Numerical simulation of positive streamer propagation in cyclohexane

A numerical 3D simulation of positive streamer propagation in a liquid, using cyclohexane as a reference case, in a needle-plane geometry is presented. The physical basis of this model is a version of the Townsend-Meek streamer criteria, known from gas discharges, adapted to a liquid containing an additive. The propagation of the streamer is modelled in the following way: Electrons located in an electric field above a given threshold (liquid dependent) create electron avalanches in the liquid. The electron avalanches leave behind positive ions that will move the high field region further into the liquid due to the field created by the high charge concentration. Subsequent avalanches in the liquid neutralize this region, but create a new highly ionized region, thus the ionization region (streamer head) moves further away from the needle, while still being connected to the needle by a weakly conducting plasma channel. The stochastic nature of streamer inception, propagation and branching is modeled through a random distribution of seed electrons in the liquid. Key results obtainable from the model includes streamer shape/degree of branching, speed (instantaneous and average), and inception delay of positive streamers as a function of applied voltage. The presented model is crude as it does not take into account the energy required for phase transition, and the dynamics of the plasma channel trailing the streamer head. In addition it is based on a rough estimate of the field in the liquid. This paper presents the model in detail.