Calculation of electric field when modeling of intense charged particles beams in complex 2D domains

In problems of modeling intense charged particles beams moving in domains with a complex configuration of boundaries, the accuracy of trajectory calculations significantly depends on the accuracy of calculation of electric fields. In this work, algorithms for calculating the strength of electric fields at the calculated points of trajectories on adaptive quasi-structured grids are developed. Special attention is given to calculations near curvilinear boundaries in order to avoid fatal errors that lead to the beam settling on the walls of the simulated device. For this purpose, special approximating functions are proposed, which are constructed at the boundary and near-boundary grid nodes based on the least squares method. Frequent cases are considered when constant values of the potential or its normal derivative are set on boundary segments, for which the developed approach, as shown by the results of numerical experiments, significantly increases the accuracy of calculations.