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Lightning optimizes a threshold mechanism ensures minimum-path flow

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Document pages: 28 pages

Abstract: A well-known property of linear resistive electrical networks is that thecurrent distribution minimizes the total dissipated energy. When the circuitincludes resistors with nonlinear monotonic characteristic, the currentdistribution minimizes in general a different functional. We show that, if thenonlinear characteristic is a threshold-like function and the energy generatoris concentrated in a single point, as in the case of lightning or dielectricdischarge, then the current flow is concentrated along a single path, which isa minimum path to the ground with respect to the threshold. We also propose adynamic model that explains and qualitatively reproduces the lightningtransient behaviour: initial generation of several plasma branches andsubsequent dismissal of all branches but the one reaching the ground first,which is the optimal one.

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