and 3-layers models (-) experlmental spectrum (---) 2-laqers T,=550eVand ,A’<=5x 10z’cm-’ and T,=280eVand VS= I x 101’cm-’ ) 3-lajer, T, = 6OOe\ and ,‘L; = 5 x lti’cm-’ 7, = 33OeI’and h, = 2 x 10-“cm-’ dnd T, = 22OcV I and ,\‘< = 5 )r IOJ’cm-’
FInally. we explore the contrlbutlons of higher order transmons This was motivated In part by the fact that our modeling fits seemed to systematically underestlmate the broadening of the LI-hke feature In all of the pre\lous results for the tz = I to n = 2 transItIons. we consldered configuratlons with all electrons In t? = I. 2. e g . for LI-hke Ar Ions this means Is%ls2121’ transItIons with / = s,p At I%‘~> I x lO”cm-’ excited states of L-shell Ar Ions with one electron m n = 3 can be slgmficantly populated, In particular, transitions of the general type Is’2131 -ls2121”31’ In Be-hke Ar can make a contnbutlon, and will have slgmficant overlappmg with ls’21-1~2121’ transltrons m Ll-hke Ar, thus contrlbutlng to Increase the observed broadening of the LI-hke feature These transItIons can be Interpreted either as higher order transitions rn Be-like Ar or as Be-like satellites (Be-S) to the transitions m Lt-like Ar To Illustrate this point. Fig 9 displays area notmdhzed. Stark broadened absorption line profiles for the transitions In Be- and LI-like Ar Ions, and the Be-S transItIons The overlapping effect IS clearly shown It IS also lnterestmg to note the Increased Stark broademng of the Be-S transItIons as compared to the transitions m Be- and LI-like Ar This IS due to the presence of the w = 3 electron In the configuratlon which makes the relevant energy levels more susceptible to plasma perturbations
05
This suggests that as density Increases. at least two effects
I
I
I
04
2 $ c3
03
3 “a 0
02
01
0
3000
3050
3100 Energy
3150
3200
WI
FIN 8 Smgle layer contrlbutlons Lo the total optIcal depth T(Y) of the Z-layers model fit of Fig 7 (-) total r(v) due to both layers (---) T(v) of the layer at T” = 280eV and N, = I x I@“cm-’ f 1 of rhe lajer at 7. = 550eV and We= 5 x lo’4cn-’
70’)
Absorptton
209
spectra III dense argon plasmas
0 12 F E
01
g
008
Ii t i s g
006 004
is 2 002 0 3050
3070
3090
3110
Energy
3130
3150
(W
Ftg 9 Area normahzed absorpuon hne profiles for T, = 400 eV and N, = I x lo?4cm-’ due to n = I to n = 2 Inner-shell transmons tn Be- (-), LI- ( ), and satelhte transtttons In Be-like (---I Ar Ions
will compete m determmmg the relevance of transulons ansmg from levels with an n = 3 electron on the one hand, the increase m the population of these energy levels which will make them more Important, and, on the other hand, the increase m Stark broadening which will broaden their line profiles and make then effect be less noticeable Figure IO shows a fit to the expenmental spectrum using a 3-layers model, mcludmg the Be-like satellite transulons. and also the n = I to n = 2 transitions m C-like Ar With the mcluslon of the Be-S transtttons, the overall broadenmg of the LI feature IS better approxtmated 4
CONCLUSIONS
We have modeled the opacity of hot, dense argon plasmas due to n = I to n = 2 Inner-shell transrtrons m t-shell Ar Ions using Stark broadened hne profiles and lomzatlon balance calculatrons For electron densrtres N, larger than ;5 5 x IO” cmm3 Stark broadening becomes dommant and modeling results indicate that the N, sensttrvity of the absorption lmeshapes together with the N, and T, dependence of the lomzatton balance result m an optlcal depth ~(11.N,, T,) that can be used to make simultaneous inferences of density and temperature AlternatIvely, If N, or T, are known from other constderatrons It can be used as a consistency check More, and better
