Influence of energy and axial momentum spreads on the cyclotron maser instability in intense hollow electron beams

The influence of energy and axial momentum spreads on the cyclotron maser instability in an intense hollow electron beam propagating parallel to a uniform axial magnetic field B0êz is investigated. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that ν/γ̂≪1, where ν is Budker’s parameter and γ̂mc2 is the characteristic electron energy. Stability properties are investigated for the choice of electron distribution function in which all electrons have a step-function distribution in energy (H=γmc2) and a step-function distribution in axial momentum (pz). The instability growth rate is calculated including the important stabilizing influence of energy spread (ε=Δγ) and axial momentum spread (Δ=Δpz). It is shown that a modest energy spread (ε≈ a few percent) is sufficient to stabilize perturbations with high magnetic harmonic number (s⩾2). Moreover, a relatively small axial momentum spread (Δ/mc≈0.1) can easily stabilize perturbations with axial wavenumber satisfying ‖kc/ωc‖≳0.2, for typical beam parameters of experimental interest.