Considering the electrons as the main element in breakdown wave propagation and using a one-dimensional, steady-state, three-fluid, hydrodynamical model, previous investigations have resulted in the completion of a set of equations for conservation of mass, momentum, and energy. We will use the terms proforce and antiforce waves, depending on whether the applied electric field force on electrons is with or against the direction of wave propagation. In the case of antiforce waves, the electron gas temperature and therefore the electron fluid pressure is assumed to be large enough to sustain the wave propagation down the discharge tube. For strong discontinuity and based on the conditions existent at the leading edge of the wave, previous investigations have concluded a minimum wave velocity condition for breakdown waves. However, allowing for a temperature derivative discontinuity at the shock front, we have been able to derive a new set of conditions at the shock front and therefore a lower range of electron drift velocity. This conforms with the experimentally observed wave speeds. The solution to the set of electron fluid-dynamical equations involves a previously discovered method of integration of the equations through the sheath (dynamical transition) region. For a wide range of wave speeds, the appropriate set of electron fluid-dynamical equations has been integrated through the sheath region.
Hemmati, Mostafa; George, Eric L.; and Terry, Frances
"Speed Range for Breakdown Waves,"
Journal of the Arkansas Academy of Science: Vol. 53, Article 16.
Available at: https://scholarworks.uark.edu/jaas/vol53/iss1/16