## 1 Introduction  
Non-Thermal Plasma (NTP) are broadly used for applications such as ozone generation, treatment of surfaces, medical treatments, disinfection, and UV production [1; 2; 3; 4; 5; 6]. In recent years, NTP has also become a rising technology for environmental protection. Many studies have reported effective removal of pollutants such as nitrogen oxides (NOx), sulfur dioxide (SO\({}_{2}\)), carbon dioxide (CO\({}_{2}\)), particulate matter, and volatile organic compounds (VOC) [1; 7], with treatments usually processed at atmospheric pressure. Dielectric Barrier Discharges (DBDs) are NTP produced in reactors, including at least one insulating layer between two metallic electrodes. In comparison with other NTP reactors, such as corona discharges and electron beams, DBDs are characterized by the absence of sparks, thanks to the dielectric barriers which limit the local current rise and by the possibility of obtaining uniform discharges, where the NTP covers the entire surface of the reactors, guaranteeing a quality treatment. DBDs operate in filamentary or homogeneous mode [8; 9]. In the homogeneous mode, the plasma is uniform and diffuse [1; 8] and it presents a glowing aspect. For some applications, it has been proven to improve the process: for instance, thin films deposit requires homogeneous discharges in order to obtain a uniform treatment and prevent local damage on the treated surface [2]. The filamentary mode is characterized by streamers, intense energy channels distributed over the electrodes surface, randomly, or sometimes following geometrical patterns [10]. Ozone generation, UV emission for instance, benefits from this mode. At atmospheric pressure, DBD generally operates in filamentary mode, and offer capabilities to initiate very valuable chemical transformations. According to their highly desirable characteristics, DBDs and packed-bed DBDs are widely used for pollutant removal applications. This is the case for the prospective application of our studies (NOx abatement) [7]. Experimental conditions such as the reactor geometry, materials, gas mixture, pressure, and electrical supply waveforms not only influence the discharge mode, but also the characteristics of the power injection into the plasma and the full or partial coverage of the reactor's surface by the NTP. Obtaining operating conditions where the surface of the reactor is fully covered by the plasma is indeed highly desirable for gas treatments: it means that each volume of the gas injected into the reactor will receive the effect of NTP treatment, contrary to the situation where only part of the reactor's surface is covered by the NTP, and thus part of the flowing gas may not receive the expected treatment. Such opposite situations are shown in Figure 1 (side view of a cylindrical reactor, detailed in Section 2, showing the streamers distribution seen through the transparent walls made with quartz). The partial discharging is quantified by the \(\beta\) (no units) percentage, which takes the 1 value when the surface is fully covered and 0 value when the discharge is OFF [8; 11; 12]. Among the diagnostic criteria used for the diagnostic of NTP delivered by DBD, this \(\beta\) discharging ratio is very important to improve the understanding of the efficiency of the gas treatments (NOx abatement in our case). Different diagnostic methods of the discharge mode, based on its appearance, have been proposed. Ref. [9] introduced a simple method that detects the homogeneous glow discharge using the Manley figure and the voltage and current waveforms. This method is based on a definition of the homogeneous APGD (Atmospheric Pressure Glow Discharge), where only one current pulse per voltage half-cycle is generated. Other diagnostic methods include Intensified Charge-Coupled Device (ICCD), high-speed imaging, optical emission spectrum, numerical simulations, and image processing [13].