Collective effects on the operation of free electron lasers with an axial guide field

The collective interaction in a free electron laser with combined helical wiggler and uniform axial guide fields is presented in the linearized regime. The analysis involves a perturbation of the Vlasov-Maxwell equations about the constant-velocity helical trajectories, and the general driving currents are derived for this configuration. The complete dispersion equation is then obtained for a monoenergetic beam. Analytic solutions are obtained in the strong pump and a space-charge dominated regimes, and an extensive numerical analysis is presented for a wide range of operating parameters. The results indicate that substantial enhancements in the gain are possible when the relativistic axial gyrofrequency is comparable to the Free Electron Laser Doppler Upshift. In addition, there is a range of parameters for which the ponderomotive potential acts to destabilize the electron beam. In this regime, we find both unstable electrostatic beam modes and largely electromagnetic modes with broad bandwidths.