Scaling Law for Ballistic Bunching on Multicavity Harmonic Gyroklystrons

It is shown that the ballistic bunching in multicavity gyroklystrons, in which different cavities operate at different cyclotron harmonics, depends only on the ratios of these harmonics, not on their absolute values. Therefore the efficiency of the bunching process is the same for all schemes of multicavity gyroklystrons with identical ratios of resonant cyclotron harmonics. Predictions based on this scaling law agree well with the results of detailed optimization of design parameters for relativistic gyroklystrons which are under development for driving future linear colliders.