The electron gas in electric discharge can be described by a set of one-dimensional fluid dynamical equations. The fundamental equations are those of a three-component (electrons, ions, and neutral particles) fluid, different from the treatment of the problem inplasma physics, a fully ionized two-component case. The leading edge of the wave is treated as a shock front driven mainly by the electron gas pressure. Integrating the one-dimensional global differential equations for mass balance, conservation of momentum and energy, and evaluating the constant of integration at the wave front permits derivation of boundary conditions on electron temperature and electron velocity. Using the boundary conditions on electron temperature and electron velocity we have been able to calculate the initial boundary condition on energy terms due to the electron random and directed motions. Using the initial boundary conditions we have been able to integrate the set of electron fluid dynamical equations through the dynamical transition region of the wave. We will present the derivation of the boundary conditions as well as the wave profile for the electric field, electron velocity, electron temperature, electron number density, and ionization rate within the dynamical transition region of the wave for a fast moving wave.
Hemmati, Mostafa and Justice, Chris
"Electric Discharge: Boundary Conditions,"
Journal of the Arkansas Academy of Science: Vol. 58
, Article 12.
Available at: https://scholarworks.uark.edu/jaas/vol58/iss1/12