(1) Iron opacity measurements on Z at 150 eV temperatures

1. (1)Iron opacity measurements on Z at 150 eV temperatures with Fe + Mg without Fe Thanks to: James E. Bailey, Sandia National Laboratories (jebaile@sandia.gov) Warm Dense Matter Winter School Lawrence Berkeley National Laboratory January 10-16, 2008 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2. Wavelength-dependent opacity governs radiation transport that is critical in HED plasmas • Bound-bound and bound free transitions in mid to high Z elements dominate opacity • As Z grows, the number of transitions becomes enormous (~ 1-100 million line transitions in typical detailed calculations) • Approximations are required and experimental tests are vital • Example 1: Solar interior • Example 2: Cu-doped Be ablator ICF capsule

3. T(eV) ne (cm-3) r/R0 0.90 54 1x1022 0.7133 182 9x1022 0.55 293 4x1023 0 1360 6x1025 Radiation controls heat transport in solar interior • boundary position depends on transport • measured with helioseismology Solar model : J.N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982) convection radiation Transport depends on opacity, composition, ne, Te

4. 1200 1025 800 1024 ne (cm-3) Te (eV) 400 1023 Bahcall et al, ApJ 614, 464 (2004). Basu & Antia ApJ 606, L85 (2004). 0 0.0 0.2 0.4 0.6 0.8 1 1022 R/R0 radiation convection Modern solar models disagree with observations. Why? • measured boundary • RCZ = 0.713 + 0.001 • Predicted RCZ= 0.726 • Thirteen s difference ne Te • Boundary location depends on radiation transport • A 1% opacity change leads to observable RCZ changes. • This accuracy is a challenge – experiments are needed to know if the solar problem arises in the opacities or elsewhere.

5. Transitions in Fe with L shell vacancies influence the radiation/convection boundary opacity solar interior 182 eV, 9x1022 cm-3 M-shell 4 105 b-f (ground states) b-f (excited states) 104 2 103 L-shell 0 opacity (cm2/g) intensity (1010 Watts/cm2/eV) Z conditions 155 eV, 1x1022 cm-3 106 2 105 104 1 103 0 200 600 1000 1400 hn (eV)

6. Cu dopant is intended to control radiation flow into Be ICF capsule ablator • Pre-heat suppression requires opacity knowledge in the 1-3 keV photon energy range • Tailoring the ablation front profile requires opacity knowledge in vicinity of Planckian radiation drive maximum • Cu transitions that influence the opacity are very similar to the Fe transitions that control solar opacity near the radiation/convection boundary

7. Goal of opacity experiments: test the physics foundations of the opacity models • Agreement at a single Te/ne value is difficult, but not sufficient • It is impractical to perform experiments over the entire Te/ne range • Therefore we seek to investigate individual processes: • charge state distribution • Term structure needed? Fine structure? • Principal quantum number range • Bundling transitions into unresolved arrays • Multiply excited states • Low probability transitions (oscillator strength cut off) • Bound free cross sections • Excited state populations • Line broadening

8. spectrometer spectrometer sample tamper (low Z) heating x-rays backlighter Anatomy of an opacity experiment Comparison of unattenuated and attenuated spectra determines transmission T = exp –{mrx} Model calculations of transmission are typically compared with experiments, rather than opacity. This simplifies error analysis.

9. Dynamic hohlraum radiation source is created by accelerating a tungsten plasma onto a low Z foam gated X-ray camera 1 nsec snapshots radiating shock CH2 foam radiating shock capsule tungsten plasma 4 mm

10. radiation temperature hn > 1 keV backlight photons 300 T (eV) 200 X-rays 100 sample 0 -10 10 -20 time (nsec) 0 radiation source The radiation source heats and backlights the sample

11. 1.0 0.8 0.6 0.4 0.2 0.0 4 6 8 10 12 14 The dynamic hohlraum backlighter measures transmission over a very broad l range Z1363-1364 Fe+Mg sample transmission bound-free Mg K-shell Fe L-shell l (Angstroms)

12. spectrometer CH heating x-rays spectrometer Fe/Mg sample CH tamper backlighter Samples consist of Fe/Mg mixtures fully tamped with 10 mm CH • Fe & Mg coated in alternating ~ 100-300 Angstrom layers • CH tamper is ~ 10x thicker than in typical laser driven experiments • Compare shots with and without Fe/Mg to obtain transmission • Mg serves as “thermometer” and density diagnostic

13. X-rays Fe + Mg at Te ~ 156 eV, ne ~ 6.9x1021 cm-3 Fe & Mg sample Mg XI 0.8 radiation source transmission 0.4 Fe XVI-XX 0.0 8.0 10.0 12.0 14.0 l (Angstroms) Z opacity experiments reach T ~ 156 eV, two times higher than in prior Fe research J.E. Bailey et al., PRL 99, 265002 (2007) • Mg is the “thermometer”, Fe is the test element • Mg features analyzed with PrismSPECT, Opal, RCM, PPP, Opas

14. 0.8 0.4 Red = PRISMSPECT J. MacFarlane, PRISM 0.0 0.8 Red = OPAL C. Iglesias, LLNL 0.4 transmission 0.0 0.8 0.4 Red = MUTA J. Abdallah, LANL 0 0.8 Red = OPAS OPAS team, CEA 0.4 0 1200 1000 1100 800 900 hn (eV) Modern detailed opacity models are in remarkable overall agreement with the Fe data

15. Both experiments used 10 mm CH | 0.3 mm Mg + 0.1 mm Fe | 10 mm CH sample • No scaling was applied for this comparison • Reproducibility is not always this extraordinary, but variations are less than approximately +10% The transmission is reproducible from shot to shot Z1650 Z1649 Intensity 7 8 9 10 11 12 l (Angstroms)

16. 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Multiple reproducible experiments enables averaging to improve transmission S/N Z1466,1467,1646,1648,1649,1650,1651,1652,1653 Fe+Mg 1.0 0.8 0.6 transmission 0.4 0.2 Mg K-shell Fe L-shell 0.0 l (Angstroms)

17. Conclusions of present work • The excellent agreement between PRISMSPECT and the measurements demonstrates a promising degree of understanding for both modeling and experiments • Comparisons with the Los Alamos ATOMIC/MUTA and OPAL are just as good, if not better. • Modern DTA opacity models are accurate, if sufficient attention is paid to setting up and running the code. • With an accurate model in hand, the accuracy penalty imposed by various approximations used in applications can be investigated • The Z dynamic hohlraum opacity platform is capable of accurate measurements in an important and novel regime

18. Future: evaluate impact of present data on solar models and design higher density experiments • Question: Can this work tell us whether prior solar opacities were accurate to better than 20%? • Construct Rosseland and Planck mean opacities • Compare: • Data to modern detailed models • Data to prior models used in solar application • Modern models to prior models (extend hn range) • With reasonable understanding for this class of L-shell transitions, now we are ready for new experiments: • Increase density • Alter sample composition (e.g., Fe & O in CH2 plasma)