Theory and simulation of the interaction between periodic multi-transmission lines with a degenerate band edge and electron beams

The interaction between a slow-wave structure (SWS) and an electron beam has been investigated by Pierce (J. R. Pierce, Bell System Technical Journal 29(3) 390–460, 1950) and several other contemporaries, leading to amplification regimes for traveling wave tubes. Slow-wave structures can be designed using homogenous or periodic waveguide structures to achieve synchronous phase velocity to the electron beam, and desirable interaction impedance. A multi-transmission line (MTL) model of homogenous SWSs has been investigated in (A. Tamma and F. Capolino, IEEE Trans. Plasma Sci. 2(4) 899–910, 2014), which accurately models wave propagating and amplification inside MTL-electron beam coupled system. Here we demonstrate a new regime of amplification for traveling wave tubes based on synchronizing the degenerate band edge in the dispersion diagram of periodic structures with the electron beam. A degenerate band edge (DBE) is a photonic band edge condition that is manifested in periodic waveguide structures supporting two modes or more, and results in a very dramatic reduction in group velocity (A. Figotin and I. Vitebskiy, Phys. Rev. E 72(3), 036619, 2005). We show that the interaction between an electron beam and SWS working at the DBE can produce simultaneous amplification in more than one propagating mode, unlike the case with uniform MTL-beam interaction where solely one mode can be amplified (M. Othman et al., arXiv:1411.1046, 2014). We develop a theoretical framework for such an unconventional interaction in both time and frequency domain, using a periodic MTL approach with the help of Floquet theorem. A MTL-electron beam finite-difference time-domain (FDTD) algorithm is also developed to show the advantages of utilizing a DBE in a traveling wave tube, where we demonstrate the required conditions for amplification and oscillation. Various considerations are taken into account, such as losses, space-charge effects in the electron beam, and loading effects. Theory developed here may have a major impact on the enhancement of the efficiency, gain, and overall performance of traveling wave tubes for high power microwave generation.