Theoretical Analysis of Effects of a Monatomic Impurity on Low-Pressure Metal Arc Discharges in a Noble Gas Matrix

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Abstract
The role of impurities in a low-pressure arc is theoretically investigated by use of a system of coupled rate equations. Some of the coefficients may be unknown; it is shown that by measuring a few parameters it is possible to obtain a set of equations at least equal in number to the number of unknown coefficients. The analysis is then particularized to the case when the introduction of the additive results in a perturbation sufficiently small that a linear treatment is applicable. This results in a system of seven linear equations, the left-hand side of which is obtained by adding seven terms, each a product of a known coefficient times perturbation on a certain plasma parameter (population of an excited level, electron density, electric field, etc.) whereas the right-hand side is linear in the pressure of the additive, the coefficient depending upon the characteristic properties of the additive.

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