S. I. Shevchenko
Institute for Analytical Instrumentation RAS, Saint-Petersburg
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.