Deficiencies of the Asymptotic Solutions Commonly Found in the Quasilinear Relaxation Theory

Abstract

Several authors have attempted to describe the dynamics of a suprathermal beam of electrons relaxing in a cold coIIisionless plasma by analytic asymptotic solutions of the quasilinear equations. These solutions are criticized on the grounds that they cannot correctly take account of the evolution of the plasma wave spectrum. A numerical solution is given which illustrates this point in the case of a homogeneous one-dimensional beam. Two important points can be made on the basis of the present work: (1) for self-consistency, the spontaneous emission terms cannot be neglected at any stage, and (2) the characteristic times of evolution in the early stages (accessible for the first time through the present numerical solutions) are found to be much longer than commonly quoted (Le. several times the linear growth time) when discussing the reasons for neglecting higher-order interactions.