# The Simulation of Dielectric Barrier Discharge for Breakdown Voltage in Starch Modification
## 3 Results and Discussion
### Effect of the Top Electrode's Mesh Size  
From Figure 1, when V = 1000 V is applied to the top electrode, the electric field between the gap is calculated using different electrode types. The electric field from the dielectric's surface to the top electrode is depicted in Figure 8. While the electric field distribution in the parallel plate electrode is uniform, it is not uniform between mesh-plate electrodes. After increasing the mesh size from 0.5 to 1.0 and 1.5 cm\({}^{2}\), the non-uniform electric field was increased. As a result, Figure 9 shows the electric field distribution for the plate and mesh electrode case when the voltage is 1000 V along the yz and xy planes. In typical plate electrodes, the field is significantly greater near the edges than in the center of the electrode. In the case  
Figure 8: The distribution of the electric field between the gaps for the four top electrodes. Figure 7: Mean value (circles) and standard deviation (triangles) of the electric field for the different meshes. of the mesh electrode, it can be seen that a stronger electric field exists not just at the outer edge of the mesh but also across every area or in every small rectangular path. The sharper edge leads to a higher field [44; 45]. A stronger electric field impacts better ionization, microdischarges, and ion collisions between atoms to produce plasma [46]. These findings lead to the conclusion that the mesh electrode is the optimum geometrical shape. Furthermore, according to Equations (4) and (7), the ionization coefficient depends on the electric field and pressure. Consider that plasma forms at atmospheric pressure (760 torr), and its ionization or breakdown of argon gas solely depends on an electric field. The breakdown voltage is determined in Equation (6) for a uniform electric field and Equation (9) for a non-uniform electric field. The value to be used is the voltage that provides the electric field value as equal to the terms on the right side of Equation (9). The breakdown voltage for each gap distance is shown in Table 2.  
The plot of the breakdown voltage and product between the pressure and gap distance (\(pd\)) of each gap is shown in Figure 10.  
Figure 10 demonstrates that the curve follows the features of the Paschen curve. The resulting curve moves upward from the theoretical curve (Figure 6) because the theoretical curve is obtained from corona discharge, which does not include dielectric material between the electrodes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Gap Distance** **(mm)**} & \multirow{2}{*}{\(pd\)** **(torr cm)**} & \multicolumn{4}{c}{**Breakdown Voltage (V)**} \\ \cline{3-5}  & & & **Plate** & **Mesh 0.5 cm\({}^{2}\)** & **Mesh 1.0 cm\({}^{2}\)** & **Mesh 1.5 cm\({}^{2}\)** \\ \hline
0.1 & 7.6 & 3094 & 3163 & 3159 & 3031 \\
0.2 & 15.2 & 2903 & 2961 & 2955 & 2847 \\
0.3 & 22.8 & 2937 & 2991 & 2981 & 2900 \\
0.4 & 30.4 & 3038 & 3087 & 3077 & 2984 \\
0.5 & 38.0 & 3166 & 3205 & 3196 & 3113 \\
0.6 & 45.6 & 3309 & 3343 & 3339 & 3259 \\
0.7 & 53.2 & 3461 & 3494 & 3491 & 3414 \\
0.8 & 60.8 & 3617 & 3651 & 3648 & 3572 \\
0.9 & 68.4 & 3777 & 3811 & 3808 & 3735 \\
1.0 & 76.0 & 3938 & 3973 & 3970 & 3899 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The breakdown voltage of different top electrodes at pressure 760 torr. Figure 9: The distribution of the electric field in the gaps along the yz planes (**top**) and xy planes (**bottom**) of the four top electrodes. The size of the mesh electrode has a significant impact on increasing the breakdown voltage. The electric field of the mesh electrode with sizes of 0.5 and 1.0 cm\({}^{2}\) was more uniform than that of 1.5 cm\({}^{2}\), and breakdown occurred at higher voltages. Following these findings, the mesh electrode with a 1.5 cm\({}^{2}\) size is the optimal shape that provides the lowest breakdown voltage.