A theoretical analysis of relativistic klystron oscillators

An electron beam pre-modulated at the first cavity in a klystron enters the second cavity opening, exciting it. Induced voltage at the second cavity in a high-power klystron forms a virtual cathode momentarily, sending back a part of the beam toward the first cavity. The relationship between the induced voltage and the return current at the first cavity is investigated. The boundary between the amplifier and oscillator operation regions is described in the parameter space defined by the return current strength and inter-cavity distance. Nonlinear saturation mechanism of the first cavity excitation is investigated for the oscillator operation region. One of the key saturation mechanisms of the cavity excitation is that the location at which the maximum current modulation occurs starts to shift toward the first cavity, if the induced voltage at the first cavity increases significantly. The saturation amplitude of the induced voltage is an increasing function of the beam intensity and energy, but it is independent of the return current