An Algorithm for Calculating Nonlinear Wave Processes in a Microwave Generator with Magnetic Insulation in the Three-Dimensional Case

The paper considers the problem of numerical modeling of nonlinear wave processes in a microwave generator with magnetic insulation, used to generate relativistic electron beams and the radiation they produce. A distinctive feature of the problem is the realistic three-dimensional geometry of the oscillator. The numerical analysis of the problem is based on a three-dimensional mathematical model involving Maxwell’s equations and the equations of motion for relativistic charged particles. The model takes into account the field emission of electrons from the cathode surface and the presence of relativistic plasma. A new numerical algorithm for solving the problem is proposed, combining explicit time-dependent schemes, the finite volume method on irregular grids, and the particle-in-cloud method. The software implementation is designed for parallel computing. To test the three-dimensional numerical approach, two relevant problems of generating relativistic electron beams in one- and two-dimensional formulations were considered. Analysis of the calculation results confirmed the reproduction of one- and two-dimensional solutions in the three-dimensional code.