## 5 Discussion  
As mentioned in Section 1, several researchers have analyzed spectroscopically comparable plasma systems to the one studied here [3, 24, 35, 36, 40, 41], but none have determined the electron number density purely experimentally using hydrogen line broadening. Some, as will be discussed in the following, calculated the electron density based on recorded molecular spectra. The electron number density is reported to range between \(10^{20}\) m\({}^{-3}\) and \(10^{21}\) m\({}^{-3}\) for low-current discharges operated with a direct current [56]. However, several researcher groups report slightly higher values for pulsed discharges. [PERSON] et al. determined a density of about \(1\times 10^{21}\) m\({}^{-3}\) (and electron temperature of about 30,000 K) for the nanosecond pulsed discharge operated in the air by 8.3 kV high voltage peaks pulsed at 30 kHz [41, 42]. For these working conditions, [PERSON] et al. measured peak current values of 30 A. The electron density was determined by the authors based on calculations of the discharge radius, which was determined from the SPS \((0,0)\)-transition spectrum, and collision frequency between electrons and heavy particles. The higher \(n_{e}\) values can be, however, caused by the current peaks, since the current density \(j\) is directly proportional to the electron density \(n_{e}\) according to \(j=-q_{e}n_{e}v_{e,d}\), with \(q_{e}\) being the electron charge and \(v_{e,d}\) the drift velocity of electrons [66]. An even higher \(n_{e}\) was calculated with a collisional-radiative model by [PERSON] et al. for a gliding arc plasmatron operated with nitrogen at a constant current of 230 mA [35]. The density was estimated to be \(1.6\times 10^{21}\) m\({}^{-3}\). Moreover, in this case, the calculations were based on the relation between the measured intensity of the SPS \((0,0)\)- and FNS \((0,0)\)-transitions of nitrogen molecules [35]. According to observations of [PERSON] et al. [65], an increase in electron density can be observed for gliding arc discharges if they are constricted by a tube, which is the case for the plasmatron studied in [35]. Another possible explanation can be the existance of short duration current peaks, which can occur during an shortening of the discharge channel, as shown by [PERSON] et al., who investigated a compact plasma torch driven by a low-current high-voltage direct current discharge [28]. Such peaks were observed at certain currents in the range between 150 mA and 400 mA, at which the discharge behaved like a gliding arc, i.e., the current peaks were caused by a reignition of the discharge at a shorter distance between the electrodes after it had been blown out by the gas flow. The discharge motion of a gliding arc plasmatron has been described in detail for an operation with \(CO_{2}\) by [PERSON] et al. [67], but the presented results were not correlated with time-resolved progressions of voltage and current. Thus, although the motion of a discharge channel depends on many factors, such as the geometry of the generator as well as the type and flow rate of the gas used, this effect may lead to an increase in electron density and cannot be excluded. The electron density values determined experimentally in this work are slightly lower compared to the above references, but this is probably the result of lower pulse current  
Figure 7: Experimental data used for estimation of \(n_{e}\) (**left hand-side**) and \(T_{h}\) (**right hand-side**). Due to imaging errors, a significantly lower intensity was recorded for a distance of 1 mm downstream from nozzle exit in both cases. amplitudes, as indicated above. Due to the design of the PG31 plasma generator and the observations made during measurements, the length of the discharge channel does not change significantly when operating at a frequency of 60 kHz. Even though the discharge is pulsed, it behaves similarly to the continuous regime described in [28], where the discharge is blown out of the nozzle, reverses and forms an attachment point at the nozzle lip.