A multi-ratio method for determination of the electric field from 2p states in transient argon discharges at atmospheric pressure

Abstract We present a theoretical analysis demonstrating that a multi-ratio optical emission spectroscopy approach can, in principle, be applied to determine the instantaneous mean electron energy and reduced electric field ( E/N ) in transient low-temperature argon discharges at atmospheric pressure, while also allowing recovery of the relative densities of the Ar 1 s 5. .2 states. The method is derived from an advanced reaction kinetic model for argon accounting for 23 species and 409 processes by means of a dominant-balance analysis used to identify negligible terms and define explicit validity conditions in terms of reduced electric field, pressure, and relative excited-state densities for simplified formulation. By combining simplified balance equations for pairs of Ar 2 p 10 … 2 states, the dependence on the unknown electron density is eliminated, and densities of the Ar 2 p 10 … 2 states appear only in mutual ratios. The influence of metastable and resonant states is incorporated through specific terms, whose impact on the method sensitivity is quantified. The neutral collision processes among the Ar 2 p 10 … 2 states has also shown to be significant. Numerical tests with various E / N waveforms confirm that the method accurately recovers the reduced electric field E / N , the mean electron energy, and relative densities of Ar 1 s 5. .2 states for a broad range of conditions, showing high sensitivity at E / N < 100 Td and robustness for atmospheric pressure conditions. Limitations arise when neglected radiative processes or electron-impact collision processes among the Ar 2 p 10 …