Electron-Temperature Dependence of Electron-Ion Recombination in Argon

A 3-mode microwave apparatus is used to study the dependence of the dissociative recombination coefficient $\alpha \left(\mathrm{Ar}_2^{}{}_{}{}^{+}\right)$ on electron temperature $T_e$ over the range ${300}^{\circ }\mathrm{K}<~T_e<~{10000}^{\circ }\mathrm{K}$ while the ion and gas temperatures remain at 300°K. A high-$Q$ cavity mode is used to ionize the gas periodically, a second high-$Q$ mode is used to determine the decay of electron density during the afterglow from the change of resonant frequency of the cavity, and a nonresonant waveguide mode is used to apply a constant microwave heating field to the electrons. At $T_e={300}^{\circ }$ K, a value $\alpha \left(\mathrm{Ar}_2^{}{}_{}{}^{+}\right)=(8.5\mathrm{}\pm 0.8)\times {10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$/sec is obtained from analysis of recombination-controlled electron-density decays using a computer solution of the electron continuity equation which includes recombination and ambipolar diffusion terms. Over the range ${300}^{\circ }\mathrm{K}<~T_e<~{10000}^{\circ }\mathrm{K}$, the coefficient $\alpha \left(\mathrm{Ar}_2^{}{}_{}{}^{+}\right)$ is found to follow a simple $T_e^{}{}_{}{}^{-0.67\mathrm{}}$ variation. This result is reconciled with Fox and Hobson's $T^{-1.3\mathrm{}}$ variation, obtained under conditions where $T_e=T_i=T$, on the basis of their changing $\mathrm{Ar}_2^{}{}_{}{}^{+}$ vibrational-state populations with changing temperature. Finally, it is noted that our $T_e^{}{}_{}{}^{-0.67\mathrm{}}$ variation may be evidence for appreciable electron capture via the indirect as well as the direct dissociative process.