On the calculation of axially-symmetric electrostatic fields in the space-charge regions

The electrostatic field potential in the space-charge region is found as a solution to the Dirichlet problem for the axially-symmetric Poisson equation. The problem is solved by the collocation method for the respective integral boundary equation. The contribution of the space-charge cloud to the potential at each point of the space is defined as the sum of contributions from the square grid cells computed by taking respective integrals wherein the space-charge density function is interpolated by a bilinear distribution.