Raman free-electron laser with transverse density gradients.

Abstract

The influence of the electron density gradients on the free-electron laser in the Raman regime is considered. Since in the Raman regime the electron density appears in the resonance parameter, the density gradients prevent the beam from being wholly resonant. The transverse gradients can then substantially reduce the gain even if the total current is kept constant. We solve a model problem of a free-electron laser, which employs a sheet electron beam in a planar wiggler, and which operates in the small-signal, high-gain regime. We study two cases, a density profile of uniform density gradient and a general density profile. For a uniform density gradient we write a dispersion relation explicitly in terms of Whittaker functions. For general density profiles, providing the current or the wiggler field is small, we derive an approximate dispersion relation through a solvability condition of the perturbed equations. In both cases, when the density gradient is large, the gain is expressed as a sum of contributions from the individual resonant layers, where each such contribution is inversely proportional to the density gradient at the respective resonant layer. A sufficient condition in order for the gain not to be substantially reduced by the density gradients is formulated.