Diffusion and conductivity of plasmas in strong external fields

Abstract

The diffusion tensors of a plasma in strong external fields are derived from first principles. A pair of integro-differential equations, which are the first members of a chain analogous to Yvon's hierarchy, is obtained, together with the required boundary conditions and an approximation, called the disjunctive approximation, which makes the solution determinate. It is shown how the diffusion tensors can be calculated from the solution of these equations. A study is made of the influence of the external fields on the encounters between charged particles in a plasma. A generalization of Boltzmann's equation is obtained, which takes into account many-body interactions in the plasma and the effect of the external field on the collision integral. Explicit expressions are obtained for the friction tensors, the diffusion tensors, and the electrical conductivity tensor, for a plasma subject to a strong external magnetic field.