## 3 Results and Discussion  
### The Discharge Energy and Discharge Efficiency  
Based on the multichannel discharge technique, the discharge channel number can be increased greatly. When the energy stored in the discharge capacitor is fixed, the energy deposited in each channel varies with the discharge channel number. As energy is a critical factor determining the performance of the PSJA, the energy characteristic is first investigated. The discharge capacitor is set as 10 nF, and the initial voltage is set as 6 kV. The discharge voltage of each electrode couple is set as 4 kV. The inductance is 1.65 uH. The sum of wire resistance and the equivalent serial resistance of the capacitor are chosen as 1.89 \(\Omega\). The discharge voltage and current waveforms with channel numbers of 1, 5, 10, and 20 are simulated. Based on the current and resistance of each discharge channel, the discharge power and discharge energy can be obtained. The discharge voltage and current waveforms with different actuator numbers are plotted in Figure 9. As described in [16], the breakdown of each electrode couple happens in sequence, the time to form a complete discharge channel increases with the growth of the actuator number. What's more, with the increase in the actuator number, the total length of the discharge channel is enlarged, leading  
Figure 8: The comparison between the CFD results and model results. (**a**) is the jet velocity at the throat outlet and (**b**) is the gauge pressure in the chamber. to the growth of plasma resistance. As a result, the discharge current decreases. The deposited energy in each actuator ought to decrease. The energy deposition power and the discharge energy in the first PSJA are obtained from the simulation results, as shown in Figure 10. The energy deposition power (\(P_{\text{deposition}}\)), and discharge energy (\(Q_{\text{discharge}}\)) are defined in Equation (22). With the increase in the actuator number, the energy deposition power decreases. However, as shown in Figure 10b, the deposited energy doesn't decrease linearly. Since the gap distance between electrodes in all actuators is the same, and the actuator works in series, the resistance of the plasma channel in each actuator can be considered as the same. The discharge energy in each actuator can be expressed as Equation (23), where \(Q\) is the energy stored in the capacitor, \(R_{\text{arc}}\) indicates the resistance of plasma channel, n is the actuator number, and \(R_{0}\) is the external resistance in the discharge circuit. Therefore, if the actuator number increases, the deposited energy in one actuator doesn't decrease linearly. When the actuator number increases from 1 to 20, the deposited energy in the first actuator decreases 76.7% instead of 95%. In this way, the total energy deposited in all actuators increases, as shown in Figure 11. This means more energy stored in the capacitor is released in the discharge channel, leading to the improvement of discharge efficiency \(\eta_{\text{d}}\), which is defined in Equation (24). \[Q_{\text{discharge}} =\int P_{\text{deposition}}(t)dt= \int I^{2}(t)/g(t)dt \tag{22}\] \[Q_{\text{discharge}} =Q\frac{R_{\text{arc}}}{nR_{\text{arc}}+R_{0}}=\frac{Q}{n+R_{0}/ R_{\text{arc}}}\] (23) \[\eta_{\text{d}} =\frac{\sum\limits_{k=1}^{k=n}Q_{\text{discharge},k}}{Q}=\frac{ \sum\limits_{k=1}^{k=n}\int I^{2}(t)/g_{k}(t)dt}{Q} \tag{24}\]  
Figure 12 shows the deposited energy in each actuator with different actuator numbers. This figure shows that in this multichannel discharge mode, the deposited energy in a different actuator is almost the same. The coefficient of variation with 5, 10, and 20 actuators is 3.8%, 3.32%, and 4.77%, respectively. Based on the previous research [18], the breakdown of the electrode couple in each actuator happens in sequence. Coupled with the results shown in Figure 12, it concludes that although the time when the breakdown of the electrode couple in each actuator happens is different, the deposited energy is the same.