Small-signal theory of multiple-beam relativistic klystron amplifier

Multiple-beam relativistic klystrons use multiple parallel beamlets that propagate in individual channels but interact in common cavity gaps. Multiple-beam operation takes advantage of the low current and small radius of individual beamlet to avoid non-working mode oscillation and enable more efficient bunching and consequently higher efficiency. A small-signal theory of multiple-beam relativistic klystrons is developed and validated by simulation. The method of calculating the beam coupling coefficient is studied, assuming that the electric field is a function of gap distance. Properties of current modulation are investigated, obtaining a expression of scaling law for the fundamental component of the bunching current. The results indicate that the amplitude of the beam coupling coefficient is higher in the coaxial cavity, which is better for beam-wave interaction. The influences of potential energy of individual beamlet on current modulation are crucial, using more annular electron beams helps to have a bigger amplitude of ac current. Making use of electron beams of 600 kV/5 kA, gap voltage of 30 kV, the ac current of multiple beamlets can reach 800 A behind the input cavity.