## 1 Introduction  
The dielectric barrier discharge (DBD), which is formed by applying an alternating high voltage across two electrodes between which at least one dielectric appears, is a common way to generate non-thermal plasma [1, 2]. As one form of DBD [3], the packed bed reactor excited by nanosecond pulse power is significant in the field of research and application. The rich variety of reactive species [4], the high electric field [5] and the ability of accommodating different dielectric materials [6] are the major characteristics of the packed bed reactor. Furthermore, better combination with the catalyst can change the discharge modes and generate new reactive species in the packed bed reactor (PBR) [7]. Moreover, the synergistic effects between the plasma and catalysis, which can improve the energy efficiency and the yield, make the PBR become the favorite discharge structure to generate non thermal plasma and be widely applied in the field of nitrogen fixation [8, 9], volatile organic compound (VOCs) and toluene degradation [10, 11, 12], ozone generation [13, 14], and CO\({}_{2}\) conversion [15], etc. In the field of environment and energy, such as nitrogen fixation and methane dry reforming, increasing the yield while reducing the energy consumption is always the goal, and the optimization of plasma sources is one of the important ways to achieve this. Compared with the traditional DC and AC discharge, the nanosecond pulse has the short pulse duration, the electrons can be accelerated plenty in their free range to obtain energy, and the gas heating can be prevented [16]. Moreover, the uniformity of the discharge can be optimized well by applying the nanosecond pulsed power [17]. In general, the nanosecond pulsed power has a higher energy efficiency and can prevent the glow-to-arc transition [18; 19]. Thus, it has been the preferred choice for us to initiate packed bed DBD, and it needs to be researched and applied. At the same time, the parameters of the voltage pulse and the corresponding characteristics of the discharge also need to be adjusted and investigated, respectively, to optimize the discharge in applications. Previous studies have found that the parameters of voltage pulse, such as pulse peak voltage, pulse repetition rate, pulse rising and falling time, pulse duration, and the electrode shape, have significant effects on the discharge characteristics. [PERSON] et al. [20] found that the gap length, pulse repetition rate, and the variety of the dielectrics can affect the transition between the diffuse \"glow-like\" discharge mode and filamentary mode. [PERSON] and [PERSON] et al. [21; 22] investigated the effects of the pulse peak voltage, pulse repetition rate, and gas composition to DBD and found that the generation of reactive species can be promoted by adjusting these three parameters, and the delay of the photocurrent peak decreases with the increase in the pulse peak voltage. [PERSON] et al. [23] studied the characteristics of DBD with a wedge-shaped electrode. [PERSON] et al. [24] investigated the connection between pulse duration and discharge phases, which have direct effects on the production of reactive species. Furthermore, reactive species, which play an important role in applications, have strong connections with discharge modes in a packed bed reactor. In our previous studies, the discharge evolution process and the corresponding production and quenching processes of reactive species have been studied carefully [25]. Furthermore, the gas composition is also an important influencing factor for packed bed DBD. According to studies, the homogenous discharge, which is beneficial to the material modification, has been obtained in helium, neon, and nitrogen [26]. However, considering the higher cost of the helium and neon, and the larger consumption of the gas during application, nitrogen-plasma is more preferable for researchers to study and apply.