Simulation of unipolar space charge controlled electric fields

A model is discussed, which allows in an easy way to perform electric field simulations in unipolar space charge controlled dielectric media with the finite element method. The approach is appropriate for a variety of different devices in electrical engineering, containing solid, liquid, or gaseous insulators. The main issue concerns the boundary condition at the charge injecting contacts, including ohmic contacts (leading to space charge limited currents) as well as contacts with a finite threshold field for injection (e.g., by Corona onset in gas). The model naturally contains the high-current limit, where the current is injection dominated, i.e., given by the saturation current of the contact, and the capacitive field is restored.Results for a few examples are presented, in order to validate the method by comparison with analytical results, and in order to illustrate its usefulness for applications. In particular, for gaseous insulation various steady state and transient field distributions are calculated. With this approach it is easily possible to investigate the effect of convective currents as well as the charging of dielectrics surfaces.