Nonequilibrium positive column

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Abstract
The dc positive column is modeled with a system of balance equations based on moments of the radially dependent Boltzmann equation taken after the two-term Legendre expansion of the electron energy distribution function is made. The importance of the electron energy balance equation, which is frequently ignored in positive column analysis, is emphasized. A key assumption is that electron transport coefficients and collision frequencies in the nonequilibrium regime have the same relation to the average energy as in the equilibrium regime, according to a zero-dimensional Boltzmann solution for a particular value of average energy. Because of this assumption, the model makes a smooth transition to the traditional equilibrium model with radially constant average energy at sufficiently high pressure. Model results in the nonequilibrium regime agree closely with published results of a numerical solution of the one-dimensional Boltzmann equation, including results for radial heat flow in the electron gas with radially varying average energy. It is shown that three separate processes account for radial heat flow: convection, conduction, and diffusion. In the example chosen for illustration of the method, the convection component is small, while the conduction and diffusion components are large and opposite in direction, nearly canceling each other.