A numerical model for the electrical breakdown of air within a gap under standard atmospheric conditions: one-dimensional versus two-dimensional approach

A numerical model which simulates the electrical breakdown of air between parallel-plates at atmospheric pressure is presented in this paper. The modelling techniques and results are compared using a one-dimensional and two-dimensional axisymmetrical approach. Hydrodynamic drift-diffusion equations are coupled with the Poison equation and solved for the transportation of electrons, positive ions and negative ions in an electric field. A negative DC voltage is applied to the cathode at various gap separation distances and the voltage is increased until sparking occurs. Sparking voltage to separation distance characteristic curves are derived and compared to the Paschen curve. Calculations are made for the external discharge current for varying separation gaps. A characteristic curve of current versus voltage is evaluated against typical curves found in the literature. The discharge regime regions leading to a Townsend discharge are identified from the numerical simulations.