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 $\left(E_{loc}\right)$ around the Laplacian field $\left(E_{lap}\right)$ 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.

• Received 12 April 2010

DOI:https://doi.org/10.1103/PhysRevE.82.041106