## 4 Discussion
### Validity of Results  
The results achieved with laser scattering are considered to be plausible, according to the comparison with previously published works given in [39]. Furthermore, the results of laser scattering and emission spectroscopy can be considered to be in good agreement, although discrepancies are observed in absolute values between the two diagnostic techniques. The values are of the same order of magnitude and show similar trends for both electron number density and temperature of heavy particles. With both diagnostic methods, higher \(\overline{n}_{e}\) and lower \(\overline{T}_{h}\) values are obtained for the lower operating frequency of 43 kHz. The differences in the electron densities determined by the scattering experiment between the two frequencies studied are much more subtle than those estimated by means of spectroscopy. Furthermore, the spectroscopically determined number densities are only half or even only a third as large as the corresponding values determined by laser scattering (compared to each other at the same frequency).  
The discrepancy between the \(n_{e}\) values might be related to the evaluation methodology of the Stark broadening, as indicated in [48]. According to [40], the Stark effect can be approximated with two limiting cases, the linear and the quadratic case. The approximation formula given in [47], used by most authors [48; 49; 50] and also used in this work, is derived for the linear case, in which the line broadening is proportional to \(\sim\)\(n_{e}^{2/3}\)[51]. Such a linear method assumes a non-spherically symmetric distribution of electrons within an atom, i.e., that the emitting atom already displays a dipole moment, and that the free electrons act collectively. In contrast, the quadratic Stark effect assumes a sequence of two consecutive interactions between the atom and the free plasma electrons. The first interaction \"deforms\" an initially spherical symmetric atom inducing a short-lived dipole moment, while the second interaction with another free electron is responsible for the eventual emission of radiation by the atom. As a consequence, the line broadening is directly proportional (in a good first approximation) to \(\sim\)\(n_{e}\)[51]. However, if the effects occurring in the analyzed plasma correspond to an intermediate situation between both limiting approximations, for example, due to the complicated ionization process of nitrogen plasmas in non-equilibrium, then the estimation of \(n_{e}\) is more complex, and the values cannot be calculated directly with the approximation formula corresponding to the linear case. This may be the reason for the difference between the \(n_{e}\) values determined spectroscopically  
Figure 5: Mean plasma parameters estimated for different power settings at an axial distance of 1 mm from nozzle exit while the scattering setup is triggered at \(I_{peak}\). A power setting of 100% corresponds to a current amplitude of \(\sim\)1.0 A.  
and by the scattering experiment. However, the observed discrepancy may also be caused by a different effect. To estimate the electron density, a commercially available canister of a nitrogen mixture with a small addition of hydrogen (1 vol.%) is used as the plasma gas. Although the gas is already premixed, segregation effects of the gas components can occur in a plasma, as reported, for example, in [52; 53]. The transient nature of a pulsed discharge, where the energy pulses lead to the creation of pressure waves [5; 54], can amplify the demixing effect. Thus, the hydrogen may not be homogeneously distributed in the measurement volume, leading to the observed differences between the two diagnostic methods. Nonetheless, as mentioned above, the values shown in Figure 2 are of the same order of magnitude and, more importantly, show the same trends, which appears to be a sufficient validation of the laser scattering results in combination with temperatures determined from molecular transitions.