A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes

TLDR

Numerical simulation of laser‑driven inertial confinement fusion experiments relies on large multidimensional hydro codes, yet these codes poorly model electron conduction, the dominant energy transport mechanism, which is known to be a nonlocal process beyond the reach of local Spitzer–Harm theory. The study aims to extend the Luciani–Mora–Virmont formula for electron conduction to two or three spatial dimensions. The multidimensional extension yields an equivalent transport equation that can be readily implemented in a two‑dimensional radiation‑hydrodynamic code. Simulations using the new model are presented and shown to agree with Fokker–Planck results in one and two dimensions. Phys.

Abstract

Numerical simulation of laser driven Inertial Confinement Fusion (ICF) related experiments require the use of large multidimensional hydro codes. Though these codes include detailed physics for numerous phenomena, they deal poorly with electron conduction, which is the leading energy transport mechanism of these systems. Electron heat flow is known, since the work of Luciani, Mora, and Virmont (LMV) [Phys. Rev. Lett. 51, 1664 (1983)], to be a nonlocal process, which the local Spitzer–Harm theory, even flux limited, is unable to account for. The present work aims at extending the original formula of LMV to two or three dimensions of space. This multidimensional extension leads to an equivalent transport equation suitable for easy implementation in a two-dimensional radiation-hydrodynamic code. Simulations are presented and compared to Fokker–Planck simulations in one and two dimensions of space.