Simulation of spark channel formation for electrical discharge technology

The impulse breakdown of dielectrics is a result of propagation of conducting discharge channels in insulators. The electric field, charge, and energy dynamics within the discharge channels and dielectric material govern the channel growth. In this paper the physical-mathematical model of the discharge channel propagation is presented. The model describes the self-consistent dynamics of temperature, electric field, charge density, and phase transition of the dielectric material to highly conducting state. The discharge channel propagation is associated with the growth of the highly conducting region into the insulator. For computer simulation the model has been realized as a three dimensional numerical algorithm on a cubic lattice. The dynamics of the electric field, charge density, and temperature are calculated on the base of finite-difference approximations of Poisson´s equation, continuity equation, and energy conservation law. The phase transition occurs when the temperature of the dielectric exceeds a critical value. The results of computer simulation of the conducting channel formation in nonhomogeneous dielectrics in needle-plane electrode geometry under DC voltage are presented. The effects of conduction inhomogeneities on the channel propagation are discussed