## Materials and Methods  
The glass, quartz, and alumina solid plates and the flexible polymer films were used as the dielectric materials for the experimental samples. The polyimide (PI), polypropylene (PP), and glass polymer (GP) were used as the dielectric materials of the flexible polymer films. Table 1 lists the information on the dielectric materials used in this experiment. Since the solid plates are fragile, they are limited to thickness reductions of less than several-hundred \(\upmu\)m. An alkaline earth boro-aluminosilicate wafer served as the glass in the experiment. Synthetic quartz was used in this study. The purity of the alumina-ceramic substrate is 99.9%. The thinnest solid plate among the commercially available ones is of the 500-\(\upmu\)m thickness (\(T\)). The dielectric constant \(K\) values are 9.0, 5.3 and 3.6 for the alumina, glass, and quartz, respectively. The selection of the samples of the flexible polymer film is based on the commercially available film thicknesses. For the PI, GP and PP, the \(T\) values are 125 \(\upmu\)m, 200 \(\upmu\)m and 300 \(\upmu\)m, respectively, while the \(K\) values are 2.8, 3.0 and 2.3, respectively. The \(T\) of the selected PI is the thickest among the commercial products. The GP film is equivalent to the smartphone-display protection film. In the flexible films, the dielectric thickness is different for each sample; accordingly, the capacitance (\(C\)-\(K/T\)) of each sample was affected by the \(K\) and \(T\) values. The PI-film properties include a high heat resistance, an excellent flexibility, and the resistance to chemicals and combustion [37]. The PI was developed for the aerospace industry in 1964 (DuPont Kapton(r)). The PI film cannot be deformed over a wide range of temperatures, ranging from \(-269\) to 400 \({}^{\circ}\)C, but it has been widely used as the substrate of the flexible printed circuit board. The PP is an inexpensive polymer material made of carbon (C) and hydrogen (H) [38; 39; 40; 41] that is used in a variety of fields such as packaging films, fibers, and daily goods. The PP film is prone to oxidation (or degradation) when it is exposed to heat or the ultraviolet light. The PP melting point is approximately 160 \({}^{\circ}\)C, so it is considered thermally weak; however, its chemical properties are excellent. The PP can withstand many organic solvents, except strong oxidizing agents. The GP has been developed to complement vulnerabilities such as the thermal deformation of the polymer materials. It is mainly used in the liquid-crystal protective films of the mobile phones and displays. In this experiment, the test sample film is SILPLUS(r) (H Global, Brooklyn, NY, USA). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**(a)** & **Glass** & **Quartz** & **Alumina** \\ \hline (T, K) & (500 \(\upmu\)m, 5.3) & (500 \(\upmu\)m, 3.7) & (500 \(\upmu\)m, 9.3) \\ Formula & B\({}_{2}\)O\({}_{3}\)-SiO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\) & SiO\({}_{2}\) & Al\({}_{2}\)O\({}_{3}\) \\ Trademark & Corning® EAGLE XGTM & Corning® 7940 Fused Silica & - \\ \hline
**(b)** & **Polymide (PI)** & **Glass Polymer (GP)** & **Polymopylene (PP)** \\ \hline (T, K) & (125 \(\upmu\)m, 3.4) & (200 \(\upmu\)m, 3.0) & (300 \(\upmu\)m, 2.3) \\ Formula & & & \\ Trademark & Dupont–Kapton® & H\&Global–SILPLUS® & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Formula of dielectric materials: (**a**) Solid plates and (**b**) Flexible polymer films. In Figure 1, the various DBD types introduced in [33; 34] were tested for the discharge-ignition experiments with the dielectric layer of the alumina-ceramic plate, as follows: spatial discharge between the face-to-face electrodes in (a), the coplanar discharge in (b), and the planar discharges between the both-side electrodes in (c-i)-(c-iv). The electrodes were coated with copper to 40-\(\upmu\)m in thickness. All the experiments were performed in the atmospheric environment.