Reverse Current Induced by Injection of a Relativistic Electron Beam into a Pinched Plasma

Abstract

A macroscopic treatment of the current induced in a dense pinched plasma because of its penetration by a relativistic electron beam of finite length is presented. The behavior of the plasma is described by the generalized Ohm's law which takes account of the inertia of the plasma electrons in addition to collisions between the plasma electrons and ions. Under some conditions, the current density induced in the plasma is found to contain both longitudinal and transverse (radial) plasma oscillations. The total induced current flowing in the axial direction due to an injected pulse which varies slowly during times on the order of magnitude of the time in which the plasma can respond significantly to the beam disturbance is also calculated and investigated for the following three cases: (1) νm ≪ωp, (2) νm ∼2ωp, and (3) νm ≫ωp, where νm is the frequency of momentum transfer collisions between plasma electrons and ions and ωp is the electron plasma frequency of the plasma electrons. In case 1, it is found that the induced current is nearly equal in magnitude and opposite in direction to the beam current and that it lies almost entirely within the beam channel over the entire length of the beam pulse. These conclusions are consistent with the results of some recently reported experiments which satisfy the conditions of case 1. The induced current in case 1 also contains an oscillatory component with a frequency near the plasma frequency of the plasma electrons. This contribution to the induced current is not significant for the experiments considered, and this conclusion is also consistent with observation. The results of case 3 are equivalent to the results obtained by treating the plasma as a simple Ohmic medium.