Cold-cavity and self-consistent approaches in the theory of mode competition in gyrotrons

On the basis of a generalized theory, the cold-cavity and the self-consistent methods of calculation of mode competition in gyrotrons are compared. This comparison enables the conditions when the cold cavity approximation is justified to be determined. Specific examples are presented and numerical problems are discussed. It is concluded that mode competition can be studied by neglecting the interaction of the electrons and the RF field in the output taper in those cases when the parameter of irregularity of the output taper is >15. Here, the results obtained in the cold-cavity approximation overestimate the starting current of the parasitic mode by ~25% in comparison with the self-consistent approach. For values of the parameter of irregularity <15, the mode competition in gyrotrons must be studied only self-consistently, taking into account the interaction of the electrons and the RF field in the output taper as well as the factors which influence the interaction along the axis