# Temporal Stability of Modified Surfaces of Insulating HV Devices Using Atmospheric Pressure Plasma
## 4 Interpretation of Modeled and Measured Data
A detailed model of the coupled microscopic concept of the model with the macroscopic one is time-consuming and therefore an experimental approach was used to supplement the model of the described problem. Experimental observation with the addition of the wave model of a partial part of the plasma discharge clarifies the origin and relevance of some lines in the RF spectrum. The following records from a high-speed camera (Photron FASTCAM SA-X2 high-speed camera parameters: 160,000 fps, shutter speed 5000 ns) and the performed experiment from the area of stochastic observation and recording were used in this analysis. In Figure 17, an X-type vertex is visible in the area of the beam impact on the dielectric substrate. It is known and theoretically explained [1]. Since this is a dynamic phenomenon and the plasma discharge is characterized by the movement of the electric charge \(q[\text{C}]\), this effect is a source of an electromagnetic wave that can be captured in the spectrum of the scanned spectral density. The moving charge forms an electric current \(i(t)\) for a time change (\(dt\)). \[i(t)=\frac{dq}{dt}. \tag{2}\]  
Figure 16: The distribution of the volume loss density \(p\) in the region of the plasma discharge in contact with the modified surface generated by the slotted chamber. Figure 17: The X-type vertex in the area of contact of the plasma discharge beam with the dielectric substrate. The specific force density \(f_{\rm q}\) acting on a moving electric charge \(q\)[20] in an electromagnetic field can be expressed by the following relation:  
\[f_{\rm q}=\rho(\mathbf{E}+\mathbf{v}\times\mathbf{B}), \tag{3}\]  
where \(B\) is the magnetic flux density vector in the space of a moving electrically charged particle with volume density \(\rho\), \(\mathbf{v}\) denotes the mean velocity of the particle, and \(\mathbf{E}\) represents the electric intensity vector. Therefore, the volume density of the force acting on moving electrically charged particles with charge \(q\) and number \(N_{\rm q}\) of volume \(V\) in the considered region is as follows:  
\[f_{\rm q}=\frac{\mathrm{d}\left(N_{\rm q}q\right)}{\mathrm{d}V}(\mathbf{E}+\mathbf{v} \times\mathbf{B}). \tag{4}\]  
Thus, the effect generates a specific spectrum for the plasma produced by the chamber, depending on the generator power, plasma atmosphere, content and type of precursors, type and quality of the sample surface and other parameters. In the observed and scanned discharge, an O-type vertex can be seen [1], as shown in Figure 18a. This has two possible origins. The first is the formation of a standing wave during the transition from the chamber area to an inhomogeneous environment with a different impedance \(Z\). The second is due to the geometry, gas composition and plasma discharge parameters, as can be observed, for example, in Figure 18b with a previously experimentally verified numerical model [28; 29]. Furthermore, from the experiment and the stochastic approach to the discharge above the sample surface, it is possible to evaluate the different shaping of the dynamic behavior of the movement of electric charge depending on the type of gas composition, as shown in Figure 19 with a dynamic discharge in pure Ar gas, depending on the discharge excitation power and the gas flow volume through the chamber. A marked difference in the discharge shape at the surface is visible in Figure 20; in the Ar atmosphere, the oxygen content was changed parametrically depending on the power supplied to the chamber and the atmospheric flow volume. These typical changes in the shape, length and distribution of the electric charge current path, of course, change the composition and distribution of the scanned RF spectrum of the power \(P_{\rm s}\) generated during the plasma discharge applied to the dielectric samples.