Mechanism of phase control in a klystron-like relativistic backward wave oscillator by an input signal

Theoretical analyses and particle-in-cell (PIC) simulations are carried out to understand the mechanism of microwave phase control realized by the external RF signal in a klystron-like relativistic backward wave oscillator (RBWO). Theoretical calculations show that a modulated electron beam can lead the microwave field with an arbitrary initial phase to the same equilibrium phase, which is determined by the phase factor of the modulated current, and the difference between them is fixed. Furthermore, PIC simulations demonstrate that the phase of input signal has a close relation to that of modulated current, which initiates the phase of the irregularly microwave during the build-up of oscillation. Since the microwave field is weak during the early time of starting oscillation, it is easy to be induced, and a small input signal is sufficient to control the phase of output microwave. For the klystron-like RBWO with two pre-modulation cavities and a reentrant input cavity, an input signal with 100 kW power and 4.21 GHz frequency can control the phase of 5 GW output microwave with relative phase difference less than 6% when the diode voltage is 760 kV, and beam current is 9.8 kA, corresponding to a power ratio of output microwave to input signal of 47 dB.