Problems of increasing the accuracy of programs for trajectory analysis of high-intense electron beams

The problems of increasing the accuracy during the numerical solution of the boundary-value problem for the system of nonlinear equations in partial derivatives describing a high-intense electron beam in the hydrodynamic approximation, when a part of a calculation area boundary is a special surface are discussed. On the base of an antiparaxial theory a new model of cathode vicinity is developed. It is valid at distances comparable with its curvature radius. For considerably different-scale flows the curvilinear orthogonal nets uniformly covering the area studied are introduced