I 3050
I 3100 Energy WI
I 3150
I 3200
Ftg IO Modehng fit to the absorptton feature of spectrum d. 3-layers model mcludmg transmons m C-hke Ar and satelhtes In Be-like Ar (-) expertmental spectrum, (---) 3-layers, T,=ZlOeV and N,=5~l~~~‘,T,=250eVandN,=IxI~‘cm-’,andT,=520eVandN~=5xl0~~~-’
210
R C MANCINIet al
quahty. results
experlmental
measurements
are needed
to further
of these modehng
nork uas supported In pan by US DOE grant DE-FGO3-92SF19199 support from NERDC through the Research Computrng lnmatrve
~~~N~n/r~~erncrrrs--Thlj
computauonal
test the capabllwes
We xknowledge
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I3 I4
I5 I6
I7 I8 I9 20 21
‘? __
B Yaakohl R L McCrory S Skupsky J Delettrez P Bourke, H Deckman C F Hooper Jr and J Soures Opt Cotnnrun 34, 213 (1980) A Hauer. R D Cowan B Yaakobt 0 Barnoum, and R Epstein. fh~~s Rer 1 34, 41 I (1986) C Chenats-Popoctcs, C Ftevet, J P Gemdre. J C Gauthter. E Luc-Koenig, J F Wyart. H Peptn and M Choker fh~s Ret A 40, 3194 (1989) J Bruneau C Chenats-Popovlcs. D Desenne J C Gauthter. J P Gemdre. M Klaptsch, J P Le Breton M Louts-Jacquet D Naccache, and J P Perrme, Phys Ra? L.ert 65, 1435 (1990) C Chenats-Popovtcs C Ftevet. J P Gemdre I Matsushtma, and J C Gauthter Phts Rev 4 42. 4788 (1990) J Bruneau A Decoster D Desenne, H Dumont, J P Le Breton, M Bolvmeau, J P Pernne. S Bayle M Lotus-Jacquet J P Gemdre. C Chenats-Popovtcs, and J C Gauthrer, fh~s Rev 4 44, R832 (1991) J Abdallah Jr and R E H Clark J Appl Phys 69, 23 (1991) J Abdalldh Jr R E H Clark, and J M Peek, Ph_rs Ray 4 44, 4072 (1991) R Epstein, Phts Rell 4 43, 961 (1991) S J Davidson J M Foster C C Smith. K A Warburton, and S J Rose, 4ppI Phls Lefr 52, 847 (1988) J M Foster. D J Hoarty. C C Smith P A Rosen S J Davrdson, S J Rose T S Perry and F J D Serduke. fhts Rev Lerr 67, 3255 (1991) T S Perry, S J Davidson F J D Serduke, D R Bach, C C Smith, J M Foster, R J Dovas. R A Ward C 4 lglestas F J Rogers J Abdallah Jr, R E Stewart, J D Ktlkenny. and R W Lee Pkrs Rec. Lert 67, 3784 (1991) J Edwards M Dunne. D Rtley. R Taylor. 0 WIIII, and S J Rose, Ph_rs Rer Lerf 67, 3780 ( 1991) R C Mancuu C F Hooper Jr, J Delettrez. R Epstein, D K Bradley, P A Jaanrmagr. and M C Rtchdrdson u-r Radtarr~~ePropertres o/ Hot Dense kfunrrer W Goldstem, C Hooper. J Gauthter, J Seely and R Lee eds World Sctenttfic Smgapore (1991) D 4 Havnes Jr R C Mancnu. and C F Hooper Jr, Laser Purrtcfe Beams II, 205 (1993) H Gnem, Specrrul Ltne Broudentng ~JP Plusmus, Academic Press, New York. NY (1974) L Waltz and C F Hooper Jr Phts Rev A 38, 4766 (1988) R C Mancu-u D P Ktlcrease. L Woltz, and C F HooperJr, Compur P~JS Commun 63,314(1991) R D Cowan %T Theorl o/ Arotnrc Sfrucrure and Spectra. Umv of Cahfomta Press, Berkeley (1981) Y T Lee JQSRT 38, 131 (1987) R L Coldwell and G J Bamford T/re TIreorr and Operurton of Spec~rul Anuhsrs C’stng ROBFIT, American lnstttute of Physics, Instrument and Measurement Sctence Serves, New York (1991) The ROBFIT code IS dvatlable from R L Coldwell upon request J Delerrez R Epstein D K Bradley, P A Jaammagt. R C Manam. and C F Hooper Jr In Rudtarrc,e Properfres oJ Hot Dense Muf/er W Goldstem C Hooper, J Gauthrer, J Seely. and R Lee eds World Scientific Singapore (1991)
kopynght c 1994 Eli&w Sxnce Lid Pnnted m Great Bntam All nghb reserved
00224073(93)EOO25-N
MODELING
OF ABSORPTION SPECTRA ARGON PLASMAS
R C MANCMI,~ C F Department of Physics
00224073:94
Unrverslty
HOOPER
of Flonda,
S6 00 + 0 00
IN DENSE
JR, and R L COLDWELL
215 Wdhamson
Hall.
