Solution of the Kinetic Equation for an Unstable Plasma in an Electric Field

Publisher Website
Google Scholar
Abstract
The response of a homogeneous plasma to the sudden application of a strong, uniform electric field, E0, is studied by solving, self-consistently, the coupled equations for the one- and two-particle distribution functions. The field is assumed to be large compared to that which produces a ``runaway'' current, so that particle-particle collisions have a negligible effect on the current flow, and particle-wave interactions dominate. The principal approximations are the neglect of intrinsic three-particle correlations (i.e., linearization in fluctuations) and the use of an adiabatic ansatz for the time dependence of the fluctuations. For the case of unequal temperatures, Te ≫ Ti, two different methods of solution are employed: a moment approximation, in which the distribution functions are assumed Maxwellian, with mean velocity and width determined self-consistently; and a more exact treatment in which the distribution function for velocities parallel to the applied field is determined by direct numerical solution of the kinetic equation using on-line computational techniques. In both cases, it is found that the unstable ion acoustic waves grow from the thermal fluctuation level to a magnitude sufficient to cause a sharp and sudden decrease in the current. Examination of the kinetic equation shows this drop to be ascribable to the dynamic friction associated with the unstable waves. Although waves propagating parallel to the applied field are most important at early times, those propagating at finite angles soon become dominant; this casts some doubt on one-dimensional approximations to this problem. The limitation of the exponential growth of unstable waves resulting from the non-linear (or quasilinear) effects is clearly evident, notwithstanding the presence of the external driving force, E0.

This publication has 9 references indexed in Scilit: