The pre-breakdown characteristics of weakly ionized media in the high non-uniform electric field

The theoretical model of pre-breakdown ions formation in a liquid dielectric and their flows, caused by high non-uniform electric field is represented. The 3D system of macroscopic pre-breakdown electrohydrodynamic equations is written. The electric field influence on the molecule dissociation rate is taken into account. The system are included the Poison equation for electric field potential, equation of ions formation and Navier-Stokes equations with electric force The our up-steady analytical electrodynamic solution of these equations for potential of electric field distribution at spherical high voltage capacitor with liquid transformer oil type dielectric is described deviations from Ohms law, observed in many experiments. The analytical non-stationary solution for velocities distributions calculations of considerable liquid dielectric flows are obtained. The theoretical and experimental micro-breakdown radius zone dependences on applied voltage at air corona discharge are obtained for edge high voltage electrode.