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 m 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 m 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. KEYWORDS Langmuir probe, PIC/MC simulation INTRODUCTIONParticle-in-cell/Monte Carlo (PIC/MC) simulation provides the most accurate and reliable tool for the calculation of electron and ion currents to a Langmuir (electrostatic) probe. The calculation of probe currents (probe theory) is necessary for the determination of electron and ion densities, electron temperatures, and electron energy distribution functions from probe measurements. Most of the analytical calculations of probe currents have been carried out under the assumption of a collisionless movement of charged particles around the probe [1] and can, therefore, be applied without error only to low-pressure plasmas.There is no widely accepted theory of probe currents for medium-pressure and high-pressure plasmas where the charged particles do collide with neutral particles in the sheath and presheath around the probe. Therefore, the probe measurements cannot be used for such plasmas. There exist three groups of collisional probe theories.

PIC/MC calculation of current–voltage characteristic of emissive probe

“…Only elastic collisions were taken into account for electron-helium atom collisions, elastic and charge transfer collisions were taken into account for helium ion-helium atom collisions. The cross sections for these collisions are given in our previous paper [17]. The ionization electron-helium collisions were not considered, because only a negligibly small fraction of electrons with an electron temperature of 10 4 K or lower has energy higher than the helium ionization energy (24.59 eV).…”

“…In this case, a particle in the cell/Monte Carlo (PIC/MC) model of plasma around the emissive probe can provide the most correct description of this situation. The PIC/MC model was already successfully used for the calculation of probe currents to spherical and cylindrical probes [16,17]. The influence of collisions between charged and neutral particles on probe currents was studied in these works and the limits of orbital motion limited current (OMLC) theory were also found.…”

Accelerated Steady-State Electrostatic Particle-in-Cell Simulation of Langmuir Probes

“…Moreover, many non-ideal conditions defeat analytical and non-kinetic computational approaches. For example, collisions can significantly affect ion current to Langmuir probes (e.g., Schulz & Brown 1955;Sternovsky & Robertson 2002;Sternovsky et al 2003;Sudit & Woods 1994;Zakrzewski & Kopiczynski 1974), and a number of studies have used PIC codes with Monte Carlo collision capabilities to study this, using 1D cylindrical or spherical models (with 3D velocities) and a Boltzmann electron distribution (Taccogna et al 2004;Tejero-del-Caz et al 2016;Voloshin et al 2015) or fully kinetic electrons (Cenian et al 2005;Iza & Lee 2006;Soberón 2006;Trunec et al 2015;Zikán et al 2019), including surface effects such as secondary electron emission (Cenian et al 2014). PIC has been critical in simulating Langmuir probes with asymmetric 3D geometries (Chiaretta 2011;Hilgers et al 2008;Hruby & Hrach 2010;Imtiaz et al 2013;Podolník et al 2018;Séran et al 2005), and has been used for probe and sheath analysis in the presence of magnetic fields (Bergmann 2002;Podolník et al 2018).…”

Influence of different particle injection methods on plasma sheath with strong production of negative ion in one-dimensional PIC simulation

“…PIC simulation of one-dimensional plasma-wall sheath formation is taken as an example. Particle production and emission on walls are discussed in [4,5], and Monte Carlo collision (MCC) method [6] is generally used in PIC simulation. In this paper, MCC and strong surface production of negative ion are taken into consideration, and PIC simulation program Nix-M [7] developed by the authors is used to compare and analyse the influence of different particle injection methods, and the advantages and disadvantages are discussed.…”