Abstract

Abstract of report at 1998 IEEE International Symposium on Electrical Insulation, 7-10 June 1998, Washington, DC, USA. Full text of presentation.

Models of Streamers Growth with "Physical" Time and Fractal Characteristics of Streamer Structures

D. I. Karpov, A. L. Kupershtokh

The results of computer simulation of the streamer growth in three-dimensional space are presented. Six models with "physical" time have been examined. Various growth criteria and different methods of including the "physical" time into the models are discussed.

The streamer propagation is considered as step by step formation of conductive phase elements in dielectrics. The streamer shape is represented by a connected graph consisting of conductive bonds. The generation of new bonds obeys simple stochastic rules in each time step. The probability of streamer structure growth is proportional to the function of local electric field   r(E).  The electric field potential is obtained by solving the Poisson equation. Charge transport along the streamer branches is calculated according to Ohm's law for each conductive element.

An implicit finite difference method for solving the system of equation for the graph was developed. The continuity equation for charge transport is taken into account to ensure the charge conservation.

The models considered can be divided into two groups. The first group consists of models in which only one new bond is added in a time step. The second allows generation of several bonds per time step. The first group includes the Biller model [1], the algorithm proposed in [2], the scale stochastic time model [3] and some its modifications. The fluctuation model [4] and the new modification of the Biller model proposed in the present work belong to the second group.

A great number of numerical experiments was carried out for different magnitude of voltage. Two types of streamer shape were obtained in simulation, namely, bush- and tree-like streamers. The differential fractal dimension of streamer structures was used to compare the results obtained within the framework of the above-mentioned models. The maximum streamer length, the total charge of the streamer structure, and the maximum electric field in front of the streamer tips were computed.

The fluctuation model and the model proposed by Biller were shown to be essentially equivalent provided that the function   r(E)  is the same. These models give the results qualitatively similar to the well-known experimental data on nanosecond dielectric breakdown in liquids in a strongly divergent field.

This work was supported in part by the Russian Foundation for Basic Research under grant No. 97-02-18416.

References

  1. Biller P., Fractal streamer models with physical time. // Proc. of the 11th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, pp. 199--203, 1993.
  2. Lopatin V.V., Noskov M.D., Kukhta V.R., Fractal description of discharge propagation in liquid. // Proc. of the 11th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, pp. 204--208, 1993.
  3. Kupershtokh A.L., Propagation of Streamer Top between Electrodes for Fluctuation Model of Liquid Dielectric Breakdown. // Proc. of the 12th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Roma, Italy, pp. 210--213, 1996.
  4. Ershov A.P., Kupershtokh A.L., Fluctuation Model of Liquid Dielectric Breakdown with Incomplete Charge Relaxation. // Proc. of the 11th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, pp. 194--198, 1993.
Full text of presentation.

Explosion Physics Laboratory or to A.L.Kupershtokh