## 5 Discussion
Thus, the channel length remains relatively constant, which in turn leads only to a small variation in the voltage and current waveforms, as shown in Figure 2.  
Furthermore, it should be noted that the above referenced \(n_{e}\) values are calculated rather than determined experimentally, which also may lead to small discrepancies. Nonetheless, the values estimated in this work are of the same order of magnitude as the referenced ones and thus are assumed to be plausible. The lower value of electron density at a distance of 1 mm downstream from nozzle outlet, as well as the high deviation from the mean values observed for the molecular temperatures at the same distance, are most likely due to an imaging error. As presented in Figure 7, a significantly lower intensity was recorded for this distance in both cases. At other distances, the progression of recorded intensities is as expected and decreases with increasing distance from the nozzle outlet. The somewhat counter-intuitive increase in \(n_{e}\) for higher distances from jet axis (see Figure 6) was also observed in [68; 69] and might be caused by an effect described by [PERSON] et al. [70]. The latter researcher group used laser scattering to estimate electron parameters of a plasma torch with axial gas injection driven by microwaves and operated with argon as well as helium at atmospheric pressure. A significant increase in both electron density and temperature was observed with increasing lateral distance from the torch axis. The effect was reduced by changing the ambient atmosphere from air to argon. Thus, the authors concluded that the increase is attributed to air entrainment from the surrounding cold atmosphere [70]. However, since the discharge in this work is operated with pure nitrogen, the above hypothesis does not seem to prove the effects satisfactorily. Another possible explanation for such an increase in values in the radial direction can be given if the beam geometry of the spectroscopic setup is considered in detail. A nearly Gaussian distribution can be assumed in a first approximation for the intensity radiated by the discharge plasma channel, which is then imaged by the spectrograph onto the sensor plane of the camera, where an integration of the signal in the viewing direction takes place. However, the integrated signal contains no information about the distribution of the emitted radiation in the direction of observation and thus an additional assumption is needed to describe the intensity distribution in the viewing direction. If again, a nearly Gaussian intensity distribution is assumed in the viewing direction, then as a result the emitted intensity can be approximated by a two-dimensional Gaussian as shown in Figure 8. If the intensity peak is now positioned slightly off-center from the nozzle axis and moves e.g., rotationally, as marked in Figure 8, then a bimodal distribution of the intensity is observed as a result of the integration on the camera sensor. Looking at such a bimodal distribution, it becomes apparent that the estimated values can increase towards further radial positions if the experimental setup is well aligned with the axis of the plasma generator. Thus, according to this discussion, the lateral motion of the discharge channel is most probably responsible for the increase in values for increasing radial distances. The effect is further increased since average images are used for the parameter evaluation. Several authors determined the temperature of molecular transitions for comparable discharges. Thus, these results can be used as a validation of the experimental setup in this work. Thereafter, the above-discussed nanosecond pulsed discharge studied by [PERSON] et al. reached a rotational temperature of 5300 K about 40 ns after a discharge pulse took place. The temperature was determined by fitting synthetic spectra to the SPS \((0,0)\)-transition [41]. [PERSON] et al.