Determining the Degree of Separation for Multiple Fractal Discharge Breakdowns in Dielectric Media Under Various Charge Distributions

Authors

  • Uzair Faruqui McMaster University

Abstract

This paper assesses the charge separation and intermingling from a double-discharge dielectric breakdown. Simulations of breakdowns are performed using the discrete Poisson's equation  under various specified charge distributions. The degree of separation between the two breakdown paths is assessed and  a measure of energy potentially storable in the system was calculated in relation to a baseline energy of simple dielectric storage. Some of the simulations showed energies that were more than 5 times the baseline energy. The effects of different charge distributions are noted, and compared to each other and the different properties of multiple discharge are discussed.

References

Niemeyer, L & Pietronero, Luciano & J. Wiesmann, H. (1984). "Fractal Dimension of Dielectric Breakdown". Physical Review Letters - PHYS REV LETT. 52. 1033-1036. 10.1103/PhysRevLett.52.1033.

P. P. Budenstein, "On the Mechanism of Dielectric Breakdown of Solids," in IEEE Transactions on Electrical Insulation, vol. EI-15, no. 3, pp. 225-240, June 1980.

Avdiaj, Sefer & Šetina, Janez. (2010). "Numerical Solving of Poisson Equation in 3D Using Finite Difference Method". Journal of Engineering and Applied Sciences. 5. 14-18. 10.3923/jeasci.2010.14.18.

P. P. Budenstein, "Dielectric Breakdown in Solids", PN (1974)

D. J. Griffiths, "Introduction to Electrodynamics", (4th Edition) Pearson 1974

S. Chapra "Numerical Methods for Engineers", (6th Edition) McGraw-Hill (2009)

L. Pietronero, A. Erzan, C. Evertsz, "Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model", In Physica A: Statistical Mechanics and its Applications, Volume 151, Issues 2–3, 1988, Pages 207-245, ISSN 0378-4371, https://doi.org/10.1016/0378-4371(88)90014-3.

(http://www.sciencedirect.com/science/article/pii/0378437188900143)

T. Vicsek "Pattern Formation in Diffusion-Limited Aggregation", Phys. Rev. Lett. 53, 2281 (1984)

T. A. Witten, L. M. Sander "Diffusion-limited aggregation", Phys. Rev. B 27, 5686 (1983)

H. J. Wiesmann and H. R. Zeller "A fractal model of dielectric breakdown and prebreakdown in solid dielectrics", Journal of Applied Physics 60, 1770 (1986)

Published

2018-01-16