Analytical and numerical computation of the electric field of a hyperboloid-plane geometry with and without space charges

In the important context of dielectric aging and space charges in dielectrics the computation of the local electric field of electrode geometries is of big significance. Therefore, a computation method for the electric field of hyperboloid-plane electrode setups with and without space charges is described in this paper. In absence of space charges the electric field can be calculated analytically. In case of space charges there is no such analytical solution. Therefore, a more general, numerical approach based on the method of the finite differences is proposed. Furthermore, some experimental examinations on this electrode configuration are presented.