## 4 Experimental Results and Their Discussions
As the charge voltage increases, the injection energy increases, resulting in a sharp increase in output energy. Once the charge voltage is greater than the optimal voltage corresponding to the optimal \(E/P\) value (w  
Figure 8: Laser energy versus charge voltage under different magnifications. Figure 7: Laser spots at different places on the heat-sensitive paper: (**a**) 1 m; (**b**) 6 m; and (**c**) 10 m distance from the laser exit; and (**d**) far-field. strength and \(P\) is pressure of the working mixture), arc discharge occurs and energy growth becomes slow. Severe arc discharge will greatly reduce the uniformity of discharge, thus reducing the laser energy and making damages on the electrodes. At each voltage, the energy does not have a linear relationship with \(M\). As we can see from Table 1, the output coupling coefficient \(C\) increased with the magnification \(M\), but the effective gain volume decreased with \(M\). Therefore, there exists an optimum magnification to balance the gain volume and output coupling. Figure 9 shows the near-field output energy and far-field energy density under different magnifications at charge voltage \(Uc\) = 42 kV. The far-field energy density was calculated by \(\rho=E/S_{\mathrm{f}}\), where \(E\) is the near-field output energy and \(S_{\mathrm{f}}\) is the far-field spot area. Considering the application in remote atmospheric monitoring, the far-field operation range is \(>\)10 km. As we can see from Figure 9, the near field energy increased at first and then decreased, with a maximum energy \(E_{\mathrm{max}}\) = 3.32 J attained at \(M\) = 1.85, while the far-field energy density increased monotonically. Table 3 contains the results of divergence and energy values of our investigation. An increase in \(M\) reduced the divergence from \(\theta\) = 1.08 mrad for M = 1.65 to 0.66 mrad for \(M\) = 2.25, and the corresponding diffraction limit factor \(\beta=\theta_{\mathrm{exp}}/\theta_{\mathrm{cal}}\) reduced from 2.25 to 1.95. Further increasing the magnification could effectively reduce the laser divergence, but restricted by the size of the electrode gap in our present equipment, the size of the concave reflecting mirror should in the range 4-5 mm, and the corresponding size of the convex mirror should be \(<\)1.7 cm for \(M\) > 3. The reduction of the size of the convex mirror would further increase the assembly difficulty of the resonator, which in turn may worsen the beam quality of the laser. The practical divergence angle of the unstable resonator in our investigation was relatively small, but it was still much larger than the theoretical value. The reasons are as follows:  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & \(M\) & \(\theta_{\mathrm{cal}}\)/mrad & \(\theta_{\mathrm{exp}}\)/mrad & \(\beta\) = \(\theta_{\mathrm{exp}}\)/\(\theta_{\mathrm{cal}}\) & _E/J_ & \(\rho\)/(m)/m\({}^{2}\))** \\ \hline stable & — & 0.190 & 7.15 & 37.63 & 3.65 & 0.91 \\ unstable & 1.65 & 0.479 & 1.08 & 2.25 & 2.76 & 30. 1. The light beam is regarded as a parallel light when calculating the theoretical divergence angle of the confocal unstable resonator. However, the actual output beam of the unstable resonator should be a near-parallel light with a certain geometric divergence angle, which is caused by factors such as cavity mirror spacing, curvature error, and mirror tilt;
2. The straight-edge diffraction caused by electrode diffraction will also increase the actual divergence of the laser beam;
3. The thermal denaturation of the output and convex mirrors increases the size of the divergence angle. Although the unstable resonator had about 10-24% energy reduction in terms of overall output energy compared with the stable resonator, the measured beam quality and 10 km far-field energy density were much better, being increased by 11 and 91 times, respectively. The laser beam and energy can be further improved by increasing the separation \(d\) between electrodes.