Increasing the output power of a long-wavelength free-electron laser (FEL), despite the destroying effects of beam energy spread, is studied using the optimal pre-bunching of the thermal electron beam along with the optimal tapering of the planar wiggler magnetic field. A set of self-consistent coupled nonlinear differential equations in three dimensional that describe the evolution of radiation and electron beam in the interaction zone are solved numerically by the Runge–Kutta method. The axial energy spread is considered and it degrades the FEL performance by reducing the saturation power and increasing the saturation length. To compensate these destroying effects, the optimum function or degree of electron beam pre-bunching and optimum parameters of wiggler tapering are found by the successive runs of the simulation code.

尽管束能量传播受到破坏，但还是要通过增加热电子束的预束聚以及平面摆动磁场的最佳锥度来研究增加长波自由电子激光器（FEL）的输出功率。用Runge–Kutta方法数值求解了一组自洽耦合的三维非线性微分方程，这些方程描述了相互作用区内辐射和电子束的演化。考虑了轴向能量散布，它通过降低饱和功率和增加饱和长度而降低了FEL性能。为了补偿这些破坏效果，通过连续运行模拟代码，可以找到电子束预聚束的最佳功能或程度以及摆动的锥度的最佳参数。