Allowance for space charge forces in a trajectory analysis of extended electron beams

A trajectory analysis of axially symmetric electron beams is described, with allowance for space charge forces. The distinctive feature of the algorithm is the use of an additional large grid of the space charge, which significantly simplifies the computation of the field of remote discrete charges. The counting time is also thus made to be linearly dependent on the length of the analyzed region for sufficiently extended beams. The method is applied to the analysis of systems with quasi-laminar helical electron beams.