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.

A model of nonlocal transport for multidimensional radiation magnetohydrodynamics codes is presented. In laser produced plasmas, it is now believed that the heat transport can be strongly modified by the nonlocal nature of the electron conduction. Other mechanisms, such as self-generated magnetic fields, may also affect the heat transport. The model described in this work, based on simplified Fokker-Planck equations aims at extending the model of G. Schurtz, Ph. Nicolaï, and M. Busquet [Phys. Plasmas 7, 4238 (2000)] to magnetized plasmas. A complete system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and simplified in order to be implemented into large laser fusion codes and coupled to other relevant physics. The model is applied to two laser configurations that demonstrate the main features of the model and point out the nonlocal Righi-Leduc effect in a multidimensional case.

Inertial confinement fusion and specifically shock ignition involve temperatures and temperature gradients for which the classical Spitzer-Harm thermal conduction breaks down and a non-local operator is required. In this article, two non-local electron thermal conduction models are tested against kinetic Vlasov-Fokker-Planck simulations. Both models are shown to reproduce the main features of thermal heat front propagation at kinetic timescales. The reduction of the thermal conductivity as a function of the scalelength of the temperature gradient is also recovered. Comparisons at nanosecond timescales show that the models agree on the propagation velocity of the heat front, but major differences appear in the thermal precursor. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4789878