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Abstract

This article will present a fluid dynamical theory for breakdown waves in which the direction of electric field force on electrons is in the opposite direction of wave propagation. We will refer to such waves as antiforce waves. The set of equations describing the model will include the equation of particle mass balance, equation of conservation of momentum, and equation of conservation of energy, coupled with Poisson's equation. This model treats the potential wave front as an electron shock wave propagating forward mainly due to the electron impact ionization. The shock front is succeeded by a thin dynamical transition region (sheath region) in which the electric field reduces to zero and the electron velocity approaches that of heavy particle velocity. Following the sheath region, ionization continues as long as electrons possess sufficient thermal energy. This thermal region is referred to as the quasi-neutral region. For antiforce waves, we have been able to integrate the set of electron fluid dynamical equations through the sheath region and through the quasi-neutral region. Our results conform to the expected physical conditions at the end of the sheath region and at the end of the quasi-neutral region. For three wave propagation velocities we will present the wave profile for each of the following: the electric field as a function of electron velocity inside the sheath, the ionization rate inside the sheath region and the quasi-neutral region, and the electron temperature and number density inside the quasi-neutral region.

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