Simulation of Smith-Purcell radiation using a particle-in-cell code

Abstract

A simulation of the generation of Smith-Purcell (SP) radiation at microwave frequencies is performed using the two-dimensional particle-in-cell code MAGIC. The simulation supposes that a continuous, thin (but infinitely wide), monoenergetic electron beam passes over a diffraction grating, while a strong axial magnetic field constrains the electrons to essentially one-dimensional motion. The code computes the time-dependent electric and magnetic fields by solving the Maxwell equations using a finite element approach. We find that the passage of the beam excites an evanescent electromagnetic wave in the proximity of the grating, which in turn leads to bunching of the initially continuous electron beam. The frequency and wave number of the bunching are determined, and found to be close to those proposed by Brau and co-workers in recent work. This frequency is below the threshold for SP radiation. However, the bunching is sufficiently strong that higher harmonics are clearly visible in the beam current. These harmonic frequencies correspond to allowed SP radiation, and we see strong emission of such radiation at the appropriate angles in our simulation, again in agreement with Brau's predictions. We also find that at the ends of the grating, some of the evanescent wave is diffracted away from the surface, and radiation below the threshold occurs. In addition, we observe a second evanescent wave at the same frequency, but with a different wave number. The existence of this wave is also predicted by the theory, although its presence in our simulation is unexpected. Numerical estimates of the growth of the evanescent wave are also in reasonable agreement with the predictions, although the precise form of the dependence of the gain on beam current remains hard to establish.

Small signal gain of a Smith-Purcell free electron laser

“…The numerical results of [18] in general are in agreement with the analysis of [13,14], but the gain calculated in [18] is within a factor of 2 of that predicted in the work [13].…”

“…c k for 0:548 (at the kinetic energy 100 keV) intersects the dispersion curve at the wave number 0.5684 and frequency 0.3115 of the resonant evanescent wave. The resonant frequency and wave number are close to those of the paper [18]. As we see the group velocity (d!=dk) of the resonant evanescent wave is negative and for this energy of an electron beam the SP FEL operates like a backward wave oscillator.…”

“…2 for a rectangular grating with w=g 0:5 and a=g 0:5. This corresponds to the setup of [18]. The abscissa is the normalized wave number and the ordinate is the normalized angular frequency.…”

“…We derive a general expression for the dispersion relation and examine various limits of small signal gain depending on the particle beam and grating parameters. Then, obtained results are applied to rectangular grating making comparisons with the results of the works [13,18].…”

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

“…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]. Several methods were suggested to enhance the SPR and to reduce the starting current, including the enhancement from surface plasmon excited by counterstreaming electron beams [31,32] and by adding sidewall to the grating [33].…”