J. E. Bailey et al- Experimental investigation of opacity models for stellar interior, inertial fusion, and high energy density plasmas
Content
PHYSICS OF PLASMAS
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058101 2009
Experimental investigation of opacity models fo r stellar interior, inertial fusion, and high energy density plasmas a… J. E. Bailey,1,b G. A. Rochau,1 R. C. Mancini,2 C. A. Iglesias,3 J. J. MacFarlane,4 I. E. Golovkin,4 C. Blancard,5 Ph. Cosse,5 and G. Fauss Faussurier urier5 1
Sandia National Laboratories, Albuquerque, New Mexico, 87185-1196, USA University of Nevada, Reno, Nevada 89557, USA 3 Lawrence Livermore National Laboratory, University of California, Livermore, California 94550, USA 4 Prism Computational Sciences, Madison, Wisconsin 53703, USA 5 CEA, DAM, DIF, F-91297 Arpajon, France 2
Received 7 December 2008; accepted 15 December 2008; published online 23 March 2009 Theoretic Theore tical al opa opaciti cities es are req requir uired ed for cal calcul culatin ating g ene energ rgy y tra transp nsport ort in pla plasma smas. s. In par partic ticula ular, r, unde un ders rsta tand ndin ing g st stel ella larr in inte teri rior ors, s, in iner erti tial al fu fusi sion on,, an and d Z pi pinc nche hess de depe pend ndss on th thee op opac acit itie iess of mid-atomicmid-a tomic-numbe numberr eleme elements nts over a wide range of tempe temperatur ratures. es. The 150–3 150–300 00 eV temperature temperature range is particularly interesting. The opacity models are complex and experimental validation is crucia cru cial. l. For exa example mple,, sol solar ar mod models els pre presen sently tly dis disagr agree ee with hel helios ioseis eismolo mology gy and one pos possib sible le explanation is inadequate theoretical opacities. Testing these opacities requires well-characterized plasmas at temperatures high enough to produce the ion charge states that exist in the sun. Typical opacity experiments heat a sample using x rays and measure the spectrally resolved transmission with a backlight. The difficulty grows as the temperature increases because the heating x-ray source mustt sup mus supply ply mor moree ene energ rgy y and the bac backli klight ght mus mustt be bri bright ght eno enough ugh to ove overwh rwhelm elm the pla plasma sma self-emission. These problems can be overcome with the new generation of high energy density HED facilities. For example, recent experiments at Sandia’s Z facility M. K. Matzen et al., Phys. Plasmas 12, 055503 2005 measured the transmission of a mixed Mg and Fe plasma heated to 156 6 eV. This capability capability will also advance opacity opacity science for other HED plasmas. plasmas. This tutorial revi re view ewss ex expe peri rime ment ntal al me meth thod odss fo forr te test stin ing g op opac acity ity mo mode dels ls,, in incl clud uding ing ex expe peri rime ment nt de desig sign, n, transmission measurement methods, accuracy evaluation, and plasma diagnostics. The solar interior serves as a focal problem and Z facility experiments illustrate the techniques. © 2009 American Institute of Physics. DOI: 10.1063/1.3089604
I. INTRODUCTION
exp − , T = I / I 0 = exp
Physical pictures for high energy density HED plasmas rely on models of the plasma properties. For example, the inner structure of astrophysical plasmas such as stars is often inacce ina ccessi ssible ble to dir direct ect mea measur sureme ements nts.. In his sem semina inall boo book k 1 “The internal constitution of the stars” Eddington pointed out this dilemma, but goes on to show that we can still build physical pictures for the inner workings of a star as long as we know the properties of the matter that lies within. More detailed information may be available for laboratory plasmas such as inertial fusion implosions and Z pinches. However, building buildi ng a comple complete te physi physical cal description description still normally requires material property models. Radiati Rad iation on oft often en pla plays ys an ess essent ential ial rol rolee in bot both h ast astrorophysic phy sical al and laborator laboratory y HED pla plasma smass and a key mat materi erial al property is the opacity, which quantifies how transparent or opaque the plasma is to radiation. In this tutorial we describe experimental methods developed to test opacity models for HED plasmas. The transmission of photons with intensity I 0 normally incident on a uniform plasma is given by a
Paper PT2 1, Bull. Am. Phys. Soc. Invited speaker.
b
1070-664X/2009/165
53,
199 2008.
/058101/16/$25.00
1
where h is the photon energy energy and I is the att attenu enuate ated d photon pho ton inte intensi nsity ty eme emerg rging ing fro from m the pla plasma sma.. The opt optica icall depth, , is related to the opacity by = x, where is the opacity per unit mass typically measured in units of cm2 / g, is the density, and x is the optical path length. Opacity Opa city mod models els are tes tested ted by mea measur suring ing T thr throug ough h a plasma with known characteristics. The opa opacit city y is gen genera erally lly a rap rapidl idly y var varyin ying g fun functio ction n of frequency. In some applications, knowledge of the frequency dependent opacity is required and this is what must be measured in benchmark experime experim ents. An example is levitation of 2 “metals” in stellar interiors. Here, metals refer to any element other than hydrogen or helium, a definition commonly employed in astrophysics. These elements diffuse toward the center cen ter of sta stars rs und under er the influence influence of gra gravity vity.. The There re is an opposing oppos ing levitating force provi provided ded by the photo photon n pres pressure sure and this for force ce is pro propor portion tional al to the fre freque quency ncy dep depend endent ent opacity. In other applications the most important quantity is the mean opacity averaged over frequency. An example is d iff uu3 sive radiation transport of energy within stellar interiors. In light of this simplification, one might ask: Why use opacity models mod els?? Why not jus justt mea measur suree the mean opa opacit cities ies we require? The problem is that the opacity depends on the plasma
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T(eV T( eV))
ne(cm-3) r /R /Rs
19 3
1x 10 1023 0.7133
measured boundary RCZ = 0.713 + 0.001 Predicted R CZ= 0.726
1000
= Planck function temperature
dB
B
dT
T =
0.8
) g / 2
100
m c (
1360 13 60
6x10 6x 1025
1.0
0.6 dB dT
N
0
0.4 radiation convection
10
0.2
FIG. 1. Color Schematic of the solar interior. The temperature and density information are from Ref. 4 and the values for the location of the radiation convection boundary are from Ref. 5.
temper temp erat atur ure, e, de dens nsity ity,, an and d el elem emen enta tall co comp mpos ositi ition on.. Th Thee breadth of plasma conditions and constituents encountered in applications makes it impractical to measure all the needed opacities. opaci ties. Furth Furthermor ermore, e, accur accurate ate opacit opacity y measu measuremen rements ts are challenging challe nging and the numbe numberr of availa available ble measu measuremen rements ts is sparse. spar se. Finally Finally,, some intere interesting sting condi conditions tions remain beyond the reach of laboratory experiments. Therefore, the main goal of opacity experiments is to test the physical underpinnings of opacity models so that they can be reliably extrapolated to conditions untested in the laboratory. Fortunately, the details of the rap rapidl idly y var varyin ying g opa opacit city y as a fun functi ction on of fre freque quency ncy provide a trove of information. The accuracy of model descriptions for the physical processes that govern opacity is severely tested by comparison with T v measurements. II. OPACITY EXPERIMENT DESIGN Given that opacity measurements are sparse and the parameter space is broad, it is important to optimize opacity experiment designs. The questions we must answer include the following.
1 What photon energy range is important? 2 What elements contribute? 3 What photon absorption processes are important? The answers to these questions depend on the application. In this tutorial we use the solar interior as an example to illustrate experiment design and execution. Figure 1 provides a schematic of the solar interior. The energy generated by thermonuclear reactions in the solar core is transported outward by radiation over approximately 70% of the solar radius, Rs. The solar opacity generally increases with radius and eventually becomes large enough that energy transport by rad radiat iation ion is ine ineffic fficien ientt and con convec vective tive tra transp nsport ort tak takes es over. The border between the radiation and convection dominated zones is known as the CZ boundary. The core temperature is roughly 1360 eV and it falls to appro approximate ximately ly 190 eV 4 just below the CZ boundary. The electron density also decrease cre ases, s, fro from m 6 1025 cm−3 at the core to 1 1023 cm−3 near ne ar th thee CZ bo boun unda dary ry.. Th Thee bo boun unda dary ry lo loca catio tion n is R / Rs =0.713 0.001, inferred with remarkable accuracy from he5 lioseismology measurements. The CZ bou bounda ndary ry loc locati ation on and the spatial temperature and density profiles depend on the mean opacity as a function of radius. However, opacity models have never been tested with laboratory experiments at the conditions that exist inside the sun.
opacity “window”
500
1000
1500 hQ (eV)
2000
2500
0.0
FIG. 2. Color Frequency dependent opacity Refs. 13 and 14 for a 17 element solar composition Ref. 6 near the base of the solar convection zone compared to dB / dT . The electron temperature and density were 193 eV and 1 1023 cm−3, respectively.
The motivation for experimental verification of theoretical opacities has grown sharper during the past decade. Solar models are constructed using estimates for the composition and the mate materia riall pro proper pertie tiess suc such h as equ equati ation on of sta state, te, opacity, and nuclear cross sections as inputs. Predictions for the CZ bound boundary ary location, interior density profile, profile, and sound speed were in good agreement with helioseismic data until roughly the year 2000. Beginning in 1999, revised estimates estimate s 6 for the sol solar ar com compos positio ition n red reduce uced d the amo amount unt of met metals als.. Solar models based ba sed on these revised estimates disagree with 5,7,8 helioseismology. One poss possible ible expla explanation nation is inacc inaccurauracies in the opacity models. Solar Sola r models models constructed with ad 5,7,9,10 adjustments ments of the opacity found that incre increasing asing hoc adjust thee me th mean an op opac acity ity by 10 10%– %–20 20% % in th thee so solar lar re regi gion on 0. 0.4 4 R / Rs 0.7 would resolve the discrepancies. The solar problem serves to define needed opacity experiments. The first question to answer is what photon energy range is most important. For plasmas such as the sun that are much larger than the photon mean free path, radiation tio n tr tran ansp spo ort is usu suaall lly y de desscr crib ibeed by a di difffu fusi sion on 11,,12 11 approximation using the Rosseland mean opacity R, 1 R
=
1 dB d dT
dB d , dT
2
where B is the Planck function, T is the plasma temper temperature ature,, and the weighting function dB / dT peaks at roughly 3.8 kT. Note that the Rosseland opacity is a harmonic mean depending on the reciprocal of and photons are most efficiently transported through the “windows” where is the lowest. Near the CZ boundary T 190 eV and and dB / dT peaks at h 750 0 eV Fig. 2. The frequency frequency depen dependent dent opacity near 75 the CZ bou ound ndar ary y ca calcu lcula lated ted us usin ing g th thee op opac acity ity pr proj ojec ectt 13,,14 13 model is di disp spla laye yed d in Fi Fig. g. 2. Co Comp mpar ariso ison n wit with h th thee weighting function for the Rosseland mean shows that the most important photon energies are approximately 300 h 1300 0 eV. We rei reiter terate ate tha thatt we req requir uiree mea measur sureme ements nts of 130 the frequency dependent opacity to test the physics in opacity models. However, familiarity with the characteristics of the Ros Rossel seland and mea mean n hel helps ps defi define ne wha whatt opa opacit cities ies are most important import ant to measu measure. re.
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100
10-1
(a)
H
n o 10-2 i t c a r f s 10-3 s a m
O Ne
Fe
10-4
10-5
1 2 6 7 8 10 11 12 13 14 16 18 20 24 25 26 28 atomic number O
0.25
(b) Fe
0.20 n o i t c 0.15 a r f y t H i c 0.10 a p o
Ne
0.05 0.00
Phys. Plasmas 16, 058101 2009
1 2 6 7 8 10 11 12 13 14 16 18 20 24 25 26 28 atomic number
FIG. 3. Color Characteristics of the solar interior composition. The histogram in a provides the mass fractions Ref. 16. The histogram in b is the fractional contribution to the Rosseland mean evaluated near the base of the solar convection zone using the OPAS opacity model Ref. 17.
The second question to answer in designing opacity experiments is: What elements should be studied? The answer is som sometim etimes es str straig aightf htforw orward ard in lab labora orator tory y pla plasma smass com com-posed of a single element. However, in many applications multiel mul tieleme ement nt pla plasma smass are use used. d. For exa exampl mple, e, mixt mixture uress of low- Z and mid- Z elements, where Z is the atomic number, are commonly used in inertial fusion capsule ablators Be/Cu ablators are described in Ref. 15. Different elements may be present in different plasma spatial regions. These differences may alter the opacity and the role each element plays in the radiation transport. Astrophysic Astro physical al plasma plasmass are more compl complicated icated since the observer does not necessarily possess certain knowledge of the com compos positio ition n and man many y ele elemen ments ts may be pre presen sent. t. The solar composition estima estimated ted from photospheric spectroscopy 16 and meteorite analysis is illustrated in Fig. 3a. This 17element mixture was was widely used prior to the revised low6 5 metallicity estimates that led to the solar CZ problem. The mass fraction for elements such as oxygen, neon, and iron is less than 1%. Nevertheless, these elements contribute a disproportiona propo rtionately tely larg largee frac fraction tion of the solar interior opacity because they are not completely ionized, as described below. The fractional opacity contribution for each element at conditions corresponding to the CZ boundary is shown in Fig. 3b. Figure 3b calculations were performed with the OPAS
model. The larg largest est contributions contributions are from oxyge oxygen, n, neon neon,, and iron and these are the elements of greatest interest for 5 solar interior opacity measurements. Obviously, the impact of errors in any single element is diminished when the element is a dilute constituent of a mixture. For example, in order to cause a 10% change in the total mean opacity we would need to multiply the iron opacity at the CZ boundary by a factor of approximately 1.5. The third question for opacity experiment design is how each eac h ele elemen mentt con contri tribut butes. es. The thr three ee mai main n abs absorp orption tion pro pro-cesses in plasmas are free-free, bound-free, and bound-bound electron transitions. These processes differ from one element to another and depend on the ionization. Consider the contributions of hydrogen, oxygen, and iron to the opacity at the base of the solar convection zone. At these conditions hydrogen is ful fully ly str stripp ipped ed and the onl only y con contrib tributio ution n is fre free-f e-free ree transitions trans itions in the ionized electr electrons ons Fig. 4a. Ox Oxyg ygen en is ionized into the K -shell -shell i.e., O+6 and O +7, isoelectronic with He and H and contributes absorption through both boundfree and bound-bound transitions. Here, “ K -shell” -shell” refers to -shell ions n =1 principal quantum number electron states. K -shell in local thermo thermodynam dynamic ic equilib equilibrium rium LTE norma normally lly have much of their population in the ground state and an important class of transitions originates from the n =1 lower level thee CZ bo boun unda dary ry,, ir iron on is io ioniz nized ed in into to th thee Fig. 4b. At th +16 +17 -shell, ell, with sig signifi nifican cantt pop popula ulation tionss of Fe , Fe , an and d L-sh Fe+18. These ions are isoelectronic with Ne, F, and O and conseq con sequen uently tly are oft often en des descri cribed bed as NeNe-like like,, F-l F-like ike,, and O-like. The greater number of bound electrons renders the Fe opacity contributions immensely complicated. Many transitions originate from the n =2 lower level, but there is also significant excited state population and transitions originate from n 3 princ principal ipal quantum numbers Fig. 4c. Of the three elements that are most important at the CZ boundary, Fe is by far the most complex and it is therefore expected to be the most suspect. The opacity plots in Figs. 4b and 4c illustrate another consequence of mixing elements together. Consider the pure iron photo photon n absor absorption ption red cur curve, ve, Fig. 4c. The deepest opacity window is in the vicinity of h 50 500– 0– 70 700 0 eV eV,, a region dominated by bound-free transitions with excited initial states. If one is interested in a pure iron plasma, then this defines the most important photon energy range. The opacity model must then have an accurate treatment for both the n 3 excited state populations and the bound-free photoionization cross sections out of those excited states. On the other hand, the comparison of pure iron opacity with the total solar mixture opacity shows that the iron contribution to the h photon ton energy energy ran range ge is neg negligi ligible ble.. The mixture mixture 500 eV pho opacity has filled in the Fe window at these energies. Instead, the Fe bound-bound transitions at 750 h 130 1300 0 eV are the mos mostt sig signifi nifican cantt iro iron n con contrib tributi ution on to the sol solar ar mixt mixture ure opacity near the CZ base. Thus, a mixture dilutes the importance of any individual element and can change which absorption processes and photon energies are important. These considerations considerations define a usef useful ul opac opacity ity exper experiment iment for the base of the solar convection zone. We should attempt to measure opacities for O, Ne, and Fe. Of these, Fe is probably the most suspect and is therefore a good place to start.
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total
(a)
0.3
n o i t c a r f
n= 3
2
10
0.4
n= 4
) 100 g / m c (
e e r f e e r f
Z experiment
R/Rsun = 0.6 R/Rsun = 0.5
R/Rsun= 0.7
0.2
H
n= 2
0.1 1
free-free 0.0
n= 1 500 1000
1000 h (eV)
total
1500
FIG. 5. Color The iron char charge ge state distributi distribution on as a func function tion of electr electron on temperature and density at different depths within the sun. The T e and ne values are from Ref. 4 and the PrismSPECT model Ref. 18 was used to calculate calcu late the charg chargee state distributi distribution. on. The red curve corre correspon sponds ds to just below the convection zone R / Rs =0.7, T e =193 eV, ne = 1 1023 cm−3, the green curve corresponds to R / R s =0.6 T e =261 eV, ne =2.5 1023 cm−3, and an d th thee bl blue ue cu curv rvee co corr rres espo pond ndss to R / Rs =0.5 T e =335 eV, ne = 7 23 cm−3 . The black curve with triangles corresponds to the distribution 10 for conditions in Z experiments.
(b) n= 4
100
n= 3
) g / 2 m c ( 10
n= 2
O ground state bound-free
1
K-shell bound-bound 500 1000
1000 h (eV)
n= 1 1500
n= 4
) 100 g / 2 m c (
e e r f d n u o b
l n = 3 l
10
1
l l e h s K
(c)
total
n= 2
window filling
e h s L
L-shell bound-bound
Fe
n= 1 500
1000 h (eV)
+21 1 +2 +22 2 +13 +1 +14 4 +1 +15 5 +16 +16 +1 +17 7 +1 +18 8 +1 +19 9 +20 +2 Fe charge state
1500
FIG. 4. Color Physical processes responsible for the contribution to opacity by different elements. The calculated Refs. 13 and 14 total opacity of the solar mixture at the base of the convection zone is compared with the contri con tribut bution ion fro from m hyd hydrog rogen, en, oxy oxygen gen,, and iro iron n in a, b, an and d c, respectively.
The most important photon energy range for Fe was already established estab lished as 750–1 750–1350 350 eV eV.. The electr electron on temper temperature ature just below the convection zone is 190 eV and the electro electron n den23 −3 sity is 10 cm . Eventually we must reproduce these conditions in order to test fully the model physics. This is a daunting goal that is beyond the ability of present day experiments. However, the ionization distribution depends on both bo th te temp mper erat atur uree an and d de dens nsity ity,, a pr prop oper erty ty tha thatt en enab able less progress progr ess while exper experimenta imentall techn techniques iques to reac reach h more extreme conditions are developed. Reproducing the charge states of interest is a key prerequisite uis ite for qua quantit ntitativ ativee tes tests ts of opa opaciti cities. es. It can det determ ermine ine whether opacity models accurately calculate the charge state distribution, energy level structur struct ure, e, and relevant photon ab18 sorption processes. Calculations of iron charge state distributions at various depths within the sun are shown in Fig. 5.
Deeper in the solar interior both the temperature and density increase. Although the temperature rise should should cause a higher degree deg ree of ion ioniza izatio tion, n, it is cou counte ntered red by the cor corres respon pondin ding g density increase. Thus, similar iron charge states exist over a broad range of the solar interior. The condition cond itionss correspond19,,20 19 ing to rec recent ent Z fac facilit ility y iro iron n exp experi erimen ments ts are supe superimrimposed on the solar interior results in Fig. 5. The Z facility experiment charge state distribution is similar to those at the CZ boundary, even though the 156 eV Z experiment temperature is 37 eV lower. lower. The rea reason son is tha thatt the density density is approximately ten times lower. Tests of high density effects such as contin continuum uum lowering and line broadening broadening require further experiment experiment advan advances ces to simulta simultaneous neously ly produ produce ce both high temperature and density. III. EXPERIMENTAL METHODS AND HISTORICAL OVERVIEW The basic strategy used to test opacity models is to compare the freq frequency uency dependent dependent exper experimental imental and theor theoretica eticall transm tra nsmiss ission ion for a sam sample ple with kno known wn con condit dition ions. s. Thi Thiss method is illustrated in Fig. 6. The sample is heated with an x-ray source and the transmission is measured by viewing a backlig bac klight ht thr throug ough h the sam sample ple with a spe spectr ctrome ometer ter.. The sample sam ple material material of int intere erest st is san sandwi dwiche ched d by lay layers ers of a low- Z tampe tamperr to promo promote te unifo uniformity rmity.. Spect Spectra ra are acquired with and without the sample material. Dividing the absorption spectrum obtained with the sample by the unattenuated tamper only spectrum provides the transmission. The requisite data can be acquired on separate experiments, as long as key experimental aspects are reproducible. Reproducibility can be evaluated by comparing spectra obtained on sequential experiments Fig. 7. The reproducibility encompasses the x-ray heating of the sample, the sample fabrication fabr ication,, the backl backlight ight absolu absolute te intens intensity ity and spect spectrum, rum, the spectrometer efficiency e.g., crystal reflectivity and the detector response e.g., film proc processin essing g repr reproducib oducibility ility. A powerf pow erful ul alt altern ernativ ativee meth method od kno known wn as poi point nt pro projec jectio tion n
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1.0
n0.8 o i s0.6 s i m s0.4 n a r0.2 t
transmission spectrum
0.0
1000
1200 h (eV)
) r e t s 2 / e V e c / n 2 a i m c 1 d / a r W
1600 FIG. 8. Color Diagram of the experiment configuration used in point pro jection opacity measurements adapted from Ref. 22.
backlighter spectrum
21,,22 21
1 1
0 1 ( 0
1400
backlighting provides the required data in a single experiment Fig. 8. This technique offers the potential for high accuracy without the need for reproducibility, at the cost of increased complexity. The three main requirements for opacity experiments are as follows:
absorption spectrum 800
1000 1200 hQ (eV)
1400
Z data without iron
1600
Z data with iron
h
h
spectrometer
spectrometer Fe/Mg sample
CH heating x-rays
(1)
CH heating x-rays
(2)
backlighter
1 uniform sample plasma, 2 accurate transmission measurements, 3 independent plasma diagnostics,
backlighter
FIG. 6. Color Method for transmission measurements used to test opacity models. A spectrometer views a backlight through an x-ray heated foil. The samplee tran sampl transmiss smission ion as a funct function ion of phot photon on ener energy gy is deter determined mined using measurements of a low-Z tamper only foil diagram 1 and measurements of the sample material of interest surrounded by the tamper diagram 2. The synthetic backlighter spectrum is a 314 eV Planckian that is representative of the backlighter used in Z iron experiments Refs. 19 and 20. The absorption spectrum was calculated with PrismSPECT Ref. 18 at the experiment temperature and density values and the transmission spectrum was obtained by dividing the absorption spectrum by the backlighter spectrum.
