Line intensities in nitrogen low-pressure microwave discharges

This paper analyzes the intensity of radiative transitions in nitrogen low-pressure (0.3-0.5 Torr) microwave (2.45GHz) discharges, using both optical emission spectroscopy (OES) measurements and a 0D non-equilibriun kinetic model. The latter solves the homogeneous and stationary electron Boltzmann equation, coupled to the rate balance equations for the N$_{2}$(X, v=1-45) vibrationally excited states, the N$_{2}$(A$^{3}\Sigma _{u}^{+}$, B$^{3}\Pi _{g}$, C$^{3}\Pi _{u}$, a$^{1}\Sigma _{u}$, a$^{1}\Pi _{g}$, w$^{1}\Delta _{u}$, a$^{1}\Sigma _{g}^{+})$ electronic states, the N($^{4}$S, $^{2}$D, $^{2}$P) atomic states, and the N$_{2}^{+}$(X,B) and N$_{4}^{+}$ molecular ions. The plasma is produced by a surface-wave discharge, within an 8mm diameter quartz tube, at $\sim $55W power and $\sim $100mm axial length. The rotational (gas) temperature of the nitrogen plasma ($\sim $ 300-600 K) is experimentally determined from measurements of the band transition with the first positive system [FPS, N$_{2}$(B)--N$_{2}$(A)]. Comparison between simulations and measurements for the line intensity ratio $R$ of the first negative system [FNS-00, N$_{2}^{+}$(B,v=0)--N$_{2}^{+}$(X,v=0) at 391.4 nm] to the second positive system [SPS-25,N2(C,v=2)--N2(B,v=5) at 394.3 nm] are used to estimated the electron density ($\sim $ 10$^{11}$ cm$^{-3})$ and temperature ($\sim $ 3eV). We discuss the calculation of $R$ using different model approximations, analyzing its evolution with variations in the working parameters: electron density, gas pressure, and gas temperature.