On the transport coefficients of hydrogen in the inertial confinement fusion regime

Abstract

Ab initio molecular dynamics is used to compute the thermal and electrical conductivities of hydrogen from 10 to 160 g cm–3 and temperatures up to 800 eV, i.e., thermodynamical conditions relevant to inertial confinement fusion (ICF). The ionic structure is obtained using molecular dynamics simulations based on an orbital-free treatment for the electrons. The transport properties were computed using ab initio simulations in the DFT/LDA approximation. The thermal and electrical conductivities are evaluated using Kubo–Greenwood formulation. Particular attention is paid to the convergence of electronic transport properties with respect to the number of bands and atoms. These calculations are then used to check various analytical models (Hubbard’s, Lee–More’s and Ichimaru’s) widely used in hydrodynamics simulations of ICF capsule implosions. The Lorenz number, which is the ratio between thermal and electrical conductivities, is also computed and compared to the well-known Wiedemann–Franz law in different regimes ranging from the highly degenerate to the kinetic one. This allows us to deduce electrical conductivity from thermal conductivity for analytical model. We find that the coupling of Hubbard and Spitzer models gives a correct description of the behavior of electrical and thermal conductivities in the whole thermodynamic regime.