Small-signal analysis of the cyclotron resonance maser in a system with axial nonuniformities

The small-signal cyclotron resonance maser (CRM) interaction in a system with axial gradients is treated analytically in order to investigate the possibility of the development of such an interaction in the gyrotron beam tunnel. The axial magnetostatic field and the tunnel diameter are both assumed with constant axial gradients, weak enough for the quadratic and higher order terms to be omitted. The monoenergetic electron beam is treated as an ensemble of test electrons, with their motion integrated analytically, under conditions of cyclotron resonance, up to second order in the amplitude of the resonant wave component. Finally, analytic expressions have been obtained for the electronic efficiency and the starting current has been calculated for a number of typical geometries. Sample comparison with experimental data is also presented.