Mathematical modeling of intense charged particles beams in extended electron-optical systems

Intense charged particles beams 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, including the calculation of electric and magnetic fields, charged particles trajectories and space charge. An extended one is understood as an electron-optical system, the size of which in the direction of the beam movement is much larger than the transverse size. The use of traditional computational approaches to modeling such systems has not yielded satisfactory results. In this paper, we propose new algorithms and technologies aimed at improving the accuracy and reducing the computation time. They are based on the domain decomposition methods and are as follows. First, the extended computational domain is divided into two subdomains: in the first of them, an intense beam is formed, and in the second, it is further accelerated and transported; the solutions are “stitched” by the alternating Schwarz method. Secondly, in each of these subdomains, an adaptive quasi-structured locally modified grid is constructed, consisting of structured subgrids. The proposed quasistructured grid can significantly reduce labor costs when calculating the charged particles trajectories. Thirdly, at the emitter, the singularity is distinguished by introducing the 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 Broyden iterative process. With the help of the proposed algorithms and technologies, the results of modeling a complex practical system were obtained, which give a good match with the results of field experiments.