The microwave generation mechanism of arelativistic electron beam propagating through the dielectric-loaded cylindrical waveguide

The general dispersion relation is derived for the fundamental transverse magnetic modes driven by a cold relativistic electron beam in a dielectric-loaded cylindrical waveguide using the fluid Maxwell equations. It is then reduced to the algebraic equation for the space charge and cyclotron modes using a tenuous beam approximation. Solutions of the resulting equation are obtained by varying several parameters, such as the external magnetic field the dielectric constant and the thickness of the dielectric material. It is shown that the growth rate of the slow cyclotron instability is greatly increased for the region of B_o≲1000 G to the extent that it becomes comparable to the growth rate of a slow space-charge instability. In this region the magnetic-field effect on the slow space-charge mode is shown to increase the growth rate by up to 10%. In the limit of the critical external magnetic field defined as the field below which no beam equilibrium exists, it is found that two slow modes of cyclotron and space-charge modes become degenerate with a finite value of growth rate