Z1650 Z1649
y t i s n e t n i
7
8
9 O
(Å)
10
11
12
FIG. 7. Color Comparison of absorption spectra from two sequential Z experiments. No scaling or other intensity adjustments were applied in this comparison, other than correcting both spectra for the film response.
as succinctly described described in Ref. 23 23.. Most research to date has compared the data with models that assume the LTE approximation is valid. In this approximation the ion energy level popula pop ulation tionss are des descri cribed bed by a Bol Boltzm tzmann ann dis distrib tributi ution. on. Methods for evaluating the validity of this approximation are 24,,25 24 described elsewhere. Techni echniques ques for opaci opacity ty resea research rch were developed using 26 laser-driven experiments beginning in the mid-1980s. The earl ea rlie iest st wo work rk us used ed a si sing ngle le-s -sid ided ed xx-ra ray y so sour urce ce to he heat at 26– 26 –30 sample sam pless com compos posed ed of Al, Fe, Br, or Ge. Later,, x-ra Later x-ray y cavities known as Hohlraums were used to provide a nearly isotropic heating x-ray x-ray flux flux and the variety of sample mate31– 31 –36 rials was expanded. Crystal spectrometers recorded photons between 1200 and 3000 eV eV,, the electron temperature temperature was 20–76 eV, and the electron density was roughly 2 – 4 21 10 cm−3 . This work established most of the principles used today for opacity research and valuable initial opacity model tests were conducted. However, the crystal spectrometerr mea ete measur sureme ements nts wer weree una unable ble to add addres resss the 40–6 40–600 00 eV photon energy energy rang rangee that dominates the tr traans nspor portt at the these se 37– 37 –39 relatively low temperatures. In later work, similar x-ray techni tec hnique quess wer weree use used d to hea heatt Fe sam sample ples, s, but the spe spectr ctraa were recorded using variable-line-spacing grating spectrometers. This enabled recording 80–300 eV photon energies that are near the peak of the Rossela Ross eland nd mean weighting function. 40 These methods were adapted to the larger x-ray flux provided by the Saturn Z-pinch facility, where a lower density LTE plasma near the conditions that exist in the envelopes of pulsating Cepheid variable stars was studied. These measurements provided provided strong evidence for the validity of the Opal 41 opacity model in this low tempera temperature ture low density regime. 42 The Opal opacities helped resolve long standing discrepancies between stellar evolution and pulsation models. In order to test opacity models used in stellar interior, inerti ine rtial al fus fusion ion,, and Z-p Z-pinc inch h res resear earch, ch, high higher er tempe temperatur raturee 19,,20 19 plasmas are required. Recent experiments have exploited the inten intense se radiation created by a dynamic Hohlraum x-ray 43– 43 – 47 source driven by the 21 106 Ampere current provided
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by the Z facility. This source is formed by accelerating an annular tungsten plasma onto a low density CH 2 cylindrical foam located on the axis. The impact of the tungsten on the foam generates shock radiation that is trapped by the tungsten plasma. This is called a “dynamic” Hohlraum because the diameter shrinks with time as the tungsten continues to be com compre presse ssed d by the mag magnet netic ic pre pressu ssure re sup supplie plied d by the large lar ge axi axiall ally y dir direct ected ed cur curren rent. t. An opa opacity city sam sample ple pla placed ced above the Hohlraum end cap is heated by the Hohlraum x rays and it is backlit when the radiating shock stagnates on the cylinder axis. These experiments measured Fe transmission at T e =156 6 eV, temperatu temperatures res high eno enough ugh to pro pro-duce the charge states, and electron configurations that exist at the base of the solar convection zone Fig. 5. As mentioned above, the density in these experiments is roughly an order of magnitude lower than at the CZ boundary.
IV. OPACITY EXPERIMENT REQUIREMENTS: SAMPLE UNIFORMITY
tamper (CH)
sample
(a)
x-rays
n0.8 o i s0.6 s i m s0.4 n a r0.2 t
hot sample
(b) cold sample
0.0 e c0.8 n a i d0.6 a r r0.4 i e v i t0.2 a l e r0.00
(c)
200 eV Planck heating spectrum
500
1000 hQ (eV)
1500
A more general expression for the transmission is
T = exp −
, T e x , ne x xdx ,
3
reducing to Eq. 1 only if the effect of plasm reducing plasmaa nonun nonuniformi iformi-ties is negligible. If nonuniformities exist it may still be possible to acquir acquiree valuab valuable le opacit opacity y infor information mation by numer numerically ically evalua eva luatin ting g the inte integra grall in Eq. 3. An example of this approach is described in Ref. 35 35.. There, the goal was to produce du ce hig high h de dens nsiti ities es an and d gr grad adie ient ntss we were re an ac acce cept ptab able le tradeoff trade off.. Such tradeoffs tradeoffs are sometimes nece necessary ssary as incre incre-mental progress progress is made toward more extre extreme me condi conditions. tions. However, the desired accuracy for validating opacity models is high and experiments with significant nonuniformities are unlikely unlike ly to provid providee defini definitive tive conclusions conclusions about the under underlylying physics embedded within the model. Volumetric heating by x rays is used to produce uniform 49 hot opacity samples. This is accomplished when a portion of the heating x-ray spectrum streams through the sample. In this case the sample is said to be “optically thin” to at least a portion of the heating x-ray spectrum. This is illustrated for the Z-pinch dynamic Hohlraum iron opacity experiments in Fig. 9. A Planckian heating spectrum at radiation brightness temperature T r =200 eV peak peakss at h max 2.8 T r 550 eV. The optical depth of the initially room tempe temperatur raturee sampl samplee is lesss tha les than n one one,, and con conseq sequen uently tly the tra transm nsmiss ission ion is hig high, h, over a broad photon energy band near the peak of the heating spectrum. As the sample temperature increases, the opacity drops further and the sample becomes even more transparent near the peak of the heating x-ray spectrum. Thus, photons deposit energy throughout the sample during the entire history of the experiment. This produces uniform heating, at the cost of an inefficient process. The desire for uniform samples is a major reason why large HED facilities are required for high temperature opacity experiments. Note that if the heating spectrum peaks at lower photon energy, then the initial energy deposition may occur primarily near the surface and the sample heating may initially be nonuniform. In this case
FIG. 9. Color X-ray heating provides provides the abil ability ity to volu volumetri metrically cally heat opacity samples a. A sig signifi nifican cantt por portio tion n of the heating heating x ray rayss str stream eam through thro ugh the sampl sample, e, prov providin iding g relat relativel ively y unif uniform orm but inef inefficien ficientt heati heating. ng. Transmiss Tran smissions ions thro through ugh room temp temperatu erature re iron iron/magn /magnesium esium foil and iron iron/ / magnesium plasma heated to 150 eV are shown in b, compared to the heating x-ray spectrum provided by a 200 eV Planckian source c. The areal density and composition of both the room temperature foil and the plasma are the same as in Refs. 19 and 20 20..
a detailed consideration of the radiation hydrodynamics of the sample evolution may be needed. Tem empo pora rall un unif ifor ormit mity y is ju just st as im impo port rtan antt as sp spat atia iall sample uniformity. Hot samples inevitably evolve with time and opacity measurements must employ some form of time resolu res olutio tion. n. The most com common mon techniqu techniquee is to use a sho short rt duration backlight source. This allows using film-based detectors, which offer the best spectral range and resolution for typical spectrometer dispersions. Time-resolved detectors are another option. In either case, the temporal evolution of the sample temperature and density must be slow enough that the transmission variation is small over the time scale of the measurement. This favors longer duration, slowly changing x-ray heat sources. Radiation hydrodynamics simulations have been used to evaluate sample uniformity. While such simulations provide valuab val uable le ins insigh ight, t, the fac factt tha thatt the they y nec necess essari arily ly emp employ loy the opacity models that are the subject of the test compounds concerns over whether the simulations provide an accurate representation of reality. Given its importance, it is desirable to measure the uniformity. Unfortunately, to date direct uniformity for mity inf inform ormati ation on obt obtain ained ed in opa opacit city y exp experi erimen ments ts has been limited. Perhaps the best certification available has been the determination that spectra used to diagnose the plasma Sec. VII are quantitatively consistent with single values of the temperature and density. Future experiments may be able to determine the uniformity directly, for example with spaceresolved measurements such as radiography or x-ray Thomson scattering. A significant challenge in this regard is the
058101-7 05810 1-7
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(a)
Phys. Plasmas 16, 058101 2009 1.0
(b) artifacts
0.8
artifacts absorption lines
absorption lines
FIG. 10. Color X-ray absorption spectra exhibiting reflectivity defects that may masquerade as spectral lines. The image in a is from Z experiments 23.. Vigi Vigilance lance is Refs. 19 and 20 and the image in b is adapted from Ref. 23 required in experiments to ensure that such defects do not introduce artifacts into the inferred transmission.
need for spatial resolution of a few microns. A possible solution may be spectroscopy of different tracer elements buried within the sample at specific depths. A problem with this approach is that each tracer absorbs a portion of the heating x-ray spectrum and consequently tracers buried near the rear of the sample are not necessarily heated to the same extent as 50 tracers near the front. V. OPACITY EXPERIMENT REQUIREMENTS: ACCURATE TRANSMISSION MEASUREMENTS Numerous technological challenges must be overcome to produce accu produce accurate rate trans transmissio mission n measu measuremen rements. ts. These challengess may be conve lenge convenientl niently y divide divided d into concerns arising from the backlight, the sample fabrication, and the spectrometer. Here we restrict the discussion to backlight and spectrometer trome ter issue issuess and we consid consider er only crystal-based crystal-based instruments operating operating in the 700– 10,00 10,000 0 eV photon energy energy range. range. Many crystal types and geometrical configurations have been employed in these spectrometers. A problem common to all of them is spectral artifacts arising from crystal defects. Examples of such artifacts are illustrated in Fig. 10 10.. These defects can masquerade as spectral features and care must be exercised to ensure that the inferred transmission is not contaminated by them. The defects are usually obvious in the two-dimensional spectral images Fig. 10, even though they may not be so easy to identify in a lineout. One possible approach is to examine the spectrum in detail, identify the artifact features, and edit or smooth the spectrum to remove their effect. An alternative is to perform multiple reproducible experiments using different crystals or different crystal alignments, so that the features change from one measurement to another. Then averaging the measurements together effectively removes their influence. The best method to avoid this problem is to procure and characterize the best possible crystals, but perfection in this regard is elusive. A second spectrometer-related issue that influences accuracy is the finite spectral resolution. resolution. Transmission Transmission spectra that illustrate the influence of spectral resolution are shown in Fig. 11 11.. The red curve is iron plasm plasmaa transmission calcu19,,20 19 lated for the Z facilit facility y experiment conditions using the 18 PrismSPECT Prism SPECT model without consi considerin dering g instr instrument ument reso reso--
n o i s0.6 s i m s n a r0.4 t
E/dE = 700
ideal
0.2
0.0
saturation
1020
1040 h (eV)
1060
1080
FIG. 11. Color Calculated Ref. 18 transmission for iron plasma at the experimental conditions in Refs. 19 and 20 20.. The blue curve is the ideal case and the red curve accou accounts nts for an inst instrumen rumentt spect spectral ral resolution resolution E / dE =700.
lution. lutio n. Th Thee bl blue ue cu curv rvee inc inclu lude dess a ty typi pica call re reso solu lutio tion n of E / dE 700 700.. Spe Spectr ctral al line liness with opt optica icall dep depth th gre greate aterr tha than n one are opt optica ically lly thi thick ck and the tra transm nsmiss ission ion at line center center approaches zero. However, if the line profile is not experimentally mental ly reso resolved, lved, then the observed transmission transmission will be 51 significantly larger. Such lines are said to be “saturated.” Saturation Satur ation eff effects ects must be incor incorpora porated ted into compa comparisons risons with opacity models. These effects are one reason opacity model calculations are converted into transmission for comparison with data, rather than the measured transmission being converted into opacity. Once the instrument blurring occurs cu rs,, in info form rmat atio ion n is lo lost st an and d it ca cann nnot ot be re reco cove vere red. d. Deconvolutio Decon volution n may be feas feasible, ible, but it typica typically lly introd introduces uces unacceptable uncertainties. If it is desired to compare opacities rather than trans transmissio mission, n, the opacity calcu calculation lationss must first be converted to transmission, the instrument resolution convolved, and then reconverted back into opacity. Thus, it is simpler and generally more informative to compare transmissions. Ultimately, the two key points of this discussion are thatt ins tha instru trumen mentt res resolu olutio tion n mus mustt be mea measur sured ed and hig higher her spectral spect ral reso resolution lution is desir desirable. able. Howev However er,, reso resource urce limitations often restrict spectral resolution measurements to relatively few photon energies, despite the fact that spectral resolut ol ution ion is a fu func nctio tion n of ph photo oton n en ener ergy gy.. If th thee me meas asur ured ed spectral range is relatively small, then the impact of spectral resolution uncertainty may be negligible. In other cases the portion of the transmission uncertainty that arises from the spectral spect ral resol resolution ution uncer uncertainty tainty may be signifi significant. cant. A third technological challenge associated with the spectrometer is the type of detector used. Time-resolved detectors such as streak cameras or microchannel plate MCP ca camer meras as 37,,40 37 40,,52 havee bee hav been n suc succes cessfu sfully lly use used d in som somee exp experi erimen ments. ts. These detectors may be essential for rapidly evolving sample conditions or if the late-time sample self-emission is bright enough to compete with the backlight see discussion of selfemission emissi on eff effects ects below. However, the active area of such
0581 05 8101 01-8 -8
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spectrometer
(a)
self emission tamper (CH)
sample backlighter
FIG. 12. Color Comparison of x-ray absorption spectra recorded on two different types of film, Kodak DEF and 101–07. The agreement between the two implies implies tha thatt th thee con conver versio sion n of film density density to film exposure exposure was self-consistent.
absorption spectrum ) r 2 s / V e /
self emission
2
detectors often restricts the spectral range. An effort to circumvent this this problem problem with larg largee forma formatt MCP configurations configurations 52,,53 52 is underway. Nevertheless, the spatial resolution element sizee of exi siz existi sting ng time time-r -reso esolve lved d det detect ectors ors is app approx roximat imately ely 80 m or larger. This limits the spectral resolution that can be achieved in most cases. The detector used in most opacity experiments to date has been x-ray film. Film has the advantage of larger effective number of pixels. Spatial resolutions of 5 m are routinely available. However, film has the disadvantage of nonlinear response and it requires both accurate calibrations and careful attention to developing procedures. Calibrations Calibr ations are resou resource rce intens intensive ive and rare rarely ly perfo performed. rmed. This raises a concern that the film sensitivity may change, especially espe cially since film manuf manufactur acturers ers regard film desig design n and fabric fab ricatio ation n det details ails as pro propri prieta etary ry.. For exa example mple,, the mos mostt commonly commo nly used x-ra x-ray y film calibrations calibrations are those of Henke et 54,,55 54 al., performed more than twenty years ago. In order to evaluate concerns over possible film development or fabrication problems, problems, an experiment experiment using two different different types of x-ray film was performed using a tamped Al and Mg opacity 56 sample placed to the side of a Z pinch Fig. 12. The resu results lts agree, supporting the sustained validity of the Henke calibrations. tio ns. Nev Nevert erthel heless ess,, vig vigila ilance nce ove overr film dev develo elopme pment nt and possible manufacturing changes is certainly warranted. X-ray charge coupled devices have a linear response and are probably a desirable optio option n to consider in future opacity experi57 ments. Image plates are another attractive detector technology,, alth ogy althoug ough h not all ima image ge pla plates tes and sca scanni nning ng sys system temss provid pro videe the nee needed ded spa spatial tial res resolu olutio tion. n. Sen Sensit sitivit ivity y to hig high h photon energy x-ray backgrounds may also limit the utility of image plates for opacity measurements in the keV photon energy range. Produc Pro ducing ing a hig high h qua quality lity backligh backlightt is a key enabling enabling technology for opacity experiments. The desired characteristics are broad spectral range, a smooth featureless spectrum, and high brightness. Broad spectral coverage is needed both to probe a wide range of features in the element of interest and to measu measure re simulta simultaneous neously ly spect spectral ral lines in diagn diagnostic ostic tracers added to the sample see below. A relati relatively vely smooth and featureless backlight spectrum is needed because if the backlig bac klight ht spe spectr ctral al fea featur tures es ove overla rlap p with fea featur tures es in the sample sam ple,, the then n the acc accura uracy cy req requir uireme ements nts of mea measur suring ing the backlighter spectrum increase dramatically. Thi T hiss problem is 58 aggravated by limited instrumental resolution. High backlight brightness is needed both to supply an
m c / W
emission limit 125 eV
0 1
0 1 ( 1 e c n a i d a r
0
(b)
backlight 170 eV
900
1000 1100 h (eV)
1200
FIG. 13. Color Self-emission can contribute to the signal recorded by the spectrometer a. A hypothetical situation is quantitatively illustrated in b using PrismSPECT Ref. 18 calcu calculati lations ons for iron plasm plasmaa selfself-emiss emission ion green curve and absorption spectra red curve. The plasma temperature is assume ass umed d to be 125 eV and th thee bac backli klight ghter er is ass assume umed d to be a 170 eV Planckian. The most optically thick lines have self-emission that peaks at the blackbody limit, corresponding in this case to a 125 eV Planckian.
adequate adequa te exp exposu osure re at the det detect ector or and to ove overwh rwhelm elm the 23 sample selfself-emissi emission. on. The com complic plicatio ations ns intr introdu oduced ced by sample self-emission are illustrated using calculated signals for a hypothetical experiment in Fig. 13 13.. The spectrometer detects the desired backlight photons and also samples selfemission contributions. In Fig. 13b examp example, le, the backli backlight ght source is a 170 eV Planckian and the iron sample temperature is 125 eV. The density and op tical path length corre corre-19,,20 19 spond spo nd to typ typica icall sam sample ple con conditi ditions ons.. The selfself-emiss emission ion and absor absorptio ption n spe spectr ctraa wer weree com comput puted ed usi using ng the Pri Prismsm18 SPECT model. The brightest spectral lines emitted by the sample are optically thick and peak at the blackbody limit: a Planckian corr orreesponding to the sample electr tro on 59,,12 59 temperature. The exper experimenta imentall trans transmissio mission n deter determined mined from Eq. 1 is affected most for the strongest spectral lines since they have the brightest self-emission. Clearly, the problem is amplified if the self-emission is an appreciable fraction of the backlight. Thus, the problem gets worse as the sample tempe temperatur raturee incre increases ases Fig. 14. The selfself-emiss emission ion signals from 125 and 150 eV samples are compared to the 170 eV Planckian backlight in Fig. 14a and the corresponding transmission with and without the 150 eV sample selfemission is shown in Fig. 14b. In this case, an inadequate treatment of self-emission would provide misleading information for opacity model comparisons. The conse consequenc quences es of selfself-emissi emission on are potentially sig-
058101-9 05810 1-9
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) r s / V2 e / 2
m c / W 0 1 01 1 ( e c n a i d a r0 1.0 0.8 n o i s0.6 s i m s0.4 n a r t 0.2 0.0
Phys. Plasmas 16, 058101 2009
laser
170 eV Planckian backlighter
0.8
125 eV emission
900
0.4
e r
h (eV) 1100
1300
(b)
ideal
0.2
with rare earth
820
860 hQ (eV) 900
940
315 eV Planckian backlighter
(a) 170 eV Planckian backlighter 150 eV self emission
500
1000 h (eV)
1500
2000
1.0 with selfemission
n0.8 o i s s0.6 i m s n0.4 a r t 0.2
(b)
ideal 820
Nd (Z=60) Back et al . JQSRT 1997 La (Z=57) Chenais-Popovics et al . JQSRT 2000 1000 1400 h (eV)
1800
FIG. 16. Color Pioneering opacity experiments primarily used laser heated fibers coated with rare-earth elements to produce the backlighter. The La spectrum is adapted from Ref. 31 and the Nd spectrum is adapted from Ref. 34.. 34
with 150 eV emissi emission on
2
0.0
fiber coated
0.0
) r s / V e2 /
01 1 ( e c n a i d a r0
e v i t a l
150 eV emission
nificant and two courses of action are possible to mitigate their effect: the backlight should be rendered much brighter than the sample self-emission and the sample self-emission should be measured during the experiment. Calculations of the self-emission and approximate approxi mate backlight brightness for 19,,20 19 the Z facility iron experiment are shown in Fig. 15a. The corresponding transmission with and without the self-
1 1
0.6
(a)
FIG. 14. Color Self-emission grows with sample temperature and competes more strongly with a specified backlighter a. The transmission calculated Ref. 18 for a portion of the spectrum is illustrated both with and without self-emission in b. The backlighter was assumed to be a 170 eV Planckian and the sample temperature was 150 eV. Both transmission spectra include convolution with E / dE =700 instrument resolution.
m c / W
e c n a i d a r
860
h (eV)
900
940
FIG. 15. Color Self-emission from iron plasma at 150 eV electron temperature is compared with 170 and 314 eV Planckian backlighter spectra in a. The ideal transmission without self-emission and the transmission including self-emission are almost the same if the backlighter spectrum corresponds to a 314 eV Planckian b. Both transmission spectra include convolution with E / dE =700 instrument resolution.
emission Fig. 15b shows that the 315 eV Planckian backlight overwhelms the sample self-emission; thus, it has negligible effect on the transmission. The sample self-emission and absorption can be measured using the same spectrometer as long as the spatial extent of the backlight is small compare pa red d to th thee si size ze of th thee he heate ated d sa samp mple le.. Bo Both th th thee sp spac aceeresolved spectrometer and point projection configuration enable the selfself-emissi emission on to be reco recorded. rded. These self-emission self-emission measurements require high detector dynamic range since we desire des ire self-emi self-emissi ssion on tha thatt is les lesss tha than n a few percent percent of the backlight. The quest for a high brightness, broad spectral coverage, and a spectrally featureless backlight is an ongoing topic in opacity opa city res resear earch. ch. Ear Early ly ef effor forts ts pro produc duced ed poi pointli ntlike ke bri bright ght sources by irradiating small fibers with lasers. Emission in the desired spectral range was obtained by coating the fiber 26,,31 26 31,,34 with a high Z material often a rare-earth element Fig. 16. The emission from these high Z laser produced plasmas consis con sists ts of man many y mill million ionss of spe spectr ctral al line liness tha thatt ble blend nd int into o unresolved unres olved trans transition ition arra arrays ys UTAs. The 3d -4 -4 f UT UTAs As are partic par ticula ularly rly bri bright ght and can bac backlig klight ht an app approx roximat imately ely keV photon energy energy regime. regime. 200– 400 eV range in the 1–3 keV In addition, these sources are inherently spectral line sources and very careful measurements are required to account correctly for the spectral structure. This introduces a potential systematic error that is hard to quantify. Recentt opaci Recen opacity ty rese research arch has empha emphasized sized the devel developopment of backlight sources that span a larger photon energy range and that are inher inherently ently continuum emission sources. sources. This is challenging because bright sources are required. As laser facilities grow in energy it may be possible to create “conventional” “conventiona l” Hohlraums th that at re reac ach h hi high gh br brig ight htne ness ss 60 temperatures. The most suc succes cessfu sfull app approa roach ch to dat datee has been the production of dynamic Hohlraums driven either by high power Z pinches or lasers. These sources are heated by a radiating shock. The shock emission is trapped by a high Z plasma that is compressed over time. The use of a Z pinch to create such a source was briefly described above and more details are given in Ref. 20 20.. Spherically convergent dynamic Hohlraum Hohlra umss ha have ve al also so be been en pr prod oduc uced ed at the Ome Omega ga la lase serr 61 facility. In these experiments the laser typically illuminates a spherical plastic shell filled with xenon gas. The emission
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detector Fe/Mg shocked foam
(a)
CH
n a e t s m g s a l n u p t
(b)
n a e t s m g s a l n u p t
)
I1(
I0(
)
)
I2(
)
(a)
D ~ 400 m Tr ~ 314 eV x1
1 ns snapshot
x2 Iron
y8 t i s n6 e t n i 4 e v i t 2 a l e r
0
I0(
equivalent brightness Tr ~ 314 eV
1000
1200
1400 h (eV)
(c)
(b)
n o i s s i m s n a r t
Red = thick Blue = scaled thin T1 = T2 (x1/x2)
1600
FIG. 17. Color Dynamic Hohlraum backlighter diagram a. The stagnation of a radi radiatin ating g shoc shock k on the pinc pinch h axis produces produces a brig bright ht continuum continuum source. sour ce. A timetime-gated gated x-ray pinhole image is show shown n in b and a plot of relative intensity as a function of photon energy is shown in c.The equivalent brightness temperature is T r 314 eV Ref. 20.