GameswIle
FL 3261 I, U S A
Abstract-We have modeled the optical depth of hot, dense Ar plasmas due to lme absorpuon m n = I to n = 2 Inner-shell tranatlons m L-shell Ar Ions by performmg Stark broadened absorption hne profile and tomzatlon balance calculations Our results have built-m the temperature and density dependence charactenstlc of the level populations as well as the density sensmvlty Inherent m the Stark broadening of these transItIons Results are presented that Illustrate the temperature and density dependence of the optical depth As an apphcatlon. we use these results to analyse absorption spectra recorded dunng the collapse of laser dnven lmploslons of Ar-filled plastic mlcroballoons
I
INTRODUCTION
Lme absorption spectroscopy has been used m the past m the analysis of laser-dnven lmploslon expenments to study regions of the pusher where self-emlsslon was not useful for dlagnostlc apphcatlons I ’ More recently, laser-produced plasma expenments usmg layered planar targets have been diagnosed by absorption spectroscopy Analysis of these expenments rehed on detalled atomic structure and level population calculations m order to model complex absorption spectra m multlelectron Ions In turn, these models were used to make quantltatlve estimates of the temperature dlstnbutlon and lomzatlon balance m the absorbing medium ‘-9 Also, expenments usmg x-rays to heat the absorbmg medium have been performed m connection with detalled opacity measurements ‘&I3In the aforementioned work, Stark broadened absorption lme profiles were not used m the spectroscopic analysis either because they were not available at the moment or the absorbmg media were not dense enough for Stark broadenmg to be Important The widths of the absorption features were density independent and due pnmanly to Doppler and mstrumental effects Hence, analysis of the absorption spectra ylelded mformatlon about the temperature and lomzatlon balance condltlons m the absorbmg media while density estimates came from other conslderatlons Laser dnben lmploslons of Ar-filled plastic mlcroballoons performed at the Laboratory for Laser Energetlcs of the Umverslty of Rochester produced condmons during the collapse of the implosion such that contmuum radlatlon emltted from the central hot spot was absorbed by regions of Ar close to the core gas-pusher interface These outer, cooler layers of Ar were dense enough (N, 3 10”cm-3) for the absorption features to display slgmficant Stark broadenmg which could be used to estimate the electron density N, m the absorbmg region I”’ In this paper we model the opacity of a dense Ar plasma In the photon energy range 2900-3200 eV due to n = I to n = 2 Inner-shell transltlons m the L-shell Ions of Ar usmg Stark broadened absorption hne profile and romzatlon balance calculations. and we apply these results to analyse expenmental absorption spectra Our results have built-m the temperature and density dependence charactenstlc of the level populations as well as the density sensltlvlt] Inherent In the Stark broadening of the absorbing transltlons In Set 2 we present the model to compute the optical depth, m Set 3 we descnbe the analysis of the absorption spectra, and m Set 4 we present our conclusions 2
MODELING OF THE OPTICAL DEPTH OF A UNIFORM ABSORBING MEDIUM We begin by consldermg the formula for the photoexcltatlon cross sectlon m the dipole
tPresent address Department of Physics Umversity of Nevada. Reno NV 89557. U S A QSRT3, I-I--lu
201
202
R C MAN~INI et al
approxlmatton
for an Isolated
Ion m state I to absorb
a photon
of energy hv and end up m state
1
a,,(e) =
where hi,, IS the energy
of the transmon,
E/;,d(\,-
\I,,),
f;, IS the absorptton
e and m are the electron charge and mass, the absorbing Ion If we multiply a,,(v) probablhty that an ton IS In state I, p,, and range, we obtam the frequency dependent
osctllator
strength,
c IS the speed of hght, and d IS the dipole moment of by the denstty matnx element assoctated wtth the sum over all transmons that he m a given frequency photoexcttatlon cross sectton for the Ion, (3)
To render this expresston mto a form amenable for Stark broadenmg calculattons, we note that the primary frequency dependence of thts cross sectlon IS due to the delta functions, provided that the frequency range IS sufficiently narrow In that case. we can approximate the cross sectlon as follows.
