Analytic theory of multicavity klystron

Multicavity Klystron (MCK) is a high power microwave (HPM) vacuum electronic device used to amplify radio-frequency (RF) signals with numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. The microwave-generating interactions in klystrons take place in resonant cavities at discrete locations along the beam. Importantly, there is no electromagnetic coupling between cavities, they are coupled only by the bunched electron beam, which drifts from one cavity to the next. We advance here an analytic theory of MCKs operating in voltage amplification mode associated with the maximal gain. This theory features in particular exact formulas for the MCK instability frequencies, its dispersion relations and optimal values of the MCK parameters providing for maximal gain