THE INSTABILITY OF HOLLOW ELECTRON BEAM INTERACTING WITH PLASMA-LIKE MEDIUM

Abstract

Nowadays a good deal of attention is focused on problems of generation of millimeter and submillimeter electromagnetic waves under the interaction of fluxes of charged particles with solids. However, today there is no consistent theoretical description of this type of effects. In this connection we present the detailed theoretical research on the instability effect of non-relativistic infinitely thin hollow electron beam which moves in vacuum above a dielectric (plasma) cylinder. The calculations have been performed in electrostatic approximation due to the non-relativistic velocity of the beam electrons. The cases where the dielectric permittivity is constant and depends on the frequency have been considered. The dispersion curves of exited modes have been constructed. The dependences of the increments (decrements) of the modes on the value of the bunch radius and on the azimuth mode index have been studied. It has been shown that for both the dielectric and plasma media the largest values of the increments (decrements) of the excited modes occur for zero value of the azimuth mode index. The maximum values of the increments (decrements) decrease with increasing the azimuth mode index. It has been established that the frequency dependence of the dielectric permittivity leads to the absolute instability. This instability exists in the corresponding finite interval of the longitudinal wave number.

Keywords

• beam instability
• electron beam
• instability increment
• space-charge wave