## 3 Results and Discussions
The line intensities of N\({}_{2}\)* species initially increased with the enhancement in the voltage from 90 V to 130 V. Meanwhile, the further increase in the voltage up to 210 V led to the slight reduction in the N\({}_{2}\)* line intensities (Figure 7a). The intensity of the N\({}_{2}\)* emission line (located at 316 nm) at the highest voltage became analogous to that in the results obtained at 90 V (Figure 7a). The intensities of the NO\({}_{\gamma}\) lines were enhanced by \(\sim\)1.71 and \(\sim\)2.16 times, with the increase in the voltage, when the air flow rates were 11.2 L/min and 13.4 L/min, respectively. The N\({}_{2}\)+ line intensity was increased by 1.95 times (from 6390 counts to 12,450 counts) with the enhancement of voltage at a 13.4 L/min flow rate (Figure 7b). It should be noted that the densities of the molecular nitrogen ion were increased, as the intensity of the emission line was enhanced by 1.65 times at an 11.2 L/min air flow rate with the increase in the voltage. The lowest intensity (1860 counts) of the atomic oxygen peak was observed at the lowest voltage when the air flow rate of 11.2 L/min was used. The enhancement of the voltage up to 210 V increased the O peak value up to 4690 counts. However, the intensity of the O peak was slightly reduced (by 6%) to 4400 counts when 250 V was applied. The intensities of excited atomic oxygen peaks were more intense when the flow rate ranged from 11.2 L/min to 13.4 L/min. The increase in the voltage from 90 to 210 V increased the O peak intensity from 1610 counts to 5760 counts, respectively. The line intensity of the O particle was 5620 counts at 250 V (Figure 7b). Figure 6: Variation in intensities of the N\({}_{2}\)* (**a**) and NO\({}_{\gamma}\), O, and N\({}_{2}\)+ (**b**) species with the direct air flow rates (from 6.7 to 15.6 L/min), when the voltage was kept at 130 V, and frequency, at 270 kHz. It was demonstrated that the enhancement in the discharge voltage led to the higher electric field as the discharge arc propagated to higher distances. As a result, the ionization degree of plasma was increased leading to the formation of higher densities of nitrogen ions, molecular nitrogen ions, atomic oxygen, or oxygen ions in the air plasmas [23, 30, 31, 32]. The calculation of the vibrational temperatures of the N\({}_{2}\)* particles in the air plasma was performed according to the methodology given in ref. [30, 32]. Equation (1), with the parameters of the vibration states (\(\
u\) = 0 and \(\
u\) = 1) of N\({}_{2}\) second positive system (C\({}^{3}\)TI-B\({}^{3}\)TI), was used:  
\[T_{vib}=\frac{E_{v1}-E_{v2}}{k_{B}}\left[ln\left(\frac{I_{\lambda 1}\cdot A_{1}^{ 4}\cdot FCF_{\lambda 2}}{I_{\lambda 2}\cdot A_{2}^{4}\cdot FCF_{\lambda 1}} \right)\right]^{-1} \tag{1}\]  
where \(I_{\lambda 1}\) and \(I_{\lambda 2}\) are the emission intensities of the transitions at the 337 nm (\(\lambda_{1}\)) and 316 nm (\(\lambda_{2}\)) wavelengths; \(k_{B}\) is the Boltzmann constant; E\({}_{v1}\) and \(E_{v2}\) are the energy of the upper energy levels; and \(FCF_{\lambda 1}\) and \(FCF_{\lambda 2}\) are the Frank-Condon factors for the \(\lambda_{1}\) and \(\lambda_{2}\) wavelengths, respectively. It was demonstrated that \(E_{v1}\) and \(E_{v2}\) values of 88,957 cm\({}^{-1}\) and 90,893 cm\({}^{-1}\) should be used. The \(FCF_{\lambda 1}\) value was 0.455 and \(FCF_{\lambda 2}\)--0.388. After evaluating these parameters, we can rewrite Equation (1) in the following form [30]:  
Figure 3.0  
The vibrational temperatures of excited N\({}_{2}\)* particles were determined for all measured emission spectra of the air plasma. It was found that the vibration temperature was -5970 K when the lowest frequency (230 kHz) at 130 V was used. A slight reduction in the vibration temperature down to 5930 K was obtained with the increase in the discharge frequency up to 250 kHz. The highest temperature of 6405 K was reached when the air plasma was created using 260 kHz discharge.