from the shock launched into the xenon is trapped because of the high opacity of the xenon plasma behind the shock. The Z-pinch driven dynamic Hohlraum described above used the Z facility to produce a backli gh ghtt with peak radiation 20 temperature of approximately 314 eV. This backlight spans an ef effec fective tive ran range ge of h 800– 200 2000 0 eV, it is essential essentially ly line-free, and it is bright enough to backlight samples at temperatures up to 16 160 0 eV Fig. 17. The characteristics of the Omega laser-driven backlight in the 800–2000 eV spectral rang ra ngee th that at is of int inter eres estt fo forr op opac acity ity ex expe peri rime ment ntss at T e = 100– 160 eV have not been publishe published. d. However, However, measuremeasure61 ments at higher photon energies have been documented and the characteristics of this source for future experiments may be attractive. VI. OPACITY EXPERIMENT ACCURACY EVALUATION Performin Perfor ming g hig high h acc accura uracy cy opa opacit city y exp experi erimen ments ts is not simple since many potential pitf alls alls exist. However, a rela23 tively straig straightfor htforward ward method is availa available ble to exper experimenimentally assess the accuracy of the measurements. The method depends on Beer’s law relationship Eq. 1 between transmission missio n and sample thickn thickness. ess. Suppose we measu measure re transmission through two uniform samples with identical conditions tio ns bu butt wi with th di diff ffer eren entt th thic ickn knes esse sess x1 and x2. The transm tra nsmiss ission ion through through sam sample ple 2 is rel relate ated d to the sample 1 2/ x 1 x x2 x1 transmission by T 2 = T 1 Fig. 18. Measuring the transmission through different thickness samples and evaluating whether the scaling obeys Beer’s law is an extremely effective means to assess possible errors. Problems that will cause deviation devia tion from Beer’ Beer’ss law includ includee sample nonuniformity nonuniformity,, self-emission, background subtraction, crystal artifacts, and inaccu ina ccurat ratee film res respon ponse se cor correc rection tions. s. For exa example mple,, if the heating hea ting x ray rayss dep deposi ositt mor moree ene energ rgy y nea nearr the fro front nt sam sample ple edge and produce nonuniform conditions, then the nonuniformity will be worse with increasing sample thickness and the transmission will deviate from the expected scaling. As another example, the sensitivity of the transmission to self-
1050
h (eV) 1150
1250
Aluminum
(c)
n o i s s i m s n a r t
1530
1550 h (eV)
1570
1590
FIG. 18. Color Evaluation of transmission accuracy using experiments with different thickness samples a. Examples of experiments that demonstrated high quality using the sample thickness scaling method are shown in 62,, respectively. b and c, adapted from Refs. 19 and 62
emission problems depends emission depends on the optica opticall depth and thus the sample thickness. thickness. As a third example, example, artif artifacts acts that are introduced because of crystal defects will not change when the sample thickness changes and examination of transmission scaling with thickness therefore serves to identify those artifacts. Finally, the exposure at the detector will depend on the sample thickness thickness and verific verification ation that trans transmissio mission n scale scaless correctly according to Beer’s law can detect inaccuracies in the conversion of film density to exposure. A host of problems can be detected with such scaling tests and the tests are straightforward to perform. One limitation is that problems arisin ari sing g fro from m ins insuffi ufficie cient nt spe spectr ctral al res resolu olutio tion n whe when n nar narrow row spectral featu features res in the backlight and sample coincide are not 58 detectable. Furthermore, performing scaling tests requires greate gre aterr res resour ources ces,, sin since ce eith either er add additio itional nal exp experi erimen mentt s or 19,,62 19 more complicated targets are needed. Two experiments which demonstrated a high degree of scaling accuracy are shown in Figs. 18b and 18c. Note that in these experiments both the weak and strong absorption features exhibit accura acc urate te sca scaling ling.. Thi Thiss is sig signifi nifican cantt bec becaus ausee man many y of the proble pro blems ms tha thatt migh mightt ari arise se pre prefer ferent ential ially ly af affec fectt eit either her the strong str ong or wea weak k fea featur tures, es, alte alterin ring g the relative absorption strengths. The tra transm nsmiss ission ion sca scalin ling g des descri cribed bed abo above ve is the mos mostt powerful test to evaluate experiment accuracy. Supplemental valuable valua ble information may also be obtain obtained ed by perfo performing rming multiple measurements within each experiment and/or mul-
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1.0
(a)
Mg +9 satellites e.g., 1s2 2s 1s2s2p
0.8
n o i t c a r f
160 eV
n o i s 0.6 s i m s 0.4 n a r t
Mg+11 Ly 1s 2p
0.2
0.1
150 eV
0.0 1300
155 eV
Mg+11 Ly 1s 3p
Mg+10 He 1s2 1s2p
1400
Mg+10 He 1s2 1s3p
1500 h (eV)
Mg+10 He 1s2 1s4p
1600
Mg+10 He 1s2 1s5p
1700
1.0
(b)
+9
+10 charge
+11
FIG. 19. Color Calculated Ref. 18 charge state distribution for Mg at 150 eV black , 155 eV red, and 160 eV blue electron temperatures. The electron density was 7 1021 cm−3 in all cases. These 5 eV temperature changes induce less than 1% change in the He-like Mg Mg+10 population, but the H-like Mg Mg+11 population changes by approximately 40%. The Li-like MgMg+9 population changes by a smaller amount.
tiple reproducible experiments. Multiple measurements using varying detector sensitivity provides signals recorded at different fer ent exp exposu osure re lev levels els.. Com Compar pariso ison n of the mea measur sureme ements nts theref the refore ore rev reveal ealss whe whethe therr det detect ector or res respon ponse se is lin linear ear or if film densit density-toy-to-expos exposure ure conv conversio ersions ns have been accu accurately rately performed perf ormed.. Multiple measu measuremen rements ts using diff different erent cryst crystals als can reveal whethe whetherr cryst crystal al artif artifacts acts have affe affected cted the resul results. ts. Averaging the results of multiple multiple reproducible experiments 19 improves impro ves signa signal-to-n l-to-noise oise value valuess and can be ess essent ential ial for accurate accu rate trans transmissio mission n measu measuremen rements ts of weak spectral features. VII. PLASMA DIAGNOSTICS Opacity is a function of the plasma electron temperature and den densit sity y and qua quantit ntitativ ativee opa opacity city mod model el tes tests ts req requir uiree sample characterization. Here, we emphasize electron density rather than mass density since it is the electron density that directly affects the collisional ionization and excitation rates. rat es. Pla Plasma sma dia diagno gnosis sis oft often en rel relies ies on K -shell -shell absor absorption ption spectra under the assumption that the models used to interpret these relatively simple spectra are reliable. The de dettail ailss of 63– 63 – 66 K -shell -shell spectral diagnostics are described elsewhere and we pro provid videe onl only y a bri brief ef rev review iew of the physical physical basis for K -shell -shell spectral diagnostics. The value of K -shell -shell spectra to diagnose electron temperature depends on two facts. First, the plasma ionization distribution is a strong function of the electron temperature but has a weak dependence on the electron density Fig. 19 19;; see also Fig Fig.. 5. Sec Second ond,, the K -shell -shell spec spectral tral line photon energ ene rgies ies shi shift ft with ion ioniza izatio tion. n. The for former mer mea means ns tha thatt the relative relat ive absor absorption ption stren strengths gths of K -shell -shell spectral lines from different charge states depends on electron temperature. The latter means that the features from particular charge states are readily discerned from each other. other. K -shell -shell spectr spectral al absorption lines are defined as lines with an initial principal
n 0.8 o i s s i m s0.6 n a r t
n=3 Ly
Ly 1s-2p
Li-like satellites
0.4 He 0.2
1350
1400 h (eV)
n=2
1450
n=1 Mg +11 Mg XII H-like
He Li-like 1s2 1s2p satellite Mg +10 Mg XI He-like
Mg +9 Mg X Li-like
FIG. 20. Color Typical K -shell -shell absorption spectrum with features from H-, He-, and Li-like Mg a. The spectrum in a represents the average transmission from the experiments in Ref. 19 19.. PrismSPECT calculations of an expanded view of the n =1 to n =2 transitions in these three charge states and a simplified energy level diagram illustrate the energy shift from nuclear screening by additional spectator electrons in He-like and Li-like ions b.
quantum number n = 1. Absorption Absorption transitions transitions betwee between n the 1 s and 2 p configurations are possible if there are vacancies in the n =2 shell. Thus, K -shell -shell absorption may arise in atoms ionized ionize d into either the K - or L-shel -shell. l. These transitions transitions are conveniently divided into two classes according to whether they occur in K -shell -shell H- and He-like ions that have only one or two bound electrons or L-shell Li-, Be-, B-, C-, O-, N-, and F-like ions that have three to nine bound electrons. This distinction has value because the diagnostics available from these two classes are somewhat different. Both these transition classes can diagnose T e, with comparable accuracy. In addition, transitions between the 1s or 1 s2 ground states states 67 and the n =2 or 3 levels are affected by Stark broadening and provide valuable density information, as described below. However, the Stark broadening of L-shell ions has not been used extensively and its reliability is less certain. A measured K -shell -shell trans transmissio mission n spect spectrum rum forme formed d by the H-, He-, and Li-like charge states of Mg is shown in Fig. 20a. The bound bound-boun -bound d trans transitions itions that contr contribute ibute n =1 to n =2 spectral lines are displayed with a calculated synthetic spectrum in Fig. 20b. The strongest absorption line from H-like ions is the 1s-2 p transition, known as Ly , while the strongest line from He-like ions is the 1 s2 − 1s2 p transition, known as He . The He photon energy is 120 eV lower lower than the Ly because of the nuclear screening provided by the second 1 s electron. Similarly, the 1s22s − 1s2s2 p Li-like transition has lower photon energy than He , but the energy separation between the Li-like lines and He is only of order 15–20 eV because the additional screening by the 2 s electron is less than that by the 1 s electron. The extra electron that
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Phys. Plasmas 16, 058101 2009
0.9 0.8
n o0.8 Ly i s 1s-2p s i m 0.7 s n a r t 0.6 150 eV
HeE 1s2-1s2p
n o i s0.6 s i m s 0.4 n a r t
155 eV 0.5 160 eV
150 eV 155 eV 160 eV
0.2
1465 1470 1475 1480 hQ (eV)
1565
1575 1585 h (eV)
FIG. 21. Color Calculated Ref. 18 absorption from Mg Ly and He at the three temperatures corresponding to Fig. 19 charge state distributions. The E / dE =700 instrument resolution effect is included.
does not partic participate ipate in the transition is someti sometimes mes referred referred to as a “spectator” electron and these Li-like lines are known as “satellites” because they appear near the resonant He transition. The Li-like spectator electron may also reside in an excited n = 3 or higher state. In this case the satellite transitions are only slightly shifted from the He photon energy and these lines may not be resolved Fig. 20b. A careful accounting of this transition blending must be incorporated into accurate plasma diagn diagnostics ostics.. Note that He-lik He-likee satel satellites lites also appear on the low photon energy side of Ly , arising from fr om in init itia iall lly y ex exci cite ted d He He-l -lik ikee co confi nfigu gura rati tion onss e.g., 1s2s − 2s2 p. Satell Satellite ite lines often provi provide de additio additional nal valua valuable ble diagno dia gnosti stics cs bec becaus ausee the they y dep depend end on the mec mechan hanism ism tha thatt populates the excited states. The sensitivity of typical H- and He-like Mg ion spectral lines to small temperature changes is illustrated illustrated in Fig. 21 21.. 19,,20 19 This example is drawn from the Z experiments investigating gat ing iron opa opacit city y mod models els and we emp employ loy the He 1s2 − 1 s3 p tra transi nsition tion bec becaus ausee iro iron n spe spectr ctral al lin lines es are ble blende nded d with the He . The He absorption line strength is not sensitive to changes in temperature because the fractional population of the closed-shell He-like Mg ions changes very little
0.5 ne = 7x1021 cm-3
e0.4 H / y L0.3
ne = 5x1021 cm-3 measured ratio
0.2
0.1
ne = 9x1021 cm-3 145
155 Te (eV)
165
FIG. 22. Color Calculated Mg Ly / He absorption line strength ratio as a function of electron temperature. The three curves correspond to three different electron densities. The horizontal line corresponds to the mean ratio value measured in the experiments in Refs. 19 and 20 and the dashed lines are the 1 ratio uncertainties. The experimental temperature lies within the cross-hatched region.
in this temperature range. On the other hand, the Ly absorption changes rapidly with temperature. Thus, measurements men ts of the int integr egrate ated d Ly / He absor absorption ption line stren strength gth ratio provide a temperature diagnostic Fig. 22. The three different curves in Fig. 22 correspond to three different electron density values, illustrating the simultaneous dependence of the ionization distribution on both temperature and density mentioned above. In this case a 30% change in electron density den sity alt alters ers the inf inferr erred ed tem temper peratu ature re by app approx roximat imately ely 3–4 eV. Thus, accurate temperature diagnostics using this method depend on knowledge of the electron density. Preliminary temperature estimates may be obtained by a visual comparison of measured and synthetic spectra calculated at different temperatures. However, quantitative opacity model tests require estimates for the temperature and density uncertainties. These may be obtained using the spectral line fitting techniques described in Refs. 20 and 68 to deter determine mine the uncertainties in the measured absorption line strengths. High quality measurements combined with careful analysis may provide temperature values accurate to typically 5%, with rou roughl ghly y hal halff the unc uncert ertain ainty ty ari arisin sing g fro from m the typ typica icall 30% density uncertainty and the other half from the absorption sorpt ion line measu measuremen rementt accu accuracy racy.. Note that these estimates mat es do not inc includ ludee any unc uncert ertain ainty ty ass associ ociate ated d with the spectral synthesis model used to interpret the data. The systematic model errors can be reduced by using as many line ratios as possible to infer the temperature, reducing the probability abi lity that tra transi nsitio tion n rat ratee err errors ors for any single line migh mightt bias the resu results. lts. Analysis performed performed with seve several ral diff different erent K -shell -shell opacity models can also solidify the reliability of the temperature temper ature result, althou although gh the extra resource investment investment renders this type of duplicate analysis uncommon. The class of transitions in ions with three to nine bound electrons is still reasonably simple and the ionization distribution but ion is typ typica ically lly bro broade aderr. The These se ion ionss inv involv olvee an ope open n n = 2 shell and they normally possess strong strong features from four or five charge states. This broader distribution may enhance accuracy accur acy and reliab reliability ility of electr electron on tempe temperatur raturee measu measurerements. men ts. The tra transi nsition tionss inv involv olved ed are gen genera erally lly 1s22sm2 pl − 1s2sm2 pl+1. These lines are sometimes referred to as “ K satellites” because they appear on the high energy side of the transition and they were first observed in neutral atom K experiments exper iments that direc directed ted high energy particle beams onto transitions. As with the transolid surfaces to investigate K sitions described above, the n =2 spectator electrons do not partic par ticipa ipate te dir direct ectly ly in the tra transi nsition tion,, but the they y do pro provid videe nuclear screening that shifts the transition energy. This class of transitions is critically important for diagnosing low temperature perat ure plasm plasmas as e.g., T e 10 100 0 eV. At low tem temper peratu atures res the simple H- and He-like charge states described above occur only for ions with atomic atomic num number ber less tha than n app approx roxiimately 10. These low- Z atoms have K -shell -shell lines that appear in the x-ray ultraviolet XUV spectral range and are consequently quent ly more difficult to measu measure. re. K satellite ite trans transitions itions satell may be observed in the soft x-ray 1 ke keV V range even for temperatures as low as 10 eV eV.. The diagnostic utility of this type of transition was first developed for emission sp spectra ectra arising in energetic electron 69 or ion beam experiments and for early laser-driven capsule
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Experimen Expe rimental tal inves investigati tigation on of of opacity opacity models… initial sample, known thickness
laser
Phys. Plasmas 16, 058101 2009 1.0
thickness radiograph
backlight hot sample
Mg He 0.8 1s2- 1s4p
y t i c a0.6 p o e v0.4 i t a l e r0.2
2.0 x 1022 cm-3 1.0 x 1022 cm-3 0.5 x 1022 cm-3
(a)
He
(b) He
50 ) Å m 40 (
He
m h 30 w f
He
20
FIG. 23. Color Diagram of point projection radiography method used to measure sample expansion and thus measure the sample density. A dispersive element such as a crystal is often inserted in front of the detector to provide spectrally resolved information, greatly enhancing the radiograph contrast.
70
implosions. Later, it was extensively employed in absorption spectra used to diagn diagnose ose a wide array of HED experi26,,71 26 71,,72 ments, including opacity. The usefulness of this transition class is also supported by the fact that adjacent 1 s to 2 p transitions in Li-like to F-like ions shift enough to be measured, but not so much as to make broad spectral coverage necessary. Thus, such diagnostics are especially appropriate if a more limited spectral range backlight is available. Transitionss involv sition involvin ing g initial initial states with an excited electron arise 73,,74 73 in these spectra and the resulting lines may blend with lines from the ground state of adjacent charge states. This is similar to the illustration provided above for Li-like ions and this charge state blending must be included in models used to infer temperature from such data. Transitions with higher- n final states e.g., 3 p have been observed, but they are typically relatively weak and the models needed to interpret the line broadening are less certain. Consequently, the class of transitions in Li-like to F-like ions has been only rarely em29 ployed in plasma electron density diagnostics up until now. Several types of electron density diagnostics have been developed devel oped for opaci opacity ty exper experiments iments.. Radiog Radiographi raphicc measu measurerements of the sample plasm plasmaa expan expansion sion and Stark broadening broadening of K -shell -shell spectral lines are two techniques that provide relatively direct density measurements. Optical laser interferometry measurements of the sample rear surface ex pa pansion nsion have 75 also been used to infer opacity sample density. However, the plasma that is actually probed at optical wavelengths is the low density edge of the sample plasma and these techniques must rely heavily on radiation hydrodynamic simulations to infer the behavior of the higher density interior of the opacity sample. Point projection spectrally-resolved radiography wa s the 21– 21 –23 firstt met firs method hod emp employ loyed ed to det determ ermine ine sam sample ple den density sity.. These measurements measurements are conce conceptuall ptually y straig straightfor htforward: ward: The sample thickness is measured after it is heated by the x-ray source and the density is obtained by comparing with measurements of the initial sample thickness performed prior to the experiment Fig. 23. A major challenge for this method is the experiment complexity introduced by the need to acquir qu iree si simu multa ltane neou ousl sly y an ed edge ge-o -on n ra radi diog ogra raph ph an and d th thee spectrallyspec trally-resol resolved ved trans transmissio mission n measu measuremen rementt used to infer the temperature and to test the opacity model for the element of inte interes rest. t. Add Additio itional nal pro proble blems ms inc includ ludee acc accura urate te init initial ial samplee compo sampl composition sition and thickn thickness ess measu measuremen rements, ts, accu accuracy racy limitations imposed by the finite point projection backlight
0.0
1650
1660 1670 h (eV)
0.5
1.0 1. 1.5 5 2. 2.0 0 2.5 ne ( x 1022 cm-3)
FIG. 24. Color Example of Stark-broadened line profile calculations Refs. 76 and 77 a. The red, green, and blue curves correspond to 0.5, 1.0, and 2.0 1020 cm−3 electron densities, respectively. These opacity profiles are converted to transmission and then convolved with the instrument resolution before comparing with the experiment Ref. 20. The plot in b illustrates the full width at half maximum as a function of electron density. The areal density and instrument resolution in b correspond to the Z experiments in Refs. 19 and 20 20..
size, assumption of one-dimensional expansion, and simultaneity of the density measurement radiograph with the transmission missio n measu measuremen rement. t. Despi Despite te these problems, density measureme sur ements nts acc accura urate te to app approx roxima imatel tely y 30 30% % ha have ve be been en acquired in a few opacity experiments. 67 K -shell Measuremen Measu rements ts of Stark Stark-broa -broadened dened -shell spect spectral ral lines also enable determination of the sample sample density. density. Atomic line transitio transitions ns in tra tracer cer ion ionss are per pertur turbed bed by the ele electr ctric ic microfields due to the other electrons and ions in the plasma. The net result is a characteristic Stark-broadened line shape that is mainly dependent on the density. In the standard Stark broadening broad ening theory appro approximatio ximation n the ions are considered considered static while the lighter electrons are considered dynamic, i.e., they move while the line trans transition ition takes place. The distri distribubution of static ion microfields causes energy levels to split and shift due to the Stark effect of the electric fields. The photon energy of dipole-allowed line transitions shifts accordingly, and the atomic state mixing by the electric field can even cause non-dipole-allowed transitions to appear. In addition, radiator ions experience a time-varying electric field due to the dynamic electrons. This broadens the line transitions that arise between shifted energy levels. The final line shape is obtained by averaging over the distribution function that the weights the static ion microfields according to their probability of occu occurrenc rrence, e, incorporating incorporating the broa broadening dening due to the dynamic electrons. Thus, the line profile broadening depends on both the ion and electron density and is typically used to infer the electron density, as long as the plasma composition is known. 76,,77 76 Calculations of Stark Stark-broa -broadened dened Mg He line pro19,,20 19 files used to diagnose the Z facility iron opacity samples are shown in Fig. 24a. The sensitivity of the line opacity profile to density is clear. However, a complication arises in applying apply ing this diagn diagnostic ostic to absor absorption ption spectra because the transmis transm ission sion lin linee pr profi ofile le is no nott th thee sa same me as th thee op opac acity ity 20,,59 20 59,,78 profile. The trans transmissio mission n T =exp − approx roxii x is app mately T 1 − x , if x 1. Such a line is said to be optically thin and the transmission profile essentially appears to be an upside down opacity line profile. However, as the optical depth = x grows to approach and then exceed unity,
0581 05 8101 01-1 -14 4
Baililey Ba ey et al.
this approximation is no longer valid. In this case the transmission profile depends on the optical depth and the areal density x of the ions in the lower level of the transition typically the ground state is required in order to relate the transm tra nsmiss ission ion line pro profile file to the opa opacity city lin linee pro profile file.. For Fortutunately, such knowledge may be reliably obtained by measuring the integrated strength of the absorption line family that arises from a given charge state. Once the optical depth has been determined, determined, the trans transmissio mission n may be compu computed ted from the opacity profile. Convolution with the instrument function must be performed prior to comparison with measured spectrall line profiles. tra profiles. The dep depend endenc encee of HeHe-like like Mg spe spectr ctral al linewid lin ewidths ths on ele electr ctron on den density sity is illu illustr strate ated d for the He , He , He , and He lines in Fig. 24b. The widths in Fig. 24b corre correspond spond to trans transmissio mission n widths after convo convolution lution with the instrument function. They include the optical depth effect and instrume instrument nt widths appropriate for the Z iron opac19,,20 19 ity exper experiment. iment. A more detailed description of this procedure is given in Ref. 20 20.. Stark broadening broadening incre increases ases and the opac opacity ity decre decreases ases with pri princi ncipal pal qua quantu ntum m num number ber.. Thu Thus, s, bot both h the abi ability lity to resolve the profile and the problems introduced by the requirement quire ment for areal density information information to inter interpret pret optically thick line broadening favor the use of high n spectral lines. However Howev er,, high-n spe spectr ctral al line liness are typ typica ically lly wea weaker ker and therefore they are measured less accurately. The most accurate density diagnostics are obtained by measuring as many lines as possible possi ble and quantitatively accounting for the signal20 to-noise ratio. Typical density accuracy obtained with this method is 30%. However, this does not account for possible uncertainties introduced by the Stark broadening models. Stark broadening measurements of HED plasma densitiess ha tie have ve be been en pe perf rfor orme med d fo forr mo more re tha than n 2 de deca cade dess an and d calculations of H-like and He-like profiles are generally considered reliable. However, only limited experimental information directly designed to test broadening models in this 79 densit den sity y reg regime ime is ava availa ilable ble and fut future ure opa opacity city res resear earch ch would benefit from more extensive tests.
