A new numerical model applied to bipolar charge transport, trapping and recombination under low and high dc voltages

In this paper, we present a new numerical formulation that we have applied to the model for bipolar charge transport, trapping and recombination in polymeric insulators, such as low density polyethylene. The numerical model is based on the high precision Runge-Kutta method for determining mobile and trapped charge local density within the sample, during the application of a dc voltage. In addition, we have applied the finite element method considered as the most general one, which can be applied to any sample shape and boundary conditions. It is applied to resolve Poisson's equation, thus providing the potential and its gradient within the sample and at the dielectric-electrode interfaces. In a first step, the new formulation is validated for the charge dynamic under low dc applied voltage. In a second step, model outputs are analyzed under high dc applied voltage. The appearance of charge packets is revealed for the first time in modelling works although they have long been reported in experimental studies on polyethylene materials. The conditions for the appearance of such packets are discussed