Emittance, Brightness, Free-Electron Laser Beam Quality, and the Scaled Thermal Velocity

Abstract

We discuss the role of emittance, brightness, and other factors affecting the quality of beams in the free electron laser. Since the key parameters in the dynamics of the free electron laser interaction depend on the beam density and axial energy spread of the beam, the ratio of the current density to the relative axial energy spread is taken as a figure of merit for comparing the quality of electron beam sources as potential drivers of free electron lasers. The scaled thermal velocity is introduced as a parameter in estimating the effect of thermal spread in a high gain free electron laser. We find that the effective thermal spread regime can be made small near the cyclotron resonance in field immersed free electron lasers, and the unusual possibility that the efficiency of the fastest growing mode with warm beams can be higher than cold beams. A detailed dispersion relation for the free electron laser interaction where the beam energy distribution is determined by pitch angle scattering and the total beam energy is conserved is presented. Numerical solutions for the growth rate and efficiency are calculated which show a shift to lower phase velocity as a function of momentum spread and an increase in efficiency of the fastest growing mode.