VIII. STATUS AND FUTURE PROSPECTS FOR HED PLASMA OPACITY RESEARCH The methods described above provide a framework for experiments designed to test opacity models. However, the range of temperatures, densities, and elements examined up until now is small. The vast majority of experiments investig ti gat ateed pl plas asma mass wi with th 20 20– –76 eV te temp mpeera ratu turres and 3 0.01–0.03 0. 01–0.03 g / cm mass densities. Only a few experimental results exist outside of this range. range . Ex Examples amples include the Sat40,,42 40 urn Z-pinc Z-pinch h drive driven n exper experiments iments that invest investigated igated iron opacities for envelopes of Cepheid variable stars and the Z facility experiments investigating opacity of the iron charge ch arge 19,,20 19 states that exist at the base of the solar convection zone. The former extended the density range down by two orders of magnitude while the latter pushed the temperature range up by approximately a factor of 2. These experiments provided vid ed val valuab uable le opa opacity city mod model el tes tests, ts, yet the they y are probably probably best regarded as proof-of-principle experiments that establish
Phys. Plasmas 16, 058101 2009
platforms for furth platforms further er invest investigatio igations. ns. Compre Comprehensiv hensivee resul results ts require more experiments. The parameter space of applications that would benefit from opacity experiments is large. Here, we mention only a few obv obviou iouss exa example mpless tha thatt mig might ht be add addres ressed sed with within in the coming years. We also reiterate that, while applications provide impor important tant motiva motivation tion that guide guidess rese research arch directions, directions, advances in opacity science require sustained focus on the physic phy sicss with within in the opa opacity city mod models els.. The dis discre crepan pancie ciess between helioseismology and solar models motivates investigations of iron plasma opacity at temperatures similar to the existing Z facility experiments, but at densities an order of magnitude higher. Measurements of oxygen and neon opacities are also needed, even though the atomic physics of the -shell is more certain than the Fe L-shell. For example, the K -shell bound-free opacities of these elements play an important role in the total opacity. The bound-free process is important over a large photon energy range, implying that a relatively small error err or migh mightt hav havee imp import ortant ant con conseq sequen uences ces.. Fur Furthe thermo rmore, re, atomic physics is just one issue. Questions also remain rer e80 garding the accuracy of ionization distribution calculations. Finally,, opaci Finally opacity ty exper experiments iments to date have measu measured red either pure elements or mixtures of two similar atomic number elements. It is a fair question to ask whether the model treatments men ts mid mid-- Z ele elemen ments ts mix mixed ed as dilu dilute te con consti stitue tuents nts in a mostly hydrogen plasma are adequate. Inertial fusion capsule implosion designs typically employ Be shells doped with Cu or CH shells doped with Ge. The motivation motivation for the dop dopant antss is to mod modify ify the abl ablati ation on pressu pre ssure re as a fun functio ction n of dep depth th usi using ng the opa opacit city y cha change ngess caused by introducing the dopant. Thus, the success of these capsule designs depends on accurate knowledge of the dopant opacity in the 50–300 eV temperature range, at a variety of densities between 0.01 and 10.0 times solid. Experiments have measured Ge opacity at temperatures up to 76 eV and densities densi ties of appro approximate ximately ly 0.01 solid. These inves investigatio tigations ns provided provi ded initial tests of basic opaci opacity ty model questi questions. ons. However, these experiments did not measure the charge states and electron configurations that will arise in inertial fusion implosions. Furthermore, to the best of our knowledge, Cu transitions have not been measured at all, let alone Cu diluted in a mos mostly tly Be pla plasma sma at hig high h tem temper peratu ature re and density density.. Improved prove d opaci opacity ty knowle knowledge dge would enabl enablee exper experimenter imenterss to emphasize other issues such as laser plasma interaction or equation of state in tuning inertial fusion implosions to reach ignition. The opacity research methods developed over the past 20 years, combined with the advent of megajoule class HED facil facilities, ities, should enab enable le near near-term -term opacity inves investigatigations for matter found in stellar interiors, inertial fusion implosions, and Z pinches. ACKNOWLEDGMENTS We thank the Z facility teams for invaluable and dedicated technical assis assistance tance.. Speci Special al assis assistance tance was prov provided ided by P. W. Lake, D. S. Nielsen, L. Nielsen-Weber, and L. P. Mix. We are grateful to R. J. Leeper, T. A. Mehlhorn, J. L. Porter, and M. K. Matzen for support and encouragement. Special thanks are due to T. S. Perry, C. Back, and F. Gille-
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Experimen Expe rimental tal inves investigati tigation on of of opacity opacity models…
ron for graci gracious ous permi permission ssion to share previously previously publis published hed results here. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Co., for the United States Department of Energy under Contract No. DE-AC0494AL85000. Work by CAI performed under the auspices of the Department of Energy by Lawrence Livermore National Laboratory under Contract No. W-7405-ENGF-48. 1
A. S. Eddington, The Internal Constitution of the Stars Cambridge University Press, Cambridge, 1926 . 2 F. Delahaye and M. Pinsonneault, Astrophys. J. 625, 563 2005 . 3 D. Mihalas, Stellar Atmospheres W.H. Freeman, San Fransisco, 1970 . 4 J. N. Bah Bahcal call, l, A. M. Ser Serene enelli lli,, and S. Bas Basu, u, Astrophys. J. 621, L8 L85 5 2005; J. N. Bahcall, W. F. Huebner, S. H. Lubow, P. D. Parker, and R. K. Ulrich, Rev. Mod. Phys. 54, 767 1982 ; see: www.sns.ias.edu/~jnb. 5 S. Basu and H. M. Antia, Phys. Rep. 457, 217 2008. 6 M. Asplund, Annu. Rev. Astron. Astrophys. 43, 481 2005 and references therein. 7 J. N. Bahcall, A. M. Serenelli, and M. Pinsonneault, Astrophys. J. 614, 464 2004. 8 S. Turck-Chieze, S. Couvidat, L. Piau, J. Ferguson, P. Lambert, J. Ballot, R. A. Garcıa, and P. Nghiem, Phys. Rev. Lett. 93, 211102 2004 . 9 H. M. Antia and S. Basu, Astrophys. J. 620, L129 2005. 10 S. Basu and H. M. Antia, Astrophys. J. 606, L85 2004 ; J. N. Bahcall, S. Basu, M. Pinsonneault, and A. M. Serenelli, ibid. 618, 1049 2005. 11 Ya. B. Zel’dolvich and Yu. P. Raizer, in Physics of Shock Waves and High Temperature Tem perature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein Dover, Mineola, 1966 . 12 J. P. Apruzese, J. Davis, K. G. Whitney, J. W. Thornhill, P. C. Kepple, R. W. Cl Clark ark,, C. Dee Deeney ney,, C. A. Co Cover verdal dale, e, and T. W. L. San Sanfor ford, d, Phys. Plasmas 9, 2411 2002. 13 M. J. Seaton, Y. Yu, D. Mihalas, and A. K. Pradhan, Mon. Not. R. Astron. Soc. 266, 805 1994 ; M. J. Seaton, ibid. 382, 245 2007. 14 C. Men Mendoz doza, a, M. J. Sea Seaton ton,, P. Bue Buerg rger, er, A. Bel Bello lorín rín,, M. Mel Melénd éndez, ez, J. González, Gonz ález, L. S. Rodr Rodrígue íguez, z, F. Delah Delahaye, aye, E. Palaci Palacios, os, A. K. Pradhan, and C. J. Zeippen, Mon. Not. R. Astron. Soc. 378, 1031 2007. 15 D. C. Wilson, P. A. Bradley, N. M. Hoffman, F. J. Swenson, D. P. Smitherman, R. E. Chrien, R. W. Margevicius, D. J. Thoma, L. R. Foreman, J. K. Hoffer, S. R. Goldman, S. E. Caldwell, T. R. Dittrich, S. W. Haan, M. M. Marinak, S. M. Pollaine, and J. J. Sanchez, Phys. Plasmas 5, 1953 1998; S. W. Haan, M. C. Herrmann, T. R. Dittrich, A. J. Fetterman, M. M. Marinak, D. H. Munro, S. M. Pollaine, J. D. Salmonson, G. L. Strobel, and L. J. Suter, ibid. 12, 056316 2005. 16 N. Grevesse and A. J. Sauval, Space Sci. Rev. 85, 161 1998. 17 P. Renau Renaudin, din, L. Lecher Lecherbour bourg, g, C. Blan Blancard, card, P. Coss Cosse, e, G. Fauss Faussurie urier, r, P. Audebert, S. Bastiani-Ceccotti, J.-P. Geindre, and R. Shepherd, AIP Conf. Proc. 926, 24 2007. 18 J. J. MacFar MacFarlane, lane, I. E. Golo Golovkin vkin,, P. R. Woodr oodruff uff,, D. R. Welch, B. V. Oliver, T. A. Mehlhorn, and R. B. Campbell, Inertial Fusion Science and Applications, edited by B. A. Hammel, D. D. Meyerhofer, J. Meyer-terVehn, and H. Azechi American Nuclear Society, La Grange Park, 2004 , p. 457; J. J. MacFarlane, I. E. Golovkin, P. Wang, P. R. Woodruff, and N. A. Pereyra, High Energy Density Phys. 3, 181 2007 . 19 J. E. Bailey, G. A. Rochau, C. A. Iglesias, J. Abdallah, Jr., J. J. MacFarlane, I. Golovkin, P. Wang, R. C. Mancini, P. W. Lake, T. C. Moore, M. Bump, O. Garcia, and S. Mazevet, Phys. Rev. Lett. 99, 265002 2007. 20 J. E. Bailey, G. A. Rochau, R. C. Mancini, C. A. Iglesias, J. J. MacFarlane, I. E. Golovkin, J. C. Pain, F. Gilleron, C. Blancard, Ph. Cosse, G. Faussurier, G. A. Chandler, T. J. Nash, D. S. Nielsen, and P. W. Lake, Rev. Sci. Instrum. 79, 113104 2008 . 21 C. L. S. Lewis and J. McGlinchey, Opt. Commun. 53, 179 1985 . 22 T. S. Perry, S. J. Davidson, F. J. D. Serduke, D. R. Bach, C. C. Smith, J. M. Foster, R. J. Doyas, R. A. Ward, C. A. Iglesias, F. J. Rogers, J. Abdallah, Jr., R. E. Stewart, J. D. Kilkenny, and R. W. Lee, Phys. Rev. Lett. 67, 3784 1991. 23 T. S. Perry, P. T. Springer, D. F. Fields, D. R. Bach, F. J. D. Serduke, C. A. Iglesi Igl esias, as, F. J. Rog Rogers ers,, J. K. Nas Nash, h, M. H. Ch Chen, en, B. G. Wilson, Wilson, W. H. Goldstein, B. Rozsynai, R. A. Ward, J. D. Kilkenny, R. Doyas, L. B. Da Silva, C. A. Back, R. Cauble, S. J. Davidson, J. M. Foster, C. C. Smith, A. Bar-Shalom, and R. W. Lee, Phys. Rev. E 54, 5617 1996 . 24 H. Griem Griem,, Princi Principles ples of Plasm Plasma a Spect Spectros roscopy copy Cambridge University Press, New York, 1997 .
Phys. Plasmas 16, 058101 2009 25
J. E. Bailey, G. A. Rochau, S. B. Hansen, C. A. Iglesias, J. J. MacFarlane, I. Golovkin, P. Wang, R. C. Mancini, C. Blancard, Ph. Cosse, G. Faussurier, F. Gilleron, and J. C. Pain, “Evaluation of non-LTE effects on iron plasma transmission measurements at temperatures above 150 eV,” High Energy Density Phys. to be submitted . 26 S. J. Davidson, J. M. Foster, C. C. Smith, K. A. Warburton, and S. J. Rose, Appl. Phys. Lett. 52, 847 1988 . 27 J. M. Foster, D. J. Hoarty, C. C. Smith, P. A. Rosen, S. J. Davidson, S. J. Rose, T. S. Perry, and F. J. D. Serduke, Phys. Rev. Lett. 67, 3255 1991. 28 J. Bruneau, C. Chenais-Popovics, D. Desenne, J.-C. Gauthier, J.-P. Geindre, M. Klapisch, J.-P. Le Breton, M. Louis-Jacquet, D. Naccache, and J.-P.. Perrine, Phys. Rev. Lett. 65, 1435 1990. J.-P 29 D. J. Hoarty, C. D. Bentley, B. J. B. Crowley, S. J. Davidson, S. G. Gales, P. Graham, J. W. O. Harris, C. A. Iglesias, S. F. James, and C. C. Smith, J. Quant. Spectrosc. Radiat. Transf. 99, 283 2006; D. J. Hoarty, J. W. O. Harris, P. Graham, S. J. Davidson, S. F. James, B. J. B. Crowley, E. L. Clark, C. C. Smith, and L. Upcraft, High Energy Density Phys. 3, 325 2007. 30 J. E. Bailey, P. Arnault, T. Blenski, G. Dejonghe, O. Peyrusse, J. J. MacFarlane, R. C. Mancini, M. E. Cuneo, D. S. Nielsen, and G. A. Rochau, J. Quant. Spectrosc. Radiat. Transf. 81, 31 2003. 31 C. Chenais-Popovics, F. Gilleron, M. Fajardo, H. Merdji, T. Mißalla, J. C. Gauthier, P. Renaudin, S. Gary, J. Bruneau, F. Perrot, T. Blenski, W. Fölsner, and K. Eidmann, J. Quant. Spectrosc. Radiat. Transf. 65, 117 2000. 32 C. Chenais-Popovics, H. Merdji, T. Mißalla, F. Gilleron, J. C. Gauthier, T. Blenski, F. Perrot, M. Klapisch, C. Bauche-Arnoult, J. Bauche, A. Bachelier, and K. Eidmann, Astrophys. J., Suppl. Ser. 127, 275 2000. 33 C. Chenais Popovics, M. Fajardo, F. Gilleron, U. Teubner, J.-C. Gauthier, C. Bauche-Arnoult, A. Bachelier, J. Bauche, T. Blenski, F. Thais, F. Perrot, A. Benuzzi, S. Turck-Chièze, J.-P. Chièze, F. Dorchies, U. Andiel, W. Foelsner, and K. Eidmann, Phys. Rev. E 65, 016413 2001 ; C. ChenaisPopovics, M. Fajardo, F. Thais, F. Gilleron, J. C. Gauthier, K. Eidmann, W. Fölsner, T. Blenski, F. Perrot, C. Bauche-Arnoult, A. Bachelier, and J. Bauche, J. Quant. Spectrosc. Radiat. Transf. 71, 249 2001 ; H. Merdji, T. Mißalla, T. Blenski, F. Perrot, J. C. Gauthier, K. Eidmann, and C. ChenaisPopovics, Phys. Rev. E 57, 1042 1998 . 34 C. A. Back, T. S. Perry, D. R. Bach, B. G. Wilson, C. A. Iglesias, O. L. Landen, S. J. Davidson, and B. J. B. Crowley, J. Quant. Spectrosc. Radiat. Transf. 58, 415 1997 . 35 F. Thai Thais, s, S. Basti Bastiani, ani, T. Blen Blenski, ski, C. Chena Chenais-P is-Popov opovics, ics, K. Eidm Eidman, an, W. Fölsner, J.-C. Gauthier, F. Gilleron, and M. Poirier, J. Quant. Spectrosc. Radiat. Transf. 81, 473 2003 . 36 P. Renaudin, C. Blancard, J. Bruneau, G. Faussurier, J.-E. Fuchs, and S. Gary, J. Quant. Spectrosc. Radiat. Transf. 99, 511 2006. 37 L. Da Silva, B. J. MacGowan, D. R. Kania, B. A. Hammel, C. A. Back, E. Hsieh, R. Doyas, C. A. Iglesias, F. J. Rogers, and R. W. Lee, Phys. Rev. Lett. 69, 438 1992. 38 P. T. Springer, D. J. Fields, B. G. Wilson, J. K. Nash, W. H. Goldstein, C. A. Iglesias, F. J. Rogers, J. K. Swenson, M. H. Chen, A. Bar-Shalom, and R. E. Stewart, Phys. Rev. Lett. 69, 3735 1992. 39 G. Winhart, K. Eidmann, C. A. Iglesias, A. Bar-Shalom, E. Mínguez, A. Ricker Ric kert, t, and S. J. Ros Rose, e, J. Quan Quant. t. Spect Spectrosc. rosc. Radiat. Transf. 54, 43 437 7 1995; G. Winhart, K. Eidmann, C. A. Iglesias, and A. Bar-Shalom, Phys. Rev. E 53, R1332 1996. 40 P. T. Springer, K. L. Wong, C. A. Iglesias, J. H. Hammer, J. L. Porter, A. Toor, To or, W. H. Gold Goldstein stein,, B. G. Wi Wilson lson,, F. J. Rogers, C. Deene Deeney, y, D. S. Dearbo Dea rborn, rn, C. Bru Bruns, ns, J. Emi Emig, g, and R. E. Ste Stewar wart, t, J. Quant Quant.. Spect Spectrosc. rosc. Radiat. Transf. 58, 927 1997 . 41 C. A. Iglesias and F. J. Rogers, Astrophys. J. 464, 943 1996. 42 F. J. Rogers and C. A. Iglesias, Science 263, 50 1994 . 43 M. K. Matze Matzen, n, Phys Phys.. Plasm Plasmas as 4, 1519 1997; V. P. Smirnov, Plasma Phys. Controlled Fusion 33, 1697 1991; J. H. Brownell, R. L. Bowers, K. D. McLenthan, and D. L. Peterson, Phys. Plasmas 5, 2071 1998. 44 J. E. Bailey, G. A. Chandler, S. A. Slutz, G. R. Bennett, G. Cooper, J. S. Lash, S. Lazier, R. Lemke, T. J. Nash, D. S. Nielsen, T. C. Moore, C. L. Ruiz, D. G. Schroen, R. Smelser, J. Torres, and R. A. Vesey, Phys. Rev. Lett. 89, 095004 2002; J. E. Bailey, G. A. Chandler, R. C. Mancini, S. A. Slutz, G. A. Rochau, M. Bump, T. J. Buris-Mog, G. Cooper, G. Dunham, I. Golovkin, J. D. Kilkenny, P. W. Lake, R. J. Leeper, R. Lemke, J. J. MacFarlane, T. A. Mehlhorn, T. C. Moore, T. J. Nash, A. Nikroo, D. S. Nielsen, K. L. Peterson, C. L. Ruiz, D. G. Schroen, D. Steinman, and W. Varnum, Phys. Plasmas 13, 056301 2006 .
0581 05 8101 01-1 -16 6 45
Baililey Ba ey et al.
T. W. L. San Sanfor ford, d, T. J. Nash, R. C. Mock, J. P. Apr Apruze uzese, se, and D. L. Peterson, Phys. Plasmas 13, 012701 2006. 46 S. A. Slutz, K. J. Peterson, R. A. Vesey, R. W. Lemke, J. E. Bailey, W. Varnum, C. L. Ruiz, G. W. Cooper, G. A. Chandler, G. A. Rochau, and T. A. Mehlhorn, Phys. Plasmas 13, 102701 2006. 47 G. A. Rochau, J. E. Bailey, G. A. Chandler, G. Cooper, G. S. Dunham, P. W. Lake, R. J. Leeper, R. W. Lemke, T. A. Mehlhorn, A. Nikroo, K. J. Peterson, C. L. Ruiz, D. G. Schroen, S. A. Slutz, D. Steinman, W. A. Stygar, and W. Varnum, Plasma Phys. Controlled Fusion 49, B591 2007. 48 D. D. Ryutov, M. S. Derzon, and M. K. Matzen, Rev. Mod. Phys. 72, 167 2000; M. K. Matzen, M. A. Sweeney, R. G. Adams, J. R. Asay, J. E. Bailey, G. R. Bennett, D. E. Bliss, D. D. Bloomquist, T. A. Brunner, R. B. Campbell, G. A. Chandler, C.A. Coverdale, M. E. Cuneo, J.-P. Davis, C. Deeney, M. P. Desjarlais, G. L. Donovan, C. J. Garasi, T. A. Haill, C. A. Hall, D. L. Hanson, M. J. Hurst, B. Jones, M. D. Knudson, R. J. Leeper, R. W. Lemke, M. G. Mazarakis, D. H. McDaniel, T. A. Mehlhorn, T. J. Nash, C. L. Olson, J. L. Porter, P. K. Rambo, S. E. Rosenthal, G. A. Rochau, L. E. Ruggles, C. L. Ruiz, T. W. L. Sanford, J. F. Seamen, D. B. Sinars, S. A. Slutz, I. C. Smith, K. W. Struve, W. A. Stygar, R. A. Vesey, E. A. Weinbrecht, D. F. Wenger, and E. P. Yu, Phys. Plasmas 12, 055503 2005. 49 D. R. Kania, H. Kornblum, B. A. Hammel, J. Seely, C. Brown, U. Feldman, G. Glendinning, P. Young, E. Hsieh, M. Hennesian, L. DaSilva, B. J. MacGowan, D. S. Montgomery, C. A. Back, R. Doyas, J. Edwards, and R. W. Lee, Phys. Rev. A 46, 7853 1992 ; T. S. Perry, R. I. Klein, D. R. Bach, K. S. Budil, R. Cauble, H. N. Kornblum, Jr., R. J. Wallace, and R. W. Lee, Phys. Rev. E 58, 3739 1998. 50 G. A. Rochau, J. E. Bailey, and J. J. MacFarlane, Phys. Rev. E 72, 066405 2005. 51 C. Chenais-Popovics, C. Fievet, J. P. Geindre, I. Matsushima, and J. C. Gauthier, Phys. Rev. A 42, 4788 1990. 52 R. F. Heeter, S. G. Anderson, R. Booth, G. V. Brown, J. Emig, S. Fulkerson, T. McCarville, D. Norman, M. B. Schneider, and B. K. F. Young, Rev. Sci. Instrum. 79, 10E303 2008. 53 T. McCarville, S. Fulkerson, R. Booth, J. Emig, B. Young, S. Anderson, and B. Heeter, Rev. Sci. Instrum. 76, 103501 2005 ; S.G. Anderson, R. F. Heeter, Heete r, R. Booth, J. Emig, S. Fulk Fulkerson erson,, T. McCarville McCarville,, D. Norm Norman, an, and B. K. F. Young, ibid. 77, 063115 2006 . 54 B. L. Henke, F. G. Fujiwara, M. A. Tester, C. H. Dittmore, and M. A. Palmer, J. Opt. Soc. Am. B 1, 828 1984 . 55 B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, and F. G. Fujiwara, J. Opt. Soc. Am. B 3, 1540 1986. 56 J. E. Bailey, G. A. Chandler, D. Cohen, M. E. Cuneo, M. E. Foord, R. F. Heeter, D. Jobe, P. W. Lake, J. J. MacFarlane, T. J. Nash, D. S. Nielson, R. Smelser, and J. Torres, Phys. Plasmas 9, 2186 2002. 57 N. Izumi, Izumi, R. Snavely Snavely,, G. Gregori, Gregori, J. A. Koch, H.-S. H.-S. Par Park, k, and B. A. Remington, Rev. Sci. Instrum. 77, 10E325 2006. 58 C. A. Iglesias, J. Quant. Spectrosc. Radiat. Transf. 99, 295 2006 . 59 A. Thorne, Spectrophysics Wiley, New York, 1974 .
Phys. Plasmas 16, 058101 2009 60
M. Schneider and R. Heeter, personal communication 2008. M. C. Hermann, Bull. Am. Phys. Soc. 48, 21 2003 ; J. F. Hansen, S. G. Glendinning, R. F. Heeter, and S. J. E. Brockington, Rev. Sci. Instrum. 79, 013504 2008. 62 T. S. Perry, S. J. Davidson, F. J. D. Serduke, D. R. Bach, C. C. Smith, J. M. Foster, R. J. Doyas, R. A. Ward, C. A. Iglesias, F. J. Rogers, J. Abdallah, Jr., R. E. Stewart, R. J. Wallace, J. D. Kilkenny, and R. W. Lee, Astrophys. J., Suppl. Ser. 127, 433 2000. 63 A. V. Vinogradov, I. Yu. Skobelev, and E. A. Yukov, Sov. Phys. Usp. 22, 771 1979. 64 M. H. Key and R.J. Hutcheon, Advances in Atomic and Molecular Physics 16 Academic, New York, 1980 , pp. 201–280. 65 C. De Michelis and M. Mattioli, Nucl. Fusion 21, 677 1981. 66 H. R. Griem, Phys. Fluids 4, 2346 1992. 67 H. R. Griem, Phys. Scr. T83, 142 1999. 68 G. Dunham, J. E. Bailey, G. A. Rochau, P. W. Lake, and L. B. NielsenWeber, Rev. Sci. Instrum. 78, 063106 2007 ; G. Dunham, G. A. Rochau, P. Lake, L. Nielsen-Weber, and D. Schuster, ibid. 75, 3687 2004; J.E. Bailey, R. Adams, A. L. Carlson, C. H. Ching, A. B. Filuk, and P. Lake, ibid. 68, 1009 1997. 69 E. Nardi and Z. Zinamon, J. Appl. Phys. 52, 7075 1981; J. E. Bailey, J. J. MacFarlane, P. Wang, A. L. Carlson, T. A. Haill, D. J. Johnson, P. Lake, E. J. McGuire, and T. A. Mehlhorn, Phys. Rev. E 56, 7147 1997. 70 J. D. Hares, J. D. Kilkenny, M. H. Key, and J. G. Lunney, Phys. Rev. Lett. 42, 1216 1979 ; A. Hauer, R. D. Cowan, B. Yaakobi, O. Barnouin, and R. Epstein, Phys. Rev. A 34, 411 1986 . 71 R. C. Mancini, C. F. Hooper, Jr., and R. L. Caldwell, J. Quant. Spectrosc. Radiat. Transf. 51, 201 1994 . 72 D. Hoarty, O. Willi, L. Barringer, C. Vickers, R. Watt, and W. Nazarov, Phys. Plasmas 6, 2171 1999. 73 J. Abdallah, Jr., R. E. H. Clark, and J. M. Peek, Phys. Rev. A 44, 4072 1991. 74 R. Epstein, Phys. Rev. A 43, 961 1991. 75 L. Lecherbourg, P. Renaudin, S. Bastiani-Ceccotti, J.-P. Geindre, C. Blancard, P. Cosse, G. Faussurier, R. Shepherd, and P. Audebert, High Energy Density Phys. 3, 175 2007 . 76 L. A. Woltz and C. F. Hooper, Jr., Phys. Rev. A 38, 4766 1988. 77 R. C. Mancini, D. P. Kilcrease, L. A. Woltz, and C. F. Hooper, Jr., Comput. Phys. Commun. 63, 314 1991. 78 A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms Cambridge University Press, London, 1934 . 79 P. T. Springer, T. S. Perry, R. E. Stewart, C. A. Iglesias, F. J. Serduke, B. G. Wilson, R. W. Lee, J. M. Foster, C. C. Smith, D. J. Hoarty, and S. J. Davidson, Proceedings of the Fourth International Workshop on Radiative Properties of Hot Dense Matter , edited by W. Goldstein, C. Hooper, J. Gauthier, J. Seely, and R. Lee World Scientific, River Edge, 1991 , p. 42. 80 C. A. Iglesias and F. J. Rogers, Astrophys. J. 408, 371 1991. 61
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Experimental investigation of opacity models fo r stellar interior, inertial fusion, and high energy density plasmas a… J. E. Bailey,1,b G. A. Rochau,1 R. C. Mancini,2 C. A. Iglesias,3 J. J. MacFarlane,4 I. E. Golovkin,4 C. Blancard,5 Ph. Cosse,5 and G. Fauss Faussurier urier5 1
Sandia National Laboratories, Albuquerque, New Mexico, 87185-1196, USA University of Nevada, Reno, Nevada 89557, USA 3 Lawrence Livermore National Laboratory, University of California, Livermore, California 94550, USA 4 Prism Computational Sciences, Madison, Wisconsin 53703, USA 5 CEA, DAM, DIF, F-91297 Arpajon, France 2
Received 7 December 2008; accepted 15 December 2008; published online 23 March 2009 Theoretic Theore tical al opa opaciti cities es are req requir uired ed for cal calcul culatin ating g ene energ rgy y tra transp nsport ort in pla plasma smas. s. In par partic ticula ular, r, unde un ders rsta tand ndin ing g st stel ella larr in inte teri rior ors, s, in iner erti tial al fu fusi sion on,, an and d Z pi pinc nche hess de depe pend ndss on th thee op opac acit itie iess of mid-atomicmid-a tomic-numbe numberr eleme elements nts over a wide range of tempe temperatur ratures. es. The 150–3 150–300 00 eV temperature temperature range is particularly interesting. The opacity models are complex and experimental validation is crucia cru cial. l. For exa example mple,, sol solar ar mod models els pre presen sently tly dis disagr agree ee with hel helios ioseis eismolo mology gy and one pos possib sible le explanation is inadequate theoretical opacities. Testing these opacities requires well-characterized plasmas at temperatures high enough to produce the ion charge states that exist in the sun. Typical opacity experiments heat a sample using x rays and measure the spectrally resolved transmission with a backlight. The difficulty grows as the temperature increases because the heating x-ray source mustt sup mus supply ply mor moree ene energ rgy y and the bac backli klight ght mus mustt be bri bright ght eno enough ugh to ove overwh rwhelm elm the pla plasma sma self-emission. These problems can be overcome with the new generation of high energy density HED facilities. For example, recent experiments at Sandia’s Z facility M. K. Matzen et al., Phys. Plasmas 12, 055503 2005 measured the transmission of a mixed Mg and Fe plasma heated to 156 6 eV. This capability capability will also advance opacity opacity science for other HED plasmas. plasmas. This tutorial revi re view ewss ex expe peri rime ment ntal al me meth thod odss fo forr te test stin ing g op opac acity ity mo mode dels ls,, in incl clud uding ing ex expe peri rime ment nt de desig sign, n, transmission measurement methods, accuracy evaluation, and plasma diagnostics. The solar interior serves as a focal problem and Z facility experiments illustrate the techniques. © 2009 American Institute of Physics. DOI: 10.1063/1.3089604
I. INTRODUCTION
exp − , T = I / I 0 = exp
Physical pictures for high energy density HED plasmas rely on models of the plasma properties. For example, the inner structure of astrophysical plasmas such as stars is often inacce ina ccessi ssible ble to dir direct ect mea measur sureme ements nts.. In his sem semina inall boo book k 1 “The internal constitution of the stars” Eddington pointed out this dilemma, but goes on to show that we can still build physical pictures for the inner workings of a star as long as we know the properties of the matter that lies within. More detailed information may be available for laboratory plasmas such as inertial fusion implosions and Z pinches. However, building buildi ng a comple complete te physi physical cal description description still normally requires material property models. Radiati Rad iation on oft often en pla plays ys an ess essent ential ial rol rolee in bot both h ast astrorophysic phy sical al and laborator laboratory y HED pla plasma smass and a key mat materi erial al property is the opacity, which quantifies how transparent or opaque the plasma is to radiation. In this tutorial we describe experimental methods developed to test opacity models for HED plasmas. The transmission of photons with intensity I 0 normally incident on a uniform plasma is given by a
Paper PT2 1, Bull. Am. Phys. Soc. Invited speaker.
