Modeling relativistic electron beams with finite-element ray-tracing codes

Ray-tracing codes determine self-consistent electric fields in high-current electron devices by an iterative procedure of orbit tracking and space-charge deposition with field recalculation. Methods to find beam-generated magnetic fields for relativistic beams are less standardized. Existing approaches (like ray counting or the relativistic transverse force approximation) have limited accuracy and do not include effects of current flow in source and collector electrodes. We describe a new method for two-dimensional finite-element codes where the beam current is deposited on the faces of the conformal elements of the electrostatic mesh. The resulting balanced calculations of electric and magnetic forces are resistant to numerical filamentation instabilities. With simple rules it is possible to assign boundary currents even in complex structures