We now relate this to the hne shape function
which 1s defined
as,‘”
notmg that this same expression IS used for both emlsston and absorption lme profiles. the only difference being whtch set of states IS averaged over (mltlal states) and whtch IS summed over (final states) Using this defimtlon of cp(v) we wrote uT(v) as.
Multlplymg and dlvldrng normahzed hne profile as.
the
r h s
of this equation
by 5 q(v) dv, and
denotmg
V(V)
ij(v) =
the area
(7)
cp(v) dv s we obtain.
and. agam usmg the approxlmatlon the hv mslde the Integral. perform
that hv varies neghgtbly m the v range of Interest, we can brmg the Integration. and wrote (recalhng the defimtton ofJ;,),
Finally. we define an average or efTecttve oscillator set of lruttal states to the set of final states 7 as,
dnd wnte
strength
for the set of transitions
from the
for Ok, (11)
Absorption
703
spectra m dense argon plasmas
The mteractlon between the absorbrng ron and the plasma mrcrofields perturbs the he profile mtrodunn_e Stark hroabemng e?iects, these eflects are mc’mdeb m the caIcula’l)on o’i she Imes’nape function $j( v) A recently developed multi-electron radiator hne profile formahsm and code.” I5was used to calculate Stark-broadened absorption hne profiles for Inner-shell n = I to n = 2 transmons m Ar L-shell Ions The electron temperature T, range of Interest was IOCMOOeVand the electron number density N, ranged from 5 x IO” cm-’ to 5 x Iti cm-’ Doppler broadenmg IS Included by convolvmg the Stark profile with a Gaussian profile Ion broadening 1s treated m the static-ron approxlmatlon and the effects of dynamic electrons are Included using a second order relaxation theory Ion- and electron-radiator mteractlons are computed m the dipole approxlmatlon All the necessalr) alomrc ph_vsIcs data {eflergv let& and reduced rnalrrh demenrs’r were ca\cu’taIed usrng Cowan’s multlconfiguratlon atomic structure codes mcludlng relatlvlstlc correctlons ” A detailed descrlptlon of the results obtamed for the Stark broadened absorption lme profiles was presented elsewhere ” For IV, larger than z 5 x 102’cm-’ Stark broadenmg becomes the dominant broddenmg mec+r3trrsn, -.imi *fl *fmi-&uc~~ ^a 3iAfla “&13fSj pS?3fSfUVfij lfh “Cdl~ +.R v.f& 5%i T3qgmmi apphcatlons, the temperalure dependence of lhe hne profifes 1s weak for the plasma condmons consldered here The !!&‘r~& &o&en& a?rs~~f~~ r’cnc~RZ&& &II,-&e L-s&=8 ~7~s & rlr cczrz USed (‘~7 L-&XY&Y the frequency dependem opllca’, beprh o!i a ~mn~‘iormabsorbing layer 03 _g)v~n Bensn_v &, temperature T,,and thickness I Using Eq (I 1) the optical depth due to absorption by tons m a particular lomzatlon stage, e g Be-like Ar, Tag. IS given by. TB~(\‘)= r~e(l’..IV,. T,.I)=oTdv.N,.T,)N,B,eI = ~f:&(v.N,)N,,(N,. T,)I
(12)
where N, BcIS the number density of Ions In the mltlal states of the Inner-shell transltlons In Be-like Ar, and 9ne lemperalure anb &-nwly bepenr5enres &J jhe 1meshapp anb IMP ~~slr>~ul>M 05 populations are explicitly dlsplayed We Ignore the weak temperature sensltlvity of the lmeshape For specr4 ra~gcs 5~ W+Y&&XQ~OQ~ de. ‘ro ‘rr~-i~~,~~~~ KI ‘rw~ DT more. ~5’Tr12’at~l~~ s$agE K important, the optical depths due to all relevant lomzatlon stages are added to yeld the total optlcal depth
a[ the layer
Hence. T(V) = TF(V) + To(V) +
+ 7L,(Y) + q-k(l')
where F refers to F-(rke Ar, 0 to O-hke Ar, etc The total r\pwal depth of the contnburrons from Wansrrlons m a3 rhe relevant IonJzarJon sfages ar rhe given baturs N, Effwwe br>soqxlon osc3Ialor slreqj2ins~7 3~ IBPSP Tra_nwrms haw JXY~Jralrtiatfd L-shell Ions I5 The distnbutlon of population among the mltlal states of the absorption
(13)
layer has nl^ 7, and
J~J aJ .4r transltlons
4
3 5 % G
3 % 0
2
He
1
0 3040 Energy
3060
3120
3160
WI
IF& I Oowal dqoth r{v\ tnr a unltarm laqw nT Irum rtwkwz~~ ~V.TJ y =L Y W’PK’ ,(---,\ 7, = i50et’, I---J I: = .Z.ZSeV In tnls figure. as well as the rest okhe tigures the peak structure IS labeled accordmg lo the dommant absorbmg Ar Ion
