A quantitative physical model is presented for the breakdown of solids by void or channel discharges. It is found that fractal treelike structures only occur when the ‘‘fields’’ at the growth tips are allowed to fluctuate about their Laplace values. By treating the local-field enhancement factor as a white noise produced by the breakdown mechanism itself, it is shown that the amount of branching depends only on the range of fluctuations allowed.

• Received 2 August 1993

DOI:https://doi.org/10.1103/PhysRevB.48.16261