Boundary and Current Elements for Simulation of Electromagnetic Fields

An important scientific and engineering problem is the control of charged particle fluxes using electric and/or magnetic fields. The paper develops a mathematical apparatus and algorithms for modeling the electric field in electro-optical systems by the Boundary Element Method (BEM) and the magnetic field of a set of arbitrarily oriented circular solenoids by the new Current Elements Method (CEM). The Boundary Element Method is used to solve the external problem for the double layer potential. Formulas for calculating integrals with singular and quasi-singular kernels are obtained, which ensured the calculations accuracy, limited only by round-off errors. The approximation of each of the loops of the solenoid by current elements has become a prerequisite for a high count rate in the Current Elements Method. The developed methods were integrated into homemade software FOCUS and used to create wide-range physical and analytical equipment, including microfocus X-ray tubes. The software is built as a combination of several modules: a graphical editor, a module for calculating electric field, a module for calculating magnetic field, modules for calculating trajectories of charged particles in an electromagnetic field.