Mathematical Modeling of Intense Beams of Charged Particles in Extended Electron-Optical Systems

Abstract

Intense beams of charged particles serve as a working element in electrophysical devices for a wide range of scientific and practical applications. Mathematical modeling of intense beams leads to the solution of a self-consistent nonlinear problem, which includes the calculation of electric and magnetic fields, trajectories of charged particles, and space charge. An extended electron-optical system is understood as an electron-optical system whose size in the direction of the beam’s motion is much larger than the transverse size. The use of traditional computational approaches to modeling such systems did not give satisfactory results. In this paper, we propose new algorithms and technologies aimed at improving their accuracy and reducing the calculation time. They are based on computational domain decomposition methods and are as follows. First, the extended computational domain is divided into two subdomains: in the first subdomain, an intense beam is formed, and in the second subdomain, it is additionally accelerated and transported. The solutions are “stitched” by the alternating Schwarz method. Second, in each of these subdomains, an adaptive quasi-structured locally modified grid is constructed, consisting of structured subgrids. The proposed quasi-structured grid can significantly reduce labor costs when calculating the trajectories of charged particles. Third, on the emitter, the singularity is isolated by introducing a near-emitter subdomain. In this subdomain, an approximate analytical solution is constructed, which is stitched with the numerical solution in the main subdomain in the iterative Broyden process. On the example of a model problem about a flat diode, the fast convergence of the Broyden method is shown. With the help of the proposed algorithms and technologies, the results of modeling a complex practical system are obtained, which closely match the results of natural experiments.