Abstract
A local and nonlinear simulation of two-beam and tapered free-electron laser (FEL) is presented self-consistently. The slippage of the electromagnetic wave with respect to the electron beam is ignored and the relativistic electron beams are assumed to be cold. The fundamental resonance and the third harmonic radiation of the beam with lower energy are considered, in which the third harmonic is at the fundamental resonance of the beam with higher energy. The wiggler field is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point of tapering and the slope of the reduction in the amplitude of wiggler are found by successive run of the code. Using the slowly varying envelope approximation, a set of nonlinear equations is derived which describes this system. These equations are solved numerically by the Runge–Kutta method. This method can be used to improve the efficiency of the two-beam FEL in the extreme ultraviolet and x-ray regions of spectrum.
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