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

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 (such as oxygen) and recombination-dominated gases (such as chlorine) are examined. It is concluded that it is valid to use a Boltzmann relation n(e) = n(e0)exp(eV/kT) for the electrons of density n(e), where the temperature T is approximately the electron temperature T-e, and that the density n(n) of the negative ions at low pressures obeys n(n) = n(n0)exp(eV/kT(n)), where T-n 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 sim-pie relationship. Thus to put n(n)/n(e) = const, n(n) = n(e0)exp(eV/kT(e)) and n(n) = n(n0) exp(eV/kT(n)) simultaneously is mathematically inconsistent and physically unsound. Accordingly, expressions deduced for a ambipolar diffusion coefficients based on these assumptions have no validity. The correct expressions for the situation where n(n)/n(e) = const are obtained without invoking a Boltzmann relation for the negative ions.