Dispersion relations and sum rules for the transport coefficients of dilute ionized gases in a magnetic field

Abstract

Abstract In the presence of a homogeneous magnetic field B the thermal conductivity and shear viscosity tensors of ionized gases are anisotropic. The thermal conductivity tensor contains three independent components, one independent of B, one even and one odd in B. The shear viscosity tensor contains five independent components, one field independent, two even and two odd in B. For pure gases, the transport coefficients which are even in B can be written as the real part of complex functions of the parameter ζ=eB/nM, while the coefficients odd in B are the imaginary parts of these functions. Here e is the charge, M the mass and n the density of the gas under consideration. Using the Chapman-Enskog equations it is then shown that these functions possess an analytic extension in one complex half plane and fall off as 1 |ζ| for large |ζ|; these facts enable one to obtain dispersion relations, connecting the transport coefficients odd in B to those even in B. For mixtures the situation is more complicated. Dispersion relations hold only if all charges have the same sign. However, a number of sum rules hold under more general conditions.