A New Amplification Regime for Traveling Wave Tubes with Third Order Modal Degeneracy

This material is based upon work supported by the Air Force Office of Scientific under the Multidisciplinary University Research Initiative award number FA9550-12-1-0489 administered through the University of New Mexico, and under award number FA9550-15- 1-0280. F. Yazdi, M. A. K. Othman, M. Veysi, and F. Capolino are with the Department of Electrical Engineering and Computer Science, University of California, Irvine, CA 92697 USA. (e-mail: fyazdi@uci.edu, mothman@uci.edu, mveysi@uci.edu, f.capolino@uci.edu). A. Figotin is with the Department of Mathematics, University of California, Irvine, CA 92697 USA. (e-mail: afigotin@uci.edu, a.figotin@uci.edu).

A New Amplification Regime for Traveling Wave Tubes with Third Order Modal Degeneracy

Abstract— Engineering of the eigenmode dispersion of slow- wave structures (SWSs) to achieve desired modal characteristics, is an effective approach to enhance the performance of high power traveling wave tube (TWT) amplifiers or oscillators. We investigate here for the first time a new synchronization regime in TWTs based on SWSs operating near a third order degeneracy condition in their dispersion. This special three-eigenmode synchronization is associated with a stationary inflection point (SIP) that is manifested by the coalescence of three Floquet-Bloch eigenmodes in the SWS. We demonstrate the special features of “cold” (without electron beam) periodic SWSs with SIP modeled as coupled transmission lines (CTLs) and investigate resonances of SWSs of finite length. We also show that by tuning parameters of a periodic SWS one can achieve an SIP with nearly ideal flat dispersion relationship with zero group velocity or a slightly slanted one with a very small (positive or negative) group velocity leading to different operating schemes. When the SIP structure is synchronized with the electron beam potential benefits for amplification include (i) gain enhancement, (ii) gain-bandwidth product improvement, and (iii) higher power efficiency, when compared to conventional Pierce-like TWTs. The proposed theory paves the way for a new approach for potential improvements in gain, power efficiency and gain-bandwidth product in high power microwave amplifiers.
I. INTRODUCTION The classical approach for designing high power microwave amplifiers provides for an efficient energy transfer from high energy electron beams to electromagnetic fields at radio and microwave frequencies [1], [2]. A traveling wave tube (TWT) amplifier is a conventional high power device comprising of a slow-wave structure (SWS) whose interacting mode has a synchronous phase velocity to the average electron’s velocity of the electron beam [1]–[4]. Pierce and his contemporaries [3], [5]–[8] developed a ubiquitous framework and design procedure for such devices through circuit theory. According to simple but physically incisive Pierce model [3], the amplification in a TWT is attributed to amplification of a slow wave radio frequency (RF) signal in an equivalent transmission line (TL) due to perturbation of the electron charge density thanks to bunching of the electron beam (the charge wave). Remarkably, Pierce predicted the small signal gain of a TWT and provided design rules for TWT amplifiers in terms of the SWS and electron beam parameters [2], [9]. In essence, state of the art of the high power TWT technology employs all-metallic slow-wave guiding structures whose dispersion is engineered for (i) matching phase velocity to an electron beam over a wide bandwidth; and (ii) high interaction impedance [10]–[17]. Consequently, dispersion engineering of the SWS eigenmodes would potentially enhance the gain, efficiency and bandwidth of conventional TWTs [18]–[22] and backward wave oscillators (BWOs) [23]–[26]. We investigate here a novel amplification regime based on special dispersion characteristics of SWS potentially leading to a higher gain and larger gain- bandwidth product (typical figure of merit for amplifiers) compared to a conventional Pierce-type TWT. In particular, the proposed regime of operation relies on electromagnetic eigenmode degeneracy in periodic SWS, namely, the third order degeneracy typically referred to as the stationary inflection points (SIP). The SIP condition is found when three Floquet-Bloch eigenmodes in the “cold” periodic structure coalesce [27]–[30] and cause an inflection point in the dispersion diagram. The “cold” term refers to a SWS which is not coupled to an electron beam. In [31]–[33], some of the authors have developed the theory of a SWS-electron beam interaction based on a different modal degeneracy, the degenerate band edge (DBE) [34]–[38], which inherently has limited bandwidth. The theory in [31]–[33], [39] describes four Floquet-Bloch eigenmodes synchronous schem

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