Plasma oscillations of an electron beam in an external electric field

Abstract

Many papers have been devoted to the problem of the interaction of beams of charged particles with a plasma (a detailed bibliography is given, for example, in [1]). Analysis of the dispersion equation shows that in the case of a sufficiently slow monoenergetic electron beam of low density, growing longitudinal waves are not excited in a system consisting of such a beam and a plasma [2–4]. The problem of the penetration of an external longitudinal electric field into a semiconfined plasma with an electron beam in the absence of instabilities in the system is studied (the boundary-value problem for growing waves was examined in [5]). This problem is, in a certain sense, an extension of the second part of L. D. Landau's well-known work [6] to include the case of a plasma with a beam. On the other hand, in the absence of an external electric field, this problem may be considered a boundary-value problem of the interaction of a weakly modulated electron beam with a plasma.