R C MANCINIet al
ii960
3000
3040 Energy
Fig 2 Optical T,=2OOeV,(---)
3060
3120
3160
WI
depth r(e) for a umform laqer of I pm thickness I-) A,=5 x I@‘cm-’ Ne= I x IO”cm-‘and T,=235eV ( ) N,=2 x 10?4cm-‘and T,=278eV ,I,=5 x 10z4cm~’ and T,=353eV
I-
and -b
IS calculated with the Saha equation For the temperatures and densltles consldered here the results of this LTE assumption have been compared to the correspondmg results from an NLTE model ‘O and agreement wlthm 5% was found between the two calculations Using these assumptions the total optlcal depth of d uniform absorbing layer due to tz = I to n = 2 Inner-shell transitions In the L-shell Ar Ions can be calculated as a function of the temperature T,. density N,, and thickness I of the layer We emphasize that the optical depth incorporates the electron temperature and density dependence of the dlstrlbutlon of population (through N,). and the density dependence of the Stark broadening effect [through q(v)] Figure I displays the optical depth for a layer of I pm thickness, N, of 5 x lO”cm-‘. and two temperatures I50 and 225 eV The change In r(\l) as the temperature rises reflects the shift m the lomzatlon balance. for T, = 150eV the absorption spectrum IS dominated by F-, 0-, N-. and C-like Ar. while for T, = 225 eV C-. B-. Be-. and LI-like Ar are prominent Note that. for the latter case the maxmium values of ~(19) for absorption by the dominant Ions are In general larger than m the former case because of an increase m absorption oscillator strength More Interesting from the point of view of Stark broadening IS the dependence of T(Y) on electron number density N, Changing NC affects both the lomzatlon balance and the Stark broadening of balance the absorption line profiles For a given T,. Increasing N< will shift the lonlzatlon downwards. as an Increase In three-body recomblnatlon will preferentially populate lower Ionization stages The Increase In V, will also Increase the Stark broadening of the absorption features To focus on the broadening effect. Fig 2 shows results for d layer thickness of I /urn and several combmatlons of N, and T, such that the lomzatlon balance remains approximately constant Hence. m each case ?(I#) IS dominated by the same Ions As the density rises from 5 x IO” cm-’ to 5 x lO”‘cm-’ the optical depth becomes less structured and the width of the absorption peaks become broader due to the density dependence of the lmeshapes Note that the values of the local maxima of the optical depth do not increase linearly alth density. ds might be expected For example. T(P) at the peak of the optical depth due to B-like Ar for the 5 x lO”cm~ cur\e IS 2 6 and when the density IS Increased by a factor of IO It IS 5 I The peaks of T(P) mcrease bj factors In the range of 24 This reflects the competition between tbo effects the Increase In the number of absorbing Ions which would tend to Increase the optical depth and the Increase m the strength of the plasma perturbation on the transitions which would tend to broaden the lmeshape and lower the peak optical depth In order to see the density dependence of the optical depth more clearly. note that the number density of Ions In the lower (mltlal) states of the absorption transltlons. for Ions m a particular lomzatlon stage, can be written as,
205
Absorption spectra m dense argon plasmas
where F,( T,, N,) IS the fractlonal Ion population, NT IS the total Ion number density and 2( T,. N,) IS the average lomzatlon stage Then we can write for the optlcal depth due to the Ions m this particular ionization stage, ne2 F,(T,. N,) T(V) = -_s G(l’, Ne)NJ mc z(T,, NC)
(15)
