Competition of modes resonant with arbitrary cyclotron harmonics in a gyrotron with nonfixed axial structure of the high-frequency field

A general theory is developed for self-consistent calculations of mode competition in a gyrotron with nonfixed axial structure of the RF field for arbitrary cyclotron harmonics. The theory is applied to the gyrotron operating at the Kernforschungszentrum Karlsruhe with a frequency of 150 GHz. The formalism presented allows a self-consistent calculation of mode competition for the operating and parasitic modes at the cyclotron resonance at arbitrary harmonics. Specific calculations are carried out for the cases n₀=1, n₁ =2 and n₀=2, n₁=1. It is emphasized that the formalism considered applies only to the case in which the azimuthal orthogonality condition is satisfied: n₀m₁≠n₁ m₀. There are circumstances when this condition is not satisfied