## 2 Experimental Setup and Methods
### Parameters Calculation and Kinetic Model  
After the reaction, the tail gas was transferred to 10 mL of 0.005 mol/L H\({}_{2}\)SO\({}_{4}\) dilute, and 0.5 mL of absorbed H\({}_{2}\)SO\({}_{4}\) dilute was transferred to the ammonium nitrogen detector to determine the ammonium concentration. The chemical formula of the reaction is shown in Equation (1):  
\[2\mathrm{NH_{3}}\cdot\mathrm{H_{2}O}+\mathrm{H_{2}SO_{4}}=(\mathrm{NH_{4}})_{2 }\mathrm{SO_{4}}+2\mathrm{H_{2}O} \tag{1}\]  
Figure 1: Experimental setup for ammonia synthesis by DBD. The measured ammonium concentration was the ammonia concentration. From Equation (2), the ammonia synthesis rate could be calculated as follows:  
\[\text{NH}_{3}\text{ synthesis rate}\Big{(}\mu\text{mol}\cdot\text{g}^{-1} \cdot\text{h}^{-1}\Big{)}=\frac{C\Big{(}\text{mg}\cdot\text{L}^{-1}\Big{)} \times 10(\text{mL})\times 60\Big{(}\text{min}\cdot\text{h}^{-1}\Big{)}}{18 \Big{(}\text{g}\cdot\text{mol}^{-1}\Big{)}\times t(\text{min})} \tag{2}\]  
where \(C\) is the NH\({}_{3}\) concentration. \(t\) is reaction time. Equation (3) was used to determine the energy yield (g kWh\({}^{-1}\)):  
\[\text{E}_{\text{NH}_{3}}\Big{(}\text{g}\cdot\text{kWh}^{-1}\Big{)}=\frac{ \frac{C\big{(}\text{mg}\cdot\text{L}^{-1}\big{)}\times 10(\text{mL})}{t( \text{min})}\times 60\Big{(}\text{min}\cdot\text{h}^{-1}\Big{)}}{P(\text{W})} \times 10^{-3} \tag{3}\]  
\[P=f\int V(t)\times I(t)\text{d}t \tag{4}\]  
In Equation (4), \"\(V(t)\)\" is the voltage in \"V\", \"\(I(t)\)\" is the current in \"A\", \"\(f\)\" is the frequency in s\({}^{-1}\). The experimentally measured spectra of N\({}_{2}\) (C\({}^{3}\Pi_{\text{u}}\)\(\rightarrow\)B\({}^{3}\Pi_{\text{g}}\)) were imported into the Specair software (Version 3.0), and the OES curves were fitted to them by setting the parameters of spectral species and the narrow peak coefficient, and adjusting the set values of rotation and vibration temperatures to derive the rotation and vibration temperatures of the nitrogen molecules under the experimental conditions. Given the minimal energy gap between rotational energy levels, the plasma's gas temperature can be closely estimated by the rotational temperature of N\({}_{2}\). A 0D plasma chemistry model was used to understand the key intermediates and chemical pathways following the addition of noble gases. The electron temperature in a non-equilibrium plasma is much higher than the gas temperature, and the electron energy distribution function deviates from the Maxwell distribution, which is subject to the Boltzmann equations, which are too complicated to solve because they include all possible transport and collision terms. The BOLSIG+ Boltzmann equation solver, developed by [PERSON] et al. [30], provided a swift method to approximate the solution of the Boltzmann equation. It utilized two approximations to calculate the electron energy distribution function, \(F_{0}\). After the Boltzmann equation was solved and \(F_{0}\) determined, the rate coefficients for every substance involved in the electron collision reaction process were calculated using Equation (5). \[k_{\text{je}}=v\int_{0}^{\infty}\varepsilon\sigma F_{0}\text{d}\varepsilon \tag{5}\]  
In Equation (5), \(k_{\text{je}}\) is the electron collision reaction rate coefficient in \"m\({}^{3}\)/s\"; \(v\) is the viscosity coefficient in \"Pa-s\", \(\varepsilon\) is the electron energy in \"eV\"; \(\sigma\) is the electron collision cross section, and \(F_{0}\) is the obtained electron energy distribution function. When simulating the discharge process, the ZDPlaskin Fortran90 program calls the BOLSIG+ solver to solve the electron transport coefficients and the reaction rate coefficients quickly and in real time, and calls the DVODE_90 solver to solve the component concentration equations to obtain the reaction rate and the evolution of reactive particles over time during the discharge process.