If we keep the lomzatlon balance approximately constant the mam density dependence of the optlcal depth IS m the product @(v. N,)N,, thus as N, Increases. peak values of r(\p) do not Increase at the same rate due to the drop m value at lme center of 4(\1. N,) However, values of T(V) m between peaks (dips, where the wmgs of the hneshapes overlap) Increase at a faster rate than does the density, Indeed, for Fig 2 values of ~0’) at the dips Increase by factors In the range between I2 and 30 while the density Increases by a factor of IO Here, at the dips, Instead of competmg, the two density dependent effects cooperate to Increase the value of the optlcal depth The Stark broadenmg effect on the absorption hne profiles removes the amblgulty of the lomzatlon balance alth respect to T, and N, As seen m Fig 2. several combmatlons of N, and T, can produce approximately the same lomzatlon dlstnbutlon but the corresponding optlcal depths are different because of the Stark broadenmg dependence on N,
3
4PPLICATION
TO THE
ANALYSIS
OF EXPERIMENTAL
SPECTRA
Laser driven lmploslon experiments of Ar-filled plastic mlcroballoons performed at the Laboratory for Laser Energetlcs of the Umverslty of Rochester produced core gas condltlons during the collapse of the lmploslon such that contmuum radlatlon emitted from the central hot spot was absorbed In the outermost layers of Ar near the pusher Interface ” In Fig 3 we shah a sequence of time-resolved spectra recorded on one of these expenments Early m time (spectrum a) we see the K-shell emlsslon from the He- and H-hke Ar Ions Later. this emlsslon gradually disappears and an absorption feature develops In the 305&3 I20 eV energy range These absorption features can be Interpreted as due to n = I to n = 2 Inner-shell transItIons m L-shell
2
3 5 @l
0 I 3000
I
3100
I
3200 Energy WI
I
3300
I 3400
Fig 3 Senes of time-resolved spectra Spectrum a IS earhest m time The spectra have been shifted vertically by arbitrary amounts for the purpose of display m the same picture
R C MANCINI
206
et al
absorbing Ions are B- ( 5 3060 eV), Be- ( z 3080 eV) and LI-hke ( z 3 IIOeV)
Ar Ions The dominant 4r
The temperature and density dependence of the optlcal depth dlscussed m the previous sectlon can be used to analyse these absorption spectra Preklous studies of absorptron spectroscopy In laser produced plasmas hdve mainly relied on the lntenslty of absorptton features to Infer plasma emlronmental condltlons ‘-’ Here. we combme mtenslty analIsIs with a study of the detailed shape of the absorption spectrum If we write for the experimental absorption spectrum I”p(11). IcXP(\’ ) = [;,‘P(\’ ) e - pr’p(y )
(16)
u here F”p(~v) IS the experimental
optical depth and I;;‘P(\q) IS the unattenuated (Incident) contmuum mtensitj. we can approximate J-erp(\l) / using our modeled T( \I) In order to Infer X”p( IV) from le’p( Y) tt IS necessary to know I,;“p(\v) In the case of the spectra of Fig 3 where parts of the Ar core gas are playing the role of the backlighting source while other parts are the absorbing media we did not have an independent characterization of the backlight source spectrum [I e. I;P(Y)] We overcame this problem bq using the spectral analysis code ROBFIT ROBFIT IS a general purpose spectral analysis code based on a least square mmlmlzatlon procedure ” The weights asslgned to each channel are determined from the fluctuations In the data The background fit IS robust m the sense that channels contalnmg peaks are weighted down relative to those free of peaks ROBFIT performed a fit to the data by slmultaneouslq and consistently karymg absorption and emlsslon peaks. and the contmuum background Figure 4 shows the details of the decon\olutton produced by ROBFIT for spectrum d of Fig 3 In thrs application we were Interested m the continuum determlnatlon done by ROBFIT which was used In Eq ( 16) to obtain Xe‘p(~~) To dpproxlmate ~‘P(Y) we mlmmlze the sum of squares. (17)
,= I
