Analysis of a low-pressure mercury rare-gas positive column with a dynamic two-temperature representation of electron energy

A method for analyzing the dynamic behavior of a low-pressure mercury rare-gas positive column is presented. An eight-state scheme analysis for mercury and argon mixture under a non-Maxwell distribution of electron energy is established. The computing time is shortened by using the two-temperature model for electron energy distribution which I have developed to give an analytical expression for the non-Maxwellian distribution. Two-temperature parameters Tt and Tb for the tail and bulk temperature, respectively, are determined from a two-term Legendre polynomial expansion of the Boltzmann equation. Then a useful empirical result is that the ratio rT=Tt/Tb is a function of a single variable of electron density times electric field strength. By storing rT calculated as a function of this variable, the electron energy distribution, which should be calculated from the Boltzmann equation at each iteration step of solving the rate equations, is found simply by a table-looking-up procedure, whereby the computing time is shortened. The examination of the eight-state scheme is done by comparing calculated and experimental results, discussing physical processes occurring among the eight states.