## 3 Experimental Results and Discussion  
In our experiment, we tested the leakage of the regenerative amplifier by monitoring the output power with the PC2 turning on and off. At the maximum pump power of 50 W, the output power of the regenerative amplifier increases with the Pockels cells switching time, however, the leakage appears when the PC2 switching time more than 69 ns. For example, with the switching time of 79 ns, the leakage reached 2 W when the maximum regenerative amplified power was about 18 W at 500 kHz. Accordingly, in order to obtain maximum power regenerative output without leakage, the switching time of Pockels cells is set to be 68 ns, corresponding to the five round trips in the regenerative cavity. The pump power of the regenerative amplifier is set to be 50 W because higher power may result in the self-excited oscillation between the M4 and M8. Next, improvement of the leakage and self-excitedoscillation threshold to increase the output power of regenerative amplifier will be studied, including the optimization of cavity design and Pockels cell structure (e.g., employing bidirectional voltage switching power supply to achieve a faster and more thorough switch [29]).  
The injected pulse energy into the regenerative amplifier was about 1 nJ, and the output pulse energy saturated with the increase number of round trips in the cavity. Figure 2a,b illustrates the dependence of the output power and pulse energy of the regenerative and final amplifier output on the repetition rate from 200 to 500 kHz, respectively. At the same pump power, the out power of the regenerative amplifier increases with the repetition rate, while the single pulse energy decreases, which is shown in Figure 2a. At 500 kHz, maximum regenerative amplified power of 9.73 W was obtained corresponding to the pulse energy of 0.02 mJ. After passing through the traveling-wave amplifier, the maximum output power of the laser system was 24.5 W at 500 kHz, corresponding to the peak power of 2.9 MW; while the maximum output pulse energy obtained was 0.11 mJ at 200 kHz, corresponding to the peak power of 6.5 MW. No leakage occurred when the repetition rate continuously adjusting from 200 to 500 kHz with the measured root-mean-square-error (RMSE) of output power less than 0.04%.  
The amplified pulses are monitored using a photodiode. At 500 kHz, oscilloscope trace of the output pulse train with 4 us/div and single pulse with 10 ns/div are illustrated in Figure 3, respectively. We can observe that the amplifier generates very clean output pulses without any noticeable pulse fluctuation or stray signal.  
Figure 4a shows the autocorrelation trace of the amplified pulses with the measured width of 16.9 ps at a repetition rate of 500 Hz. The pulse width of the output was slightly broadened compared with that of the seed pulses 11.5 ps, which is mainly caused by the gain narrowing [30; 31]. The measured beam quality factor \(M^{2}\) and near-field beam intensity profile are shown in Figure 4b.  
Figure 3: Oscilloscope trace of the regenerative amplified pulse train (a) 4 us/div; and (b) 10 ns/div.  
Figure 2: Average output power and pulse energy of the amplifier in dependence on the repetition rate of (**a**) regenerative amplifier output; and (**b**) final amplifier output.  
The \(M^{2}\) measured were 1.27 and 1.22 for the horizontal and vertical axes of the output, respectively. The roundness of the near-field intensity distribution is higher than 99%.