An Electrostatic Approach to the Numerical Simulation of Combined Corona and Electrostatic Field in Three-Electrode System

Numerical Analysis of Electric Field in Three-Electrode Corona System Containing Ionized and Non-Ionized Areas

“…Separatrix is a line denoting the geometric place of points where the imaginary part of complex potential v(x, y) is equal to 0. An equation of separatrix dividing the field into two areas: an area occupied by an electric flux related to electrodes u1 and u2 and an area with the flux between electrodes u1 and u3 is derived in [9]. The field in the first area is strongly inhomogeneous, and the field between electrodes u1 and u3 is quasi-homogeneous.…”

“…where E is electric field strength, J is current density,  is space charge density, u is potential,  is permittivity, and k is ion mobility. We use [9] the system (11) reduced to the Poisson's and charge conservation equations as in [2], [4]:…”

“…Coordinates of separatrix points are being computed in the Stage 4, and their potentials are determined in the Stage 5. Boundary conditions for the points of separatrix are described in details in [15]. Initial conditions for the Laplacean field in polar coordinates are established in Stage 6, Stages 7 and 8 are the solution of Poisson equation.…”

“…Equation of separatrix, dividing the field of the system into two areas: the area occupied by electric flux directed from the corona wire to the one of plane electrodes and the area of the flux between plane electrodes was constructed in [8]. Parameters of corona field electrometer [9] are determined as a result of field computation by use the Deutsch´s assumption: vector of the corona field strength differs in magnitude from the strength of Laplacean field, but their directions coincide [10], [11].…”