Stabilization of the cyclotron autoresonance maser instability by axial momentum spread

This paper investigates the stabilizing influence of axial momentum spread on the linear growth properties of the cyclotron autoresonance maser (CARM) instability. The stability analysis is based on the linearized Vlasov-Maxwell equations for a relativistic electron beam and right-circularly-polarized electromagnetic waves propagating parallel to a uniform magnetic field B₀e^_z. Detailed stability properties are investigated for a choice of beam equilibrium f_b⁰(p_⊥²,p_z) that incorporates both an inverted population in perpendicular momentum p_⊥ and a spread Δ in axial momentum p_z. For simplicity, the analysis neglects the influence of finite radial geometry (k_⊥→0 and no radial waveguide structure). The resulting dispersion relation is analyzed numerically in parameter regimes of interest for CARM applications, and approximate analytical estimates of the (reduced) growth rate are presented.