An asymptotic-series solution for the vicinity of emitting surfaces of an axially symmetric bipolar beam

Abstract

A solution in the form of an asymptotic expansion in small parameter is obtained for an electrostatic bipolar beam with the density of the compensating component on the order of unity. The second approximation of this solution is expressed in quadratures. For a planar diode, in the case of the perturbation of the initial solution on the order of with respect to physical and geometric parameters of the flow, the solution is expressed in elementary functions. The boundary value problem of determination of the emission current density in the ρ mode and the electric field in the T mode, which is a necessary element of numerical models for calculation of bipolar beams or beams with bulk processes, is solved.