KINETIC EQUATION OF A PLASMA IN A STRONG STATIC MAGNETIC FIELD

Abstract

In an extension of the recent works on the kinetic equation of a plasma in (1) the spatially homogeneous case by Guernsey, (2) the spatially inhomogeneous case by Wu and Rosenberg, and (3) the presence of "weak" static electric and magnetic fields by Sundaresan and Wu, the present work deals with the formulation of the kinetic equation of a plasma in a "strong" static magnetic field B, on the basis of the "initial condition" of Bogoliubov that introduces the time arrow, or irreversibility, into the theory. By a "strong" field, it is meant that the cyclotron frequencies of the charged particles ωσ = zσeB/mc are large compared with the "collision" frequencies, so that the randomizing effect of the interparticle interactions can be regarded as a "perturbation" on the dynamical motion of the particles. For the spatially homogeneous plasma, the kinetic equation is formulated in an expansion in powers of (1/ωσ) [Formula: see text] (1/B). For the spatially inhomogeneous case, the kinetic equation is given in a further expansion in powers of the wave vector κ measuring the spatial variation of the inhomogeneity. The theory gives the formal scheme in which the distribution functions F1(r, p, σ, t) of particles of charge zσe can be obtained to various orders in1/B and κ.