Self-consistent theory of cyclotron maser instability for intense hollow electron beams

Abstract

A self-consistent theory of the cyclotron maser instability, assuming azimuthally symmetric perturbations about a slowly rotating hollow electron beam propagating parallel to a uniform axial magnetic field B0êz is developed. The stability analysis is carried out within the framework of the linearize Vlasov–Maxwell equations. It is assumed that the beam is thin with radial thickness (2a) much smaller than the beam radius (R0), and that ωp2/ω2c≪1, where ωp and ωc are the electron plasma frequency and electron cyclotron frequency, respectively, in a frame of reference moving with the beam axial velocity cβb. The analysis is carried out for the specific choice of equilibrium electron distribution function in which all electrons have the same value of canonical angular momentum and the same value of energy in a frame of reference moving with axial velocity cβb. Stability properties are investigated including the important influence of finite radial geometry, finite beam temperature, and transverse magnetic perturbations (δB≠0). It is shown that instability exists for a very narrow range of axial wavenumbers satisfying ‖k−βbω/c‖≪1/R0. Detailed stability properties are calculated for a variety of system parameters.