Resistive growth of the relativistic cyclotron wave

Growth of the negative energy axisymmetric cyclotron eigenmode of an unneutralized relativistic electron beam propagating interior to a cylindrical conducting guide along a guide magnetic field can be induced by resistive liner structures interior to the guide. Analysis shows these liners yield sharply peaked growth rates of the order of 5·10⁻³Ω, where Ω is the relativistic cyclotron frequency. However, such liners are plagued by resistive kink instabilities, unless 1) the magnetic field is operated above optimum for axisymmetric growth or 2) azimuthal shorting rings are included in the liner configuration. Unfortunately, such rings may then allow a hydrodynamic kinking instability at high phase velocity and growth rates (. 1Ω) if 4ωp² >Ω², where ωp is the relativistic beam plasma frequency. Although undesirable for growth of the axisymmetric modes, such an instability may be of interest for the generation of microwave power.