Electrical tree structures generated by the ab-initio discharge-avalanche model

Initially the discharge-avalanche model for electrical tree formation treated the local Poisson fields as being derived from the applied Laplace field via a modification factor that was regarded as a random variable in time and space. Recently we have removed this approximation by calculating the local Poisson fields from the space charge arrangement produced by discharges in the tree tubules and avalanches in the surrounding polymer. This “ab-initio” version of the model has now been fully implemented. The ac-cycle is divided into 16 time segments. In each time segment tube-discharges are allowed to occur if the potential difference along a tube is greater than an onset threshold. Positive space charge is regarded as being deposited on the tube walls in the form of positive ions. Negative charge is allowed to penetrate the polymer where it can be used to initiate avalanches and thereby generate damage. The avalanches compete with a field dependant mobility in rearranging the charge around the tree tips.