Electrostatic instability of electron beams in a planar E x B amplifier

Abstract

A wave equation is kinetically derived for an electron beam to describe the linear electrostatic perturbations propagating in the perpendicular direction with respect to the applied magnetic field in a planar E x B amplifier in which the operating electric field is inhomogeneous. For omega(c) > omega(p), the massless guiding center limit is taken to obtain the wave equation for the analysis of the electrostatic instability encountered in the planar E x B amplifier. In this work the plasma density profile is assumed to be a step function with vacuum boundaries between the cathode and the anode. The growth rates of the perpendicular electrostatic wave are obtained for the parameters such as the location and the thickness of the electron beam as well as the wave number.