b
1070-664X/2009/165
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199 2008.
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1
where h is the photon energy energy and I is the att attenu enuate ated d photon pho ton inte intensi nsity ty eme emerg rging ing fro from m the pla plasma sma.. The opt optica icall depth, , is related to the opacity by = x, where is the opacity per unit mass typically measured in units of cm2 / g, is the density, and x is the optical path length. Opacity Opa city mod models els are tes tested ted by mea measur suring ing T thr throug ough h a plasma with known characteristics. The opa opacit city y is gen genera erally lly a rap rapidl idly y var varyin ying g fun functio ction n of frequency. In some applications, knowledge of the frequency dependent opacity is required and this is what must be measured in benchmark experime experim ents. An example is levitation of 2 “metals” in stellar interiors. Here, metals refer to any element other than hydrogen or helium, a definition commonly employed in astrophysics. These elements diffuse toward the center cen ter of sta stars rs und under er the influence influence of gra gravity vity.. The There re is an opposing oppos ing levitating force provi provided ded by the photo photon n pres pressure sure and this for force ce is pro propor portion tional al to the fre freque quency ncy dep depend endent ent opacity. In other applications the most important quantity is the mean opacity averaged over frequency. An example is d iff uu3 sive radiation transport of energy within stellar interiors. In light of this simplification, one might ask: Why use opacity models mod els?? Why not jus justt mea measur suree the mean opa opacit cities ies we require? The problem is that the opacity depends on the plasma
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T(eV T( eV))
ne(cm-3) r /R /Rs
19 3
1x 10 1023 0.7133
measured boundary RCZ = 0.713 + 0.001 Predicted R CZ= 0.726
1000
= Planck function temperature
dB
B
dT
T =
0.8
) g / 2
100
m c (
1360 13 60
6x10 6x 1025
1.0
0.6 dB dT
N
0
0.4 radiation convection
10
0.2
FIG. 1. Color Schematic of the solar interior. The temperature and density information are from Ref. 4 and the values for the location of the radiation convection boundary are from Ref. 5.
temper temp erat atur ure, e, de dens nsity ity,, an and d el elem emen enta tall co comp mpos ositi ition on.. Th Thee breadth of plasma conditions and constituents encountered in applications makes it impractical to measure all the needed opacities. opaci ties. Furth Furthermor ermore, e, accur accurate ate opacit opacity y measu measuremen rements ts are challenging challe nging and the numbe numberr of availa available ble measu measuremen rements ts is sparse. spar se. Finally Finally,, some intere interesting sting condi conditions tions remain beyond the reach of laboratory experiments. Therefore, the main goal of opacity experiments is to test the physical underpinnings of opacity models so that they can be reliably extrapolated to conditions untested in the laboratory. Fortunately, the details of the rap rapidl idly y var varyin ying g opa opacit city y as a fun functi ction on of fre freque quency ncy provide a trove of information. The accuracy of model descriptions for the physical processes that govern opacity is severely tested by comparison with T v measurements. II. OPACITY EXPERIMENT DESIGN Given that opacity measurements are sparse and the parameter space is broad, it is important to optimize opacity experiment designs. The questions we must answer include the following.
1 What photon energy range is important? 2 What elements contribute? 3 What photon absorption processes are important? The answers to these questions depend on the application. In this tutorial we use the solar interior as an example to illustrate experiment design and execution. Figure 1 provides a schematic of the solar interior. The energy generated by thermonuclear reactions in the solar core is transported outward by radiation over approximately 70% of the solar radius, Rs. The solar opacity generally increases with radius and eventually becomes large enough that energy transport by rad radiat iation ion is ine ineffic fficien ientt and con convec vective tive tra transp nsport ort tak takes es over. The border between the radiation and convection dominated zones is known as the CZ boundary. The core temperature is roughly 1360 eV and it falls to appro approximate ximately ly 190 eV 4 just below the CZ boundary. The electron density also decrease cre ases, s, fro from m 6 1025 cm−3 at the core to 1 1023 cm−3 near ne ar th thee CZ bo boun unda dary ry.. Th Thee bo boun unda dary ry lo loca catio tion n is R / Rs =0.713 0.001, inferred with remarkable accuracy from he5 lioseismology measurements. The CZ bou bounda ndary ry loc locati ation on and the spatial temperature and density profiles depend on the mean opacity as a function of radius. However, opacity models have never been tested with laboratory experiments at the conditions that exist inside the sun.
opacity “window”
500
1000
1500 hQ (eV)
2000
2500
0.0
FIG. 2. Color Frequency dependent opacity Refs. 13 and 14 for a 17 element solar composition Ref. 6 near the base of the solar convection zone compared to dB / dT . The electron temperature and density were 193 eV and 1 1023 cm−3, respectively.
The motivation for experimental verification of theoretical opacities has grown sharper during the past decade. Solar models are constructed using estimates for the composition and the mate materia riall pro proper pertie tiess suc such h as equ equati ation on of sta state, te, opacity, and nuclear cross sections as inputs. Predictions for the CZ bound boundary ary location, interior density profile, profile, and sound speed were in good agreement with helioseismic data until roughly the year 2000. Beginning in 1999, revised estimates estimate s 6 for the sol solar ar com compos positio ition n red reduce uced d the amo amount unt of met metals als.. Solar models based ba sed on these revised estimates disagree with 5,7,8 helioseismology. One poss possible ible expla explanation nation is inacc inaccurauracies in the opacity models. Solar Sola r models models constructed with ad 5,7,9,10 adjustments ments of the opacity found that incre increasing asing hoc adjust thee me th mean an op opac acity ity by 10 10%– %–20 20% % in th thee so solar lar re regi gion on 0. 0.4 4 R / Rs 0.7 would resolve the discrepancies. The solar problem serves to define needed opacity experiments. The first question to answer is what photon energy range is most important. For plasmas such as the sun that are much larger than the photon mean free path, radiation tio n tr tran ansp spo ort is usu suaall lly y de desscr crib ibeed by a di difffu fusi sion on 11,,12 11 approximation using the Rosseland mean opacity R, 1 R
=
1 dB d dT
dB d , dT
2
where B is the Planck function, T is the plasma temper temperature ature,, and the weighting function dB / dT peaks at roughly 3.8 kT. Note that the Rosseland opacity is a harmonic mean depending on the reciprocal of and photons are most efficiently transported through the “windows” where is the lowest. Near the CZ boundary T 190 eV and and dB / dT peaks at h 750 0 eV Fig. 2. The frequency frequency depen dependent dent opacity near 75 the CZ bou ound ndar ary y ca calcu lcula lated ted us usin ing g th thee op opac acity ity pr proj ojec ectt 13,,14 13 model is di disp spla laye yed d in Fi Fig. g. 2. Co Comp mpar ariso ison n wit with h th thee weighting function for the Rosseland mean shows that the most important photon energies are approximately 300 h 1300 0 eV. We rei reiter terate ate tha thatt we req requir uiree mea measur sureme ements nts of 130 the frequency dependent opacity to test the physics in opacity models. However, familiarity with the characteristics of the Ros Rossel seland and mea mean n hel helps ps defi define ne wha whatt opa opacit cities ies are most important import ant to measu measure. re.
058101-3 05810 1-3
Experimen Expe rimental tal inve investigat stigation ion of opac opacity ity model models s… 17
100
10-1
(a)
H
n o 10-2 i t c a r f s 10-3 s a m
O Ne
Fe
10-4
10-5
1 2 6 7 8 10 11 12 13 14 16 18 20 24 25 26 28 atomic number O
0.25
(b) Fe
0.20 n o i t c 0.15 a r f y t H i c 0.10 a p o
Ne
0.05 0.00
Phys. Plasmas 16, 058101 2009
1 2 6 7 8 10 11 12 13 14 16 18 20 24 25 26 28 atomic number
FIG. 3. Color Characteristics of the solar interior composition. The histogram in a provides the mass fractions Ref. 16. The histogram in b is the fractional contribution to the Rosseland mean evaluated near the base of the solar convection zone using the OPAS opacity model Ref. 17.
The second question to answer in designing opacity experiments is: What elements should be studied? The answer is som sometim etimes es str straig aightf htforw orward ard in lab labora orator tory y pla plasma smass com com-posed of a single element. However, in many applications multiel mul tieleme ement nt pla plasma smass are use used. d. For exa exampl mple, e, mixt mixture uress of low- Z and mid- Z elements, where Z is the atomic number, are commonly used in inertial fusion capsule ablators Be/Cu ablators are described in Ref. 15. Different elements may be present in different plasma spatial regions. These differences may alter the opacity and the role each element plays in the radiation transport. Astrophysic Astro physical al plasma plasmass are more compl complicated icated since the observer does not necessarily possess certain knowledge of the com compos positio ition n and man many y ele elemen ments ts may be pre presen sent. t. The solar composition estima estimated ted from photospheric spectroscopy 16 and meteorite analysis is illustrated in Fig. 3a. This 17element mixture was was widely used prior to the revised low6 5 metallicity estimates that led to the solar CZ problem. The mass fraction for elements such as oxygen, neon, and iron is less than 1%. Nevertheless, these elements contribute a disproportiona propo rtionately tely larg largee frac fraction tion of the solar interior opacity because they are not completely ionized, as described below. The fractional opacity contribution for each element at conditions corresponding to the CZ boundary is shown in Fig. 3b. Figure 3b calculations were performed with the OPAS
model. The larg largest est contributions contributions are from oxyge oxygen, n, neon neon,, and iron and these are the elements of greatest interest for 5 solar interior opacity measurements. Obviously, the impact of errors in any single element is diminished when the element is a dilute constituent of a mixture. For example, in order to cause a 10% change in the total mean opacity we would need to multiply the iron opacity at the CZ boundary by a factor of approximately 1.5. The third question for opacity experiment design is how each eac h ele elemen mentt con contri tribut butes. es. The thr three ee mai main n abs absorp orption tion pro pro-cesses in plasmas are free-free, bound-free, and bound-bound electron transitions. These processes differ from one element to another and depend on the ionization. Consider the contributions of hydrogen, oxygen, and iron to the opacity at the base of the solar convection zone. At these conditions hydrogen is ful fully ly str stripp ipped ed and the onl only y con contrib tributio ution n is fre free-f e-free ree transitions trans itions in the ionized electr electrons ons Fig. 4a. Ox Oxyg ygen en is ionized into the K -shell -shell i.e., O+6 and O +7, isoelectronic with He and H and contributes absorption through both boundfree and bound-bound transitions. Here, “ K -shell” -shell” refers to -shell ions n =1 principal quantum number electron states. K -shell in local thermo thermodynam dynamic ic equilib equilibrium rium LTE norma normally lly have much of their population in the ground state and an important class of transitions originates from the n =1 lower level thee CZ bo boun unda dary ry,, ir iron on is io ioniz nized ed in into to th thee Fig. 4b. At th +16 +17 -shell, ell, with sig signifi nifican cantt pop popula ulation tionss of Fe , Fe , an and d L-sh Fe+18. These ions are isoelectronic with Ne, F, and O and conseq con sequen uently tly are oft often en des descri cribed bed as NeNe-like like,, F-l F-like ike,, and O-like. The greater number of bound electrons renders the Fe opacity contributions immensely complicated. Many transitions originate from the n =2 lower level, but there is also significant excited state population and transitions originate from n 3 princ principal ipal quantum numbers Fig. 4c. Of the three elements that are most important at the CZ boundary, Fe is by far the most complex and it is therefore expected to be the most suspect. The opacity plots in Figs. 4b and 4c illustrate another consequence of mixing elements together. Consider the pure iron photo photon n absor absorption ption red cur curve, ve, Fig. 4c. The deepest opacity window is in the vicinity of h 50 500– 0– 70 700 0 eV eV,, a region dominated by bound-free transitions with excited initial states. If one is interested in a pure iron plasma, then this defines the most important photon energy range. The opacity model must then have an accurate treatment for both the n 3 excited state populations and the bound-free photoionization cross sections out of those excited states. On the other hand, the comparison of pure iron opacity with the total solar mixture opacity shows that the iron contribution to the h photon ton energy energy ran range ge is neg negligi ligible ble.. The mixture mixture 500 eV pho opacity has filled in the Fe window at these energies. Instead, the Fe bound-bound transitions at 750 h 130 1300 0 eV are the mos mostt sig signifi nifican cantt iro iron n con contrib tributi ution on to the sol solar ar mixt mixture ure opacity near the CZ base. Thus, a mixture dilutes the importance of any individual element and can change which absorption processes and photon energies are important. These considerations considerations define a usef useful ul opac opacity ity exper experiment iment for the base of the solar convection zone. We should attempt to measure opacities for O, Ne, and Fe. Of these, Fe is probably the most suspect and is therefore a good place to start.
0581 05 8101 01-4 -4
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total
(a)
0.3
n o i t c a r f
n= 3
2
10
0.4
n= 4
) 100 g / m c (
e e r f e e r f
Z experiment
R/Rsun = 0.6 R/Rsun = 0.5
R/Rsun= 0.7
0.2
H
n= 2
0.1 1
free-free 0.0
n= 1 500 1000
1000 h (eV)
total
1500
FIG. 5. Color The iron char charge ge state distributi distribution on as a func function tion of electr electron on temperature and density at different depths within the sun. The T e and ne values are from Ref. 4 and the PrismSPECT model Ref. 18 was used to calculate calcu late the charg chargee state distributi distribution. on. The red curve corre correspon sponds ds to just below the convection zone R / Rs =0.7, T e =193 eV, ne = 1 1023 cm−3, the green curve corresponds to R / R s =0.6 T e =261 eV, ne =2.5 1023 cm−3, and an d th thee bl blue ue cu curv rvee co corr rres espo pond ndss to R / Rs =0.5 T e =335 eV, ne = 7 23 cm−3 . The black curve with triangles corresponds to the distribution 10 for conditions in Z experiments.
(b) n= 4
100
n= 3
) g / 2 m c ( 10
n= 2
O ground state bound-free
1
K-shell bound-bound 500 1000
1000 h (eV)
n= 1 1500
n= 4
) 100 g / 2 m c (
e e r f d n u o b
l n = 3 l
10
1
l l e h s K
(c)
total
n= 2
window filling
e h s L
L-shell bound-bound
Fe
n= 1 500
1000 h (eV)
+21 1 +2 +22 2 +13 +1 +14 4 +1 +15 5 +16 +16 +1 +17 7 +1 +18 8 +1 +19 9 +20 +2 Fe charge state
1500
FIG. 4. Color Physical processes responsible for the contribution to opacity by different elements. The calculated Refs. 13 and 14 total opacity of the solar mixture at the base of the convection zone is compared with the contri con tribut bution ion fro from m hyd hydrog rogen, en, oxy oxygen gen,, and iro iron n in a, b, an and d c, respectively.
The most important photon energy range for Fe was already established estab lished as 750–1 750–1350 350 eV eV.. The electr electron on temper temperature ature just below the convection zone is 190 eV and the electro electron n den23 −3 sity is 10 cm . Eventually we must reproduce these conditions in order to test fully the model physics. This is a daunting goal that is beyond the ability of present day experiments. However, the ionization distribution depends on both bo th te temp mper erat atur uree an and d de dens nsity ity,, a pr prop oper erty ty tha thatt en enab able less progress progr ess while exper experimenta imentall techn techniques iques to reac reach h more extreme conditions are developed. Reproducing the charge states of interest is a key prerequisite uis ite for qua quantit ntitativ ativee tes tests ts of opa opaciti cities. es. It can det determ ermine ine whether opacity models accurately calculate the charge state distribution, energy level structur struct ure, e, and relevant photon ab18 sorption processes. Calculations of iron charge state distributions at various depths within the sun are shown in Fig. 5.
Deeper in the solar interior both the temperature and density increase. Although the temperature rise should should cause a higher degree deg ree of ion ioniza izatio tion, n, it is cou counte ntered red by the cor corres respon pondin ding g density increase. Thus, similar iron charge states exist over a broad range of the solar interior. The condition cond itionss correspond19,,20 19 ing to rec recent ent Z fac facilit ility y iro iron n exp experi erimen ments ts are supe superimrimposed on the solar interior results in Fig. 5. The Z facility experiment charge state distribution is similar to those at the CZ boundary, even though the 156 eV Z experiment temperature is 37 eV lower. lower. The rea reason son is tha thatt the density density is approximately ten times lower. Tests of high density effects such as contin continuum uum lowering and line broadening broadening require further experiment experiment advan advances ces to simulta simultaneous neously ly produ produce ce both high temperature and density. III. EXPERIMENTAL METHODS AND HISTORICAL OVERVIEW The basic strategy used to test opacity models is to compare the freq frequency uency dependent dependent exper experimental imental and theor theoretica eticall transm tra nsmiss ission ion for a sam sample ple with kno known wn con condit dition ions. s. Thi Thiss method is illustrated in Fig. 6. The sample is heated with an x-ray source and the transmission is measured by viewing a backlig bac klight ht thr throug ough h the sam sample ple with a spe spectr ctrome ometer ter.. The sample sam ple material material of int intere erest st is san sandwi dwiche ched d by lay layers ers of a low- Z tampe tamperr to promo promote te unifo uniformity rmity.. Spect Spectra ra are acquired with and without the sample material. Dividing the absorption spectrum obtained with the sample by the unattenuated tamper only spectrum provides the transmission. The requisite data can be acquired on separate experiments, as long as key experimental aspects are reproducible. Reproducibility can be evaluated by comparing spectra obtained on sequential experiments Fig. 7. The reproducibility encompasses the x-ray heating of the sample, the sample fabrication fabr ication,, the backl backlight ight absolu absolute te intens intensity ity and spect spectrum, rum, the spectrometer efficiency e.g., crystal reflectivity and the detector response e.g., film proc processin essing g repr reproducib oducibility ility. A powerf pow erful ul alt altern ernativ ativee meth method od kno known wn as poi point nt pro projec jectio tion n
058101-5 05810 1-5
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Phys. Plasmas 16, 058101 2009
1.0
n0.8 o i s0.6 s i m s0.4 n a r0.2 t
transmission spectrum
0.0
1000
1200 h (eV)
) r e t s 2 / e V e c / n 2 a i m c 1 d / a r W
1600 FIG. 8. Color Diagram of the experiment configuration used in point pro jection opacity measurements adapted from Ref. 22.
backlighter spectrum
21,,22 21
1 1
0 1 ( 0
1400
backlighting provides the required data in a single experiment Fig. 8. This technique offers the potential for high accuracy without the need for reproducibility, at the cost of increased complexity. The three main requirements for opacity experiments are as follows:
absorption spectrum 800
1000 1200 hQ (eV)
1400
Z data without iron
1600
Z data with iron
h
h
spectrometer
spectrometer Fe/Mg sample
CH heating x-rays
(1)
CH heating x-rays
(2)
backlighter
1 uniform sample plasma, 2 accurate transmission measurements, 3 independent plasma diagnostics,
backlighter
FIG. 6. Color Method for transmission measurements used to test opacity models. A spectrometer views a backlight through an x-ray heated foil. The samplee tran sampl transmiss smission ion as a funct function ion of phot photon on ener energy gy is deter determined mined using measurements of a low-Z tamper only foil diagram 1 and measurements of the sample material of interest surrounded by the tamper diagram 2. The synthetic backlighter spectrum is a 314 eV Planckian that is representative of the backlighter used in Z iron experiments Refs. 19 and 20. The absorption spectrum was calculated with PrismSPECT Ref. 18 at the experiment temperature and density values and the transmission spectrum was obtained by dividing the absorption spectrum by the backlighter spectrum.
