Exact solutions to stationary relativistic electron beam equations and the problem of testing programs of track analysis

Exact two-dimensional solutions to stationary relativistic electron beam equations while accounting for the intrinsic magnetic field of the beam are studied. These solutions define beams starting from an equipotential half-plane or a spiral cylinder with planar and three-dimensional (under nonzero external magnetic field) tracks when the emission current has a nonuniform density. For planar currents, the solution to the external boundary problem is derived and includes the solution for a high-compression stream from a spiral cylinder. The applicability of these solutions to the testing of track-analysis programs is examined. The task of incorporating exact solution data into the testing of programs is discussed.