Experimental and theoretical study on the N₂(X¹Σ⁺_g) vibrational temperatures estimation in nitrogen glow discharges

In the present work, we develop an experimental route for determining the N₂(X¹Σ⁺_g) vibrational temperature in low-pressure flowing nitrogen glow discharges using only the Optical Emission Spectroscopy (OES) technique. The emissions of the nitrogen Second Positive System (SPS) transitions, originated from the N₂(C³Π_u, 0 ≤ v' ≤ 4) states, are used to indirectly determine the N₂(X¹Σ⁺_g, 0 ≤ v ≤ 4) distribution. For the first time, we explicitly derive the relation between the different electronic states populations solving the rate balance equations, using the definition of 'vertical' excitation from the N₂(C³Π_u, v') excitation cross-sections. Subsequently, the N₂(X¹Σ⁺_g) vibrational distribution is fitted by either Boltzmann and Treanor functions furnishing two different experimental estimations for the vibrational temperature. The vibrational temperatures are estimated in two different discharge set-ups, for experimental conditions of discharge current from 15 to 75 mA, gas pressure from 160 to 1000 Pa, and gas flow rate from 0.2 to 1.0 Sl m^-1 varying independently. A well-established state-to-state kinetic numerical model we constructed to the study of the nitrogen discharges positive columns is modified to calculate the N₂(X¹Σ⁺_g) vibrational temperature for our experimental conditions. The experimentally determined vibrational temperatures are quite well validated by our calculations for an extensive range of electron density (10¹⁰-10¹¹ cm^-3), reduced electric field (37-115 Td), and gas residence time (0.3-16 ms) discharges conditions. The work provides an original detailed analysis of experimental and theoretical routes to the N₂(X¹Σ⁺_g) vibrational temperature determination in low-pressure nitrogen DC discharges.