On the self-oscillation in a pulsed RF amplifying-accelerating system

A number of resonant accelerators of charged particles are fed by high power RF amplifiers loaded by resonant accelerating structures. Some of the accelerators such as linacs and racetrack microtrons are employed in self-oscillating mode using a positive feedback loop. That scheme allows a self-adjusted operation tolerable to significant changes in temperature and beam loading. However, in general such a system may develop instabilities. In this paper we consider a simplified model of an amplifier (e.g., a klystron) self-starting generation from noise and loaded by a resonant structure. Some typical transients including reflected power and influence of group delays are evaluated numerically.