## 3 Results
### Application to Rectangular Current Power Supply Operated in Burst Mode  
As shown in Figure 16, results obtained with the rectangular current power supply are difficult to analyze through the equivalent circuit approach: indeed, each burst of  
Figure 14: Partial discharging ratio \(\beta\) variation during the startup transient. Figure 15: Partial discharging ratio \(\beta\) obtained with image processing and equivalent circuit analyzes. Results are grouped by values of supply frequency; adjustments of injected power are achieved with the peak value of imposed \(v_{DBD}\) voltage. Displayed values are obtained in steady state. current pulses injected into the DBD creates an electrical transient (see voltage and current waveforms on Figure 16a), which has no time to vanish before the end of the burst. As a result, the Q-V Manley diagram exhibits a poorly trapezoidal shape, as can be appreciated in Figure 16b: this makes it very difficult to select the slopes to be used for the calculation of the circuit's parameters. Taking advantage of the very good convergence of both methods for \(\beta\) ratio diagnostic highlighted on Figure 15, it is proposed to admit:  
* the parameter set (\(C_{d}\), \(C_{g}\), \(V\)th), acquired thanks to previously achieved experiment, where the discharge fully covers the surface of the reactor (\(\beta\) = 100%), sketched by the equivalent circuit of Figure 10;
* the \(\beta\) ratio obtained by the image processing. Using Equations (4) and (5), which translate the behavior of the equivalent circuit of Figure 12, it becomes possible to build and to draw the parallelepipedal figure, which should be considered. Note that the image acquisition shows an averaged behavior of the system. As for the \(\beta\) value provided by the analysis of this image, therefore, this approach provides an equivalent average behavior over the burst. The image processing of the acquired picture shown in Figure 17a gives: \(\beta\) = 56%. Together with already known circuit parameters (\(C_{d}\) = 90 pF, \(C_{g}\) = 135 pF, \(V\)th = 2585 V, independent from operating conditions), Figure 17b shows the Manley figure (red). Figure 16: Rectangular current supplied system: electrical measurements of a whole burst (**a**), with DBD voltage (blue) and current (green), and associated Q-V Manley diagram (**b**). Figure 17: Rectangular current supplied system: processed image corresponding to Figure 16 (**a**), giving a value: \(\beta\) = 56% experimental Manley diagram (**b**), blue and the theoretical one (red), obtained with the known parameter set for the equivalent circuit: \(C_{d}\) = 90 pF, \(C_{g}\) = 135 pF, \(V\)th = 2585 V.  
Effect of the Supply Waveform on the Discharge Uniformity: Additional Diagnostic Provided by the Image Processing  
In addition to the segmentation process, other statistical diagnostics of the images can provide very useful information about the discharge. We now consider the operating conditions obtained with the electrical waveforms shown in Figure 3, with two different generators; the waveforms are completely different but, in fact, they have the same power level (approx. 40 W). The appearance of the discharges [26] shown in Figure 18 are very different: the discharge obtained with the sinusoidal voltage source (column (b)) appears much more diffuse than the one pumped with the rectangular current source (column (a)): in the original picture (column (a)), the spots which can be related to the streamers are clearly visible. Figure 18: Image diagnostic of operating conditions obtained with square current source (column (**a**)) and sine voltage power supply (column (**b**))—electrical waveforms presented in Figure 3—from top to bottom: original image, grayscale, result of geometrical transformation, segmented image (central area), gray levels frequency.