Non-linear theory of CRM instability in plasma-filled gyrotron

In this paper plasma influence on gyrotron efficiency was investigated. Numerical equations for plasma-filled gyrotron was solved and obtained in a stationary single mode approximation for 140-GHz 1-MHz CW gyrotron developed in Kralsruhe. It is shown that low density plasma decreases the resonance mismatch of the operation frequency (omega-omega_c0), where omega_c0 is the initial gyro-frequency of beam electrons and oscillation region shifts to smaller beam currents. Therefore the influence of plasma on the operation of the gyrotrons, which were designed and tuned without taking into account plasma presence in the cavity, is mostly negative due to detuning the tube out of the optimal regime. However, if the optimal mismatch (for example, by adjusting the magnetic field) was provided taking into account the appearance of a low density background plasma in the gyrotron cavity, the maximal efficiency of the operating mode will be the same as in the absence of plasma, but it shows a substantial increase for higher current values. The range of currents where the efficiency is close to the maximal one substantially extends depending on plasma density. This is caused by the plasma-induced decrease of the beam-wave coupling coefficient. So keeping the mismatch near the optimal value for the plasma-filled cavity, one can achieve higher output power than for the optimized vacuum gyrotron.