Lightning optimizes: a threshold mechanism ensures minimum-path flow

TL;DR

This paper investigates how lightning-like discharges follow a minimum path to ground by modeling nonlinear resistive networks with threshold characteristics, explaining the transient plasma branching behavior.

Contribution

It introduces a threshold-based model for nonlinear resistive networks that captures lightning discharge paths and transient plasma branching phenomena.

Findings

Lightning discharges follow a minimum path to ground.

The proposed model reproduces plasma branch formation and elimination.

Discharges optimize their path based on threshold-like nonlinear resistances.

Abstract

A well-known property of linear resistive electrical networks is that the current distribution minimizes the total dissipated energy. When the circuit includes resistors with nonlinear monotonic characteristic, the current distribution minimizes in general a different functional. We show that, if the nonlinear characteristic is a threshold-like function and the energy generator is concentrated in a single point, as in the case of lightning or dielectric discharge, then the current flow is concentrated along a single path, which is a minimum path to the ground with respect to the threshold. We also propose a dynamic model that explains and qualitatively reproduces the lightning transient behaviour: initial generation of several plasma branches and subsequent dismissal of all branches but the one reaching the ground first, which is the optimal one.