Particle-in-Cell Simulation of Electrical Gas Discharges

A fluid particle-in-cell (PIC) model is proposed for the numerical solution of the continuity equation of electrons and ions in transient electrical gas discharges. The reactions occurring in a gaseous discharge, such as ionization of neutral molecules, electron attachment, and recombination between electrons and ions, are implemented through the variation of the mass of the computational particles used in the simulation. Two different forms of interpolation of the gain/loss rates from the grid to the computational particles are suggested, depending on the reaction type. The PIC model is first applied to the problem of an idealized electron avalanche in a non-attaching gas. This problem possesses an analytical solution where the electron density grows exponentially in time as it propagates, but keeps the square-wave form of the initial electron distribution. This problem is used to validate the optimum interpolation of the gain/loss rate and to analyze the effect of the mass matrix formulation of the PIC model. Then, a more realistic model is applied to simulate the propagation of a Trichel pulse between a sphere and a plate. In this case, the continuity equation for electrons and positive and negative ions, coupled to the Poisson equation, has been solved. This second test has proved the ability of the present numerical method to deal with those discharges dominated by the space charge effect. The results of the PIC simulation are compared with those obtained from the application of a flux-corrected transport method.