Use of Langmuir Probes to Study Ion-Electron Recombination

Abstract

Between about 0.1 and 20 mm Hg, ion concentration is related to the current collected by a negative cylindrical probe by the equation (in practical units) $${\text{n=1.78×10}}^{13}{\lambda }_e^{\text{−1/2}}{\mu }^{\text{−5/8}}{\mathrm{(V}}_p{r}_p{)}^{\text{−1/4}}{i}^{\text{5/8}}$$ , where λ_e is the electron mean free path, μ is the ion mobility, V_p and r_p are the probe voltage and radius, and i is the probe current per unit length. The plasma is not perturbed because the probe current is supplied by ionization occurring at the sheath boundary. Using this equation, the following values of the dissociative‐recombination coefficient α in cm³/sec were obtained from pulse discharge afterglow measurements: argon, 3.6×10⁻⁷ for high excitation and 1.4×10⁻⁶ for moderate excitation; oxygen, 2.0×10⁻⁶; mercury, 3.5×10⁻⁶. For nitrogen α was found to be proportional to pressure and equal to 1.7×10⁻⁷ at 1 mm Hg. For cesium the above equation does not apply, and the value α = 1.7×10⁻⁷ was obtained from experimental results using conventional probe theory. The frequency of three‐body conversion of atomic to molecular ions was found to be 151 sec⁻¹ for argon and 37 sec⁻¹ for helium.