with respect to the layer thickness I for given T,and ,Y, Since r(v) depends linearly on I this can he reddily done analytically We emphasize that while the values of T,and N, WIII determine the details of the shdpe of s(r). the value of 1~111 merely adJuSt the overall lekel of absorption to best reproduce the observed one Fits can be obtained for several comblnatlons of T,and ;Ve In order to see \thlch one best approximates the experimental spectrum Figure 5 displays two fits for N, s of I x IO” and 5 x lO”‘cm ml The photon energy range for the mlmmlzatlon IS 3045-31’5 eV which IS relevant for the leading absorbing Ions (B-. Be- and Ll-like Ar) Note that the fits do not reproduce effectlvelq the relative mtensltles of the absorption dips characterlstlc of each lonlzatlon state This suggests that the absorption feature was formed while the continuum radiation Has passing through a gradient of temperatures
To test this Idea we performed
fits using two absorbing
0 75 07 0 65 ;
06 0 55
I 3075 Fig 4 Detads of the deconvolwon spectrum
I 3175 Energy (ev)
I 3275
of spectrum d produced by the ROBFIT ) mdl~ldual peaks and background
(
I 3375 code
I-)
expernnental
207
Absorption spectra m dense argon plasmas
3050
3100 Energy WI
3150
3200
Fig 5 Modehng fits fo the absorption fealure of spectrum d, i-layer model (---_) expenmental ) T,=525eV and NC=5 x l@‘cn~’ spectrum, (---) T, = 325 eV and NC= I x lO”cm-‘, (
layers, and allowlng the radlatlon commg out of the first layer to be further transmltted through the second one Here, layers are characterized by the same N, but they can have different T,‘s, the mmmuzatlon IS done with respect to both layers thicknesses Figure 6 shows the result obtamed for N, = 1 x IO”cn-) It IS apparent that the two temperature model allows a better matching of the relative absorption mtensltles but the details of the broadenmg are not well reproduced At this pomt, we tned to Improve the fit by usmg also different densltles m the two layers. the new result IS shown m Fig 7 Now the Improvement IS even more significant since relative absorption dips as well as the broadening of each absorption feature can be better approximated. suggestmg that the absorption spectrum was produced whde the contmuum radlatlon was going through gradients of both temperature and density A study was done using a 34ayers model and the result IS also dlsplayed m Fig 7 The 34ayers result shows a small Improvement with respect to the 24ayers case To better understand the 24ayers model result, Fig 8 shows the contnbutlons to T(Y) from each layer The absorption m Be- and LI-hke Ar IS dommated by contnbuuons at higher density as compared to B-hke Ar This picture 1s consistent with radiation-hydrodynamics slmulatlon results which Indicate that the absorption features were produced when contmuum radlatlon emltted from the central hot spot behmd the reflected shock IS absorbed by cooler layers of Ar m front of the shock where density and temperature gradients are present 2z
145
139 3050
3150 3200 3100 Energy (W Fig 6 Modehng fits to the absorption feature of spectrum d, I- and 2-layers models (-) expenmenlal spectrum, (---) l-layer, same as (---) m Rg 5, ( ) 2-layers, 7, = 400 eV and N, = I x 10z”cm-‘. and T,= 25OeV and N,= I x IW’cm-
208
R C MANCINI et al
I 3000
LI
I
3050
3100 Energy
I 3150
3200
WI
Fig 7 Modehng fits to the absorption feature of spectrum d 2- and 3-layers models (-) experlmental spectrum (---) 2-laqers T,=550eVand ,A’<=5x 10z’cm-’ and T,=280eVand VS= I x 101’cm-’ ) 3-lajer, T, = 6OOe\ and ,‘L; = 5 x lti’cm-’ 7, = 33OeI’and h, = 2 x 10-“cm-’ dnd T, = 22OcV I and ,\‘< = 5 )r IOJ’cm-’
