Analytic Solution for the Problem of Gridded Gap-Electron Flow Interaction

摘要

The present study is motivated by the modelling of high-power klystrons. The two basic components of a Klystron are the resonant cavities and the drift spaces. This paper addresses only the first of these two components. Modelling of the drift spaces is deferred to future work. The formulation is not restricted to Klystron modelling, but is applicable to any problem involving the interaction of an electron beam with a resonant cavity. While the theory of Klystrons has been worked out in detail in the small signal limit, the problem remains largely unsolved when the signals are large. In particular, the hydrodynamic models of electron beams used to derive the small signal theories fail when particle trajectories cross each other. In this paper, we employ a Vlasov description of the electron beam to study the Klystron problem. In the Vlasov formulation we follow the evolution of the electron distribution function in phase-space. The general framework can naturally accommodate particle crossing, and the beam dynamics is accurately described even when the signals are large. (ERA citation 09:025053)