Study of “source sheath” problem in PIC/MC simulation: Spherical geometry

A method for treatment of boundary conditions and particle loading in a self-consistent semi-infinite Particle-In-Cell/Monte Carlo simulation is presented. A non-ionizing, collisional plasma in contact with an electrode was assumed. The simulation was performed for a spherical probe with constant probe potential. The motion of charged particles was calculated in three dimensions, but only the radial charge distribution and thus only radial electric field were assumed. The particle loading has to be done with an appropriate velocity distribution with a radial drift velocity. This drift velocity has to be calculated from the probe current, and therefore, a self-consistent (iterative) approach is necessary. Furthermore, correct values of particle densities and electric field potential at the outer boundary of the computational domain have to be set using asymptotic formulae for particle density and electric field potential. This approach removes the “source sheath” which is created artificially, if incorrect boundary conditions and velocity distributions of loaded particles are used. This approach is, however, feasible only for the case of a negative probe where asymptotic formulae are known.