Spontaneous emission of free electron laser with planar wiggler and ion-channel guiding is calculated analytically and possibility of emission at up-shifted wiggler or ion-channel betatron frequency and their harmonics has been found. To investigate the nonlinear odd harmonics, a set of self-consistent nonlinear differential equations that governs the evolution of radiation and electron beam are derived and solved numerically by Runge-Kutta method. Using the simulation code, gain improvement of third harmonic is studied in the range of microwave frequency by applying ion-channel guiding for a cold beam. It is shown that the combination of the ion-channel and a prebunched electron beam increases the amplitude of the third harmonic of the radiation and decreases its saturation length. The relation between the linear and nonlinear harmonics is discussed.
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.
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