Fractal multiplication of electron avalanches and streamers: new mechanism of electrical breakdown?

Abstract

Long-lasting problems concerning peculiar statistical behaviour of high populated electron avalanches have been analysed. These avalanches are precursors of streamer breakdown in gases. The present streamer theory fails in explaining severe systematic deviations from the Furry statistics that is believed to be a governing statistical law. Such a deviated behaviour of high populated avalanches seems to be a consequence of a special pre-breakdown mechanism that is rather different from that known so far in discharge physics. This analysis tends towards formulating a modified theoretical concept supplementing the streamer theory by a new statistical view of pre-streamer states. The correctness of the concept is corroborated by a series of experiments.

Electron Avalanche Statistics

“…The Pareto statistics is a "typical fractal" statistics since it governs statistical features of all self-similar fractals with dimension D. This fact was taken into account when formulating the scenario of fractal avalanche multiplication [11]. The multiplication counts on displaced smaller avalanches that accompany big parent avalanches.…”

“…The mentioned anomaly consists in systematic deviations [1,4,5] from the Furry/exponential distribution [6,7], w(n) = 1/ n [1 − 1/ n ] n−1 ≈ 1/ n exp(−n/ n ), which has been considered as a general statistical law holding for all avalanches regardless of their size. Experimental evidence based on different testing methods [8][9][10][11][12][13] has identified the Pareto probability density function w(n) = const · n −(1+D) as a reliable distribution of high populated avalanches. However, this result would imply the existence of two independent statistics (Furry's and Pareto's) governing simultaneously one group of identical objects but such a dual concept is hardly acceptable.…”

“…So far the anomalous statistics of big avalanches have been considered as experimental artifact [1]. Experimental evidence employing various experimental techniques [8][9][10][11] has shown that this is not the case and that the phenomenon has a real physical background. Our derivation of the generalized statistical distribution demonstrates how a special superposition of elementary functions may generate a new functional form showing perfect power law behavior, which is characteristic for fractal phenomena.…”