1. M. S. Tillack Radiation-Hydrodynamic Analysis of Doped Underdense Targets for HED Studies 8 February 2005 Mechanical and Aerospace Engineering Department and the Center for Energy Research, Jacobs School of Engineering

2. We are collaborating with LLNL on a 3-year study of non-LTE laser plasmas Overall goal is to develop absolutely calibrated spectroscopic diagnostics and benchmark data from well-characterized “non-LTE” plasmas Address a class of problems in which temperature can not be uniquely related to energy Establish credibility in non-LTE calculations Resolve long-standing problems in the literature concerning emission from low density plasmas TGS “Non-LTE”: energy content and radiation emission depend on the full time-dependent set of rate equations for atomic processes Collisional ionization, recombination, excitation, and deexcitation Photoionization and stimulated recombination Photoexcitation and stimulated emission Spontaneous decay Radiative recombination Dielectronic recombination, autoionization, and electron capture

3. A generic problem with laser plasmas is the large gradients and transient nature, which complicate analysis and data interpretation T e and n e in 100  m DT film at 1 ns, 5x10 14 W/cm 2 Low density targets (gas bags or foams) can provide more uniform density and temperature: 1. mass limited so that all of the target mass heats 2. optical thickness comparable to target thickness at desired T e 3. larger than the hydrodynamic expansion length during the pulse >1 mm thick, 1-10 mg/cm 3 for 4 ns laser pulse

4. 40 shots (7 days) were obtained at Nike in 2004; Future experiments are planned at Janus Obtained absolutely calibrated Ti L-shell emission from aerogel targets – Measured time-resolved spectra in 470-3000 keV region covering Ti L-shell Determined accessible plasma conditions by variation of laser parameters – Able to heat plasma to threshold of K-shell emission (He-like Ti emission) – Determined experimental conditions for creating L-shell emission (135 J, 4 ns, 940 µm spot) – Time-integrated measurements of plasma T e via Si and Ti K-shell line ratios Examined plasma uniformity with x-ray imaging diagnostics Nike chamber (5 kJ)

5. Model predictions often disagree with data, and with each other Non-LTE plasma simulations are computationally expensive and often not self-consistent To model realistic plasmas, simulations must implement approximations in the atomic physics data and radiation algorithm –A relatively complete model of a Ti ion can have up to 20,000 levels –An approximate model of the same ion may be reduced to ~100 levels in order to run simulations

6. This project is an element of the growing field of High Energy Density (HED) physics 1. Material Properties 2. Compressible Dynamics * HED in NNSA Facilities, “Bruce Remington (LLNL), Chris Deeney (SNLA), David Hammer (Cornell), Dick Lee (LLNL), David Meyerhofer (LLE), Dieter Schneider (LLNL), Isaac Silvera (Harvard), Bernie Wilde (LANL),” A presentation to the High Energy Density Physics Workshop, May 24-26, 2004, Gaithersburg, Maryland. http://www.ofes.fusion.doe.gov/More_HTML/HEDPWorkshop5-04.html The topic of HED on NNSA facilities is divided into 4 thrust areas: * Our work addresses two of these “Compelling question” for material properties thrust area: Can matter in the difficult warm dense matter (WDM) regime be isolated, defining its state while measuring the material properties of interest? 3. Radiative Hydrodynamics 4. Inertial Confinement Fusion “Compelling question” for radiation hydrodynamics area: Can HED experimental facilities become a routine tool for testing rad-hydro models and simulations of powerful astronomical phenomena in a scaled laboratory setting?

7. The goal of the material properties thrust is to map material properties across the WDM regime Hot Dense Matter occurs in: stellar interiors, accretion disks laser plasmas, z-pinches radiatively heated foams ICF capsule impoded cores Warm Dense Matter occurs in: cores of giant planets strongly shocked solids radiatively heated solid foils 1. Prepare the state (at desired density, temperature, etc.) – verify that gradients are small, time-dependent effects are unimportant 2. Measure the material property of interest – opacity, ionization state, EOS, conductivity, etc. The methodology involves two steps:

8. The Radiative Hydrodynamics thrust focuses on “hot flowing matter”, where the radiation and material flows are coupled Quantitative modeling of such flows is difficult; benchmark data is needed Examples : radiative shocks & jets, supersonic radiation flow, photoionized plasmas, radiation-dominated dynamics Radiative hydrodynamics abounds in astrophysical plasmas Radiative shock in Janus Radiative shocks in the Cygnus loop SNR

