Three-dimensional theory of the Smith-Purcell free-electron laser with side walls

Abstract

We present an analytic theory for the operation of a Smith-Purcell free-electron laser with side walls that includes the effects of transverse diffraction in the optical beam. We allow the width of the electron beam and the width of the grating to vary independently and require the walls to be high compared to the wavelength of the evanescent wave. The results show that the side walls change the empty-grating dispersion relation in important ways. When the separation of the walls is not too large, it is sufficient to consider only the lowest-order transverse mode of the grating. In this case, we obtain excellent agreement with numerical simulations and experimental results. © 2009 American Institute of Physics.