Finite-element analysis of corona discharge onset in air with artificial diffusion scheme and under Fowler-Nordheim electron emission

A complete finite-element analysis method for corona discharge process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into second order by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite-element formulation which is well-developed for second-order equations. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2-D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 μm. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the finite-element method, finer meshes, a higher-order shape function, and artificial diffusion scheme were employed.