This is the author's final draft of the paper presented at the 4th International Conference on Electric Charge in Solid Insulators (CSC4), 2-6 July 2001 and published in pp. 170-177 of the Proceedings. The final version may be available from http://www.vide.org/.Electrical trees are branched damage structures produced in polymeric insulation subject to high divergent fields. The density of branching ranges from a sparse form like a tree in winter to a dense compact form like a bush. This variation in form is significant as the bush structure occurs at higher voltages but grows slower. We present here a deterministic model for the formation of electrical trees based on damage produced by charges injected into the polymer from discharges taking place within the gas-filled tubules of the tree. A number of processes within the mechanism cause the space charge fields to fluctuate chaotically, and this is held to be responsible for the branching that is observed. Different tree shapes are found depending on whether or not injected/extracted charges reach a kinetic energy high enough for damage only at a few tree tips or everywhere around the tree periphery
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