中文摘要：

利用光场的高斯-赫米特源项展开法，推导了粒子运动一维方程加三维修正和光场幅度、光束半径、瑞利参数的非线性方程组，编制稳态MatlabFELcode程序，初始粒子加载与国际通用软件Genesis进行对比，吻合很好。新程序对于X射线FEL理论研究的深化，实验装置的设计和改进具有重要意义。

英文摘要：

Using light field Gaussian-Hermite source term expansion method to derive the nonlinear equations of one-dimensional FEL equation plus three-dimensional correction for particle and amplitude, the beam radius, Rayleigh parameters for light field, the steady-state Matlab code has been developed. The initial particle loading is consistent with each other for self-amplified spontaneous emission （SASE） single pass using new code and Genesis. The presented code is valuable for improving the X-ray FEL design.