Gain of a Smith-Purcell free-electron laser

Abstract

A formula is derived for the small-signal gain of a Smith-Purcell free-electron laser. The theory describes the electron beam as a moving plasma dielectric, and assumes that the electron beam interacts with an evanescent mode traveling along the surface of a periodic waveguide with a rectangular profile. The phase velocity of the evanescent wave is synchronous with the electron velocity, but the group velocity is actually negative. The electron beam amplifies the evanescent wave, which does not itself radiate. According to this picture, the radiation observed emanating from the grating is Smith-Purcell radiation enhanced by the bunching of the electrons due to the interaction with the evanescent mode. There will also be radiation from the part of the evanescent mode that is outcoupled from the ends of the grating. This radiation appears at a lower frequency than the Smith-Purcell radiation. The new results explain both the gain and the radiation observed in the experiments of Urata and Walsh, and the cube-root current dependence of the gain inferred by Bakhtyari, Walsh, and Brownell.

Small signal gain of a Smith-Purcell free electron laser

“…A different result has been obtained in Ref. [13]. In this paper it is considered a rectangular grating, assuming that the entire space above the grating is filled by a uniform electron beam.…”

Enhancement of coherent Smith-Purcell radiation at terahertz frequency by optimized grating, prebunched beams, and open cavity

“…(2) becomes identical to Eq. (33) of Andrews and Brau [22], when setting m ¼ n ¼ 0 there. The open grating dispersion curve, Eq.…”

“…In this paper, by using particle-in-cell (PIC) simulations, we identify the optimized grating parameters for minimizing the threshold (starting) current for coherent SPR. Contrary to previous simulation work [28,34], we present the frequency spectrum of both the radiated waves and the beam current, which helps to directly verify the model of Andews et al [22]. A simple analytical dispersion relation is derived for the open grating Smith-Purcell structure, which accurately predicts the operating frequency of the (evanescent surface mode) backward wave oscillation and the consequent coherent (superradiant) harmonic SPR.…”

“…The parameters of the grating are optimized to minimize the starting current for achieving coherent SPR. The results are compared to the theoretical analysis of Andrews et al [22] and Kim et al [26]. Next, we investigate the coherent SPR from prebunched electron beams.…”

“…It was achieved due to the appearance of periodic electron bunching, induced by strong nonlinear interaction of the electron beam with an oscillating-evanescent wave (or grating surface mode) that is excited on the grating structure. The physics of coherent SPR has been studied extensively [21][22][23][24][25][26]. Many simulation works have been performed to investigate coherent SPR from continuously injected electron beam [27][28][29][30].…”