Influence of Electromagnetic Effects on the Two Stream Instability in a Relativistic Electron Beam

摘要

This paper investigates the influence of electromagnetic effects on the two stream instability in a relativistic electron beam propagating through a collisionless plasma channel. The analysis is carried out within the framework of a macroscopic cold fluid model in which beam and plasma fluid element is in a laminar flow. Axisymmetric electromagnetic stability properties are calculated for the case in which the equilibrium beam and plasma density profiles are rectangular. Consistent with the two stream instability, the perturbed fields are assumed to be the transverse magnetic mode. The resulting eigenvalue equation for the perturbed axial electric field del E sub z is solved to give a closed algebraic dispersion relation for the complex eigenfrequency omega. This dispersion relation is solved and it is shown that the electromagnetic effects have a strong stabilizing influence for a relativistic electron beam with gamma sub b > > 1, where gamma sub b is the relativistic mass ratio of beam electrons. For example, the critical beam current for instability is proportional to the electromagnetic current enhancement factor xi = (gamma sub b + 1)/2. Thus, the critical current from the electromagnetic calculation increases more drastically with the beam energy than that from the electrostatic approximation.