Ab initio benchmarking of the thermal conductivity models for hydrogen under ICF conditions

We present the first ab initio evaluation of the thermal conductivity of hydrogen for a density ($\rho$ = 80 g/cc) and in a range of temperatures (50 eV $<$ T $<$ 1000 eV) which corresponds to the Inertial Confinement Fusion regime. Such simulations are made possible by the use of nearly coulombic pseudo-potentials whith a high cutoff in energy, and by the high density which translates into a moderate T/T$_F$ ratio (where T$_F$ is the Fermi temperature), and thus a moderate number of electronic orbitals to consider. With rising temperature, the hydrogen plasma evolves from the strongly coupled degenerate regime ($\Gamma=14$) to the kinetic semi-degenerate regime. The thermal conductivity is computed from the general Kubo-Geenwood expression of the Onsager relations for transport coefficients. Results are compared with the usual Lee-More and Spitzer-Hubbard formulations.