The propagation of breakdown waves in a gas, which is primarily driven by electron gas pressure, is described by a one-dimensional, steady-state, three-component (electrons, ions, and neutral particles) fluid model. We consider the electron gas partial pressure to be much larger than that of the other species and the waves to have a shock front. Our set of equations consists of the equations of conservation of the flux of mass, momentum, and energy coupled with Poisson’s equation. This set of equations is referred to as the electron fluid dynamical equations. In this study we are considering breakdown waves propagating in the opposite direction of the electric field force on electrons (return stroke in lightning) and moving into a neutral medium. For Breakdown waves with a significant current behind the shock front, the set of electron fluid dynamical equations and also the boundary condition on electron temperature need to be modified. For a range of experimentally observed current values and also some larger current values which few experimentalists have been able to observe, we have been able to solve the set of electron fluid dynamical equations through the dynamical transition region of the wave. Some experimentalists have reported the existence of a relationship between return stroke lightning wave speed and current behind the shock front; however, some others are skeptical of the existence of such a relationship. Our solutions to the set of electron fluid dynamical equations within the dynamical transition region of the wave confirm the existence of such a relationship. We will present the method of solution of the set of electron fluid dynamical equations through the dynamical transition region of the wave and also the wave profile for electric field, electron velocity, electron temperature and electron number density, within the dynamical transition region of the wave.
Newberry, H. D.; Hemmati, M.; Moore, H. D.; Ledbetter, K.; and Bowman, M. W.
"Electron Shock Waves with a Large Current Behind the Shock Front,"
Journal of the Arkansas Academy of Science: Vol. 70
, Article 29.
Available at: https://scholarworks.uark.edu/jaas/vol70/iss1/29