Rate of charging of spherical particles by monopolar ions in electric fields

This paper presents a numerical algorithm to simulate the charging dynamics of high-resistivity spherical particles by the ionic bombardment in an electric field. The algorithm is based on solving the Poisson equation, governing the electric field distribution, and the differential equation expressing the charge conservation law. The Poisson equation is solved be means of the finite-element method using the triangular discretization and the first of interpolation. The finite-volume method (in a version called the donor-cell method) is used to handle the charge conservation equation. Results of simulation are also presented and they illustrate the effect of different parameters on the charging dynamics. For high-conductivity particles, the charging rate is practically identical to that given by the Pauthernier formula. Charging of high-resistivity particles leads to more complicated solutions and is much slower.