A coupled-monotron analysis of band-edge oscillations in high-power traveling-wave tubes

Abstract

A theoretical analysis of the interaction of an electron beam with a coupled-cavity structure near a band-edge frequency is presented. The analysis utilizes the resonant modes of the individual cavities in a way such that the details of the electronic interaction within each distinct cavity are identical to those of the monotron theory, but the coupling between adjacent cavities is taken into account via the circuit equations. There are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> equations obtained for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> cavities, and an algebraic rather than a characteristic wave type of approach is chosen for their solution. The theory is applied to finding the starting conditions for band-edge oscillations in an untapered structure. The results are verified experimentally. The theory also indicates that it is probably valid to use the simple monotron theory to find the minimum start-oscillation length or current.