Analytic theory of multicavity klystrons

Abstract

Multicavity Klystron (MCK) is a high power microwave vacuum electronic device used to amplify radio frequency (RF) signals. MCKs have numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. The microwave-generating interactions in klystrons take place mostly in coupled resonant cavities positioned periodically along the electron beam axis. Importantly, there is no electromagnetic coupling between cavities. The cavities are coupled only by the flow of bunched electrons drifting from one cavity to the next. We advance here a Lagrangian field theory of MCKs with the space being represented by a one-dimensional continuum. The theory integrates into it the space-charge effects, including the so-called debunching (electron-to-electron repulsion). The corresponding Euler–Lagrange equations are ordinary differential equations with coefficients varying periodically in the space. Utilizing the system periodicity, we develop the instrumental features of the Floquet theory, including the monodromy matrix and its Floquet multipliers. We use them to derive closed form expressions for a number of physically significant quantities. Those include, in particular, the dispersion relations and the frequency dependent gain foundational to the RF signal amplification. We assume that MCKs operate in the voltage amplification mode associated with the maximal gain.