## 3 Results and Discussion
Due to ionization of water vapor, the on-axis electron density of UV pulses in wet air is much greater than that in dry air, which can be clearly seen in Figure 1b. At a larger z, the pulse ultimately diffracts as \(\rho\) decreases to zero. In addition, the simulation results from the measured MPA parameters are very close to those from the theoretical calculation results in dry air (as shown with black dash lines). Figure 2 shows the number of electrons ionized from N\({}_{2}\), O\({}_{2}\), and H\({}_{2}\)O. The number of electrons was calculated by \(N_{e}(z)=\int_{0}^{z}dz\int_{0}^{\tau_{\mathrm{max}}}dr\int_{0}^{2\pi}d\phi \rho(r,\tau_{\mathrm{max}},z)r\sin\phi\). The solid lines represent the results from the measured MPA parameters under wet conditions. It clearly shows that the number of electrons increased substantially in wet air compared with dry air, which demonstrates the remarkable contribution of H\({}_{2}\)O molecules to the air ionization. The MPA process is a crucial mechanism for the pulse's energy loss [14]. As shown in Figure 2b, the pulse energy decreases rapidly during the filamentation stage. The filamentation tends to deposit more energy in wet air conditions. To investigate the underlying physics behind the filamentation for the two cases in the spatial regime, we plot the fluence distribution as a function of the propagation distance, which is shown in Figure 3. The fluence distribution is defined as \(F(x,y,z)=\int_{-\infty}^{+\infty}\abs{E(x,y,t)}^{2}dt\). The several highlighted core areas in Figure 3 clearly indicate defocusing-refocusing cycles in the filaments [12]. There are mainly three cycles in dry air and wet air. The longer bright core in wet air further indicates that the laser pulse forms longer filaments in wet air. Compared with filamentation in dry air, the radius of filament gets slightly wider and the intensity of fluence becomes lower in wet air. These results are consistent with the experimental results reported by [PERSON] et al. [18]. Figure 1: Evolution of the on-axis (**a**) intensity, (**b**) electron density as functions of z for a UV pulse propagating in air. The blue and green solid lines represent the simulated results in dry and wet air conditions, respectively. The cross section \(\sigma^{\mathrm{K}}\) for N\({}_{2}\), O\({}_{2}\), and H\({}_{2}\)O is obtained from the measured results by [PERSON] [17]. The dry air is assumed to only consist of N\({}_{2}\) and O\({}_{2}\) in a ratio of 0.78 to 0.21. For wet air, we impose a composition of 78.0% N\({}_{2}\), 21.0% O\({}_{2}\), and 1.0% H\({}_{2}\)O (gas). The black dash line represents the simulated results of dry air when its cross section \(\sigma^{\mathrm{K}}\) for N\({}_{2}\) and O\({}_{2}\) are obtained from the theoretical formula in Reference [9]. The input beam is a Gaussian shape with P\({}_{\mathrm{in}}\) = 10P\({}_{\mathrm{cr}}\), w\({}_{0}\) = 1 mm, and \(\tau_{\mathrm{P}}\) = 90 fs. The evolution of the radius and intensity of the filament can also be clearly seen from the transverse energy flux distributions, as shown in Figure 4. The energy is concentrated into the central area with a slightly higher peak fluence in dry air (Figure 4a) than in wet air (Figure 4d) at the initial position of the filament. During the intensity clamping, an obviously higher peak fluence takes place in dry air  
Figure 3: Evolution of the fluence distribution along the propagation distance. (**a**) Dry air and (**b**) wet air. Figure 2: Evolution of (**a**) number of electrons ionized from N\({}_{2}\), O\({}_{2}\), and H\({}_{2}\)O, and (**b**) pulse energy as functions of z. The number of electrons is calculated by \(N_{e}(z)=\int_{0}^{z}dz\int_{0}^{z_{max}}dr\int_{0}^{2n}d\phi\rho(r,\tau_{\max},z)r\sin\phi\). In Figure 2a, the blue dash line is the results for O\({}_{2}\) gas, the red dash line denotes the results for N\({}_{2}\) gas, and the black dash line represents the results for dry air gas. The results are obtained from the calculated multiphoton absorption (MPA) parameters in Reference [9].