Resonant Diffusion of Plasma across a Magnetic Field

Abstract

The particle transport associated with low-frequency waves is calculated for a nonuniform plasma immersed in a magnetic field. Electrons and ions in a model plasma obey E × B drift across B, and are accelerated by Ez along B. Their distribution function is given by the solution of the kinetic drift equation. The first-order density perturbation, n(1), is made consistent with the first-order electric field, E, and the flux cEyn(1)/B is averaged over large periods in t and z. The method of calculation is equivalent to quasi-linear theory and yields the following results: the process for transport may be described as a diffusion in (x, vz) phase space which, for each Fourier component, is restricted to resonant particles (i.e., particles moving along B = ẑB with zero-order velocity vz = ω/kz) and to lines in (x, vz) space with the slope (qB/mc)(Ẽz/Ẽy)—hence ``resonant diffusion''; the transport is ambipolar, the direction of transport can be parallel or anti-parallel not only to −dn/dx, but also to −∂f0(x, ω/kz)/∂x, leading to situations of ``pump-out,'' ``normal pump-in'' or ``anomalous pump-in''; using a zero-order velocity distribution in which the density, parallel flow velocity, and temperature may be functions of x, it is possible to balance destabilizing and damping forces against each other to create states of marginal stability—these states, for which small-amplitude theory is valid, still show pump-in or pump-out. As a final result, it is found that the wave-energy conservation equation can be restated in a manner which relates cross-B particle fluxes to the product of instability growth rate and wave energy density.