## 3 Results and Discussion
To investigate the transformation mechanism from P1 discharge to P2 discharge, Figure 7 gives the spatial distributions of charged particle density and electric field at the moments a-i in P2 discharge, and the moments a-i have been marked in Figure 6. As shown in Figure 7a, at the beginning of the first voltage period, the density of charged particles is very low, and the uniform distributions of the charged particles and electric field are obtained. This means that the heavy ions produced by the previous discharge can reach the surface of dielectric barriers during the power-off phase. Figure 7b shows the spatial distributions of charged particles and electric field at the moment when the positive current reaches the peak value. The discharge operates in glow discharge, the maximum positive charge density in the cathode fall region is \(1.6\times 10^{11}\) cm\({}^{-3}\), and the maximum value of the electric field is 8.5 kV/cm. After the discharge is quenched, the electron density drops rapidly as shown in Figure 7c. According to the simulation results, the electrons are  
Figure 5: Spatial distributions of positive charge density, negative charge density, electron density, and electric field at several key moments in P1 discharge. dissipated at about 13.5 \(\upmu\)s with a gap width of 4.2 mm. At 17 \(\upmu\)s, there is a positive column with a width of 0.15 mm in the discharge region in Figure 7d, while in the P1 discharge, the positive column at this moment has been completely dissipated. Then, at the end of the first voltage period shown in Figure 7e, the electrons have completely dissipated, but the CO\({}_{2}^{+}\) and CO\({}_{3}^{-}\) ions cannot reach the electrodes and remain in the sheath region. These ions make the plasma easy to be ignited, reducing the breakdown voltage of the subsequent discharge event. Figure 6: Temporal evolutions of current density, applied voltage, gas voltage, and memory voltage in P2 discharge with a gap width of 4.2 mm. Figure 7: Spatial distributions of positive charge density, negative charge density, electron density, and electric field at several key moments in P2 discharge. In the second voltage period, the discharge current density reaches the maximum value at 2.5 \(\upmu\)s after the voltage application, which is earlier than that in the first voltage period. Figure 7f plots the spatial distributions of charged particle density and electric field at the moment f. Similar to the first discharge, the second discharge also operates in glow mode. The maximum positive charge density in the cathode fall region is only \(1.1\times 10^{11}\) cm\({}^{-3}\), which is obviously smaller than the charged particle density produced by the first discharge event shown in Figure 7b. The second discharge is weak and less charged particles are produced; thus, these charged particles can be completely dissipated during the power-off phase. In fact, the electrons are dissipated completely at about 13 \(\upmu\)s in Figure 7g, the heavy CO\({}_{3}^{-}\) ions reach the anode at about 17 \(\upmu\)s in Figure 7h, and CO\({}_{2}^{+}\) ions reach the cathode at about 19 \(\upmu\)s according to the simulation results. As shown in Figure 7i, there are no heavy ions remaining in the sheath region at the end of the second voltage period, which does not affect the discharge of the next voltage period. In general, the increase in the gap width prolongs the time for the charged particles to reach the electrodes, so that the heavy ions with small mobility cannot be dissipated during the power-off phase and remain in the sheath region, effectively reducing the breakdown voltage of the next discharge. Then, fewer ions generated by the second discharge event can be completely dissipated during the power-off phase without affecting the third discharge. When the gap width is increased to 5.1 mm, the discharge turns into a RP2 discharge, a small positive current pulse is followed by a large negative current pulse.