The Boltzmann relation in electronegative plasmas: When is it permissible to use it?

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Abstract
This paper reports the results of computations to obtain the spatial distributions of the charged particles in a bounded active plasma dominated by negative ions. Using the fluid model with a constant collision frequency for electrons, positive ions and negative ions the cases of both detachment-dominated gases (such as oxygen) and recombination-dominated gases (such as chlorine) are examined. It is concluded that it is valid to use a Boltzmann relation ne = ne0exp(eV/kT) for the electrons of density ne, where the temperature T is approximately the electron temperature Te, and that the density nn of the negative ions at low pressures obeys nn = nn0exp(eV/kTn), where Tn is the negative-ion temperature. However, at high pressure in detachment-dominated gases where the ratio of negative-ion density to electron density is constant and greater than unity, and when the attachment rate is larger than the ionization rate, the negative ions are distributed with the same effective temperature as the electrons. In all other cases there is no simple relationship. Thus to put nn/ne = const, nn = ne0exp(eV/kTe) and nn = nn0exp(eV/kTn) simultaneously is mathematically inconsistent and physically unsound. Accordingly, expressions deduced for ambipolar diffusion coefficients based on these assumptions have no validity. The correct expressions for the situation where nn/ne = const are obtained without invoking a Boltzmann relation for the negative ions.

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