Z1650 Z1649
y t i s n e t n i
7
8
9 O
(Å)
10
11
12
FIG. 7. Color Comparison of absorption spectra from two sequential Z experiments. No scaling or other intensity adjustments were applied in this comparison, other than correcting both spectra for the film response.
as succinctly described described in Ref. 23 23.. Most research to date has compared the data with models that assume the LTE approximation is valid. In this approximation the ion energy level popula pop ulation tionss are des descri cribed bed by a Bol Boltzm tzmann ann dis distrib tributi ution. on. Methods for evaluating the validity of this approximation are 24,,25 24 described elsewhere. Techni echniques ques for opaci opacity ty resea research rch were developed using 26 laser-driven experiments beginning in the mid-1980s. The earl ea rlie iest st wo work rk us used ed a si sing ngle le-s -sid ided ed xx-ra ray y so sour urce ce to he heat at 26– 26 –30 sample sam pless com compos posed ed of Al, Fe, Br, or Ge. Later,, x-ra Later x-ray y cavities known as Hohlraums were used to provide a nearly isotropic heating x-ray x-ray flux flux and the variety of sample mate31– 31 –36 rials was expanded. Crystal spectrometers recorded photons between 1200 and 3000 eV eV,, the electron temperature temperature was 20–76 eV, and the electron density was roughly 2 – 4 21 10 cm−3 . This work established most of the principles used today for opacity research and valuable initial opacity model tests were conducted. However, the crystal spectrometerr mea ete measur sureme ements nts wer weree una unable ble to add addres resss the 40–6 40–600 00 eV photon energy energy rang rangee that dominates the tr traans nspor portt at the these se 37– 37 –39 relatively low temperatures. In later work, similar x-ray techni tec hnique quess wer weree use used d to hea heatt Fe sam sample ples, s, but the spe spectr ctraa were recorded using variable-line-spacing grating spectrometers. This enabled recording 80–300 eV photon energies that are near the peak of the Rossela Ross eland nd mean weighting function. 40 These methods were adapted to the larger x-ray flux provided by the Saturn Z-pinch facility, where a lower density LTE plasma near the conditions that exist in the envelopes of pulsating Cepheid variable stars was studied. These measurements provided provided strong evidence for the validity of the Opal 41 opacity model in this low tempera temperature ture low density regime. 42 The Opal opacities helped resolve long standing discrepancies between stellar evolution and pulsation models. In order to test opacity models used in stellar interior, inerti ine rtial al fus fusion ion,, and Z-p Z-pinc inch h res resear earch, ch, high higher er tempe temperatur raturee 19,,20 19 plasmas are required. Recent experiments have exploited the inten intense se radiation created by a dynamic Hohlraum x-ray 43– 43 – 47 source driven by the 21 106 Ampere current provided
0581 05 8101 01-6 -6
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Phys. Plasmas 16, 058101 2009
48
by the Z facility. This source is formed by accelerating an annular tungsten plasma onto a low density CH 2 cylindrical foam located on the axis. The impact of the tungsten on the foam generates shock radiation that is trapped by the tungsten plasma. This is called a “dynamic” Hohlraum because the diameter shrinks with time as the tungsten continues to be com compre presse ssed d by the mag magnet netic ic pre pressu ssure re sup supplie plied d by the large lar ge axi axiall ally y dir direct ected ed cur curren rent. t. An opa opacity city sam sample ple pla placed ced above the Hohlraum end cap is heated by the Hohlraum x rays and it is backlit when the radiating shock stagnates on the cylinder axis. These experiments measured Fe transmission at T e =156 6 eV, temperatu temperatures res high eno enough ugh to pro pro-duce the charge states, and electron configurations that exist at the base of the solar convection zone Fig. 5. As mentioned above, the density in these experiments is roughly an order of magnitude lower than at the CZ boundary.
IV. OPACITY EXPERIMENT REQUIREMENTS: SAMPLE UNIFORMITY
tamper (CH)
sample
(a)
x-rays
n0.8 o i s0.6 s i m s0.4 n a r0.2 t
hot sample
(b) cold sample
0.0 e c0.8 n a i d0.6 a r r0.4 i e v i t0.2 a l e r0.00
(c)
200 eV Planck heating spectrum
500
1000 hQ (eV)
1500
A more general expression for the transmission is
T = exp −
, T e x , ne x xdx ,
3
reducing to Eq. 1 only if the effect of plasm reducing plasmaa nonun nonuniformi iformi-ties is negligible. If nonuniformities exist it may still be possible to acquir acquiree valuab valuable le opacit opacity y infor information mation by numer numerically ically evalua eva luatin ting g the inte integra grall in Eq. 3. An example of this approach is described in Ref. 35 35.. There, the goal was to produce du ce hig high h de dens nsiti ities es an and d gr grad adie ient ntss we were re an ac acce cept ptab able le tradeoff trade off.. Such tradeoffs tradeoffs are sometimes nece necessary ssary as incre incre-mental progress progress is made toward more extre extreme me condi conditions. tions. However, the desired accuracy for validating opacity models is high and experiments with significant nonuniformities are unlikely unlike ly to provid providee defini definitive tive conclusions conclusions about the under underlylying physics embedded within the model. Volumetric heating by x rays is used to produce uniform 49 hot opacity samples. This is accomplished when a portion of the heating x-ray spectrum streams through the sample. In this case the sample is said to be “optically thin” to at least a portion of the heating x-ray spectrum. This is illustrated for the Z-pinch dynamic Hohlraum iron opacity experiments in Fig. 9. A Planckian heating spectrum at radiation brightness temperature T r =200 eV peak peakss at h max 2.8 T r 550 eV. The optical depth of the initially room tempe temperatur raturee sampl samplee is lesss tha les than n one one,, and con conseq sequen uently tly the tra transm nsmiss ission ion is hig high, h, over a broad photon energy band near the peak of the heating spectrum. As the sample temperature increases, the opacity drops further and the sample becomes even more transparent near the peak of the heating x-ray spectrum. Thus, photons deposit energy throughout the sample during the entire history of the experiment. This produces uniform heating, at the cost of an inefficient process. The desire for uniform samples is a major reason why large HED facilities are required for high temperature opacity experiments. Note that if the heating spectrum peaks at lower photon energy, then the initial energy deposition may occur primarily near the surface and the sample heating may initially be nonuniform. In this case
FIG. 9. Color X-ray heating provides provides the abil ability ity to volu volumetri metrically cally heat opacity samples a. A sig signifi nifican cantt por portio tion n of the heating heating x ray rayss str stream eam through thro ugh the sampl sample, e, prov providin iding g relat relativel ively y unif uniform orm but inef inefficien ficientt heati heating. ng. Transmiss Tran smissions ions thro through ugh room temp temperatu erature re iron iron/magn /magnesium esium foil and iron iron/ / magnesium plasma heated to 150 eV are shown in b, compared to the heating x-ray spectrum provided by a 200 eV Planckian source c. The areal density and composition of both the room temperature foil and the plasma are the same as in Refs. 19 and 20 20..
a detailed consideration of the radiation hydrodynamics of the sample evolution may be needed. Tem empo pora rall un unif ifor ormit mity y is ju just st as im impo port rtan antt as sp spat atia iall sample uniformity. Hot samples inevitably evolve with time and opacity measurements must employ some form of time resolu res olutio tion. n. The most com common mon techniqu techniquee is to use a sho short rt duration backlight source. This allows using film-based detectors, which offer the best spectral range and resolution for typical spectrometer dispersions. Time-resolved detectors are another option. In either case, the temporal evolution of the sample temperature and density must be slow enough that the transmission variation is small over the time scale of the measurement. This favors longer duration, slowly changing x-ray heat sources. Radiation hydrodynamics simulations have been used to evaluate sample uniformity. While such simulations provide valuab val uable le ins insigh ight, t, the fac factt tha thatt the they y nec necess essari arily ly emp employ loy the opacity models that are the subject of the test compounds concerns over whether the simulations provide an accurate representation of reality. Given its importance, it is desirable to measure the uniformity. Unfortunately, to date direct uniformity for mity inf inform ormati ation on obt obtain ained ed in opa opacit city y exp experi erimen ments ts has been limited. Perhaps the best certification available has been the determination that spectra used to diagnose the plasma Sec. VII are quantitatively consistent with single values of the temperature and density. Future experiments may be able to determine the uniformity directly, for example with spaceresolved measurements such as radiography or x-ray Thomson scattering. A significant challenge in this regard is the
058101-7 05810 1-7
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(a)
Phys. Plasmas 16, 058101 2009 1.0
(b) artifacts
0.8
artifacts absorption lines
absorption lines
FIG. 10. Color X-ray absorption spectra exhibiting reflectivity defects that may masquerade as spectral lines. The image in a is from Z experiments 23.. Vigi Vigilance lance is Refs. 19 and 20 and the image in b is adapted from Ref. 23 required in experiments to ensure that such defects do not introduce artifacts into the inferred transmission.
need for spatial resolution of a few microns. A possible solution may be spectroscopy of different tracer elements buried within the sample at specific depths. A problem with this approach is that each tracer absorbs a portion of the heating x-ray spectrum and consequently tracers buried near the rear of the sample are not necessarily heated to the same extent as 50 tracers near the front. V. OPACITY EXPERIMENT REQUIREMENTS: ACCURATE TRANSMISSION MEASUREMENTS Numerous technological challenges must be overcome to produce accu produce accurate rate trans transmissio mission n measu measuremen rements. ts. These challengess may be conve lenge convenientl niently y divide divided d into concerns arising from the backlight, the sample fabrication, and the spectrometer. Here we restrict the discussion to backlight and spectrometer trome ter issue issuess and we consid consider er only crystal-based crystal-based instruments operating operating in the 700– 10,00 10,000 0 eV photon energy energy range. range. Many crystal types and geometrical configurations have been employed in these spectrometers. A problem common to all of them is spectral artifacts arising from crystal defects. Examples of such artifacts are illustrated in Fig. 10 10.. These defects can masquerade as spectral features and care must be exercised to ensure that the inferred transmission is not contaminated by them. The defects are usually obvious in the two-dimensional spectral images Fig. 10, even though they may not be so easy to identify in a lineout. One possible approach is to examine the spectrum in detail, identify the artifact features, and edit or smooth the spectrum to remove their effect. An alternative is to perform multiple reproducible experiments using different crystals or different crystal alignments, so that the features change from one measurement to another. Then averaging the measurements together effectively removes their influence. The best method to avoid this problem is to procure and characterize the best possible crystals, but perfection in this regard is elusive. A second spectrometer-related issue that influences accuracy is the finite spectral resolution. resolution. Transmission Transmission spectra that illustrate the influence of spectral resolution are shown in Fig. 11 11.. The red curve is iron plasm plasmaa transmission calcu19,,20 19 lated for the Z facilit facility y experiment conditions using the 18 PrismSPECT Prism SPECT model without consi considerin dering g instr instrument ument reso reso--
n o i s0.6 s i m s n a r0.4 t
E/dE = 700
ideal
0.2
0.0
saturation
1020
1040 h (eV)
1060
1080
FIG. 11. Color Calculated Ref. 18 transmission for iron plasma at the experimental conditions in Refs. 19 and 20 20.. The blue curve is the ideal case and the red curve accou accounts nts for an inst instrumen rumentt spect spectral ral resolution resolution E / dE =700.
lution. lutio n. Th Thee bl blue ue cu curv rvee inc inclu lude dess a ty typi pica call re reso solu lutio tion n of E / dE 700 700.. Spe Spectr ctral al line liness with opt optica icall dep depth th gre greate aterr tha than n one are opt optica ically lly thi thick ck and the tra transm nsmiss ission ion at line center center approaches zero. However, if the line profile is not experimentally mental ly reso resolved, lved, then the observed transmission transmission will be 51 significantly larger. Such lines are said to be “saturated.” Saturation Satur ation eff effects ects must be incor incorpora porated ted into compa comparisons risons with opacity models. These effects are one reason opacity model calculations are converted into transmission for comparison with data, rather than the measured transmission being converted into opacity. Once the instrument blurring occurs cu rs,, in info form rmat atio ion n is lo lost st an and d it ca cann nnot ot be re reco cove vere red. d. Deconvolutio Decon volution n may be feas feasible, ible, but it typica typically lly introd introduces uces unacceptable uncertainties. If it is desired to compare opacities rather than trans transmissio mission, n, the opacity calcu calculation lationss must first be converted to transmission, the instrument resolution convolved, and then reconverted back into opacity. Thus, it is simpler and generally more informative to compare transmissions. Ultimately, the two key points of this discussion are thatt ins tha instru trumen mentt res resolu olutio tion n mus mustt be mea measur sured ed and hig higher her spectral spect ral reso resolution lution is desir desirable. able. Howev However er,, reso resource urce limitations often restrict spectral resolution measurements to relatively few photon energies, despite the fact that spectral resolut ol ution ion is a fu func nctio tion n of ph photo oton n en ener ergy gy.. If th thee me meas asur ured ed spectral range is relatively small, then the impact of spectral resolution uncertainty may be negligible. In other cases the portion of the transmission uncertainty that arises from the spectral spect ral resol resolution ution uncer uncertainty tainty may be signifi significant. cant. A third technological challenge associated with the spectrometer is the type of detector used. Time-resolved detectors such as streak cameras or microchannel plate MCP ca camer meras as 37,,40 37 40,,52 havee bee hav been n suc succes cessfu sfully lly use used d in som somee exp experi erimen ments. ts. These detectors may be essential for rapidly evolving sample conditions or if the late-time sample self-emission is bright enough to compete with the backlight see discussion of selfemission emissi on eff effects ects below. However, the active area of such
0581 05 8101 01-8 -8
Bail Ba iley ey et al.
Phys. Plasmas 16, 05810 058101 1 2009
spectrometer
(a)
self emission tamper (CH)
sample backlighter
FIG. 12. Color Comparison of x-ray absorption spectra recorded on two different types of film, Kodak DEF and 101–07. The agreement between the two implies implies tha thatt th thee con conver versio sion n of film density density to film exposure exposure was self-consistent.
absorption spectrum ) r 2 s / V e /
self emission
2
detectors often restricts the spectral range. An effort to circumvent this this problem problem with larg largee forma formatt MCP configurations configurations 52,,53 52 is underway. Nevertheless, the spatial resolution element sizee of exi siz existi sting ng time time-r -reso esolve lved d det detect ectors ors is app approx roximat imately ely 80 m or larger. This limits the spectral resolution that can be achieved in most cases. The detector used in most opacity experiments to date has been x-ray film. Film has the advantage of larger effective number of pixels. Spatial resolutions of 5 m are routinely available. However, film has the disadvantage of nonlinear response and it requires both accurate calibrations and careful attention to developing procedures. Calibrations Calibr ations are resou resource rce intens intensive ive and rare rarely ly perfo performed. rmed. This raises a concern that the film sensitivity may change, especially espe cially since film manuf manufactur acturers ers regard film desig design n and fabric fab ricatio ation n det details ails as pro propri prieta etary ry.. For exa example mple,, the mos mostt commonly commo nly used x-ra x-ray y film calibrations calibrations are those of Henke et 54,,55 54 al., performed more than twenty years ago. In order to evaluate concerns over possible film development or fabrication problems, problems, an experiment experiment using two different different types of x-ray film was performed using a tamped Al and Mg opacity 56 sample placed to the side of a Z pinch Fig. 12. The resu results lts agree, supporting the sustained validity of the Henke calibrations. tio ns. Nev Nevert erthel heless ess,, vig vigila ilance nce ove overr film dev develo elopme pment nt and possible manufacturing changes is certainly warranted. X-ray charge coupled devices have a linear response and are probably a desirable optio option n to consider in future opacity experi57 ments. Image plates are another attractive detector technology,, alth ogy althoug ough h not all ima image ge pla plates tes and sca scanni nning ng sys system temss provid pro videe the nee needed ded spa spatial tial res resolu olutio tion. n. Sen Sensit sitivit ivity y to hig high h photon energy x-ray backgrounds may also limit the utility of image plates for opacity measurements in the keV photon energy range. Produc Pro ducing ing a hig high h qua quality lity backligh backlightt is a key enabling enabling technology for opacity experiments. The desired characteristics are broad spectral range, a smooth featureless spectrum, and high brightness. Broad spectral coverage is needed both to probe a wide range of features in the element of interest and to measu measure re simulta simultaneous neously ly spect spectral ral lines in diagn diagnostic ostic tracers added to the sample see below. A relati relatively vely smooth and featureless backlight spectrum is needed because if the backlig bac klight ht spe spectr ctral al fea featur tures es ove overla rlap p with fea featur tures es in the sample sam ple,, the then n the acc accura uracy cy req requir uireme ements nts of mea measur suring ing the backlighter spectrum increase dramatically. Thi T hiss problem is 58 aggravated by limited instrumental resolution. High backlight brightness is needed both to supply an
m c / W
emission limit 125 eV
0 1
0 1 ( 1 e c n a i d a r
0
(b)
backlight 170 eV
900
1000 1100 h (eV)
1200
FIG. 13. Color Self-emission can contribute to the signal recorded by the spectrometer a. A hypothetical situation is quantitatively illustrated in b using PrismSPECT Ref. 18 calcu calculati lations ons for iron plasm plasmaa selfself-emiss emission ion green curve and absorption spectra red curve. The plasma temperature is assume ass umed d to be 125 eV and th thee bac backli klight ghter er is ass assume umed d to be a 170 eV Planckian. The most optically thick lines have self-emission that peaks at the blackbody limit, corresponding in this case to a 125 eV Planckian.
adequate adequa te exp exposu osure re at the det detect ector or and to ove overwh rwhelm elm the 23 sample selfself-emissi emission. on. The com complic plicatio ations ns intr introdu oduced ced by sample self-emission are illustrated using calculated signals for a hypothetical experiment in Fig. 13 13.. The spectrometer detects the desired backlight photons and also samples selfemission contributions. In Fig. 13b examp example, le, the backli backlight ght source is a 170 eV Planckian and the iron sample temperature is 125 eV. The density and op tical path length corre corre-19,,20 19 spond spo nd to typ typica icall sam sample ple con conditi ditions ons.. The selfself-emiss emission ion and absor absorptio ption n spe spectr ctraa wer weree com comput puted ed usi using ng the Pri Prismsm18 SPECT model. The brightest spectral lines emitted by the sample are optically thick and peak at the blackbody limit: a Planckian corr orreesponding to the sample electr tro on 59,,12 59 temperature. The exper experimenta imentall trans transmissio mission n deter determined mined from Eq. 1 is affected most for the strongest spectral lines since they have the brightest self-emission. Clearly, the problem is amplified if the self-emission is an appreciable fraction of the backlight. Thus, the problem gets worse as the sample tempe temperatur raturee incre increases ases Fig. 14. The selfself-emiss emission ion signals from 125 and 150 eV samples are compared to the 170 eV Planckian backlight in Fig. 14a and the corresponding transmission with and without the 150 eV sample selfemission is shown in Fig. 14b. In this case, an inadequate treatment of self-emission would provide misleading information for opacity model comparisons. The conse consequenc quences es of selfself-emissi emission on are potentially sig-
058101-9 05810 1-9
Experimen Expe rimental tal inve investigat stigation ion of opac opacity ity models…
) r s / V2 e / 2
m c / W 0 1 01 1 ( e c n a i d a r0 1.0 0.8 n o i s0.6 s i m s0.4 n a r t 0.2 0.0
Phys. Plasmas 16, 058101 2009
laser
170 eV Planckian backlighter
0.8
125 eV emission
900
0.4
e r
h (eV) 1100
1300
(b)
ideal
0.2
with rare earth
820
860 hQ (eV) 900
940
315 eV Planckian backlighter
(a) 170 eV Planckian backlighter 150 eV self emission
500
1000 h (eV)
1500
2000
1.0 with selfemission
n0.8 o i s s0.6 i m s n0.4 a r t 0.2
(b)
ideal 820
Nd (Z=60) Back et al . JQSRT 1997 La (Z=57) Chenais-Popovics et al . JQSRT 2000 1000 1400 h (eV)
1800
FIG. 16. Color Pioneering opacity experiments primarily used laser heated fibers coated with rare-earth elements to produce the backlighter. The La spectrum is adapted from Ref. 31 and the Nd spectrum is adapted from Ref. 34.. 34
with 150 eV emissi emission on
2
0.0
fiber coated
0.0
) r s / V e2 /
01 1 ( e c n a i d a r0
e v i t a l
150 eV emission
nificant and two courses of action are possible to mitigate their effect: the backlight should be rendered much brighter than the sample self-emission and the sample self-emission should be measured during the experiment. Calculations of the self-emission and approximate approxi mate backlight brightness for 19,,20 19 the Z facility iron experiment are shown in Fig. 15a. The corresponding transmission with and without the self-
1 1
0.6
(a)
FIG. 14. Color Self-emission grows with sample temperature and competes more strongly with a specified backlighter a. The transmission calculated Ref. 18 for a portion of the spectrum is illustrated both with and without self-emission in b. The backlighter was assumed to be a 170 eV Planckian and the sample temperature was 150 eV. Both transmission spectra include convolution with E / dE =700 instrument resolution.
m c / W
e c n a i d a r
860
h (eV)
900
940
FIG. 15. Color Self-emission from iron plasma at 150 eV electron temperature is compared with 170 and 314 eV Planckian backlighter spectra in a. The ideal transmission without self-emission and the transmission including self-emission are almost the same if the backlighter spectrum corresponds to a 314 eV Planckian b. Both transmission spectra include convolution with E / dE =700 instrument resolution.
emission Fig. 15b shows that the 315 eV Planckian backlight overwhelms the sample self-emission; thus, it has negligible effect on the transmission. The sample self-emission and absorption can be measured using the same spectrometer as long as the spatial extent of the backlight is small compare pa red d to th thee si size ze of th thee he heate ated d sa samp mple le.. Bo Both th th thee sp spac aceeresolved spectrometer and point projection configuration enable the selfself-emissi emission on to be reco recorded. rded. These self-emission self-emission measurements require high detector dynamic range since we desire des ire self-emi self-emissi ssion on tha thatt is les lesss tha than n a few percent percent of the backlight. The quest for a high brightness, broad spectral coverage, and a spectrally featureless backlight is an ongoing topic in opacity opa city res resear earch. ch. Ear Early ly ef effor forts ts pro produc duced ed poi pointli ntlike ke bri bright ght sources by irradiating small fibers with lasers. Emission in the desired spectral range was obtained by coating the fiber 26,,31 26 31,,34 with a high Z material often a rare-earth element Fig. 16. The emission from these high Z laser produced plasmas consis con sists ts of man many y mill million ionss of spe spectr ctral al line liness tha thatt ble blend nd int into o unresolved unres olved trans transition ition arra arrays ys UTAs. The 3d -4 -4 f UT UTAs As are partic par ticula ularly rly bri bright ght and can bac backlig klight ht an app approx roximat imately ely keV photon energy energy regime. regime. 200– 400 eV range in the 1–3 keV In addition, these sources are inherently spectral line sources and very careful measurements are required to account correctly for the spectral structure. This introduces a potential systematic error that is hard to quantify. Recentt opaci Recen opacity ty rese research arch has empha emphasized sized the devel developopment of backlight sources that span a larger photon energy range and that are inher inherently ently continuum emission sources. sources. This is challenging because bright sources are required. As laser facilities grow in energy it may be possible to create “conventional” “conventiona l” Hohlraums th that at re reac ach h hi high gh br brig ight htne ness ss 60 temperatures. The most suc succes cessfu sfull app approa roach ch to dat datee has been the production of dynamic Hohlraums driven either by high power Z pinches or lasers. These sources are heated by a radiating shock. The shock emission is trapped by a high Z plasma that is compressed over time. The use of a Z pinch to create such a source was briefly described above and more details are given in Ref. 20 20.. Spherically convergent dynamic Hohlraum Hohlra umss ha have ve al also so be been en pr prod oduc uced ed at the Ome Omega ga la lase serr 61 facility. In these experiments the laser typically illuminates a spherical plastic shell filled with xenon gas. The emission
0581 05 8101 01-1 -10 0
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Phys. Plasmas 16, 058101 2009
detector Fe/Mg shocked foam
(a)
CH
n a e t s m g s a l n u p t
(b)
n a e t s m g s a l n u p t
)
I1(
I0(
)
)
I2(
)
(a)
D ~ 400 m Tr ~ 314 eV x1
1 ns snapshot
x2 Iron
y8 t i s n6 e t n i 4 e v i t 2 a l e r
0
I0(
equivalent brightness Tr ~ 314 eV
1000
1200
1400 h (eV)
(c)
(b)
n o i s s i m s n a r t
Red = thick Blue = scaled thin T1 = T2 (x1/x2)
1600
FIG. 17. Color Dynamic Hohlraum backlighter diagram a. The stagnation of a radi radiatin ating g shoc shock k on the pinc pinch h axis produces produces a brig bright ht continuum continuum source. sour ce. A timetime-gated gated x-ray pinhole image is show shown n in b and a plot of relative intensity as a function of photon energy is shown in c.The equivalent brightness temperature is T r 314 eV Ref. 20.
