## 4 Discussion
### Temporal Evolution of the Estimated Plasma Parameters
For higher currents, for which LTE conditions are assumed by the authors, lower \(E/n\) and higher \(T_{h}\) values are expected; hence, the excitation process leading to ionization is reported to be controlled instead by associative ionization of metastable states [64]. A comparable statement can be found in the works of [PERSON] et al., who reported that the excitation and de-excitation rates of nitrogen electronic states change with increasing temperature of heavy particles [65, 66]. While the excitation of the ground state \(X^{1}\Sigma_{S}^{+}\) is mainly governed by electron impact, the excitation of metastables such as \(A^{3}\Sigma_{u}^{+}\) to higher energy states as well as most de-excitation reactions are caused by collisions with other heavy particles. Thus, according to [PERSON] et al., for low \(E/n\) values the resulting free electrons are predominantly provided by associative ionization of following states:  
\[N_{2}\left(A^{3}\Sigma_{u}^{+}\right)+N_{2}\left(a^{\prime 1} \Sigma_{u}^{-}\right) \to N_{4}^{+}+q_{e}\,,\] \[N_{2}\left(a^{\prime 1}\Sigma_{u}^{-}\right)+N_{2}\left(a^{\prime 1 }\Sigma_{u}^{-}\right) \to N_{4}^{+}(X)+q_{e}\,,\]  
although both initial states, \(A^{3}\Sigma_{u}^{+}\) and \(a^{\prime 1}\Sigma_{u}^{-}\), have been mutually formed by collisions with electrons. [PERSON] developed further the mathematical models presented in [64] and performed calculations for nanosecond repetitively pulsed sparks operated in air [56]. The initial pulse conditions were adopted from experiments with a voltage amplitude of 5 kV, a pulse length of 5 ns and repetition rate of 30 kHz. According to the simulated results, the number density decreases after a pulse due to electron-ion recombination with a characteristic time constant of approximately 30 \(\upmu\)s. Electron recombination times in a similar range of about 10 \(\upmu\)s are also reported by [PERSON] et al. [67]. A slow recombination rate of electrons is furthermore observed by [PERSON] et al. while investigating a nanosecond pulsed microgap discharge operated in air at a frequency of 8 kHz [68]. Similarly to others, the researchers postulated that the slower-than-expected recombination rate may originate from a combination of associative and stepwise ionization processes during the recombination phase. Moreover, they suggest that a high density of excited nitrogen atoms may also play a significant role in slowing down the recombination of free electrons [68]. The correlation of the above discussion with the experimental results obtained in this work suggests that the excitation and de-excitation processes of heavy particles may be responsible not only for the \"memory effect\" but also for the relatively slow decay of electron parameters observed here (especially since the plasma generator operates at pulse repetition rates comparable to those of electron recombination). Hence, when the current is rising, the excitation and dissociation of nitrogen molecules is mainly caused by electron collisions. Both electron density and electron temperature increase with increasing current and energy is transferred to heavy particles. After a pulse, the reduction in the electron density does not immediately follow the current trajectory due to complex de-excitation reactions, which slow down the recombination rate of free plasma electrons. This maintains a relative high electron density and may lead to the formation of further electrons, even during a phase of low current. The above hypothesis may also explain the difference in the electron parameters observed for both frequencies. As shown in Figure 2, a higher electron density and higher electron temperature are measured for the lower operating frequency of 43 kHz. At this frequency, however, a lower power is coupled into the generator, as discussed above. Furthermore, nitrogen is a plasma gas whose recombination displays a somewhat slower rate due to de-excitation channels consisting of several steps.