FInally. we explore the contrlbutlons of higher order transmons This was motivated In part by the fact that our modeling fits seemed to systematically underestlmate the broadening of the LI-hke feature In all of the pre\lous results for the tz = I to n = 2 transItIons. we consldered configuratlons with all electrons In t? = I. 2. e g . for LI-hke Ar Ions this means Is%ls2121’ transItIons with / = s,p At I%‘~> I x lO”cm-’ excited states of L-shell Ar Ions with one electron m n = 3 can be slgmficantly populated, In particular, transitions of the general type Is’2131 -ls2121”31’ In Be-hke Ar can make a contnbutlon, and will have slgmficant overlappmg with ls’21-1~2121’ transltrons m Ll-hke Ar, thus contrlbutlng to Increase the observed broadening of the LI-hke feature These transItIons can be Interpreted either as higher order transitions rn Be-like Ar or as Be-like satellites (Be-S) to the transitions m Lt-like Ar To Illustrate this point. Fig 9 displays area notmdhzed. Stark broadened absorption line profiles for the transitions In Be- and LI-like Ar Ions, and the Be-S transItIons The overlapping effect IS clearly shown It IS also lnterestmg to note the Increased Stark broademng of the Be-S transItIons as compared to the transitions m Be- and LI-like Ar This IS due to the presence of the w = 3 electron In the configuratlon which makes the relevant energy levels more susceptible to plasma perturbations
05
This suggests that as density Increases. at least two effects
I
I
I
04
2 $ c3
03
3 “a 0
02
01
0
3000
3050
3100 Energy
3150
3200
WI
FIN 8 Smgle layer contrlbutlons Lo the total optIcal depth T(Y) of the Z-layers model fit of Fig 7 (-) total r(v) due to both layers (---) T(v) of the layer at T” = 280eV and N, = I x I@“cm-’ f 1 of rhe lajer at 7. = 550eV and We= 5 x lo’4cn-’
70’)
Absorptton
209
spectra III dense argon plasmas
0 12 F E
01
g
008
Ii t i s g
006 004
is 2 002 0 3050
3070
3090
3110
Energy
3130
3150
(W
Ftg 9 Area normahzed absorpuon hne profiles for T, = 400 eV and N, = I x lo?4cm-’ due to n = I to n = 2 Inner-shell transmons tn Be- (-), LI- ( ), and satelhte transtttons In Be-like (---I Ar Ions
will compete m determmmg the relevance of transulons ansmg from levels with an n = 3 electron on the one hand, the increase m the population of these energy levels which will make them more Important, and, on the other hand, the increase m Stark broadening which will broaden their line profiles and make then effect be less noticeable Figure IO shows a fit to the expenmental spectrum using a 3-layers model, mcludmg the Be-like satellite transulons. and also the n = I to n = 2 transitions m C-like Ar With the mcluslon of the Be-S transtttons, the overall broadenmg of the LI feature IS better approxtmated 4
CONCLUSIONS
We have modeled the opacity of hot, dense argon plasmas due to n = I to n = 2 Inner-shell transrtrons m t-shell Ar Ions using Stark broadened hne profiles and lomzatlon balance calculatrons For electron densrtres N, larger than ;5 5 x IO” cmm3 Stark broadening becomes dommant and modeling results indicate that the N, sensttrvity of the absorption lmeshapes together with the N, and T, dependence of the lomzatton balance result m an optlcal depth ~(11.N,, T,) that can be used to make simultaneous inferences of density and temperature AlternatIvely, If N, or T, are known from other constderatrons It can be used as a consistency check More, and better
I 3050
I 3100 Energy WI
I 3150
I 3200
Ftg IO Modehng fit to the absorptton feature of spectrum d. 3-layers model mcludmg transmons m C-hke Ar and satelhtes In Be-like Ar (-) expertmental spectrum, (---) 3-layers, T,=ZlOeV and N,=5~l~~~‘,T,=250eVandN,=IxI~‘cm-’,andT,=520eVandN~=5xl0~~~-’
210
R C MANCINIet al
quahty. results
experlmental
measurements
are needed
to further
of these modehng
nork uas supported In pan by US DOE grant DE-FGO3-92SF19199 support from NERDC through the Research Computrng lnmatrve
~~~N~n/r~~erncrrrs--Thlj
computauonal
test the capabllwes
We xknowledge
REFERENCES I 2 3 -I 5 6 7 8 9 IO II I2
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