The Plasma Nature of Lightning Channels and the Resulting Nonlinear Resistance

Abstract

Lightning channels are made of plasma. As a consequence, the driving electrical current changes the channel's resistance in a nonlinear fashion. The resistance has an intricate dependence on the history of Joule heating and various cooling processes, as well as on the various kinetic processes that dictate the population balance of electrons within the channel. Such dependence cannot be captured by an analytic function, as often attempted. In this paper, we introduce a minimal numerical model that can qualitatively capture the temporal dynamics of the key plasma properties of a lightning channel, including its electric field, temperature, plasma density, radius, and the resulting nonlinear resistance. Through a series of novel parameterizations, we introduce six zero-dimensional equations that can capture both nonequilibrium/low-temperature and local thermodynamic equilibrium/high-temperature plasma regimes. In this manuscript, we go to great lengths to validate the model, showing that it can reproduce the finite time scale of streamer-to-leader transition, replicate the negative differential resistance behavior of steady-state plasma arcs, and properly describe the temporal evolution of temperature in a return stroke channel. Finally, the model is applied to the simulation of optical emissions from rocket-triggered lightning strikes, explaining the measured delay between the rise of current and visible light, as well as reproducing the direct relationship between peak current and peak radiated power and between charge transferred to ground and total radiated energy.