Three-dimensional simulation of long-wavelength free-electron lasers with helical wiggler and ion-channel guiding

A three-dimensional simulation of a steady-state amplifier model of a long-wavelength free-electron laser (FEL) with realizable helical wiggler and ion-channel guiding is presented. The set of coupled nonlinear differential equations for electron orbits and fields of TE11 mode in a cylindrical waveguide are solved numerically by the Runge—Kutta algorithm with averages calculated by the Gaussian quadrature technique. Self-fields and space-charge effects are neglected, and the electron beam is assumed to be cold and slippage is ignored. The parameters correspond to the Compton regime. Evolution of the radiation power and growth rate along the wiggler is studied. Ion-channel density is chosen to obtain optimum efficiency. Simulations are preformed for the FEL operating in the neighborhood of 35 GHz and 16.5 GHz for the electron beam energies of 250 keV and 400 keV, respectively. The result of the saturated efficiency was found to be in good agreement with the simple estimation based on the phase-trapping model