Three-dimensional Simulation of Thermal Harmonic Lasing FEL with Detuning of the Fundamental

Detuning of the fundamental is a way to enhance harmonic generation . By this method, the wiggler is composed of two segments in such a way that the fundamental resonance of the second segment to coincide with the third harmonic of the first segment of the wiggler to generate extreme ultraviolet radiation and x-ray emission. A set of coupled, nonlinear, and first-order differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field with warm beam is solved numerically by CYRUS 3D code in the steady-state for two models (1) seeded free electron laser (FEL) and (2) shot noise on the electron beam (self-amplified spontaneous emission FEL). Thermal effects in the form of longitudinal velocity spread is considered. Three-dimensional simulation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The evolutions of the transverse modes are investigated for the fundamental resonance and the third harmonic. Also, the effective modes of the third harmonic are studied. In this paper, we found that detuning of the fundamental with shot noise gives more optimistic result than the seeded FEL.