Phase Sensitivity in Relativistic Gyrotrons

This paper is initiated by the discussion of possibilities to use free-running gyrotron oscillators for testing high-gradient accelerating structures, which took place in November 18, 2005 at the meeting "US Collaboration on High Gradient Research for Multi-TeV Linear Colliders" (University of Maryland, College Park). The main concern was the phase stability of such devices because for using the outgoing radiation in pulse compressors before introducing it into an accelerating structure, the phase deviation should not exceed pi/2. First estimates of phase stability in such devices were done by G. Nusinovich immediately after the meeting and reported to the participants on November 21. Present paper contains those initial estimates based on the general theory of gyro-devices and also contains results of MAGY simulations for 30 GHz free-running and phase-locked relativistic gyrotron oscillators