Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework

Abstract

We extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes non-negligible outside the domain of validity of the classical Landau equation. For the electron-ion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies non-monotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ∼30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ∼9%, and the shear viscosity coefficient is increased by up to ∼13%. In the Lorentz gas (Z→∞) limit, the electrical conductivity is reduced by up to ∼14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ∼39%, and the shear viscosity coefficient is not affected.