# A Simple and Compact Laser Scattering Setup for Characterization of a Pulsed Low-Current Discharge
## 5 Discussion of the Results  
To check the plausibility of the results shown in Figure 7, they are compared in the following with reference values determined experimentally or by calculations for low-current discharges operated at atmospheric pressure, although some of the experimental setups in those references do not correspond to the experiment considered in this work. The most relevant references are summarized in Table 1.  
According to [PERSON] [59], electron densities ranging between 10\({}^{20}\) m\({}^{-3}\) and 10\({}^{21}\) m\({}^{-3}\) and heavy particle temperatures below 5800 K can be expected for discharges driven by a constant current of less than 50 A, which is in good agreement with the values estimated in this work. In comparison to that, the electron temperature reported in [59]  
Figure 7: Plasma parameters (\(n_{e}\), \(T_{e}\), \(T_{h}\)) estimated from scattering measurements at an axial distance of \(d=1\) mm for a pulse frequency of 60 kHz and a power setting of 100% of the system under study. is significantly lower than that estimated in this work. It should be noted, however, that the operating frequency is quite different--the values presented in [59] are determined for direct current (constant energy supply), while the generator studied in this work is pulsed at frequencies in the range of 50 kHz. Therefore, the discrepancy may be correlated with the operating frequency of the discharge under study. As presented by [PERSON] et al., a significantly higher electron temperature is required to achieve a similar electron density in pulsed operation as is the case for a discharge driven by direct current [4]. This suggestion that the relatively high electron temperature is related to the pulsed nature of the discharge, is confirmed in further references, where pulsed discharges were studied [60, 61, 62, 63]. Subsequently, [PERSON] et al. determined an electron temperature of about 30,000 K and an electron density value of about 10\({}^{21}\) m\({}^{-3}\) for a discharge of nanosecond duration driven in air by 8.3 kV high voltage peaks pulsed at 30 kHz [61, 62]. For these working conditions, peak current values of 30 A were measured, resulting in a rotational temperature of 5300 K, reached about 40 ns after a discharge took place. The heavy particle temperature was determined by fitting synthetic spectra to the SPS \((0,0)\)-transition. Both the electron density and temperature on the other hand were estimated based on calculations of the discharge radius and collision frequency between electrons and heavy particles [61]. Although the reported electron temperature is somewhat lower according to Table 1, the values determined by [PERSON] et al. concur well with the results estimated in this work. The higher \(T_{e}\) and \(n_{e}\) values observed in this work are correlated not only with the operating frequency, but probably also with the plasma gas used. Molecular gases, especially nitrogen, are capable of accumulating energy in vibrational, metastable or dissociated states over longer periods of time [17, 18]. Reactions such as ionic recombination or metastable-induced dissociation (that can lead to the creation of secondary electrons), neutral interactions, and diffusion processes occur in nitrogen plasmas on timescales of hundreds of microseconds or even milliseconds [1, 65, 66]. Hence, the high temperature and concentration of excited species within the discharge channel cannot be cleared fast enough by the gas flow when operating at sufficiently high pulse repetition rates [67], where the recombination time scale and the inverse of the pulse frequency are similar to each other. At a pulse frequency in the range of 50 kHz, the time period (\(\sim\)20 us) between successive energy pulses lies in the same order of magnitude as the recombination time of nitrogen species and therefore an appreciable deviation of electron parameters from the steady state achieved under direct current is to be expected.