Plasmochemical modeling of transient spark in N₂-O₂ mixture

The goal of this work was to create the chemical kinetic model simulating plasma chemistry induced by atmospheric pressure discharge named Transient Spark (TS). The TS is streamer-to-spark transition discharge with very short (10-100 ns) spark phase. First part of the work focuses on the basic physical, chemical and mathematical principles necessary for the plasma chemistry understanding. Most of the described phenomena are essential not only for model construction, but also for accurate interpretation of obtained results. Then, the construction and testing of the model is presented. Fortran 90 programming language coupled with ZDPlasKin package library was used for model development. Necessary set of chemical reactions present in synthetic air (N₂-O₂ mixture) was taken from [23]. Furthermore, the experimentally obtained cross sections for electron involving reaction were found in [19]. The measured gas temperature, voltage waveform and internal circuit capacity were used as experimental input data to computational process. The validity of the model was tested using experimentally obtained electron number density and N₂(C) emission intensity. During the TS streamer phase, the E=N evolution is simulated using Gauss function. The parameters of this function were selected so that the peak E=N value reaches 270 T_d (to be in agreement with literature), and the calculated electron density reaches 10¹⁴ cm^-3 (to be in agreement with our experimental findings). Next, we achieved a very good match between experimentally observed and calculated electron number density in the post streamer phase. In addition, we were able to observe the chemical reactions with the most significant impact on free electrons production and losses. Next, the model enabled us to quantitatively describe the processes responsible for transition from streamer to spark. We revealed that the increase of T_g has not very strong direct impact on free electrons production. On the other hand, the E=N increase has much stronger influence on n_e evolution. The influence of T_g is only indirect. The heating of the gas inside the plasma channel leads to the local increase of the pressure, hydrodynamic expansion, decrease of the density of neutrals and thus increase of E=N. This accelerates the electron impact ionization processes crucial for the breakdown and spark formation. Several E=N profiles were tested to the measured evolution of ne during the TS spark phase. Finally, we created model where E=N is calculated from the time evolution of gas density N(t) and potential V (t) between the electrodes. Since we are not able to calculate N(t) with our 0D kinetic model, we used the N profile from the simulations of Naidis [24]. Besides the hydrodynamic expansion, it handles also the radial diffusion of particles from the discharge channel. We suppose that this profile is the closest match to the TS discharge we found in the literature. Concerning the calculation of V (t), we actually simulate the discharging of C via the plasma resistance R_p. The Rp is derived from calculated ne and experimentally observed dimension of plasma generated by TS. The advantage of this approach is that besides n_e, we calculate another variable that can be compared with experimental data - V (t). Our model deals also with the problem caused by high degree of ionization during the spark phase. The Bolsig+ solver used to calculate electron energy distribution functions is used only for electron density below 10¹⁶ cm^-3. Otherwise, the Maxwellian electron energy distribution functions are used. This approach provided results comparable with experimental findings also during the TS spark phase. The model presents a great tool to study and diagnose the conditions in the TS. The theoretical results enable us to 'see' the scheme of reaction mechanisms leading to more detailed understanding of TS induced chemistry. Moreover, the created model can be further extended using more complex reaction sets focusing on particular application, not only in synthetic air. However, further development is still needed to include processes during the relaxation phase of the TS discharge. This will enable to study the sequence of TS pulses and phenomena related to the memory ect observed in TS at higher repetition frequencies. (Author)