Effect of reflections on nonstationary gyrotron oscillations

We present an extension of the self-consistent time-dependent theory describing nonstationary processes in gyrotrons to allow for reflections. Different mathematical descriptions of partial reflection of the output signal are compared, and numerical algorithms for analyzing them are given. Using a novel description, we have computed a map of gyrotron oscillations which identifies the regimes of stationary, periodically modulated, and chaotic oscillations in the plane of generalized gyrotron variables when reflection is present. In general, reflections drive the gyrotron into quasi-periodic oscillations instead of chaos, but also the threshold current for chaotic oscillations decreases somewhat. The results can be exploited in the development of high-power gyrotrons for electron cyclotron resonance heating and electron cyclotron current drive of fusion plasmas, but also in low-power applications, where chaotic oscillations might be useful.