## 3 Results and Discussion  
We first considered incident laser pulses with \(w_{0}\) = 1 mm, \(\tau_{\mathrm{p}}\) = 90 fs, and \(P_{\mathrm{in}}\) = 10\(P_{\mathrm{cr}}\). The total atmospheric air molecule density \(p_{\mathrm{at}}\) was assumed to be \(2.7\times 10^{25}\)/m\({}^{3}\). For simplicity, dry air was assumed to only consist of N\({}_{2}\) and O\({}_{2}\) at a ratio of 0.78 to 0.21. For wet air, we imposed a composition of 78.0% N\({}_{2}\), 21.0% O\({}_{2}\), and 1.0% H\({}_{2}\)O (gas). Figure 1 presents the on-axis intensity and on-axis electron density along the propagation axis. The solid blue and green lines represent the results for pulses in dry and wet air conditions, respectively. The multiphoton ionization cross section \(\sigma^{\mathrm{K}}\) for N\({}_{2}\), O\({}_{2}\), and H\({}_{2}\)O are taken from the measured results by [PERSON] [17], as listed in Table 1. The black dash line represents the simulated results for dry air when the cross section \(\sigma^{\mathrm{K}}\) for N\({}_{2}\) and O\({}_{2}\) were obtained from the theoretical formula by [PERSON] and [PERSON] [9]. As shown in Figure 1a, the beam intensity in both dry air and wet air first increased rapidly at about z = 2.0 m, which implies that the water vapor had no influence on the self-focusing position (defined as the distance between the initial transmission position of the beam and the position where the on-axis light intensity increases sharply). Almost simultaneously, the on-axis electron density also obviously increases, as shown in Figure 1b. This is in accord with the characteristics of intense a femtosecond laser pulse at its first propagation stage, as identified by [PERSON] et al. [10]. During the first stage, the beam intensity increases due to the optical Kerr effect focusing and the electron density being excited when the beam intensity becomes sufficiently large. Subsequently, the generated electron density has a threshold-like response, which limits the further increase of peak intensity inside the filament by defocusing the beam in turn [9]. When a balance of these two processes is achieved, the laser intensity inside the filament gradually stabilizes. This special phenomenon is usually named intensity clamping [9]. This light guide coupling with a significant electron density level is identified as the second stage by [PERSON] et al. [10]. Based on the values of the peak intensity, it can be clearly seen from Figure 1a that the clamping intensity in dry air is much higher than that in wet air. The clamping intensity of UV filaments decreased more obviously in wet air conditions compared with the results of \begin{table}
\begin{tabular}{c c c c} \hline
**Gas Types** & **Symbol (Units)** & **Values [9]** & **The Measured Values** \\ \hline \multirow{3}{*}{O\({}_{2}\)} & K & 3 & 3 \\  & \(\sigma^{\mathrm{K}}\) (s\({}^{-1}\) m\({}^{2\mathrm{K}}\)/\(\mathrm{W}^{\mathrm{K}}\)) & \(1.35\times 10^{-40}\) & \(1.5\times 10^{-40}\) \\  & U\({}_{\mathrm{i}}\) (eV) & 12.07 & 12.07 \\ \hline \multirow{3}{*}{N\({}_{2}\)} & K & 4 & 3 \\  & \(\sigma^{\mathrm{K}}\) (s\({}^{-1}\) m\({}^{2\mathrm{K}}\)/\(\mathrm{W}^{\mathrm{K}}\)) & \(3.22\times 10^{-60}\) & \(2.4\times 10^{-41}\) \\  & U\({}_{\mathrm{i}}\) (eV) & 15.58 & 15.58 \\ \hline \multirow{3}{*}{H\({}_{2}\)O} & K & - & 3 \\  & \(\sigma^{\mathrm{K}}\) (s\({}^{-1}\) m\({}^{2\mathrm{K}}\)/\(\mathrm{W}^{\mathrm{K}}\)) & - & \(6.8\times 10^{-38}\) \\ \cline{1-1}  & U\({}_{\mathrm{i}}\) (eV) & - & 12.62 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the model. We adopted most of the theoretically calculated parameters for O\({}_{2}\) and N\({}_{2}\) from Reference [9]. The effective multiphoton ionization cross section \(\sigma^{\mathrm{K}}\) for H\({}_{2}\)O molecules is taken from Reference [17]. mid-infrared lasers filaments [15]. The peak intensity is maintained for several meters and is coupled with a significant electron density level (Figure 1b). The laser pulse tends to form longer filaments in wet air.