## 3 Results and Discussion  
### Dielectric Properties Measurement Results of Test Time  
Measuring dielectric properties is essential for verifying and evaluating experimental results, especially in the synthesis of nitrate fertilizers using plasma technology [61]. Determining the dielectric constant and dielectric loss factor provides valuable insights into how water or solutions react to the electric field applied during the plasma process [62]. These properties directly influence plasma generation and the production of reactive compounds, such as nitrates, which are crucial components of fertilizers. This study examined the dielectric properties of water samples treated with Plasma-Activated Water (PAW) and compared them with untreated water and nitrate-mixed water (2.2 mg/L). The aim was to understand the impact of the plasma process on dielectric properties and its effect on the efficiency of nitrate fertilizer production. The results are presented graphically to demonstrate the relationship between dielectric properties and different electric field frequencies. The results presented in Figure 3a, Figure 4a, and Figure 5a provide a detailed analysis of the dielectric constant (\(\epsilon^{\prime}\)), while Figure 3b, Figure 4b, and Figure 5b illustrate the dielectric loss coefficient (\(\epsilon^{\prime\prime}\)) of water samples treated with plasma for 1, 2, and 3 h. The samples were categorized into three groups: (1) plasma-activated water (PAW), (2) nitrate-treated water (NO\({}_{3}\) + RO), and (3) untreated reverse osmosis (RO) water. The results show significant changes in dielectric properties depending on the treatment duration and flow rate used in the experiments. Figure 2: Dielectric property measurement setup. At a frequency of 0.2 GHz and a flow rate of 0.5 L/min, the dielectric constant of nitrate-treated water increased from 78.75 \(\pm\) 0.37% after 1 h of treatment to 79.75 \(\pm\) 0.26% after 2 h and further to 79.79 \(\pm\) 0.41 after 3 h, indicating the impact of treatment time on the dielectric properties. Across all frequencies, the dielectric constant (\(\epsilon^{\prime}\)) of nitrate-treated water consistently exhibited higher values than those of PAW-treated water and untreated RO water. Similarly, the dielectric loss coefficient (\(\epsilon^{\prime\prime}\)) for nitrate-treated water rose from 7.03 \(\pm\) 0.11% after 1 h to 7.53 \(\pm\) 0.33% after 2 h, and 5.64 \(\pm\) 0.10% after 3 h, demonstrating a trend of increasing dielectric loss with treatment duration. For a more precise comparison, the dielectric properties were also evaluated at a higher frequency of 3.0 GHz and the same flow rate of 0.5 L/min. The dielectric constant of nitrate-treated water was 76.55 \(\pm\) 0.18% after 1 h of plasma treatment, increasing to 77.55 \(\pm\) 0.16% after 2 h, and reaching 77.89 \(\pm\) 0.13% after 3 h, highlighting the influence of plasma exposure time on these properties across different frequency ranges. These findings suggest that plasma-activated water (PAW) has a higher energy storage capacity as the plasma treatment time increases, indicated by an increased dielectric constant. This increase may result from the enhanced polarization of nitrate ions when subjected to an electric field. As the frequency rises, the dielectric constant of all samples  
Figure 4: Measurement results of (**a**) dielectric constant (\(\epsilon^{\prime}\)) and (**b**) dielectric loss factor (\(\epsilon^{\prime\prime}\)) for different water samples (NO\({}_{3}\) + RO, RO Water, and PAW) after a test duration of 2 h.  
Figure 3: Measurement results of (**a**) dielectric constant (\(\epsilon^{\prime}\)) and (**b**) dielectric loss factor (\(\epsilon^{\prime\prime}\)) for different water samples (NO\({}_{3}\) + RO, RO Water, and PAW) after a test duration of 1 h.  
decreases, which aligns with the typical behavior of dielectric materials. This decrease indicates a reduced ability of water molecules to align themselves in response to rapidly fluctuating electric fields at higher frequencies.