Extension of Pierce model to multiple transmission lines interacting with an electron beam

TL;DR

This paper extends Pierce's model to multiple coupled transmission lines interacting with an electron beam, revealing conditions for wave growth and potential for high power microwave device applications.

Contribution

It introduces a novel extension of Pierce theory to MTLs with electron beams, providing new dispersion relations and insights into wave growth and energy exchange mechanisms.

Findings

Growing wave solutions exist when electron propagation constant exceeds the largest MTL propagation constant.

Finite bands of electron propagation constants support wave growth.

The beam acts as an energy source, influencing power flux along the transmission lines.

Abstract

A possible route towards achieving high power microwave (HPM) devices is through the use of novel slow-wave structures, represented by multiple coupled transmission lines (MTLs), and whose behavior when coupled to electron beams has not been sufficiently explored. We present the extension of the one-dimensional linearized Pierce theory to MTLs coupled to a single electron beam. We develop multiple formalisms to calculate the k-{\omega} dispersion relation of the system and find that the existence of a growing wave solution is always guaranteed if the electron propagation constant is larger than or equal to the largest propagation constant of the MTL system. We verify our findings with illustrative examples which bring to light unique properties of the system in which growing waves were found to exist within finite bands of the electron propagation constant and also present possible means to improve the gain. By treating the beam-MTL interaction as distributed dependent current generators in the MTL, we derive relations characterizing the power flux and energy exchange between the beam and the MTLs. For the growing wave, we show that the beam always behaves as an energy source causing power flux along the transmission lines. The theory developed in this paper is the basis for the possible use of degenerate band-edges in periodic MTL systems for HPM amplifiers.