# The Simulation of Dielectric Barrier Discharge for Breakdown Voltage in Starch Modification
## 1 Introduction
If \(\gamma(\mathrm{e}^{ad}-1)<1\), the discharge current will be non-self-sustaining; that is, if there are no cosmic rays or energy sources that can make the electrons escape from the cathode, the discharge current will stop flowing and will not release secondary electrons. However, if \(\gamma(\mathrm{e}^{ad}-1)=1\), the discharging current will be self-sustaining and cause a gas breakdown between electrodes. This condition is called [PERSON]'s breakdown criterion or the self-sustaining discharge criterion. \[ad=ln\left(1+\frac{1}{\gamma}\right) \tag{3}\]  
In the case of a uniform electric field, [PERSON]'s experiments showed that  
\[\alpha=Ap\;e^{-\frac{Bp}{L}} \tag{4}\]  
The results of Equations (3) and (4) demonstrate that  
\[E_{b}=\frac{Bp}{lnApd-ln\left[ln\left(\frac{1}{\gamma}+1\right)\right]} \tag{5}\]  
and  
\[V_{b}=\frac{Bpd}{lnApd-ln\left[ln\left(\frac{1}{\gamma}+1\right)\right]} \tag{6}\]  
where \(A\) and \(B\) are the constant values of each type of gas, \(p\) is the pressure of the gas, and \(d\) is the gap distance [36]. Moreover, many studies have shown that the electric field in the gap may not be uniform. This electric field non-uniformity has an impact on both the discharge ignition and the gas breakdown criteria [37; 38; 39; 40]. If \(E(z)\) is the axial electric field, this field changes according to the position between the electrodes. The ionization coefficient \(\alpha\) is altered to  
\[\alpha(z)=Ap\;e^{-\frac{Bp}{E(z)}} \tag{7}\]  
Therefore, from Equation (3), the breaking down condition is  
\[\int\limits_{0}^{L}\alpha(E(z))dz=ln\bigg{(}1+\frac{1}{\gamma}\bigg{)} \tag{8}\]  
or  
\[\int\limits_{0}^{L}Ap\;e^{-\frac{Bp}{E(z)}}dz=ln\bigg{(}1+\frac{1}{\gamma} \bigg{)} \tag{9}\]  
For argon \(A=11.5\) cm\({}^{-1}\) torr\({}^{-1}\), \(B=176\) V cm\({}^{-1}\) torr\({}^{-1}\) and \(\gamma=0.07\)[41]. In the situation of a non-uniform field, we can identify the intensity of the electric field for the ignition of the discharge via Equation (8), which means that we can find the electrical voltage that causes the breakdown. Generally, various parameters, such as electrode diameter, electrode geometries, dielectric surface, accumulation of surface charge, etc., have an impact on the electric field generated and result in its non-uniformity. As a consequence, it is challenging to develop a usable plasma-generating system. Therefore, one method before building a plasma generator system is to simulate the situation according to the specified conditions. In applying starch modification, if we have conditions for the starch, we can input them into the model to determine the starting voltage used to create plasma and then adjust the conditions for additional studies. For instance, we can adjust the electrode spacing to obtain the required initial voltage at atmospheric pressure (760 torr). On the other hand, identifying the original voltage of this breakdown can also be utilized as a criterion when the plasma generating system is designed in order to vary the pressure. Each kind of starch has unique characteristics and applications specific to its type. It is crucial to determine the appropriate DBD conditions for each starch. The aim of this study is to use COMSOL Multiphysics to simulate the generation of electric fields for the breakdown of the DBD model to determine the breakdown voltage for the starch modification process. The impact of the starch's relative permittivity, granule shape, thickness, and diameter on the breakdown voltage will be studied. Another factor to consider is the top electrode's mesh size. The results presented in this work can help to develop a highly efficient plasma production system for the starch modification process in future work.