## 3 Results and Discussion
### Electron Number Density  
To find out whether the electron collisions are the main cause of molecule dissociation in the formed discharges, the electron number density was experimentally calculated in the plasma positions focused on by the lens. The Stark broadening analysis of the spectral profile of the \(H_{\beta}\) emission line (486.1 nm) is the most usual procedure for the experimental determination of electron density in a plasma discharge [37]. The Stark broadening of this line depends on electron density according to the expression [38]:  
\[\Delta\lambda_{stark}=2\times 10^{-11}\left(n_{e}^{2/3}\right) \tag{28}\]  
where density is in cm\({}^{-3}\) and Stark broadening is in nm. The pressure broadening occurs when the energy states of the emitting species are disturbed by the neutral species in the plasma discharge. This broadening depends on resonance and van der Waals effects. In this experiment, the hydrogen atom density was very  
Figure 7: **(a)** Experimental emission spectrum of the OH \(A^{2}\Sigma\to X^{2}\Pi\) band (dots) with their SPECAIR fitting (line) for the determination of the rotational, vibrational, and excitation temperatures. **(b)** Variations of rotational, vibrational, and excitation temperatures as a function of position at the AC voltage of 22 kV and 1 cm distance between electrodes. low, and the resonance effect can be neglected. Thus, the van der Waals broadening was the only contribution to the pressure broadening, which can be described as follows [39; 40; 41]:  
\[\Delta\lambda_{Pressure}=\Delta\lambda_{van\ der\ Waals}=8.18\times 10^{-26}\ \lambda^{2}\Big{(}\alpha\Big{\langle}R^{2}\Big{\rangle}\Big{)}^{2/5}\bigg{(} \frac{T_{g}}{\mu}\bigg{)}^{3/10}\frac{P}{KT_{g}} \tag{29}\]  
where \(\mu\) is the reduced mass of the colliding particles (\(\mu\)= 0.92308 for H/CO\({}_{2}\) collision), \(\lambda\) is the wavelength of the \(H_{\beta}\) line (486.1 nm), \(\alpha\) is the molecular polarizability of the CO\({}_{2}\) disturbing particles (\(\alpha\)= 2.46 \(\times\) 10\({}^{-24}\) cm\({}^{3}\)), \(\langle R^{2}\rangle\) is the difference of the squared radius of the upper and lower levels of \(H_{\beta}\) transition, \(T_{g}\) is the gas temperature in K, and \(P\) is the pressure (1 atm for atmospheric pressure). The Stark and pressure broadenings are the main contributions to the Lorentz shape of a line. So, the full-width at half-maximum (FWHM) value of the Lorentz profile can be obtained from these broadenings [42]:  
\[\Delta\lambda_{Lorentz}=\Delta\lambda_{Stark}+\Delta\lambda_{Pressure} \tag{30}\]  
Another contribution to the line broadening is the Doppler effect through particle movement. This broadening has a Gaussian profile and can be written as follows [42]:  
\[\Delta\lambda_{D}(nm)=7.2\times 10^{-7}\sqrt{\frac{T_{g}}{M}}\lambda \tag{31}\]  
where \(\lambda\) is the wavelength of \(\beta\) hydrogen line (486.1 nm), \(M\) is the molar weight of hydrogen, which is equal to 1, and \(T_{g}\) is the gas temperature in Kelvin units. The total Gaussian profile is generally considered as a convolution of Doppler and instrumental profiles, then [43]:  
\[\Delta\lambda_{G}=\sqrt{\Delta\lambda_{D}^{2}+\Delta\lambda_{I}^{2}} \tag{32}\]  
where \(\Delta\lambda_{G}\) and \(\Delta\lambda_{I}\) are the Gaussian and instrumental broadenings, respectively. The optical components resolution directly affects the instrumental broadening. A convolution of these Gaussian and Lorentzian profiles results in a Voigt shape. Fitting of experimental data to this analytical curve allowed us to separate Lorentz and Gaussian contributions (Figure 8a). In this study, Origin software was used for this purpose. In this way, the FWHM of the Lorentzian broadening could be distinguished. Figure 8: (**a**) Detected \(H_{\beta}\) emission line with its fitting to a Voigt profile. (**b**) Variations of electron density as a function of position at the AC voltage of 22 kV and 1 cm distance between electrodes.