Kinetic Equation for an Unstable Plasma in Parallel Electric and Magnetic Fields

Abstract

The response of a homogeneous plasma, in a strong uniform magnetic field, B0, to the sudden application of a strong, uniform electric field is studied in a self-consistent formulation which treats the coupled equations for the one-particle and two-particle distribution functions resulting from neglect of three-particle correlations. As in earlier work on the case B0 = 0, the electric field is assumed to be large compared to that which produces a ``runaway current,'' so that particle-wave interactions should dominate. In the limit of strong magnetic field, use of the Bernstein-Kulsrud expansion in k⊥Ric makes the problem effectively one-dimensional, eliminating the need for factorization assumptions of the form f(v) = f∥(v∥)f⊥ (v⊥) used in the B0 = 0 case. Only the dominant contributions to the diffusion in velocity space, arising from the fastest growing waves, are retained. Other simplifications result from the assumption of unequal electron and ion temperatures, but it proves necessary to specify the ratio Te/Ti, rather than simply assuming it to be large. In sharp contrast to the case B0 = 0, it is found that the diffusion affects only those electrons which have, in the ion rest frame, velocities of order (m/M)½ of the electron thermal speed. No appreciable ``quasi-linear'' effects, such as the current limitation found in the B0 = 0 case, are therefore to be expected; the results of numerical calculations confirming this are summarized.