# Temporal Stability of Modified Surfaces of Insulating HV Devices Using Atmospheric Pressure Plasma
## 4 Interpretation of Modeled and Measured Data  
In order to better understand the cause and context of the appearance of typical spectral lines when applying plasma to the sample surface, it is necessary to consider the behavior of plasma as an electromagnetic phenomenon when in contact with the sample. For this purpose, a number of numerical models were used, which are listed below or have been previously published [13; 14; 28; 29]. A radio-frequency (RF) slot plasma nozzle with an active plasma width of \(w_{\mathrm{g}}\) = 150 mm was used for the surface treatment of the tested polymer insulation samples, as shown in Figure 14. This figure shows the geometry of the chamber, which was numerically modeled using the finite element method [30; 31] in the ANSYS [30] HFSS module, where \(P_{\mathrm{out}}\) = 500 W, under an argon and other atmosphere. The evaluation of numerical models and comparison with experiments is complemented by research from the field of radio-frequency methods [32; 33]. Currently, FEM numerical models are used from the perspective of the mechanistic concept of the matter [34; 35; 36; 37; 38] or only a narrow part of the electromagnetic spectrum from the perspective of optics [39]. Our problem and its model extend into the field of electrodynamics [1] and specifically deal with the electromagnetic field [40] with the formulation of the telegraph equation. A numerical model used for chamber geometry modelling and to evaluate electromagnetic quantities, i.e., the frequency dependence of the \(S\) and \(Z\) parameters [13] of the laboratory experiment [14; 15; 16] shown in Figure 14, was constructed based on solving the reduced Maxwell's equations and the formulated wave equation in ANSYS [30]. \[\
abla^{2}\hat{\mathbf{A}}+\hat{k}^{2}\hat{\mathbf{A}}=-\mu\hat{\mathbf{f}}^{c},\ \Delta\hat{\varphi}+\hat{k}^{2}\hat{\varphi}=-\frac{\hat{ \rho}^{c}}{\varepsilon} \tag{1}\]  
where \(\hat{\mathbf{A}}\) is the complex vector magnetic potential, \(\hat{\varphi}\) denotes the complex scalar electric potential, \(\hat{k}\) represents the complex wave number, \(\varepsilon\) stands for the electric permittivity, \(\mu\)  
Figure 14: The geometrical arrangement of the slot plasma chamber, where \(w_{\mathrm{g}}\) = 150 mm. \begin{table}
\begin{tabular}{c c c} \hline
**Plasma Atmosphere** & **Thermoplastic Sample, \(P_{\mathrm{slog}}\) [dBm]** & **Sample from Thermoset, \(P_{\mathrm{slog}}\) [dBm]** \\ \hline Argon + O\({}_{2}\) & Thermoplastic, Ar+O, without background \\  & & \\  & & \\ \end{tabular}
\end{table} 
Table 1: _Cont._signifies the magnetic permeability, \(\hat{\rho}^{e}\) is the complex specific electric charge, and \(\vec{\hat{J}}\) is the current density. Model (1) and the modeling method were previously described in detail and verified experimentally in the papers [16; 28]. The analysis results for the critical parts of the chamber are shown in Figures 15 and 16. The figures show the distribution of the magnetic field intensity components \(H\) in the area of the chamber winding and the plasma discharge slot, in addition to the distribution of the electric field intensity components \(E\). Figure 15: The field intensity component distribution in a chamber with a slit for plasma discharge in contact with a dielectric substrate and modified sample surface, with (**a**) \(H\) for the magnetic field and (**b**) \(E\) for the electric field. The analysis results provide quantitative evaluation of the electromagnetic field distribution at the sample surface, as shown in Figure 15. Figure 16 illustrates the distribution of the power volume loss density \(p[\text{Wm}^{-3}]\) in the area of the plasma discharge in contact with the modified dielectric surface generated by the slot chamber at the nominal chamber excitation power \(P_{\text{out}}\) = 500 W for an argon atmosphere. The above-mentioned deterministic analyses can be considered as an evaluation of the discharge from the macroscopic concept of the model, especially of a quantitative nature.