Cold-Beam-Plasma Interaction Theory for Finite Transverse Dimensions and Finite Magnetic Fields

Abstract

The dispersion relation for interaction between a cold electron beam and the electrons of a cold, uniform density plasma of a circular cylindrical cross section and of a radius equal to that of the beam inside a conducting pipe of a larger radius has been solved on a computer for a number of values of finite magnetic field, the ratio of plasma density to beam density, and beam perveance. Complete ω-k diagrams are given for various cases along with more extensive data on the growing wave gain that occurs below the plasma frequency and the cyclotron frequency. A comparison with experimental data on a beam-generated plasma is given and the theory is shown to provide a satisfactory explanation for the onset of oscillations in such a system with a finite length.