A small-signal theory for the radial-line relativistic klystron amplifier

A small-signal theory describing the electron beam modulation in the radial-line relativistic klystron amplifier (RL-RKA) is developed in this paper. We first derive theoretically the space-charge limited current, the dispersion relation of space-charge waves on the radial-radiated electron beam, and the beam coupling coefficient for the radial-line electromagnetic structure. Then, a smallsignal theory is established to analyze the beam current bunching during the initial modulation period. With particle-in-cell simulations, the theoretical analysis is verified through observing the fundamental harmonic current of an input cavity in a previous Ku-band RL-RKA. More importantly, the presented small-signal theory can provide a theoretical guidance for the RL-RKA design.