## 1 Introduction  
Dielectric barrier discharge (DBD) actuator in plasma flow control is an active research field in the past few years. The advantages of the DBD actuators are low weight, small size, low energy consumption, without moving parts, fast response, and wide-band control authority. Conventional DBD actuators produce electrodynamic (EHD) flow acceleration (ion wind) of the electric field, which can control the flow separation when the free stream Mach number is less than 0.4. Recently, nanosecond pulsed dielectric barrier discharge (NS-DBD) actuators have been proposed. NS-DBD actuators are driven by nanosecond high voltages repetitively. The discharge is featured by the local ionization at a nanosecond time scale, which induces a fast and slow gas heating at different timescales. The fast gas heating usually occurs at 0.01\(\sim\)1 \(\upmu\)s, which can induce compression waves. However, the slow gas heating occurs at a time scale of about 200 \(\upmu\)s. It can introduce wide-band perturbations of temperature, pressure, and density, which can trigger instabilities in the shear flows. NS-DBD plasma actuators can be applied in the high-speed flow controls [1; 2]. The air discharge of NS-DBD involves complex reactions, which makes the kinetic numerical modeling of the discharge very complicated. The governing equations of lots of species introduce a very large partial differential equation system. As the reaction rates of different reactions and number densities of different species are much more different, the equation systems are very stiff to solve. Because different chemical reactions of the multi-species contribute much more differently to the energy balance, an appropriate modeling of chemical reactions is very crucial. [PERSON] et al. [3] developed a kinetic model of \(N_{2}/O_{2}\) mixtures having 46 species and 395 reactions, which includes electronic excitation, electron impact destruction and ionization, electron attachment and detachment, recombination of electron-ion and ion-ion, associative ionization, ion conversion, and chemical transformations of neutral particles. It is very difficult to adopt all the reactions in a physical modeling of the NS-DBD discharge, due to the very large governing equation system and huge computational cost. Therefore, most of the work adopted different reduced reaction models. [PERSON] et al. [4] adopted a kinetic model that consists 20 species and 176 reactions to do multiscale modeling of a pulsed NS-DBD. [PERSON] and [PERSON] [5] developed a 20 species and 49 reactions kinetic model for the low-density plasma and a 19 species and 73 reactions model for the high-density plasma. [PERSON] and [PERSON] [6] also adopted an 8 species and 15 reactions kinetic model simulated the plasma formation in a nanosecond pulse plane to plane dielectric barrier discharge at atmospheric pressure and 340 K. [PERSON] et al. [7] developed a reduced model with 23 species and 50 processes to study the main species and reactions in energy storage and thermalization of an NS-DBD. They [7] also developed a 15-species and 42-process model to simulate a NS-DBD discharge. [PERSON] et al. adopted two models in plasma simulations, which contain 16-species, 44-process [8], and 13-species, 37-process [9], [PERSON] et al. [10] simulated an airglow discharge at pressure \(\sim\)1 Torr by an 11 species and 21 reactions plasma model. [PERSON] et al. [11] used an 8 species, 28 reactions air chemical model modeled plasmas for computational aerodynamics. The reduced kinetic models neglect some minor species and the corresponding reactions, however, the effects of the neglected species on the preserved major species need to be addressed.