Microwave Excitation by a Constrained Large-Orbit Electron Beam—A Unified Dispersion Relation for Slow- and Fast-Wave Devices

Abstract

A unified linear dispersion relation that describes both slow-and fast-wave devices excited by a constrained large gyration orbit (LO) monoenergetic electron beam of infinitely small thickness has been derived and studied numerically. Beam electrons in a sufficiently long sinusoidally corrugated metal slow-wave structure are assumed completely neutralized by the background ions in equilibrium state. An exact dispersion relation of an LO backward-wave oscillator that can reasonably describe instabilities in the slow-wave device region has been obtained. A parameter , defined as a ratio of the transverse to the longitudinal component of the electron velocity, is found to have a critical value above which the excitation of a nonaxisymmetric quasi-TE 11 mode caused by the fast cyclotron instability dominates the conventional Cherenkov instability. However, for an SWS having infinitely small amplitude of corrugation, radiation with in the fast-wave device region is obtained. Here, and are, respectively, microwave angular frequency and relativistic electron cyclotron frequency. The conventional cyclotron resonance maser (CRM) instability with is altogether suppressed; instead, an alternate mechanism, namely, Cherenkov instability in the azimuthal direction with found first in the current paper leads to the excitation of microwaves. This suggests that the radiation from some previous CRM experiments with a high current density electron beam neutralized by ions might have been caused not by CRM instability but by the present Cherenkov instability in the azimuthal direction.Index Terms-Backward-wave oscillator (BWO), Cherenkov instability, cyclotron maser instability, cyclotron resonance maser, fast-wave devices, gyrotron, high-power microwaves, slow-wave devices.

Proposal of a new principle of cyclotron emission from neutralized electron beams

“…The CIAD was found to be non-relativistic in nature, because it survived under the approximation c → ∞ in the dispersion relation (10) as shown in Fig. 6(a)-(d) in [11]. In order to investigate further the distinction between the two instabilities that arise for ω >Ω and ω <Ω, incompletely constrained gyrations of the electrons near the LO circle, namely the intermediate cases between Figs 7 and 8 in [11], are investigated in this paper.…”

“…However, the CRM instability may not be the unique principle of cyclotron emission nearΩ. Another principle of radiation, different from CRM instability, was found to exist theoretically, if high-density electron beams were neutralized by ions [11]. It was named Cherenkov instability in the azimuthal direction (CIAD) and was expected to arise at an oscillation frequency ω <Ω + V z k z .…”

“…In our previous analysis, conventional CRM instability [2][3][4][5][6][7][8][9][10] and the CIAD [11,Fig. 6(a), (b)] were distinguished in Figs 7 and 8 in [11] by tracking trajectories of 128 test electrons without mutual interactions, initially distributed uniformly on a large orbit (LO) circle with a radius equal to their Larmor radius, in the presence of a right-hand circularly polarized electric field E ⊥ . In the particle simulation in Fig.…”

“…In the particle simulation in Fig. 7 in [11], the radial displacements of the electrons were allowed in the rf field in the vacuum, and a well-known CRM instability with ω >Ω + V z k z (ω >Ω, hereafter) was obtained. In Fig.…”

“…In Fig. 8 in [11], on the other hand, the electrons were constrained to stay on the original LO circle in the rf field, when the radial displacements were completely prohibited. The CIAD with ω <Ω + V z k z (ω <Ω, hereafter) was observed instead of the CRM instability.…”