Fokker-Planck Modeling of Heat Conduction in NIF Hohlraums

We use the Vlasov-Fokker-Planck code OSHUN to model electron heat conduction in a realistic plasma profile for a NIF “rugby-shaped” hohlraum. Please attend my talk on 25 August 2015 to see NIF results.

Andrew H. Dublin1,2, David J. Strozzi1, Adam Tableman3, Benjamin Winjum3 Lawrence Livermore National Laboratory1 | University of Rochester2 | University of California at Los Angeles3

Results:

Introduction: Methods: •  Electron heat conduction is a key process in inertial fusion

targets, like NIF hohlraums. •  Radiation-hydrodynamics codes routinely use the collisional

Spitzer-Harm model, with an ad-hoc “flux limit” to match data. •  Kinetic and non-local effects can sometimes be important.

•  The code OSHUN (Tzoufras et. al, Phys. Plasmas 2013), developed at UCLA, solves the Vlasov-Fokker-Planck equation:

•  OSHUN uses the spherical harmonic expansion:

•  Spherical coordinates: •  Electron-ion collision operator (electron-electron is more complicated)

•  Thermal conductivity κ:

•  Spitzer-Härm, local collisional result (Zi >>1):

•  We ran OSHUN on the 1-D green path from above: Z=2 helium •  We compare OSHUN results with Spitzer-Härm theory.

LLNL-POST-675603 This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Lasnex simulation of NIF hohlraum. We study heat conduction along the green path.

Gold wall

Capsule: ablator and fusion fuel Helium plasma

electron-electron collisions

electron-ion collisions

fe(r,p,t) = electron distribution

Discussion: •  OSHUN displays non-local reduction in thermal conductivity for

large temperature gradients. •  Future work: 2D simulations, mobile ions, and gold wall

conditions.

Spitzer-Härm Result

Non-local reduction in κ

λ0 = mean free path

1-D NIF profile for OSHUN 4.5 0.12

ne

Te

0 0

0.05 Non-locality Parameter

0