Klystron beam-bunching lecture

摘要

Electron beam current modulation in a klystron is the key phenomenon that accounts for klystron gain and rf power generation. Current modulation results from the beams' interaction with the rf fields in a cavity, and in turn is responsible for driving modulation in the next rf cavity. To understand the impact of the current modulation in a klystron, we have to understand both the mechanism leading to the generation of the current modulation and the interaction of a current-modulated electron beam with an rf cavity. The cavity interaction is subtle, because the fields in the cavity modify the bunching of the beam within the cavity itself (usually very dramatically). We will establish the necessary formalism to understand klystron bunching phenomena which can be used to describe rf accelerator cavity/beam interactions. This formalism is strictly steady-state; no transient behavior will be considered. In particular, we will discuss the following: general description of klystron operation; beam harmonic current; how beam velocity modulation induced by an rf cavity leads to current modulation in both the ballistic and space-charge dominated regimes; use of Ramo's theorem to define the power transfer between a bunched electron beam and the cavity; general cavity model with external coupling (including an external generator if needed), used to describe the input cavity, idler cavities, and the output cavity, including the definition of beam loaded-cavity impedance. Although all these are conceptually straight-forward, they represent a fair amount of physics, and to derive some elements of the formalism from first principles requires excessive steps. Our approach will be to present a self-consistent set of equations to provide a mechanism that leads to a quantifiable description of klystron behavior; derivations for moderately complex formulas will be outlined, and a relatively complex derivation of the self-consistent set of equations can be found in the Appendix. 6 figs.