Ion injection in electrostatic particle-in-cell simulations of the ion sheath

•An ion injection algorithm is proposed for PIC simulations of ion sheaths.•The goal of the algorithm was to avoid the appearance of “source sheaths”.•It self consistently obtain the drift velocity that ions acquire in the presheath.•Validation and verification of the algorithm has been carried out.•The algorithm has a huge impact in the correct prediction of ion current.

A particle injection algorithm has been developed for its use in electrostatic particle-in-cell (PIC) simulations of the ion sheath which takes place in the surroundings of a planar electrode immersed in a plasma when negatively biased. The algorithm takes into account the acceleration of ions along the presheath and evaluates their flux and velocity distribution when entering the simulation at the sheath edge. It has been verified by comparing the results obtained from the PIC simulation with those provided by fluid models of the ion sheath. The algorithm can be easily extended to cylindrical or spherical geometries and, in fact, it has already been successfully used to study the transition from radial to orbital behaviour of ions in the surroundings of cylindrical Langmuir probes.