Tree growth simulation associated with dielectric breakdown

In many dielectric failures the final disruption is preceded by the sporadically progressive development of many minute branched channels(i.e., trees or dendrites), and the ultimate failure follows one of these channels. Trees often exhibit a strong tendency to branch into complicated patterns. Treeing, in general, is a weak-link phenomenon [1]. It has been shown that a simple stochastic model naturally leads to characteristic structures of the discharge pattern [2]. The type of tree dealt with in this paper is the one in which the configuration grows rapidly with a single discharge, and consists of a highly conducting gaseous plasma generated by the rapid dissociation of the solid. Tree growth is simulated by a Monte Carlo method based on a probability field associated with the electric potential, similar to that of Reference 2. Tree growth involves two competing factors, stochastic and deterministic. The patterns developed in the simulation depend upon the size of the lattice (the density of mesh points between two parallel electrode surfaces) and the way that the next growth site is selected from the local electric field and a stochastic algorithm. The tip effect and anisotropy due to lattice size are discussed in detail. The results of simulation give an insight into the mechanism of tree growth associated with dielectric breakdown.