Nonlinear third harmonic radiation in thermal free electron laser with modified wiggler

Simulation of free electron laser (FEL) with modified wiggler consisting of a conventional planar wiggler with third harmonic field component is presented. A set of self consistent nonlinear differential equations is derived and solved numerically by Runge-Kutta method. The optimum amplitudes of fundamental and third harmonic wiggler filed are obtained to increase the third harmonic radiation in comparison with conventional wiggler and also to have lower electron beam energy compared to conventional wiggler with the same wavelength. For the thermal effect the axial energy spread of electron beam, without any spread in the transverse velocity, is assumed. A peculiar region is found in which there is a sharp increase of the radiation amplitude. Thermal effect of the electron beam was found to be irregular in this peculiar region.