A deterministic model for branched structures in the electrical breakdown of solid polymeric dielectrics

We present a completely deterministic model for the electrical-tree breakdown mechanism in solids, and show that it is capable of generating branched structures even when the polymer is assumed to be homogeneous. The model is non-linear in the local electric fields and contains feedback features. These generate deterministic chaos in the discharges driving the breakdown, such as have been observed in laboratory experiments. It is surmised that it is this chaotic behaviour which is responsible for the branching.