Space-charge-Cerenkov and cyclotron-Cerenkov instabilities in an electron-beam dielectric system

Abstract

A relativistic electron beam propagating along a constant magnetic field has four normal modes: the slow and fast space charge and the slow and fast cyclotron modes. When propagating through a dielectric where the beam velocity is greater than the velocity of light in the dielectric, the slow modes may become unstable. We call these the space-charge-Cerenkov and cyclotron-Cerenkov instabilities. In this paper we use the cold fluid model in the small signal limit to obtain a general dispersion relation for propagation at an arbitrary direction with respect to the magnetic guide field. This describes both of the above instabilities as special cases. This result is then generalized to include the effects of a thermal spread. Implications for possible application for generation or amplification of microwaves, where the beam passes near the dielectric, are also considered. We conclude that the cyclotron-Cerenkov instability is a strong candidate for the short wavelength microwave regime.