This paper considers the pressing problem of numerical modeling of nonlinear wave processes in a magnetically insulated microwave generator used to generate relativistic electron beams and the radiation they generate. A distinctive feature of the problem formulation is the realistic three-dimensional geometry of the generator. A three-dimensional mathematical model, including Maxwells equations and the equations of motion for relativistic charged particles, was used for the numerical analysis. The model takes into account the field emission of electrons from the cathode surface and the presence of relativistic plasma. A new numerical algorithm is proposed for solving the problem, combining explicit time-dependent schemes, the finite volume method on irregular grids, and the cloud particle method. The software implementation is designed for parallel computing. To test the three-dimensional numerical approach, two relevant problems of generating relativistic electron beams are considered in one- and two-dimensional settings. Analysis of the calculation results confirmed the reproduction of one- and two-dimensional solutions in the three-dimensional code.
S. V. Polyakov (Wed,) studied this question.