The Positive Column of the Nitrogen Arc at Atmospheric Pressure

Abstract

Extending earlier work by one of ${\mathrm{u}\mathrm{s},}^1$ a theory of the positive column in an arc has been developed, from considerations of energy balance, from which good values of nitrogen arc parameters are calculated from known properties of the gas. The power generation per unit volume is obtained in terms of the potential gradient, the electron mobility and the electron concentration. The electron concentration is computed with the aid of the Saha equation for thermal ionization. The power loss is calculated in terms of a generalized heat conductivity which includes the heat transport that results from the diffusion of dissociated atoms. Convection is neglected, so that the theory applies only to low current arcs in ordinary space or to arcs below 30 amperes in gravity-free space. Equating power generation and power loss leads to a differential equation that can be solved numerically once the center temperature is known. Without solving the equation a change of variable is evident, which shows the potential gradient to be independent of the total power. This gives an arc equation of the Ayrton type. The arc is shown to be free from certain constraints which might otherwise set the center temperature. However, the center temperature is determined by introducing the additional consideration that the arc operates to make the power loss a maximum. The agreement with experiment is satisfactory. The inclusion of convection in a more complete theory is discussed, and it can be asserted that departure from the above simplified theory, for arcs of larger currents, is qualitatively of the type to be expected from the influence of convection. These results supply convincing evidence that the mechanism of the positive column of arcs is now understood.