# The Simulation of Dielectric Barrier Discharge for Breakdown Voltage in Starch Modification
## 1 Introduction
[24] stated that cold plasma treatments had a significant impact on the shapes of starch granules, reducing aggregations and developing fissures on granule surfaces as a result of plasma species' etching and making an improvement to the surface topography and roughness of treated starch. Additionally, there were significant modifications in amylose concentration, paste clarity, solubility, freezing thawing stability, color characteristics, whiteness index, molecular weight distribution, and in vitro digestibility, depending on the cold plasma voltage and treatment time. Also, [PERSON] et al. [25] investigate the impact of pin-to-plate cold plasma at atmospheric pressure on physicochemical, functional, powder flow, thermal, and structural factors. The study demonstrates that a reduction in the amylose concentration through plasma-induced depolymerization resists the tendency for retrogradation and increasing paste clarity. Depolymerized proso-millet starch that forms a soluble, low-viscous, stable, and clear paste is produced using cold plasma. Furthermore, several works further discuss topics that are applicable to using cold plasma in medicinal products, functional foods, and food packaging [4; 5; 26; 27; 28; 29; 30]. Cold plasma has seen a significant increase in use in modifying starch. Basic DBD configurations are constructed using parallel planar electrodes, which have a dielectric covering on at least one of the electrodes. The electric field will be generated when applying the electric voltage between two electrodes. When the electric field in the gap is strong enough, electrons are accelerated between collisions to an increasing rate until their energy exceeds the ionization value of neutral molecules, which causes gas ionization. The electric voltage of this process is called the breakdown voltage. A breakdown can be identified using a Paschen curve of the discharge, described by [PERSON]'s law, and examined at various pressures and electrode gap distances. A Paschen curve is one of the essential characteristics for explaining gas discharge behavior, and its use defines plasma production conditions. Designing and fabricating suitable plasma production systems to apply various aspects requires knowing the conditions for each application. This curve, based on [PERSON]'s law, describes the electrical breakdown of gas or gas discharge, and if the uniform electric field applied is strong enough, then the Townsend avalanche process is started, which leads to the breakdown of the gas and the formation of plasma. [PERSON] observed that the minimal voltage that must be provided for a breakdown when a distance \(d\) separates two electrodes is provided by the following equation:  
\[V_{b}=f(pd), \tag{1}\]  
where \(p\) is the gas pressure and \(d\) is the electrode separation [31]. In this work, we would like to study factors that affect the breakdown voltage value in plasma caused by DBD discharge. Additionally, this factor discharge is used in various fields, such as ozone generation [32], cold plasma for medicine [33], environmental applications [34], and agriculture [35]. The breakdown voltage value is important for the approach to designing the system used to create the plasma. The system consists of two main parts: the power supply and the discharge chamber. In the discharge chamber part, there are two electrodes and at least one dielectric on the electrode. The initial plasma production mechanism in DBD is determined using the Townsend breakdown mechanism, which obtains the number of electrons from one electrode to the other electrode terminal, leading to an exponential occurrence (avalanche) and breakdown between gap distance \(d\):  
\[N_{t}=\frac{N_{0}\mathrm{e}^{ad}}{1-\gamma\left(\mathrm{e}^{ad}-1\right)} \tag{2}\]  
where \(N_{t}\) is the electrons from the cathode reaching the anode, \(N_{0}\) is the initial free electrons produced at the cathode, \(\alpha\) is the first Townsend ionization coefficient, and \(\gamma\) is the secondary electron emission coefficient.