For analytical solution of breakdown waves with a large current behind the wave front, we employ a one-dimensional, steady-state, three-component (electrons, ions, and neutral particles) fluid model. This project involves breakdown waves propagating in the opposite direction of the electric field force on electrons, anti-force waves (return stroke in lightning); and the electron gas partial pressure is considered to provide the driving force for the propagation of the wave. The basic set of equations consists of the equation of conservation of mass flux, equation of conservation of momentum, equation of conservation of energy, plus Poisson’s equation. The waves are considered to have a shock front. In this study, we examine the possibility and validity of large currents measured and reported by few investigators. Existence of a relationship between wave speed and peak current values is investigated as well.

Existence of a large current behind the wave front alters the equation of conservation of energy and Poisson’s equation, as well as the shock boundary condition on electron temperature. Considering a current behind the shock front, we have made appropriate modifications in our set of electron fluid dynamical equations. Using the modified set of equations and the shock condition on electron temperature, we have been able to integrate the set of electron fluid dynamical equations for current bearing anti-force waves. For a range of wave speeds and with the largest current possible for a specific wave speed, we present the wave profile for electric field, electron velocity, and the ionization rate within the dynamical transition region of the wave for anti-force waves.