Laser Energy Transport and Deposition Package for CRASH Fall 2011 Review

1. Laser Energy Transport and Deposition Package for CRASHFall 2011 Review Ben Torralva

2. We developed the laser package to reduce uncertainty and enable productive UQ • Perform simulations that reproduce the experimentally observed shock morphology • Eliminate the use of H2D • Rezoner fidelity issues • Differences between models • H2D is manpower intensive • UQ is problematic • Code revisions are slow • Develop a self-contained multi-physics model • Reduce coupled-model uncertainties • Enables more complete UQ studies Experimental Radiograph Auto-rezoner Comparison

3. Laser energy transport is modeled using an efficient, parallel ray-tracing algorithm via geometric optics At each time step the rays are traced by numerically solving using Boris’s scheme, which automatically conserves the ray direction vector, The relative gradient, , can be determined from the plasma density distribution: The critical density, ,at which the the refractive index goes to zerois

4. Laser energy is absorbed by electron-ion collisions The modify laser-plasma interactions cause laser energy to be deposited in the plasma. The dielectric permittivity becomes: were the effective electron-ion collision frequency is The absorption coefficient is calculated to be:

5. The laser energy is smoothly deposited in the plasma The electric field propagates through the plasma with the complex index of refraction , and At each time step the laser energy is deposited in the right-hand-side of the electron heat conduction equation to be solved implicitly The delta-function is implemented by distributing the energy between the nearest cells with the total of the interpolation coefficients equal to one.

6. We verify the laser package nightly The laser-ray turning point and the energy deposition of an obliquely incident laser ray are tested. The closest approach to the critical surface is: The energy deposition is: is held constant, and at the critical surface. Linear Density Profile Laser Ray Absorption – Weak Laser Ray Absorption – Strong

7. We tested convergence and scaling of shock breakout in 1-D Shock breakout of 20 μm Be foils are being simulated. Our experiments indicate that the average shock breakout is ~ 450 ps with systematic error of ± 50 ps. Convergence as a function of zone size

8. Shock breakout occurs at ~ 400 ps in the model The laser intensity is scaled relative to the full CRASH intensity of 7x1014 w/cm2

9. CRASH shows more sensible behavior near the tube wall Comparison of breakout with H2D at the Au-Be-Xe interface Full CRASH at 0.88 ns H2D at 0.7 ps 3 vs. 6 zones in auto-rezoner

10. We validate the laser package in 2-D against shock breakout data 2-D breakout test of the full CRASH problem with a full-intensity laser profile and 2 levels of AMR

11. 2-D breakout test of the full CRASH problem indicates breakout at 420 ps with the full-intensity laser profile and 2 levels of AMR Electron Temperature [keV] at 420 ps Log Density [g/cm3] at 420 ps R [μm] R [μm] Z [μm] Z [μm]

12. We developed the laser package to reduce uncertainty and enable productive UQ • We successfully implemented a laser energy transport and deposition package in CRASH • The implementation is parallel, utilizes the Block Adaptive Tree Library (BATL), and adaptive mesh refinement (AMR) • We conduct nightly verification tests of turning point and energy deposition of an obliquely incident ray • We are conducting code comparison and validation tests, and are simulating shock breakout experiments • We are currently using this package in UQ studies • We are developing full 3-D ray-tracing in 2-D and 3-D CRASH