On the Theory of the Mercury Arc

The theory of heat balance at the cathode is extended (1) by the introduction of the accommodation coefficient of neutralized ions, (2) by evaluation of all processes which absorb the energy gained by electrons in the cathode fall space, and (3) by correction of a previous assumption that fields sufficient to extract electrons will affect the heat of neutralization of postive ions at the surface. Test of the two resulting equations by existing experimental data shows that Langmuir's theory of extraction of electrons by the field at a Hg arc cathode is consistent with the cathode heat equations, but cannot be uniquely proved by them on account of uncertainty in two factors whose order of magnitude only is known: the fraction F of energy brought to the cathode by unelectrified carriers, $1.0>F>0.5$; the fraction 1(1+δ) of positive ions formed near the cathode which go to it, 1>δ>0.From the net rate of evaporation an equation is obtained between vapor pressure and temperature at the cathode which, when combined with the vapor pressure-temperature equation of Hg, gives uniquely the temperature of the cathode spot and the vapor pressure outside it, provided the fraction f of total current carried by electrons is known. It is shown that the temperature of the cathode spot does not exceed 200^∘{}C, and that the thickness of the cathode fall space is less than the electron mean free path.It is shown that ionization just beyond the cathode fall space must be of the cumulative, multiple stage type. From this it is shown that the fraction f must exceed 0.67 (if δ=0) or 0.80 (if δ=1), since these minimum values depend on 100 per cent efficiency of two stage ionization.Mechanical pressure against the cathode by the arc is explained by the fact that the accommodation coefficient a is less than 1.0. If this accommodation coefficient of Hg ions at a liquid Hg surface should be independently measured, it would give an independent method of estimating the important fraction f.The paper points out the causes of present limitations in our knowledge of conditions at the arc cathode and also the manner in which, and the extent to which, these limitations may be removed.