Influence of voltage rise time on two parallel klystron-like relativistic backward wave oscillators

The influence of voltage rise time on two parallel klystron-like relativistic backward wave oscillators (RBWOs) is investigated through 3-D particle-in-cell (PIC) simulations. With a short voltage rise time, the axially symmetrically mode is excited, the frequency spectrum is pure, and phase locking is realized for both RBWOs. As the rise time increases, asymmetric modes appear in one or two channels, modes competition occurs, and the output power reduces. This can be explained as the transient excitation in the resonant reflector initiated by the current change in beam head, which generates an induced voltage with magnitude inversely proportional to the rise time. Furthermore, the induced voltage caused by the beam head is equivalent to an externally injected radio frequency signal. At a large rise time, an external signal can also suppress the asymmetric modes and lock the two RBWOs.