## 4 Discussion  
In this section, we use a simplified analytical model to discuss the characteristic phases of SDBD evolution over a single voltage cycle. We also investigate the influence of the electrode geometry on the plasma formation process. We assume that the SDBD is generated using a typical reactor, similar to the one used in our experiment, operating in stationary air at atmospheric pressure. For clarity, only the reactor with a planar electrode configuration is shown in the diagram in Figure 6. The SDBD plasma reactor is powered by a sinusoidal high voltage waveform applied to the discharge electrode, and the progression of voltage phase stages is indicated by arrows in the diagram. It is further assumed that a steady-state SDBD has already been established and that the spatial distribution of the bound charge in the volume of the dielectric is constant. We begin the analysis at the positive voltage half-cycle, when the voltage applied to the discharge electrode is at its maximum (Figure 6A). At this phase, the material of the dielectric barrier is already electrically polarized so that the negative-bound charge accumulates near its upper surface. This negative-bound charge electrostatically attracts positive charges from the surrounding air, forming a thin layer of positive charges on the dielectric surface. Although the attraction of these positive charges has been reported in other studies [56; 57; 58], the mechanism behind their generation remains partially unexplained. It is likely that these charges consist of positive gas ions produced in the discharge during the previous voltage cycles. In Section 3.2, we confirmed the presence of N\({}_{2}\)\({}^{+}\) ions in the  
Figure 5: Typical emission spectra of the SDBD plasma, measured and simulated. SDBD plasma (using the OES method), which are produced in the discharge by collisions with energetic free electrons, as described with Reaction (1). \[e+N_{2}\Big{(}X^{1}\Sigma^{+}\Big{)}\to N_{2}^{+}\Big{(}A^{3}\Sigma\Big{)}+e. \tag{1}\]  
The second phase (Figure 6B) begins as the applied voltage begins to decrease. Despite the decreasing potential of the discharge electrode, the polarization of the dielectric barrier does not dissipate immediately; rather, it is sustained during the dielectric relaxation time and maintains the layer of positive particles. As the applied voltage continues to decrease, the electric potential of the discharge electrodes becomes lower than that of the dielectric barrier surface, creating a strong electric field between the electrode and the dielectric. This field initiates electron emission from the electrode edge. The emitted electrons, along with free electrons in the air, are accelerated along the dielectric surface in the electric field. When the energy of these electrons exceeds the ionization threshold of the air molecules, electron avalanches occur, similar to the negative DC corona discharge that we observed in the form of plasma plumes (shown in Figure 2). These plasma plumes are longer and more randomly distributed when emitted from the planar electrode, probably due to its sharp edges, which are the source of spots of higher electric field intensity. In contrast, the cylindrical electrode produces a more uniform electric field with no points of higher field intensity, so the plasma plumes are shorter and more evenly distributed along the electrode length. Meanwhile, the polarization of the dielectric barrier shifts, and its upper boundary becomes positively polarized. This leads to the accumulation of electrons and negative ions generated in this pseudo-Trichel discharge on the dielectric surface. As the negative charge accumulates, it gradually neutralizes the electric field until the accelerated electrons no longer have sufficient energy to ionize air molecules, at which point this diffuse discharge ceases.