Modeling of electrical field modified by injected space charge

Abstract

This paper presents the numerical solution of the coupled Poisson equation and charge conservation equation. We present an algorithm to obtain the distributions of electric field and charge density resulting from a corona discharge in the two-dimensional hyperbolic blade-ground plate configuration. We use finite elements method (FEM) to determine the potential distribution, finite volume method (FVM) and method of characteristics (MOC) to determine the distribution of charge density. The structured mesh is redefined at each iteration step to decrease artificial numerical diffusion. For solving the conservation equation, MOC with redefinition of structured mesh appears to be the best technique.

Numerical Solution and Experimental Test for Corona Discharge Between Blade and Plate

“…1, with the blade radius of curvature being small compared with the distance between blade and plate. The two coupled equations, Poisson (1) and charge conservation (2), governing the electrical potential and the charge density of the injected ionic species in the drift zone, are in nondimensional form [2], [3] (1) (2) The expression of the dimensional current density (A/m ) is , where denotes the medium permittivity (F/m), the ions diffusion constant (m /s), the electrical field (V/m), the medium conductivity (S/m), the mobility of charge carriers (m /V.s) and the velocity field of the medium (m/s). In gases, the medium conductivity is zero and the diffusion and convection currents are negligible compared with the drift current.…”

“…In gases, the medium conductivity is zero and the diffusion and convection currents are negligible compared with the drift current. After some simple derivation, we deduce the following nondimensional form for (2) [2], [3]:…”

“…Using the finite volume method (FVM) to solve (3) and obtain the charge density between the two electrodes, introduces the difficulty of a local minimum appearing in the current density at the axis of symmetry [2]. The charge (3) is solved here by using the method of characteristics (MOC) which is a good method for hyperbolic equations.…”

“…With such a law, it is possible to determine the potential and the charge density numerically. In this paper, the numerical solutions obtained by the technique described in [2] and [3] are compared with the experimental ones.…”

FE Analysis of Plasma Discharge and Sheath Characterization in Dry Etching Reactor

“…The most frequently used algorithms are the hydrodynamic diffusion-drift model incorporating flux-corrected-transport (FCT) method and particle-in-cell (PIC) method [2][3][4][5][6]. In this paper, we proposed a full finite element approach where the charge transport equations of hydrodynamic diffusion-drift model and the electric field equation were numerically solved in a fully coupled system by using a standard finite element procedure for transient analysis [7][8][9][10][11]. Numerical technique for the hydrodynamic diffusiondrift modeling using charge transport equations is used in various applications such as corona discharge, heat transfer and cooling effect of heavy electric machines [12][13][14].…”