Modeling and calculation of electron beam diffusion based on adaptive Simpson integral

The diffusive behaviour of relativistic electron beams propagating is a central issue in high-energy physics research and the design of high-energy physics devices. Traditional numerical integration methods have the defects of low accuracy and insufficient efficiency in calculating the initial diffusion integral. Aiming at the accuracy and efficiency of the diffusion prediction of the beam spot radius in relativistic electron beam transport, a high-precision computational framework based on adaptive Simpson's integral is proposed to improve the shortcomings of the traditional Alfvén current theory that relies on the rectangular integration method. In this paper, by embedding the adaptive Simpson integration algorithm into the Alfvén theoretical model, the high-precision and high-efficiency solution of the diffusion parameter of the electron beam propagation radius is achieved. Numerical experiments show that compared with the conventional method, the error of the adaptive Simpson integral in the electron beam diffusion integral is reduced to the order of 10-7, the accuracy is improved by two orders of magnitude, and the computational time consumed is reduced to 9.06%. The analysis further shows that the increase in electron energy enhances the focusing effect of the magnetic field, suppresses the spread of the beam radius.