from the shock launched into the xenon is trapped because of the high opacity of the xenon plasma behind the shock. The Z-pinch driven dynamic Hohlraum described above used the Z facility to produce a backli gh ghtt with peak radiation 20 temperature of approximately 314 eV. This backlight spans an ef effec fective tive ran range ge of h 800– 200 2000 0 eV, it is essential essentially ly line-free, and it is bright enough to backlight samples at temperatures up to 16 160 0 eV Fig. 17. The characteristics of the Omega laser-driven backlight in the 800–2000 eV spectral rang ra ngee th that at is of int inter eres estt fo forr op opac acity ity ex expe peri rime ment ntss at T e = 100– 160 eV have not been publishe published. d. However, However, measuremeasure61 ments at higher photon energies have been documented and the characteristics of this source for future experiments may be attractive. VI. OPACITY EXPERIMENT ACCURACY EVALUATION Performin Perfor ming g hig high h acc accura uracy cy opa opacit city y exp experi erimen ments ts is not simple since many potential pitf alls alls exist. However, a rela23 tively straig straightfor htforward ward method is availa available ble to exper experimenimentally assess the accuracy of the measurements. The method depends on Beer’s law relationship Eq. 1 between transmission missio n and sample thickn thickness. ess. Suppose we measu measure re transmission through two uniform samples with identical conditions tio ns bu butt wi with th di diff ffer eren entt th thic ickn knes esse sess x1 and x2. The transm tra nsmiss ission ion through through sam sample ple 2 is rel relate ated d to the sample 1 2/ x 1 x x2 x1 transmission by T 2 = T 1 Fig. 18. Measuring the transmission through different thickness samples and evaluating whether the scaling obeys Beer’s law is an extremely effective means to assess possible errors. Problems that will cause deviation devia tion from Beer’ Beer’ss law includ includee sample nonuniformity nonuniformity,, self-emission, background subtraction, crystal artifacts, and inaccu ina ccurat ratee film res respon ponse se cor correc rection tions. s. For exa example mple,, if the heating hea ting x ray rayss dep deposi ositt mor moree ene energ rgy y nea nearr the fro front nt sam sample ple edge and produce nonuniform conditions, then the nonuniformity will be worse with increasing sample thickness and the transmission will deviate from the expected scaling. As another example, the sensitivity of the transmission to self-
1050
h (eV) 1150
1250
Aluminum
(c)
n o i s s i m s n a r t
1530
1550 h (eV)
1570
1590
FIG. 18. Color Evaluation of transmission accuracy using experiments with different thickness samples a. Examples of experiments that demonstrated high quality using the sample thickness scaling method are shown in 62,, respectively. b and c, adapted from Refs. 19 and 62
emission problems depends emission depends on the optica opticall depth and thus the sample thickness. thickness. As a third example, example, artif artifacts acts that are introduced because of crystal defects will not change when the sample thickness changes and examination of transmission scaling with thickness therefore serves to identify those artifacts. Finally, the exposure at the detector will depend on the sample thickness thickness and verific verification ation that trans transmissio mission n scale scaless correctly according to Beer’s law can detect inaccuracies in the conversion of film density to exposure. A host of problems can be detected with such scaling tests and the tests are straightforward to perform. One limitation is that problems arisin ari sing g fro from m ins insuffi ufficie cient nt spe spectr ctral al res resolu olutio tion n whe when n nar narrow row spectral featu features res in the backlight and sample coincide are not 58 detectable. Furthermore, performing scaling tests requires greate gre aterr res resour ources ces,, sin since ce eith either er add additio itional nal exp experi erimen mentt s or 19,,62 19 more complicated targets are needed. Two experiments which demonstrated a high degree of scaling accuracy are shown in Figs. 18b and 18c. Note that in these experiments both the weak and strong absorption features exhibit accura acc urate te sca scaling ling.. Thi Thiss is sig signifi nifican cantt bec becaus ausee man many y of the proble pro blems ms tha thatt migh mightt ari arise se pre prefer ferent ential ially ly af affec fectt eit either her the strong str ong or wea weak k fea featur tures, es, alte alterin ring g the relative absorption strengths. The tra transm nsmiss ission ion sca scalin ling g des descri cribed bed abo above ve is the mos mostt powerful test to evaluate experiment accuracy. Supplemental valuable valua ble information may also be obtain obtained ed by perfo performing rming multiple measurements within each experiment and/or mul-
058101-1 05810 1-11 1
Experimen Expe rimental tal inves investigati tigation on of of opacity opacity model models s…
Phys. Plasmas 16, 058101 2009 1.0
1.0
(a)
Mg +9 satellites e.g., 1s2 2s 1s2s2p
0.8
n o i t c a r f
160 eV
n o i s 0.6 s i m s 0.4 n a r t
Mg+11 Ly 1s 2p
0.2
0.1
150 eV
0.0 1300
155 eV
Mg+11 Ly 1s 3p
Mg+10 He 1s2 1s2p
1400
Mg+10 He 1s2 1s3p
1500 h (eV)
Mg+10 He 1s2 1s4p
1600
Mg+10 He 1s2 1s5p
1700
1.0
(b)
+9
+10 charge
+11
FIG. 19. Color Calculated Ref. 18 charge state distribution for Mg at 150 eV black , 155 eV red, and 160 eV blue electron temperatures. The electron density was 7 1021 cm−3 in all cases. These 5 eV temperature changes induce less than 1% change in the He-like Mg Mg+10 population, but the H-like Mg Mg+11 population changes by approximately 40%. The Li-like MgMg+9 population changes by a smaller amount.
tiple reproducible experiments. Multiple measurements using varying detector sensitivity provides signals recorded at different fer ent exp exposu osure re lev levels els.. Com Compar pariso ison n of the mea measur sureme ements nts theref the refore ore rev reveal ealss whe whethe therr det detect ector or res respon ponse se is lin linear ear or if film densit density-toy-to-expos exposure ure conv conversio ersions ns have been accu accurately rately performed perf ormed.. Multiple measu measuremen rements ts using diff different erent cryst crystals als can reveal whethe whetherr cryst crystal al artif artifacts acts have affe affected cted the resul results. ts. Averaging the results of multiple multiple reproducible experiments 19 improves impro ves signa signal-to-n l-to-noise oise value valuess and can be ess essent ential ial for accurate accu rate trans transmissio mission n measu measuremen rements ts of weak spectral features. VII. PLASMA DIAGNOSTICS Opacity is a function of the plasma electron temperature and den densit sity y and qua quantit ntitativ ativee opa opacity city mod model el tes tests ts req requir uiree sample characterization. Here, we emphasize electron density rather than mass density since it is the electron density that directly affects the collisional ionization and excitation rates. rat es. Pla Plasma sma dia diagno gnosis sis oft often en rel relies ies on K -shell -shell absor absorption ption spectra under the assumption that the models used to interpret these relatively simple spectra are reliable. The de dettail ailss of 63– 63 – 66 K -shell -shell spectral diagnostics are described elsewhere and we pro provid videe onl only y a bri brief ef rev review iew of the physical physical basis for K -shell -shell spectral diagnostics. The value of K -shell -shell spectra to diagnose electron temperature depends on two facts. First, the plasma ionization distribution is a strong function of the electron temperature but has a weak dependence on the electron density Fig. 19 19;; see also Fig Fig.. 5. Sec Second ond,, the K -shell -shell spec spectral tral line photon energ ene rgies ies shi shift ft with ion ioniza izatio tion. n. The for former mer mea means ns tha thatt the relative relat ive absor absorption ption stren strengths gths of K -shell -shell spectral lines from different charge states depends on electron temperature. The latter means that the features from particular charge states are readily discerned from each other. other. K -shell -shell spectr spectral al absorption lines are defined as lines with an initial principal
n 0.8 o i s s i m s0.6 n a r t
n=3 Ly
Ly 1s-2p
Li-like satellites
0.4 He 0.2
1350
1400 h (eV)
n=2
1450
n=1 Mg +11 Mg XII H-like
He Li-like 1s2 1s2p satellite Mg +10 Mg XI He-like
Mg +9 Mg X Li-like
FIG. 20. Color Typical K -shell -shell absorption spectrum with features from H-, He-, and Li-like Mg a. The spectrum in a represents the average transmission from the experiments in Ref. 19 19.. PrismSPECT calculations of an expanded view of the n =1 to n =2 transitions in these three charge states and a simplified energy level diagram illustrate the energy shift from nuclear screening by additional spectator electrons in He-like and Li-like ions b.
quantum number n = 1. Absorption Absorption transitions transitions betwee between n the 1 s and 2 p configurations are possible if there are vacancies in the n =2 shell. Thus, K -shell -shell absorption may arise in atoms ionized ionize d into either the K - or L-shel -shell. l. These transitions transitions are conveniently divided into two classes according to whether they occur in K -shell -shell H- and He-like ions that have only one or two bound electrons or L-shell Li-, Be-, B-, C-, O-, N-, and F-like ions that have three to nine bound electrons. This distinction has value because the diagnostics available from these two classes are somewhat different. Both these transition classes can diagnose T e, with comparable accuracy. In addition, transitions between the 1s or 1 s2 ground states states 67 and the n =2 or 3 levels are affected by Stark broadening and provide valuable density information, as described below. However, the Stark broadening of L-shell ions has not been used extensively and its reliability is less certain. A measured K -shell -shell trans transmissio mission n spect spectrum rum forme formed d by the H-, He-, and Li-like charge states of Mg is shown in Fig. 20a. The bound bound-boun -bound d trans transitions itions that contr contribute ibute n =1 to n =2 spectral lines are displayed with a calculated synthetic spectrum in Fig. 20b. The strongest absorption line from H-like ions is the 1s-2 p transition, known as Ly , while the strongest line from He-like ions is the 1 s2 − 1s2 p transition, known as He . The He photon energy is 120 eV lower lower than the Ly because of the nuclear screening provided by the second 1 s electron. Similarly, the 1s22s − 1s2s2 p Li-like transition has lower photon energy than He , but the energy separation between the Li-like lines and He is only of order 15–20 eV because the additional screening by the 2 s electron is less than that by the 1 s electron. The extra electron that
0581 05 8101 01-1 -12 2
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0.9 0.8
n o0.8 Ly i s 1s-2p s i m 0.7 s n a r t 0.6 150 eV
HeE 1s2-1s2p
n o i s0.6 s i m s 0.4 n a r t
155 eV 0.5 160 eV
150 eV 155 eV 160 eV
0.2
1465 1470 1475 1480 hQ (eV)
1565
1575 1585 h (eV)
FIG. 21. Color Calculated Ref. 18 absorption from Mg Ly and He at the three temperatures corresponding to Fig. 19 charge state distributions. The E / dE =700 instrument resolution effect is included.
does not partic participate ipate in the transition is someti sometimes mes referred referred to as a “spectator” electron and these Li-like lines are known as “satellites” because they appear near the resonant He transition. The Li-like spectator electron may also reside in an excited n = 3 or higher state. In this case the satellite transitions are only slightly shifted from the He photon energy and these lines may not be resolved Fig. 20b. A careful accounting of this transition blending must be incorporated into accurate plasma diagn diagnostics ostics.. Note that He-lik He-likee satel satellites lites also appear on the low photon energy side of Ly , arising from fr om in init itia iall lly y ex exci cite ted d He He-l -lik ikee co confi nfigu gura rati tion onss e.g., 1s2s − 2s2 p. Satell Satellite ite lines often provi provide de additio additional nal valua valuable ble diagno dia gnosti stics cs bec becaus ausee the they y dep depend end on the mec mechan hanism ism tha thatt populates the excited states. The sensitivity of typical H- and He-like Mg ion spectral lines to small temperature changes is illustrated illustrated in Fig. 21 21.. 19,,20 19 This example is drawn from the Z experiments investigating gat ing iron opa opacit city y mod models els and we emp employ loy the He 1s2 − 1 s3 p tra transi nsition tion bec becaus ausee iro iron n spe spectr ctral al lin lines es are ble blende nded d with the He . The He absorption line strength is not sensitive to changes in temperature because the fractional population of the closed-shell He-like Mg ions changes very little
0.5 ne = 7x1021 cm-3
e0.4 H / y L0.3
ne = 5x1021 cm-3 measured ratio
0.2
0.1
ne = 9x1021 cm-3 145
155 Te (eV)
165
FIG. 22. Color Calculated Mg Ly / He absorption line strength ratio as a function of electron temperature. The three curves correspond to three different electron densities. The horizontal line corresponds to the mean ratio value measured in the experiments in Refs. 19 and 20 and the dashed lines are the 1 ratio uncertainties. The experimental temperature lies within the cross-hatched region.
in this temperature range. On the other hand, the Ly absorption changes rapidly with temperature. Thus, measurements men ts of the int integr egrate ated d Ly / He absor absorption ption line stren strength gth ratio provide a temperature diagnostic Fig. 22. The three different curves in Fig. 22 correspond to three different electron density values, illustrating the simultaneous dependence of the ionization distribution on both temperature and density mentioned above. In this case a 30% change in electron density den sity alt alters ers the inf inferr erred ed tem temper peratu ature re by app approx roximat imately ely 3–4 eV. Thus, accurate temperature diagnostics using this method depend on knowledge of the electron density. Preliminary temperature estimates may be obtained by a visual comparison of measured and synthetic spectra calculated at different temperatures. However, quantitative opacity model tests require estimates for the temperature and density uncertainties. These may be obtained using the spectral line fitting techniques described in Refs. 20 and 68 to deter determine mine the uncertainties in the measured absorption line strengths. High quality measurements combined with careful analysis may provide temperature values accurate to typically 5%, with rou roughl ghly y hal halff the unc uncert ertain ainty ty ari arisin sing g fro from m the typ typica icall 30% density uncertainty and the other half from the absorption sorpt ion line measu measuremen rementt accu accuracy racy.. Note that these estimates mat es do not inc includ ludee any unc uncert ertain ainty ty ass associ ociate ated d with the spectral synthesis model used to interpret the data. The systematic model errors can be reduced by using as many line ratios as possible to infer the temperature, reducing the probability abi lity that tra transi nsitio tion n rat ratee err errors ors for any single line migh mightt bias the resu results. lts. Analysis performed performed with seve several ral diff different erent K -shell -shell opacity models can also solidify the reliability of the temperature temper ature result, althou although gh the extra resource investment investment renders this type of duplicate analysis uncommon. The class of transitions in ions with three to nine bound electrons is still reasonably simple and the ionization distribution but ion is typ typica ically lly bro broade aderr. The These se ion ionss inv involv olvee an ope open n n = 2 shell and they normally possess strong strong features from four or five charge states. This broader distribution may enhance accuracy accur acy and reliab reliability ility of electr electron on tempe temperatur raturee measu measurerements. men ts. The tra transi nsition tionss inv involv olved ed are gen genera erally lly 1s22sm2 pl − 1s2sm2 pl+1. These lines are sometimes referred to as “ K satellites” because they appear on the high energy side of the transition and they were first observed in neutral atom K experiments exper iments that direc directed ted high energy particle beams onto transitions. As with the transolid surfaces to investigate K sitions described above, the n =2 spectator electrons do not partic par ticipa ipate te dir direct ectly ly in the tra transi nsition tion,, but the they y do pro provid videe nuclear screening that shifts the transition energy. This class of transitions is critically important for diagnosing low temperature perat ure plasm plasmas as e.g., T e 10 100 0 eV. At low tem temper peratu atures res the simple H- and He-like charge states described above occur only for ions with atomic atomic num number ber less tha than n app approx roxiimately 10. These low- Z atoms have K -shell -shell lines that appear in the x-ray ultraviolet XUV spectral range and are consequently quent ly more difficult to measu measure. re. K satellite ite trans transitions itions satell may be observed in the soft x-ray 1 ke keV V range even for temperatures as low as 10 eV eV.. The diagnostic utility of this type of transition was first developed for emission sp spectra ectra arising in energetic electron 69 or ion beam experiments and for early laser-driven capsule
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Experimen Expe rimental tal inves investigati tigation on of of opacity opacity models… initial sample, known thickness
laser
Phys. Plasmas 16, 058101 2009 1.0
thickness radiograph
backlight hot sample
Mg He 0.8 1s2- 1s4p
y t i c a0.6 p o e v0.4 i t a l e r0.2
2.0 x 1022 cm-3 1.0 x 1022 cm-3 0.5 x 1022 cm-3
(a)
He
(b) He
50 ) Å m 40 (
He
m h 30 w f
He
20
FIG. 23. Color Diagram of point projection radiography method used to measure sample expansion and thus measure the sample density. A dispersive element such as a crystal is often inserted in front of the detector to provide spectrally resolved information, greatly enhancing the radiograph contrast.
70
implosions. Later, it was extensively employed in absorption spectra used to diagn diagnose ose a wide array of HED experi26,,71 26 71,,72 ments, including opacity. The usefulness of this transition class is also supported by the fact that adjacent 1 s to 2 p transitions in Li-like to F-like ions shift enough to be measured, but not so much as to make broad spectral coverage necessary. Thus, such diagnostics are especially appropriate if a more limited spectral range backlight is available. Transitionss involv sition involvin ing g initial initial states with an excited electron arise 73,,74 73 in these spectra and the resulting lines may blend with lines from the ground state of adjacent charge states. This is similar to the illustration provided above for Li-like ions and this charge state blending must be included in models used to infer temperature from such data. Transitions with higher- n final states e.g., 3 p have been observed, but they are typically relatively weak and the models needed to interpret the line broadening are less certain. Consequently, the class of transitions in Li-like to F-like ions has been only rarely em29 ployed in plasma electron density diagnostics up until now. Several types of electron density diagnostics have been developed devel oped for opaci opacity ty exper experiments iments.. Radiog Radiographi raphicc measu measurerements of the sample plasm plasmaa expan expansion sion and Stark broadening broadening of K -shell -shell spectral lines are two techniques that provide relatively direct density measurements. Optical laser interferometry measurements of the sample rear surface ex pa pansion nsion have 75 also been used to infer opacity sample density. However, the plasma that is actually probed at optical wavelengths is the low density edge of the sample plasma and these techniques must rely heavily on radiation hydrodynamic simulations to infer the behavior of the higher density interior of the opacity sample. Point projection spectrally-resolved radiography wa s the 21– 21 –23 firstt met firs method hod emp employ loyed ed to det determ ermine ine sam sample ple den density sity.. These measurements measurements are conce conceptuall ptually y straig straightfor htforward: ward: The sample thickness is measured after it is heated by the x-ray source and the density is obtained by comparing with measurements of the initial sample thickness performed prior to the experiment Fig. 23. A major challenge for this method is the experiment complexity introduced by the need to acquir qu iree si simu multa ltane neou ousl sly y an ed edge ge-o -on n ra radi diog ogra raph ph an and d th thee spectrallyspec trally-resol resolved ved trans transmissio mission n measu measuremen rementt used to infer the temperature and to test the opacity model for the element of inte interes rest. t. Add Additio itional nal pro proble blems ms inc includ ludee acc accura urate te init initial ial samplee compo sampl composition sition and thickn thickness ess measu measuremen rements, ts, accu accuracy racy limitations imposed by the finite point projection backlight
0.0
1650
1660 1670 h (eV)
0.5
1.0 1. 1.5 5 2. 2.0 0 2.5 ne ( x 1022 cm-3)
FIG. 24. Color Example of Stark-broadened line profile calculations Refs. 76 and 77 a. The red, green, and blue curves correspond to 0.5, 1.0, and 2.0 1020 cm−3 electron densities, respectively. These opacity profiles are converted to transmission and then convolved with the instrument resolution before comparing with the experiment Ref. 20. The plot in b illustrates the full width at half maximum as a function of electron density. The areal density and instrument resolution in b correspond to the Z experiments in Refs. 19 and 20 20..
size, assumption of one-dimensional expansion, and simultaneity of the density measurement radiograph with the transmission missio n measu measuremen rement. t. Despi Despite te these problems, density measureme sur ements nts acc accura urate te to app approx roxima imatel tely y 30 30% % ha have ve be been en acquired in a few opacity experiments. 67 K -shell Measuremen Measu rements ts of Stark Stark-broa -broadened dened -shell spect spectral ral lines also enable determination of the sample sample density. density. Atomic line transitio transitions ns in tra tracer cer ion ionss are per pertur turbed bed by the ele electr ctric ic microfields due to the other electrons and ions in the plasma. The net result is a characteristic Stark-broadened line shape that is mainly dependent on the density. In the standard Stark broadening broad ening theory appro approximatio ximation n the ions are considered considered static while the lighter electrons are considered dynamic, i.e., they move while the line trans transition ition takes place. The distri distribubution of static ion microfields causes energy levels to split and shift due to the Stark effect of the electric fields. The photon energy of dipole-allowed line transitions shifts accordingly, and the atomic state mixing by the electric field can even cause non-dipole-allowed transitions to appear. In addition, radiator ions experience a time-varying electric field due to the dynamic electrons. This broadens the line transitions that arise between shifted energy levels. The final line shape is obtained by averaging over the distribution function that the weights the static ion microfields according to their probability of occu occurrenc rrence, e, incorporating incorporating the broa broadening dening due to the dynamic electrons. Thus, the line profile broadening depends on both the ion and electron density and is typically used to infer the electron density, as long as the plasma composition is known. 76,,77 76 Calculations of Stark Stark-broa -broadened dened Mg He line pro19,,20 19 files used to diagnose the Z facility iron opacity samples are shown in Fig. 24a. The sensitivity of the line opacity profile to density is clear. However, a complication arises in applying apply ing this diagn diagnostic ostic to absor absorption ption spectra because the transmis transm ission sion lin linee pr profi ofile le is no nott th thee sa same me as th thee op opac acity ity 20,,59 20 59,,78 profile. The trans transmissio mission n T =exp − approx roxii x is app mately T 1 − x , if x 1. Such a line is said to be optically thin and the transmission profile essentially appears to be an upside down opacity line profile. However, as the optical depth = x grows to approach and then exceed unity,
0581 05 8101 01-1 -14 4
Baililey Ba ey et al.
this approximation is no longer valid. In this case the transmission profile depends on the optical depth and the areal density x of the ions in the lower level of the transition typically the ground state is required in order to relate the transm tra nsmiss ission ion line pro profile file to the opa opacity city lin linee pro profile file.. For Fortutunately, such knowledge may be reliably obtained by measuring the integrated strength of the absorption line family that arises from a given charge state. Once the optical depth has been determined, determined, the trans transmissio mission n may be compu computed ted from the opacity profile. Convolution with the instrument function must be performed prior to comparison with measured spectrall line profiles. tra profiles. The dep depend endenc encee of HeHe-like like Mg spe spectr ctral al linewid lin ewidths ths on ele electr ctron on den density sity is illu illustr strate ated d for the He , He , He , and He lines in Fig. 24b. The widths in Fig. 24b corre correspond spond to trans transmissio mission n widths after convo convolution lution with the instrument function. They include the optical depth effect and instrume instrument nt widths appropriate for the Z iron opac19,,20 19 ity exper experiment. iment. A more detailed description of this procedure is given in Ref. 20 20.. Stark broadening broadening incre increases ases and the opac opacity ity decre decreases ases with pri princi ncipal pal qua quantu ntum m num number ber.. Thu Thus, s, bot both h the abi ability lity to resolve the profile and the problems introduced by the requirement quire ment for areal density information information to inter interpret pret optically thick line broadening favor the use of high n spectral lines. However Howev er,, high-n spe spectr ctral al line liness are typ typica ically lly wea weaker ker and therefore they are measured less accurately. The most accurate density diagnostics are obtained by measuring as many lines as possible possi ble and quantitatively accounting for the signal20 to-noise ratio. Typical density accuracy obtained with this method is 30%. However, this does not account for possible uncertainties introduced by the Stark broadening models. Stark broadening measurements of HED plasma densitiess ha tie have ve be been en pe perf rfor orme med d fo forr mo more re tha than n 2 de deca cade dess an and d calculations of H-like and He-like profiles are generally considered reliable. However, only limited experimental information directly designed to test broadening models in this 79 densit den sity y reg regime ime is ava availa ilable ble and fut future ure opa opacity city res resear earch ch would benefit from more extensive tests.
