Coupled-cavity traveling wave tube (CCTWT) is a high power microwave vacuum electronic device used to amplify radio frequency signals. CCTWTs have numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. Microwave-generating interactions in CCTWTs take place mostly in coupled resonant cavities positioned periodically along the electron beam axis. Operational features of a CCTWT, particularly the amplification mechanism, are similar to those of a multicavity klystron. We advance here a Lagrangian field theory of CCTWTs with the space being represented by 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 field equations are ordinary differential equations with coefficients varying periodically in the space. Utilizing the system periodicity, we develop 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, dispersion relations and the frequency dependent gain foundational to the RF signal amplification. Serpentine (folded, corrugated) traveling wave tubes are very similar to CCTWTs, and our theory applies to them also.

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