(1) Iron opacity measurements on Z at 150 eV temperatures Thanks to: James E. Bailey, Sandia National Laboratories 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-AC04-94AL with Fe + Mg without Fe Warm Dense Matter Winter School Lawrence Berkeley National Laboratory January 10-16, 2008

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 (~ 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

Radiation controls heat transport in solar interior T(eV) n e (cm -3 ) r/R x x x x10 22 radiation convection boundary position depends on transport measured with helioseismology Solar model : J.N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982) Transport depends on opacity, composition, ne, Te

measured boundary R CZ = Predicted R CZ = Thirteen  difference Bahcall et al, ApJ 614, 464 (2004). Basu & Antia ApJ 606, L85 (2004). 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. convection radiation R/R 0 T e (eV) n e (cm -3 ) TeTe nene Modern solar models disagree with observations. Why?

Transitions in Fe with L shell vacancies influence the radiation/convection boundary opacity opacity (cm 2 /g) intensity (10 10 Watts/cm 2 /eV) h (eV) M-shell b-f (excited states) L-shell solar interior 182 eV, 9x10 22 cm -3 Z conditions 155 eV, 1x10 22 cm -3 b-f (ground states)

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

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: 1.charge state distribution 2.Term structure needed? Fine structure? 3.Principal quantum number range 4.Bundling transitions into unresolved arrays 5.Multiply excited states 6.Low probability transitions (oscillator strength cut off) 7.Bound free cross sections 8.Excited state populations 9.Line broadening

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

Dynamic hohlraum radiation source is created by accelerating a tungsten plasma onto a low Z foam tungsten plasma 4 mm CH 2 foam radiating shock capsule gated X-ray camera 1 nsec snapshots radiating shock

The radiation source heats and backlights the sample time (nsec) T (eV) h > 1 keV backlight photons radiation temperature sample radiation source X-rays

The dynamic hohlraum backlighter measures transmission over a very broad range  (Angstroms) transmission Fe L-shell Z Fe+Mg sample bound-free Mg K-shell

Samples consist of Fe/Mg mixtures fully tamped with 10  m CH backlighter CH tamper Fe/Mg sample spectrometer heating x-rays spectrometer CH Fe & Mg coated in alternating ~ 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

(Angstroms) transmission Fe + Mg at T e ~ 156 eV, n e ~ 6.9x10 21 cm -3 Fe XVI-XX Mg XI Mg is the “thermometer”, Fe is the test element Mg features analyzed with PrismSPECT, Opal, RCM, PPP, Opas Fe & Mg sample radiation source X-rays J.E. Bailey et al., PRL 99, (2007) Z opacity experiments reach T ~ 156 eV, two times higher than in prior Fe research

Modern detailed opacity models are in remarkable overall agreement with the Fe data h (eV) Red = MUTA J. Abdallah, LANL Red = OPAL C. Iglesias, LLNL Red = PRISMSPECT J. MacFarlane, PRISM transmission Red = OPAS OPAS team, CEA

The transmission is reproducible from shot to shot  (Angstroms) Intensity Z1650 Z1649 Both experiments used 10  m CH | 0.3  m Mg  m Fe | 10  m CH sample No scaling was applied for this comparison Reproducibility is not always this extraordinary, but variations are less than approximately +10% 810

 (Angstroms) Multiple reproducible experiments enables averaging to improve transmission S/N Fe L-shell Z1466,1467,1646,1648,1649,1650,1651,1652,1653 Fe+Mg Mg K-shell transmission

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

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 h 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 CH 2 plasma)