## 3 Result and Discussion
### Spatial Distributions Characteristic of the FEGLD  
For understanding the characteristic variation of discharge plasma in space, the spatially resolved emission intensity distributions of N\({}_{2}\) (C\({}^{3}\Pi\)\({}_{\rm u}\)\(\rightarrow\) B\({}^{3}\Pi\)\({}_{\rm g}\)), N\({}_{2}^{+}\) (B\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)), OH (A\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)), O (3p\({}^{5}\)P \(\rightarrow\) 3s\({}^{5}\)S\({}^{0}\)), and He (3s\({}^{3}\)S \(\rightarrow\) 2p\({}^{3}\)P\({}^{0}\)) of FEGLD are shown in Figure 7, under the experimental conditions of 12 mm discharge gap, 30 kV pulse peak voltage, and 3.5 L/min helium flow rate. In this part, the OES emitted from the different parts of FEGLD is obtained by optical fiber which is placed on the adjustable micrometer screw lifting platform. The inconsistent spatial distributions of FEGLD reactive species emission intensities along the axial direction can be found in Figure 7. In the range of 0-10 mm, the emission intensities of N\({}_{2}\) (C\({}^{3}\Pi\)\({}_{\rm u}\)\(\rightarrow\) B\({}^{3}\Pi\)\({}_{\rm g}\)), N\({}_{2}^{+}\) (B\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)), and OH (A\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)) remains constant. But in the range of 10-12 mm which is near to the liquid surface, the emission intensities of N\({}_{2}^{+}\) (B\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)), N\({}_{2}\) (C\({}^{3}\Pi\)\({}_{\rm u}\)\(\rightarrow\) B\({}^{3}\Pi\)\({}_{\rm g}\)), and OH (A\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)) show obvious increases and attain a peak value at 12 mm. Meanwhile, the emission intensities of He (3s\({}^{3}\)S \(\rightarrow\) 2p\({}^{3}\)P\({}^{0}\)) and O (3p\({}^{5}\)P \(\rightarrow\) 3s\({}^{5}\)S\({}^{0}\)) keep decreasing in the range of 0-12 mm. This is because there are differences in the excitation mechanism of radiative states. The formation of He (3s\({}^{3}\)S \(\rightarrow\) 2p\({}^{3}\)P\({}^{0}\)) and N\({}_{2}\) (C\({}^{3}\Pi\)\({}_{\rm u}\)\(\rightarrow\) B\({}^{3}\Pi\)\({}_{\rm g}\)) is dominated by direct excitation by energetic electrons [52], which relies on the high electric field and the electron density. But near the liquid surface, there is no obvious increase in electron density which is clearly shown in Figure 8. According to the research in [53], a mushroom-like shape discharge area is generated due to the interaction with a liquid surface. The N\({}_{2}\) molecule from ambient air is involved in the discharge area. Thus, the emission intensity of N\({}_{2}\) (C\({}^{3}\Pi\)\({}_{\rm u}\)\(\rightarrow\) B\({}^{3}\Pi\)\({}_{\rm g}\)) increased here, and helium diffused here leading to the emission intensity of He (3s\({}^{3}\)S \(\rightarrow\) 2p\({}^{3}\)P\({}^{0}\)) decreasing. The significant elevation of N\({}_{2}^{+}\) (B\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)) emission intensity comes from the Penning process [52], in which the increase of nitrogen will induce the improvement of N\({}_{2}^{+}\) (B\({}^{2}\Sigma\)\({}_{\rm u}^{+}\))\({}_{\rm u}\) generation. The formation of OH (A) via direct dissociative electron excitation of water or dissociative recombination of H\({}_{2}\)O\({}^{+}\) or H\({}_{3}\)O\({}^{+}\)[54] The increase of OH (A\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)) emission intensity near the liquid surface is also shown in [52]. The H\({}_{2}\)O\({}^{+}\)(A) ion could exist in a mushroom-like shape area due to its relatively long radiative lifetime (about 10 \(\upmu\)s), so the increase of OH (A\({}^{2}\Sigma\)\(\rightarrow\) X\({}^{2}\Pi\)) emission intensity can be observed near the liquid surface. As the important parameters, gas temperature and electron density influence the gas-liquid discharge application. The spatially resolved gas temperature and electron density of FEGLD are shown in Figure 8 when the pulse peak voltage, gas flow rate, and discharge gap are kept at 30 kV, 3.5 L/min, and 12 mm, respectively.