# Coplanar Capillary Plasma Electrode Discharge Flat-Panel Lamps Based on Porous Anodic Alumina
## 3 Simulation of Coplanar CPED with Porous Anodic Alumina
### Results  
To investigate the discharge process in the simulation, the evolution of the electron density, temperature, and electric field intensity of the CPED device with the PAA dielectric layer is shown in Figures 10-12. The discharge process can be illustrated by the evolution. Electron density and temperature are the main parameters of coplanar CPED plasma. When a sinusoidal voltage is applied to the anode and cathode, the parameters change with the voltage. The voltage changes are determined using Equation (6). \[V_{app}=V_{m}\cdot\sin(\omega t), \tag{6}\]  
where \(V_{app}\), \(V_{m}\), and \(\omega\) are the applied voltage, peak voltage, and angular frequency, respectively. The \(V_{m}\) was set at 300-500 V. The calculation of the sinusoidal voltage period was 1 \(\times\) 10\({}^{-4}\) s, which was one cycle. When a frequency of 10 kHz is applied, the time points selected occur at every 1/8 cycles (1/8 T) in one cycle, that is, (a) 1/8 T, (b) 1/4 T, (c) 3/8 T, (d) 1/2 T, (e) 5/8 T, (f) 3/4 T, (g) 7/8 T, and (h) 1 T.  
The evolution of electron density in the coplanar CPED device is shown in Figure 10. In the first half of the cycle, the electron density near the anode significantly increased, whereas in the second half of the cycle, the electron density near the cathode increased. At 5.00 \(\times\) 10\({}^{5}\) s and 1.00 \(\times\) 10\({}^{4}\) s, the electrons were uniform, and the electron density was approximately 7.92 \(\times\) 10\({}^{7}\) m\({}^{3}\). The highest electron density of 1.94 \(\times\) 10\({}^{8}\) m\({}^{3}\) was obtained at 1/4 T. \begin{table}
\begin{tabular}{c c} \hline \hline
**No.** & **Reactions** \\ \hline
1 & e + Ar \(\Rightarrow\) e + Ar \\
2 & e + Ar \(\Rightarrow\) e + Ar\({}^{*}\) \\
3 & e + Ar \(\Rightarrow\) e + Ar \\
4 & e + Ar \(\Rightarrow\) e + Ar\({}^{*}\) \\
5 & e + Ar\({}^{*}\Rightarrow\) e + Ar\({}^{*}\) \\
6 & Ar\({}^{*}\) + Ar\({}^{*}\Rightarrow\) e + Ar + Ar\({}^{*}\) \\
7 & Ar\({}^{*}\) + Ar \(\Rightarrow\) Ar + Ar \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main reactions considered in porous anodic alumina CPED. The electron density was calculated to be 1/8 T and reached a maximum value at 1/4 T when the maximum voltage was applied. The same pattern was observed in the next process. The electron density was the indicator of the discharge occurrence. The electron temperature evolution in the coplanar CPED device is shown in Figure 11. In the first half of the cycle, the electron density near the anode was significantly higher, whereas in the second half of the cycle, the electron temperature near the cathode increased. This result was consistent with the electron density. At 1/2 T and 1 T, the electron density distribution was uniform in the PAA zone and the electron density was 0.52 eV. The highest electron density of approximately 3.34 eV was obtained at 1/4 T.  
Figure 10: Evolution of the electron density in the coplanar CPED device. (**a**) 1/8 T, (**b**) 1/4 T, (**c**) 3/8 T, (**d**) 1/2 T, (**e**) 5/8 T, (**f**) 3/4 T, (**g**) 7/8 T, (**h**) 1 T.  
The PAA with perforated holes functioned as the dielectric layer in CPED. The electron temperature in the PAA was much higher than that in the other part. Therefore, the PAA structure was shown to perform an important role in the CPED process. To further investigate the role of the PAA in the CPED process, the electric field intensity was analyzed. The evolution of the electric field intensity in the coplanar CPED device is shown in Figure 12. In contrast to the results shown in Figures 11 and 12, the electric field intensity between these zones was higher than that in the other zones. In the first cycle, the electric field intensity first increased. At 1/4 T, the electric field intensity was approximately 4.26 \(\times\) 10\({}^{7}\) m\({}^{3}\), which was the highest value obtained. During 1/2 T and 1.0 T, the electric field intensity near the anode and cathode was higher at low values.