Particle‐in‐cell/Monte Carlo simulation of electron and ion currents to cylindrical Langmuir probe

Abstract

Electron and ion currents to a cylindrical Langmuir (electrostatic) probe were calculated using the particle‐in‐cell/Monte Carlo (PIC/MC) self‐consistent simulation for a neutral gas in the pressure range 2–3,000 Pa. The simulation enables us to calculate the probe currents even at high neutral gas pressures when the collisions of collected charged particles with neutral gas particles near the probe are important. The main aim of this paper is the calculation of probe currents at such high gas pressures and the comparison of the results with experimentally measured probe currents. Simulations were performed for two cases: (a) probes with varying radii in a non‐thermal plasma with high electron temperature at low neutral gas pressure of 2 Pa (in order to verify the correctness of our simulations), and (b) probe with the radius of 10 μm in the afterglow plasma with low electron temperature and a higher neutral gas pressure (up to 3,000 Pa). The electron probe currents obtained in case (a) show good agreement with those predicted by the orbital motion limited current (OMLC) theory for probes with radii up to 100 μm for the given plasma conditions. At larger probe radii and/or at higher probe voltages, the OMLC theory incorrectly predicts too high an electron probe current for the plasma parameters studied. Additionally, a formula describing the spatial dependence of the electron density in the presheath in the collisionless case is derived. The simulation at higher neutral gas pressures, i.e. case (b), shows a decrease of the electron probe current with increasing gas pressure and the creation of a large presheath around the probe. The simulated electron probe currents are compared with those of measurements by other authors, and the differences are discussed.