An approach to a non-LTE Saha equation based on the Druyvesteyn energy distribution function: a comparison between the electron temperature obtained from OES and the Langmuir probe analysis

Abstract

Plasma diagnostics using the optical emission spectroscopy (OES) technique is often based on the assumption of Maxwellian distribution functions. Whenever the equilibrium condition is not fulfilled, the electron energy distribution function (EEDF) is no longer Maxwellian and there appear discrepancies between the electron temperature obtained via the spectral line ratio (e.g. Saha equation) and the effective temperature obtained from the EEDF, measured by a Langmuir probe. In this work we derive a modified version of the Saha equation by assuming a Druyvesteyn energy distribution function for the electrons. We apply the modified Saha equation to a low pressure argon plasma produced in an inductive RF discharge to obtain the electron temperature. We show that the modified version introduces substantial corrections in the measured values of the electron temperature given by OES, which approach those given by the second derivative method of Langmuir probe analysis.