A critique of methods for calculating the dielectric strength of gas mixtures

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Abstract
Three currently available methods for predicting the dielectric strength of gas mixtures are discussed and compared. All are based on the common principle of linear addition of some property of the individual gases in proportion to their concentration in the mixture. The simplest approach uses a weighted sum of the dielectric strengths of the separate gases. The other approaches are based on predicting the limiting reduced field (E/N)*m at which the net ionization coefficient of the mixture (ᾱ/N)m = 0. Wieland’s approximation for ᾱm involves a weighted sum of the ᾱ’s for the separate gases, and requires a knowledge of these over the range (E/N)*w<(E/N)<(E/N)*s, where w and s refer to the weakest and strongest gas involved. It is shown that this approach in general gives a mixture strength which varies monotonically with the fractional concentrations and lies within the above range of E/N. The simplest approach, using weighted linear addition of strengths, and the empirical rule proposed earlier by Takuma et al., are shown to be special cases of the Wieland approximation. The third and most physically realistic approach uses linear proportional addition of all the relevant electron-molecule collision cross sections of the component gases. It requires a knowledge of the electron energy distribution in the mixture, which can be obtained by numerical solution of the Boltzmann equation. In some mixtures the presence of special ’’mixture processes’’, such as Penning ionization, can be anticipated and included in this third approach. The underlying assumption in the Wieland approximation is examined in the framework of the more exact formalism, and the overall hierarchy of approximations involved in the various approaches is identified. The concept of η̄ synergism is introduced as a suitable indicator of the presence of interesting mixture effects contributing to the mixture’s dielectric strength. Comparison of the Wieland formula predictions with experimental data, or the results of more exact calculations, provides an appropriate test for η̄ synergism.