9. At UCSD we are contributing to both experiments and modeling activities 1D LTE rad-hydro simulations using Hyades and Helios –gray and spectrally resolved simulations –purpose is to explore and verify n e and T e behavior, and determine whether spectral detail affects hydro Non-LTE simulations using Cretin and Helios-CR Experimental support of T e diagnostics – Single-channel calibrated PCD detector – Multi-channel filtered diode detector

10. During 2004 we acquired several new modeling tools Cascade Applied Sciences (Jon Larsen), history of use at LLNL Limited capabilities for spectrally resolved opacities, LTE only 1. Hyades Prism Computational Sciences (MacFarlane/Golovkin), used a lot at SNLA Propaceos code provides spectral data, Helios-CR for non-LTE 2. Helios Lagrangian grid, flux limited, diffusion approximation Standard 1D rad-hydro codes 3D non-LTE collisional-radiative rate equation solver (Howard Scott) Cretin HULLAC Parametric potential method to generate atomic data (Klapisch/Busquet)

11. Cases were examined using Hyades at high and low density, high and low intensity, with and without doping t I 3.6 ns 4 ns All cases used a 4-ns flat-top intensity profile at 248 nm An unfeathered grid with 50 zones was used to simplify graphical interpretation (constant mass per zone)

12. Base case temperature evolution (5x10 12 W/cm 2, SiO 2, 2 mg/cm 3 ) Spatial profile at 2.5 ns ~50 eV ~1/2 ns

13. Base case density evolution Spatial profile at 2.5 ns (note: n cr =16x10 21 /cm 3 )

14. Charge state, target expansion, laser absorption (nodes 25-50) (100 nodes) (Denavit, PoP 1994)

15. Two key physical processes are involved in underdense laser plasma energy transfer  = 10 –16 T e –3/2 Z ln  (n e 2 /n cr ) 1. Laser absorption in underdense plasma (inverse bremsstrahlung) 2. Emission and absorption of thermal radiation L  = 1 mm

16. The radiation absorption wave propagates more slowly at higher density (8 mg/cm 3 ) Scaling depends on opacity rather than inverse bremsstrahlung ~50 eV... but the final temperature, density and charge state are remarkably similar

17. At 4x10 14 W/cm 2, the plasma is fully stripped and expands more rapidly

18. This plasma becomes transparent; the density is initially uniform, but is quickly lost due to expansion

19. Properly modeling opacities is challenging Planck averaging: Rosseland averaging: SiO 2

20. We tried several variations to explore the influence of opacity models on the results Sesame data in Hyades Built-in multi-group model in Hyades Propaceos (spectral) data averaged and imported into Hyades Propaceos (spectral) data used in Helios Sesame data used in Helios Reduced frequency group (averaged) modeling with Helios Due to problems implementing multi-group radiation transport in Hyades, we relied upon Helios to study the effect of doping

21. Unfortunately, temperatures from Hyades and Helios do not agree very well Hyades Helios spatial profiles at 2.5 ns

22. Opacity data is surely part of the reason Helios plasmas are much more opaque Which is correct? range of interest Comparison of spectrally averaged opacities

23. The energy balance looks completely different Helios stores ~50% of the energy, whereas Hyades promptly radiates 90%. Helios plasma is far more opaque. 2 kJ/cm 2 7 kJ/cm 2 8 kJ/cm 2 16 kJ/cm 2

24. The effect of 6% Ti dopant on T e (using Helios) The doped case cools faster and is less uniform base case 6% Ti

25. The effect of 6% Ti dopant on n e (using Helios) The lower temperature leads to slightly lower density base case 6% Ti

26. Summary Plasmas with uniform n e and “relatively” uniform T e were obtained and parametrically studied in the range 5x10 12 –5x10 14 W/cm 2 ; not quite good enough yet The best results seem to occur when the target is optically thick to the laser Codes disagree, even with single-group opacities. Hyades needs more work to produce accurate spectrally resolved results Doping significantly affects temperatures (based on Helios simulations); makes them worse!

27. Our plans in 2005-06 include more modeling and experimental collaborations Further optimization of rad hydro Increased use of Cretin to study non-LTE emissions Explore atomic data for non-LTE work Hullac, Propaceos, new averaging schemes,... Development of PCD detectors for T e measurements – single, calibrated diamond diode – filtered diode array Experiments at Janus