Field fluctuations and fractality in electrical breakdown trees

In the present paper, the discharge avalanche model, initially proposed by Dissado and co-workers, is modified to explore (by correlating its results with experimental information) the role of the space-charge characteristics in the fractal nature of electric trees. Stochastic fluctuations of the local electrical field in each site of the polymer sample (E(loc)) around the Laplacian field (E(lap)) are allowed and limited to intermediate values of E(lap). The major achievements of the modified model are the prediction of a nonmonotonic behavior in both the average time to failure and the average fractal dimension of the electrical trees, and the prediction of a transition from branched to runaway trees as the applied voltage is increased.