Testing of geometrized models of 2D electron beams

Geometrized models of a dense electron beam are tested using two sets of references: solutions with multiplicative separation of variables and analytic solutions with additive separation of variables. The effectiveness of the geometrized approach for describing nonparaxial flows with the nonuniform distribution of parameters over the cross section is demonstrated. Models are considered in which the length of the base current tube or the potential plays the role of the longitudinal coordinate. The effect of remarking the transverse coordinate, which determines the geometry of the current tube, is studied. The asymptotic theory is compared with the first-approximation geometrized theory. It is shown that each exact axially symmetric solution to the equations of a beam in elementary functions corresponds to the exact solution to the equation for a tubular beam in the asymptotic theory. For optimal utilization of possibilities of the geometrized approach, it is proposed to use the value of discrepancy as a criterion oor accuracy.