## 4 Discussion
### Temporal Evolution of the Estimated Plasma Parameters  
The scattering results show that slightly lower \(T_{h}\) values are observed when either the frequency or the power setting is reduced (see Figures 2 and 5). According to theoretical models of [PERSON] [55] as well as [PERSON] [56], the gas temperature in pulsed discharges is associated with the dissipated power rather than the separate behavior of voltage or current. [PERSON], who modeled nanosecond pulsed spark discharges in air, discussed two case studies in [56] and observed no significant difference in the heavy particle temperature. In the first case, the discharge was pulsed at a frequency of 30 kHz. In the second case, the frequency was reduced to 15 kHz, but the pulse duration was doubled so that the input power was similar in both cases. Assuming that the power supply delivers a nearly equal electric charge and thus also a similar energy amount into the system with each single current pulse, then a higher power is dissipated in the plasma generator with increased frequency, since, with a faster repetition of similar pulses, the power transferred to the discharge increases (under the above assumption). Such an increase for higher pulse repetition rates is measured at the exit of the power supply. Although a slower response of \(T_{h}\) to steeper current slopes can be observed in the temporal distribution of the mean plasma parameters (see Figure 3), this does not have a significant effect on the mean temperature. Thereafter, the above statement that the heavy particle temperature depends mainly on the dissipated power can be confirmed experimentally for the analyzed system. The effect of a delayed response of heavy particles to input power changes (particularly visible for 43 kHz in Figure 3) was observed by several research groups. An increase in the heavy particle temperature of a gliding arc discharge was observed by [PERSON] et al. while the current and power decreased at the same time [57]. A possible explanation for this \"memory effect\", as called by [PERSON] et al., is provided by [PERSON] et al. [58]. According to their observations, the effect is connected with the exchange of rotational and vibrational energy of molecular species leading to additional heating of heavy particles. Furthermore, taking into consideration that recombination reactions in nitrogen plasmas can occur on timescales of hundreds of microseconds or even milliseconds [59; 60; 5], this energy exchange can lead to a possible accumulation of various charged species in the discharge channel if the discharge is operated at sufficiently high frequencies (as is the case in this work). This can lead to the appearance of a space charge field that has to be first overcome by the external electric field of the next pulse [58]. Similar considerations on the influence of the heavy particle temperature and gas flow on the discharge behavior can be found in [61; 62; 63]. According to the above discussion, the effect observed in Figure 3, the fact that a higher gas temperature is measured even though the current is already decreasing is attributed to such a \"memory effect\". The parameters estimated in this work for the plasma free electrons are relatively insensitive to fast changes of the discharge current (see Figures 3 and 5). According to a theoretical model of a low-current DC discharge developed by [PERSON] and [PERSON] [64], a reduction in electron density by about one order of magnitude can be expected when the current value decreases from amperes to milliamperes (see upper left plot in Figure 3). This reduction is attributed by the authors to a change in the ionization rate. Hence, for lower current values, for which non-LTE conditions are assumed, higher values of the reduced electric field are expected, and thus the ionization rate of neutral particles is mainly controlled by the electron impact.