Plasma Kinetic Theory of Transverse Diffusion

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Abstract
The kinetic theory of Prigogine and Balescu is applied to the diffusion of a plasma column across a uniform magnetic field. The problem of deriving the kinetic equation for the single-particle distribution function is reduced to that of solving a linear integral equation with a complicated kernel. No restriction is made on the amplitude or length scale of the inhomogeneity across the magnetic field. Although a multicomponent plasma is considered, the calculation ignores macroscopic electric fields. An unusual linearization of the Vlasov equation is also examined. It yields essentially the same linear integral equation, where the kernal represents a generalized electric susceptibility. The problem of finding the unstable modes of oscillation is the eigenvalue problem for the corresponding homogeneous integral equation. If the collective terms are replaced by appropriate cutoffs in the integrations, the kinetic theory becomes relatively simple. In particular, a single kinetic equation describes the collisional transverse diffusion. For a gyrotropic plasma with slab geometry, this kinetic equation reduces to one previously obtained by Eleonskiǐ, Zyryanov, and Silin by a different method; an H-theorem has been established, and some nonequilibrium stationary distributions have been found.