Revisiting Lee-More: electronic transport coefficients from a convervative BGK model

A multitemperature Bhatnagar-Gross-Krook kinetic model is developed that includes partial degeneracy for the electrons. The model is constructed to satisfy the basic conservation laws with an H-theorem, generalized to mixed statistics (i.e., Maxwell-Boltzmann, Fermi-Dirac), that yields the desired equilibrium limit. From this model, we obtain a moment-based quantum hydrodynamics formulation closed through a Chapman-Enskog expansion to yield expressions for the transport coefficients, including electron-ion temperature relaxation and electronic thermal conductivity. The transport coefficients include both electron-electron and electron-ion collisions with degeneracy corrections valid from zero temperature to the classical limit. Comparisons in modeling philosophy and results are made with the Lee-More model.