VIII. STATUS AND FUTURE PROSPECTS FOR HED PLASMA OPACITY RESEARCH The methods described above provide a framework for experiments designed to test opacity models. However, the range of temperatures, densities, and elements examined up until now is small. The vast majority of experiments investig ti gat ateed pl plas asma mass wi with th 20 20– –76 eV te temp mpeera ratu turres and 3 0.01–0.03 0. 01–0.03 g / cm mass densities. Only a few experimental results exist outside of this range. range . Ex Examples amples include the Sat40,,42 40 urn Z-pinc Z-pinch h drive driven n exper experiments iments that invest investigated igated iron opacities for envelopes of Cepheid variable stars and the Z facility experiments investigating opacity of the iron charge ch arge 19,,20 19 states that exist at the base of the solar convection zone. The former extended the density range down by two orders of magnitude while the latter pushed the temperature range up by approximately a factor of 2. These experiments provided vid ed val valuab uable le opa opacity city mod model el tes tests, ts, yet the they y are probably probably best regarded as proof-of-principle experiments that establish
Phys. Plasmas 16, 058101 2009
platforms for furth platforms further er invest investigatio igations. ns. Compre Comprehensiv hensivee resul results ts require more experiments. The parameter space of applications that would benefit from opacity experiments is large. Here, we mention only a few obv obviou iouss exa example mpless tha thatt mig might ht be add addres ressed sed with within in the coming years. We also reiterate that, while applications provide impor important tant motiva motivation tion that guide guidess rese research arch directions, directions, advances in opacity science require sustained focus on the physic phy sicss with within in the opa opacity city mod models els.. The dis discre crepan pancie ciess between helioseismology and solar models motivates investigations of iron plasma opacity at temperatures similar to the existing Z facility experiments, but at densities an order of magnitude higher. Measurements of oxygen and neon opacities are also needed, even though the atomic physics of the -shell is more certain than the Fe L-shell. For example, the K -shell bound-free opacities of these elements play an important role in the total opacity. The bound-free process is important over a large photon energy range, implying that a relatively small error err or migh mightt hav havee imp import ortant ant con conseq sequen uences ces.. Fur Furthe thermo rmore, re, atomic physics is just one issue. Questions also remain rer e80 garding the accuracy of ionization distribution calculations. Finally,, opaci Finally opacity ty exper experiments iments to date have measu measured red either pure elements or mixtures of two similar atomic number elements. It is a fair question to ask whether the model treatments men ts mid mid-- Z ele elemen ments ts mix mixed ed as dilu dilute te con consti stitue tuents nts in a mostly hydrogen plasma are adequate. Inertial fusion capsule implosion designs typically employ Be shells doped with Cu or CH shells doped with Ge. The motivation motivation for the dop dopant antss is to mod modify ify the abl ablati ation on pressu pre ssure re as a fun functio ction n of dep depth th usi using ng the opa opacit city y cha change ngess caused by introducing the dopant. Thus, the success of these capsule designs depends on accurate knowledge of the dopant opacity in the 50–300 eV temperature range, at a variety of densities between 0.01 and 10.0 times solid. Experiments have measured Ge opacity at temperatures up to 76 eV and densities densi ties of appro approximate ximately ly 0.01 solid. These inves investigatio tigations ns provided provi ded initial tests of basic opaci opacity ty model questi questions. ons. However, these experiments did not measure the charge states and electron configurations that will arise in inertial fusion implosions. Furthermore, to the best of our knowledge, Cu transitions have not been measured at all, let alone Cu diluted in a mos mostly tly Be pla plasma sma at hig high h tem temper peratu ature re and density density.. Improved prove d opaci opacity ty knowle knowledge dge would enabl enablee exper experimenter imenterss to emphasize other issues such as laser plasma interaction or equation of state in tuning inertial fusion implosions to reach ignition. The opacity research methods developed over the past 20 years, combined with the advent of megajoule class HED facil facilities, ities, should enab enable le near near-term -term opacity inves investigatigations for matter found in stellar interiors, inertial fusion implosions, and Z pinches. ACKNOWLEDGMENTS We thank the Z facility teams for invaluable and dedicated technical assis assistance tance.. Speci Special al assis assistance tance was prov provided ided by P. W. Lake, D. S. Nielsen, L. Nielsen-Weber, and L. P. Mix. We are grateful to R. J. Leeper, T. A. Mehlhorn, J. L. Porter, and M. K. Matzen for support and encouragement. Special thanks are due to T. S. Perry, C. Back, and F. Gille-
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Experimen Expe rimental tal inves investigati tigation on of of opacity opacity models…
ron for graci gracious ous permi permission ssion to share previously previously publis published hed results here. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Co., for the United States Department of Energy under Contract No. DE-AC0494AL85000. Work by CAI performed under the auspices of the Department of Energy by Lawrence Livermore National Laboratory under Contract No. W-7405-ENGF-48. 1
A. S. Eddington, The Internal Constitution of the Stars Cambridge University Press, Cambridge, 1926 . 2 F. Delahaye and M. Pinsonneault, Astrophys. J. 625, 563 2005 . 3 D. Mihalas, Stellar Atmospheres W.H. Freeman, San Fransisco, 1970 . 4 J. N. Bah Bahcal call, l, A. M. Ser Serene enelli lli,, and S. Bas Basu, u, Astrophys. J. 621, L8 L85 5 2005; J. N. Bahcall, W. F. Huebner, S. H. Lubow, P. D. Parker, and R. K. Ulrich, Rev. Mod. Phys. 54, 767 1982 ; see: www.sns.ias.edu/~jnb. 5 S. Basu and H. M. Antia, Phys. Rep. 457, 217 2008. 6 M. Asplund, Annu. Rev. Astron. Astrophys. 43, 481 2005 and references therein. 7 J. N. Bahcall, A. M. Serenelli, and M. Pinsonneault, Astrophys. J. 614, 464 2004. 8 S. Turck-Chieze, S. Couvidat, L. Piau, J. Ferguson, P. Lambert, J. Ballot, R. A. Garcıa, and P. Nghiem, Phys. Rev. Lett. 93, 211102 2004 . 9 H. M. Antia and S. Basu, Astrophys. J. 620, L129 2005. 10 S. Basu and H. M. Antia, Astrophys. J. 606, L85 2004 ; J. N. Bahcall, S. Basu, M. Pinsonneault, and A. M. Serenelli, ibid. 618, 1049 2005. 11 Ya. B. Zel’dolvich and Yu. P. Raizer, in Physics of Shock Waves and High Temperature Tem perature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein Dover, Mineola, 1966 . 12 J. P. Apruzese, J. Davis, K. G. Whitney, J. W. Thornhill, P. C. Kepple, R. W. Cl Clark ark,, C. Dee Deeney ney,, C. A. Co Cover verdal dale, e, and T. W. L. San Sanfor ford, d, Phys. Plasmas 9, 2411 2002. 13 M. J. Seaton, Y. Yu, D. Mihalas, and A. K. Pradhan, Mon. Not. R. Astron. Soc. 266, 805 1994 ; M. J. Seaton, ibid. 382, 245 2007. 14 C. Men Mendoz doza, a, M. J. Sea Seaton ton,, P. Bue Buerg rger, er, A. Bel Bello lorín rín,, M. Mel Melénd éndez, ez, J. González, Gonz ález, L. S. Rodr Rodrígue íguez, z, F. Delah Delahaye, aye, E. Palaci Palacios, os, A. K. Pradhan, and C. J. Zeippen, Mon. Not. R. Astron. Soc. 378, 1031 2007. 15 D. C. Wilson, P. A. Bradley, N. M. Hoffman, F. J. Swenson, D. P. Smitherman, R. E. Chrien, R. W. Margevicius, D. J. Thoma, L. R. Foreman, J. K. Hoffer, S. R. Goldman, S. E. Caldwell, T. R. Dittrich, S. W. Haan, M. M. Marinak, S. M. Pollaine, and J. J. Sanchez, Phys. Plasmas 5, 1953 1998; S. W. Haan, M. C. Herrmann, T. R. Dittrich, A. J. Fetterman, M. M. Marinak, D. H. Munro, S. M. Pollaine, J. D. Salmonson, G. L. Strobel, and L. J. Suter, ibid. 12, 056316 2005. 16 N. Grevesse and A. J. Sauval, Space Sci. Rev. 85, 161 1998. 17 P. Renau Renaudin, din, L. Lecher Lecherbour bourg, g, C. Blan Blancard, card, P. Coss Cosse, e, G. Fauss Faussurie urier, r, P. Audebert, S. Bastiani-Ceccotti, J.-P. Geindre, and R. Shepherd, AIP Conf. Proc. 926, 24 2007. 18 J. J. MacFar MacFarlane, lane, I. E. Golo Golovkin vkin,, P. R. Woodr oodruff uff,, D. R. Welch, B. V. Oliver, T. A. Mehlhorn, and R. B. Campbell, Inertial Fusion Science and Applications, edited by B. A. Hammel, D. D. Meyerhofer, J. Meyer-terVehn, and H. Azechi American Nuclear Society, La Grange Park, 2004 , p. 457; J. J. MacFarlane, I. E. Golovkin, P. Wang, P. R. Woodruff, and N. A. Pereyra, High Energy Density Phys. 3, 181 2007 . 19 J. E. Bailey, G. A. Rochau, C. A. Iglesias, J. Abdallah, Jr., J. J. MacFarlane, I. Golovkin, P. Wang, R. C. Mancini, P. W. Lake, T. C. Moore, M. Bump, O. Garcia, and S. Mazevet, Phys. Rev. Lett. 99, 265002 2007. 20 J. E. Bailey, G. A. Rochau, R. C. Mancini, C. A. Iglesias, J. J. MacFarlane, I. E. Golovkin, J. C. Pain, F. Gilleron, C. Blancard, Ph. Cosse, G. Faussurier, G. A. Chandler, T. J. Nash, D. S. Nielsen, and P. W. Lake, Rev. Sci. Instrum. 79, 113104 2008 . 21 C. L. S. Lewis and J. McGlinchey, Opt. Commun. 53, 179 1985 . 22 T. S. Perry, S. J. Davidson, F. J. D. Serduke, D. R. Bach, C. C. Smith, J. M. Foster, R. J. Doyas, R. A. Ward, C. A. Iglesias, F. J. Rogers, J. Abdallah, Jr., R. E. Stewart, J. D. Kilkenny, and R. W. Lee, Phys. Rev. Lett. 67, 3784 1991. 23 T. S. Perry, P. T. Springer, D. F. Fields, D. R. Bach, F. J. D. Serduke, C. A. Iglesi Igl esias, as, F. J. Rog Rogers ers,, J. K. Nas Nash, h, M. H. Ch Chen, en, B. G. Wilson, Wilson, W. H. Goldstein, B. Rozsynai, R. A. Ward, J. D. Kilkenny, R. Doyas, L. B. Da Silva, C. A. Back, R. Cauble, S. J. Davidson, J. M. Foster, C. C. Smith, A. Bar-Shalom, and R. W. Lee, Phys. Rev. E 54, 5617 1996 . 24 H. Griem Griem,, Princi Principles ples of Plasm Plasma a Spect Spectros roscopy copy Cambridge University Press, New York, 1997 .
Phys. Plasmas 16, 058101 2009 25
J. E. Bailey, G. A. Rochau, S. B. Hansen, C. A. Iglesias, J. J. MacFarlane, I. Golovkin, P. Wang, R. C. Mancini, C. Blancard, Ph. Cosse, G. Faussurier, F. Gilleron, and J. C. Pain, “Evaluation of non-LTE effects on iron plasma transmission measurements at temperatures above 150 eV,” High Energy Density Phys. to be submitted . 26 S. J. Davidson, J. M. Foster, C. C. Smith, K. A. Warburton, and S. J. Rose, Appl. Phys. Lett. 52, 847 1988 . 27 J. M. Foster, D. J. Hoarty, C. C. Smith, P. A. Rosen, S. J. Davidson, S. J. Rose, T. S. Perry, and F. J. D. Serduke, Phys. Rev. Lett. 67, 3255 1991. 28 J. Bruneau, C. Chenais-Popovics, D. Desenne, J.-C. Gauthier, J.-P. Geindre, M. Klapisch, J.-P. Le Breton, M. Louis-Jacquet, D. Naccache, and J.-P.. Perrine, Phys. Rev. Lett. 65, 1435 1990. J.-P 29 D. J. Hoarty, C. D. Bentley, B. J. B. Crowley, S. J. Davidson, S. G. Gales, P. Graham, J. W. O. Harris, C. A. Iglesias, S. F. James, and C. C. Smith, J. Quant. Spectrosc. Radiat. Transf. 99, 283 2006; D. J. Hoarty, J. W. O. Harris, P. Graham, S. J. Davidson, S. F. James, B. J. B. Crowley, E. L. Clark, C. C. Smith, and L. Upcraft, High Energy Density Phys. 3, 325 2007. 30 J. E. Bailey, P. Arnault, T. Blenski, G. Dejonghe, O. Peyrusse, J. J. MacFarlane, R. C. Mancini, M. E. Cuneo, D. S. Nielsen, and G. A. Rochau, J. Quant. Spectrosc. Radiat. Transf. 81, 31 2003. 31 C. Chenais-Popovics, F. Gilleron, M. Fajardo, H. Merdji, T. Mißalla, J. C. Gauthier, P. Renaudin, S. Gary, J. Bruneau, F. Perrot, T. Blenski, W. Fölsner, and K. Eidmann, J. Quant. Spectrosc. Radiat. Transf. 65, 117 2000. 32 C. Chenais-Popovics, H. Merdji, T. Mißalla, F. Gilleron, J. C. Gauthier, T. Blenski, F. Perrot, M. Klapisch, C. Bauche-Arnoult, J. Bauche, A. Bachelier, and K. Eidmann, Astrophys. J., Suppl. Ser. 127, 275 2000. 33 C. Chenais Popovics, M. Fajardo, F. Gilleron, U. Teubner, J.-C. Gauthier, C. Bauche-Arnoult, A. Bachelier, J. Bauche, T. Blenski, F. Thais, F. Perrot, A. Benuzzi, S. Turck-Chièze, J.-P. Chièze, F. Dorchies, U. Andiel, W. Foelsner, and K. Eidmann, Phys. Rev. E 65, 016413 2001 ; C. ChenaisPopovics, M. Fajardo, F. Thais, F. Gilleron, J. C. Gauthier, K. Eidmann, W. Fölsner, T. Blenski, F. Perrot, C. Bauche-Arnoult, A. Bachelier, and J. Bauche, J. Quant. Spectrosc. Radiat. Transf. 71, 249 2001 ; H. Merdji, T. Mißalla, T. Blenski, F. Perrot, J. C. Gauthier, K. Eidmann, and C. ChenaisPopovics, Phys. Rev. E 57, 1042 1998 . 34 C. A. Back, T. S. Perry, D. R. Bach, B. G. Wilson, C. A. Iglesias, O. L. Landen, S. J. Davidson, and B. J. B. Crowley, J. Quant. Spectrosc. Radiat. Transf. 58, 415 1997 . 35 F. Thai Thais, s, S. Basti Bastiani, ani, T. Blen Blenski, ski, C. Chena Chenais-P is-Popov opovics, ics, K. Eidm Eidman, an, W. Fölsner, J.-C. Gauthier, F. Gilleron, and M. Poirier, J. Quant. Spectrosc. Radiat. Transf. 81, 473 2003 . 36 P. Renaudin, C. Blancard, J. Bruneau, G. Faussurier, J.-E. Fuchs, and S. Gary, J. Quant. Spectrosc. Radiat. Transf. 99, 511 2006. 37 L. Da Silva, B. J. MacGowan, D. R. Kania, B. A. Hammel, C. A. Back, E. Hsieh, R. Doyas, C. A. Iglesias, F. J. Rogers, and R. W. Lee, Phys. Rev. Lett. 69, 438 1992. 38 P. T. Springer, D. J. Fields, B. G. Wilson, J. K. Nash, W. H. Goldstein, C. A. Iglesias, F. J. Rogers, J. K. Swenson, M. H. Chen, A. Bar-Shalom, and R. E. Stewart, Phys. Rev. Lett. 69, 3735 1992. 39 G. Winhart, K. Eidmann, C. A. Iglesias, A. Bar-Shalom, E. Mínguez, A. Ricker Ric kert, t, and S. J. Ros Rose, e, J. Quan Quant. t. Spect Spectrosc. rosc. Radiat. Transf. 54, 43 437 7 1995; G. Winhart, K. Eidmann, C. A. Iglesias, and A. Bar-Shalom, Phys. Rev. E 53, R1332 1996. 40 P. T. Springer, K. L. Wong, C. A. Iglesias, J. H. Hammer, J. L. Porter, A. Toor, To or, W. H. Gold Goldstein stein,, B. G. Wi Wilson lson,, F. J. Rogers, C. Deene Deeney, y, D. S. Dearbo Dea rborn, rn, C. Bru Bruns, ns, J. Emi Emig, g, and R. E. Ste Stewar wart, t, J. Quant Quant.. Spect Spectrosc. rosc. Radiat. Transf. 58, 927 1997 . 41 C. A. Iglesias and F. J. Rogers, Astrophys. J. 464, 943 1996. 42 F. J. Rogers and C. A. Iglesias, Science 263, 50 1994 . 43 M. K. Matze Matzen, n, Phys Phys.. Plasm Plasmas as 4, 1519 1997; V. P. Smirnov, Plasma Phys. Controlled Fusion 33, 1697 1991; J. H. Brownell, R. L. Bowers, K. D. McLenthan, and D. L. Peterson, Phys. Plasmas 5, 2071 1998. 44 J. E. Bailey, G. A. Chandler, S. A. Slutz, G. R. Bennett, G. Cooper, J. S. Lash, S. Lazier, R. Lemke, T. J. Nash, D. S. Nielsen, T. C. Moore, C. L. Ruiz, D. G. Schroen, R. Smelser, J. Torres, and R. A. Vesey, Phys. Rev. Lett. 89, 095004 2002; J. E. Bailey, G. A. Chandler, R. C. Mancini, S. A. Slutz, G. A. Rochau, M. Bump, T. J. Buris-Mog, G. Cooper, G. Dunham, I. Golovkin, J. D. Kilkenny, P. W. Lake, R. J. Leeper, R. Lemke, J. J. MacFarlane, T. A. Mehlhorn, T. C. Moore, T. J. Nash, A. Nikroo, D. S. Nielsen, K. L. Peterson, C. L. Ruiz, D. G. Schroen, D. Steinman, and W. Varnum, Phys. Plasmas 13, 056301 2006 .
0581 05 8101 01-1 -16 6 45
Baililey Ba ey et al.
T. W. L. San Sanfor ford, d, T. J. Nash, R. C. Mock, J. P. Apr Apruze uzese, se, and D. L. Peterson, Phys. Plasmas 13, 012701 2006. 46 S. A. Slutz, K. J. Peterson, R. A. Vesey, R. W. Lemke, J. E. Bailey, W. Varnum, C. L. Ruiz, G. W. Cooper, G. A. Chandler, G. A. Rochau, and T. A. Mehlhorn, Phys. Plasmas 13, 102701 2006. 47 G. A. Rochau, J. E. Bailey, G. A. Chandler, G. Cooper, G. S. Dunham, P. W. Lake, R. J. Leeper, R. W. Lemke, T. A. Mehlhorn, A. Nikroo, K. J. Peterson, C. L. Ruiz, D. G. Schroen, S. A. Slutz, D. Steinman, W. A. Stygar, and W. Varnum, Plasma Phys. Controlled Fusion 49, B591 2007. 48 D. D. Ryutov, M. S. Derzon, and M. K. Matzen, Rev. Mod. Phys. 72, 167 2000; M. K. Matzen, M. A. Sweeney, R. G. Adams, J. R. Asay, J. E. Bailey, G. R. Bennett, D. E. Bliss, D. D. Bloomquist, T. A. Brunner, R. B. Campbell, G. A. Chandler, C.A. Coverdale, M. E. Cuneo, J.-P. Davis, C. Deeney, M. P. Desjarlais, G. L. Donovan, C. J. Garasi, T. A. Haill, C. A. Hall, D. L. Hanson, M. J. Hurst, B. Jones, M. D. Knudson, R. J. Leeper, R. W. Lemke, M. G. Mazarakis, D. H. McDaniel, T. A. Mehlhorn, T. J. Nash, C. L. Olson, J. L. Porter, P. K. Rambo, S. E. Rosenthal, G. A. Rochau, L. E. Ruggles, C. L. Ruiz, T. W. L. Sanford, J. F. Seamen, D. B. Sinars, S. A. Slutz, I. C. Smith, K. W. Struve, W. A. Stygar, R. A. Vesey, E. A. Weinbrecht, D. F. Wenger, and E. P. Yu, Phys. Plasmas 12, 055503 2005. 49 D. R. Kania, H. Kornblum, B. A. Hammel, J. Seely, C. Brown, U. Feldman, G. Glendinning, P. Young, E. Hsieh, M. Hennesian, L. DaSilva, B. J. MacGowan, D. S. Montgomery, C. A. Back, R. Doyas, J. Edwards, and R. W. Lee, Phys. Rev. A 46, 7853 1992 ; T. S. Perry, R. I. Klein, D. R. Bach, K. S. Budil, R. Cauble, H. N. Kornblum, Jr., R. J. Wallace, and R. W. Lee, Phys. Rev. E 58, 3739 1998. 50 G. A. Rochau, J. E. Bailey, and J. J. MacFarlane, Phys. Rev. E 72, 066405 2005. 51 C. Chenais-Popovics, C. Fievet, J. P. Geindre, I. Matsushima, and J. C. Gauthier, Phys. Rev. A 42, 4788 1990. 52 R. F. Heeter, S. G. Anderson, R. Booth, G. V. Brown, J. Emig, S. Fulkerson, T. McCarville, D. Norman, M. B. Schneider, and B. K. F. Young, Rev. Sci. Instrum. 79, 10E303 2008. 53 T. McCarville, S. Fulkerson, R. Booth, J. Emig, B. Young, S. Anderson, and B. Heeter, Rev. Sci. Instrum. 76, 103501 2005 ; S.G. Anderson, R. F. Heeter, Heete r, R. Booth, J. Emig, S. Fulk Fulkerson erson,, T. McCarville McCarville,, D. Norm Norman, an, and B. K. F. Young, ibid. 77, 063115 2006 . 54 B. L. Henke, F. G. Fujiwara, M. A. Tester, C. H. Dittmore, and M. A. Palmer, J. Opt. Soc. Am. B 1, 828 1984 . 55 B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, and F. G. Fujiwara, J. Opt. Soc. Am. B 3, 1540 1986. 56 J. E. Bailey, G. A. Chandler, D. Cohen, M. E. Cuneo, M. E. Foord, R. F. Heeter, D. Jobe, P. W. Lake, J. J. MacFarlane, T. J. Nash, D. S. Nielson, R. Smelser, and J. Torres, Phys. Plasmas 9, 2186 2002. 57 N. Izumi, Izumi, R. Snavely Snavely,, G. Gregori, Gregori, J. A. Koch, H.-S. H.-S. Par Park, k, and B. A. Remington, Rev. Sci. Instrum. 77, 10E325 2006. 58 C. A. Iglesias, J. Quant. Spectrosc. Radiat. Transf. 99, 295 2006 . 59 A. Thorne, Spectrophysics Wiley, New York, 1974 .
Phys. Plasmas 16, 058101 2009 60
M. Schneider and R. Heeter, personal communication 2008. M. C. Hermann, Bull. Am. Phys. Soc. 48, 21 2003 ; J. F. Hansen, S. G. Glendinning, R. F. Heeter, and S. J. E. Brockington, Rev. Sci. Instrum. 79, 013504 2008. 62 T. S. Perry, S. J. Davidson, F. J. D. Serduke, D. R. Bach, C. C. Smith, J. M. Foster, R. J. Doyas, R. A. Ward, C. A. Iglesias, F. J. Rogers, J. Abdallah, Jr., R. E. Stewart, R. J. Wallace, J. D. Kilkenny, and R. W. Lee, Astrophys. J., Suppl. Ser. 127, 433 2000. 63 A. V. Vinogradov, I. Yu. Skobelev, and E. A. Yukov, Sov. Phys. Usp. 22, 771 1979. 64 M. H. Key and R.J. Hutcheon, Advances in Atomic and Molecular Physics 16 Academic, New York, 1980 , pp. 201–280. 65 C. De Michelis and M. Mattioli, Nucl. Fusion 21, 677 1981. 66 H. R. Griem, Phys. Fluids 4, 2346 1992. 67 H. R. Griem, Phys. Scr. T83, 142 1999. 68 G. Dunham, J. E. Bailey, G. A. Rochau, P. W. Lake, and L. B. NielsenWeber, Rev. Sci. Instrum. 78, 063106 2007 ; G. Dunham, G. A. Rochau, P. Lake, L. Nielsen-Weber, and D. Schuster, ibid. 75, 3687 2004; J.E. Bailey, R. Adams, A. L. Carlson, C. H. Ching, A. B. Filuk, and P. Lake, ibid. 68, 1009 1997. 69 E. Nardi and Z. Zinamon, J. Appl. Phys. 52, 7075 1981; J. E. Bailey, J. J. MacFarlane, P. Wang, A. L. Carlson, T. A. Haill, D. J. Johnson, P. Lake, E. J. McGuire, and T. A. Mehlhorn, Phys. Rev. E 56, 7147 1997. 70 J. D. Hares, J. D. Kilkenny, M. H. Key, and J. G. Lunney, Phys. Rev. Lett. 42, 1216 1979 ; A. Hauer, R. D. Cowan, B. Yaakobi, O. Barnouin, and R. Epstein, Phys. Rev. A 34, 411 1986 . 71 R. C. Mancini, C. F. Hooper, Jr., and R. L. Caldwell, J. Quant. Spectrosc. Radiat. Transf. 51, 201 1994 . 72 D. Hoarty, O. Willi, L. Barringer, C. Vickers, R. Watt, and W. Nazarov, Phys. Plasmas 6, 2171 1999. 73 J. Abdallah, Jr., R. E. H. Clark, and J. M. Peek, Phys. Rev. A 44, 4072 1991. 74 R. Epstein, Phys. Rev. A 43, 961 1991. 75 L. Lecherbourg, P. Renaudin, S. Bastiani-Ceccotti, J.-P. Geindre, C. Blancard, P. Cosse, G. Faussurier, R. Shepherd, and P. Audebert, High Energy Density Phys. 3, 175 2007 . 76 L. A. Woltz and C. F. Hooper, Jr., Phys. Rev. A 38, 4766 1988. 77 R. C. Mancini, D. P. Kilcrease, L. A. Woltz, and C. F. Hooper, Jr., Comput. Phys. Commun. 63, 314 1991. 78 A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms Cambridge University Press, London, 1934 . 79 P. T. Springer, T. S. Perry, R. E. Stewart, C. A. Iglesias, F. J. Serduke, B. G. Wilson, R. W. Lee, J. M. Foster, C. C. Smith, D. J. Hoarty, and S. J. Davidson, Proceedings of the Fourth International Workshop on Radiative Properties of Hot Dense Matter , edited by W. Goldstein, C. Hooper, J. Gauthier, J. Seely, and R. Lee World Scientific, River Edge, 1991 , p. 42. 80 C. A. Iglesias and F. J. Rogers, Astrophys. J. 408, 371 1991. 61
