# A Practical Method for Controlling the Asymmetric Mode of Atmospheric Dielectric Barrier Discharges
## 3 Examples and Mechanisms of the Discharge Mode Control
### Numerical Regulating Example and the Underlying Mechanism  
Under the source parameters and initial values described in Section 2, the discharge under _f_d of 14 kHz will finally stabilize in the AP1P mode after about 10 applied voltage cycles, as shown in Figure 4a. Starting from the 15 th cycle, we change _f_d to a different frequency for 20 cycles, and then adjust the frequency back to 14 kHz at the 35 th cycle. The results indicate that the final stabilized discharge mode depends on _f_c to some extent. Figure 4b shows that when _f_c is set to 8 kHz, the discharge mode at the frequency-altered stage is SP1. However, after this stage, the discharge mode evolves back to AP1P; when _f_c is set to 20 kHz, the discharge mode of the control section and the section after the 35 th cycles are both AP1N, as shown in Figure 4c; when _f_c increases to 30 kHz, an AP1P discharge is observed at the frequency-altered stage, but the discharge mode after the 35 th cycle evolves into SP1, as shown in Figure 4d. Note that, when _f_c rises beyond 30 kHz (the largest _f_c considered in our simulation is 100 kHz), the initial AP1P discharge under 14 kHz can always be adjusted to SP1. At first sight, the discharge mode of the controlling section, as illustrated in Figure 4, is not directly relevant to that of the after-controlling section. To gain a deeper insight into how the frequency impacts the discharge mode, the evolution of the seed electron level has been extracted as a function of the breakdown number, as further given in Figure 5. Combined with two such figures, one can observe that, before the first breakdown of the controlling section, although the seed electron maintains at the same level (the first red circle in Figure 5), the discharge intensity and residual electron density of the subsequent breakdown show an obvious difference. This phenomenon may be qualitatively related to the equivalent gap resistance. Since the lower driving frequency causes lower angular frequency but higher equivalent gap resistance, the discharge intensity of the first breakdown in the controlling section is relatively weak when _f_c is lower than _f_d (14 kHz). On this basis, when _f_c is set to a lower value like 8 kHz, the discharge in the controlling section develops from a relatively lower seed electron density and provides sufficient dissipative time for the residual electrons before the next breakdown, leading to an SP1 mode. The opposite leading to AP1 mode can be inferred by analogy. Figure 4: Temporal profiles of current density when the controlling frequency _f_c is set to be (**a**) 14 kHz, (**b**) 8 kHz, (**c**) 20 kHz and (**d**) 30 kHz respectively. Through 20 controlling cycles, the driving frequency is adjusted back to 14 kHz. Theoretically speaking, the period of controlling section is not fixed, and the criteria considered here is to choose one relatively long period of time that ensures the discharge in the controlling section to achieve the steady state. As can be observed in Figure 5a,b, both low and high seed electron levels (the second red circle) will trigger the AP1 mode in the after-controlling section. In this case, one can understand that, in order to generate an SP1 discharge, the seed electron must retain a moderate level. Figure 6 presents the space-average seed electron relationship and the peak current density under the driving frequency of 14 kHz. In particular, the seed electron density in Figure 6a indicates the value before the breakdown, whereas the one in Figure 6b represents the residual value after the breakdown and dissipative stage. Obviously, if the seed electron density maintains at a low level at the beginning of a discharge (\(<\)2 \(\times\) 10\({}^{13}\) m\({}^{-3}\)), then the discharge intensity of the subsequent discharge will be strong (\(>\)1.23 mA/cm\({}^{2}\)). Correspondingly, the residual electron density after the breakdown, as further depicted in Figure 7a, can not be dissipated completely and exceeds 1 \(\times\) 10\({}^{17}\) m\({}^{-3}\) (Figure 6b).