3.2. Analysis of the Observed H-β and He I 492 nm Lines
Figure 5 shows the experimental spectra of H-β and He I 492 nm lines recorded simultaneously for different pressure values in the test cell, at 0.1, 0.2, and 0.3 MPa.
It can be seen, by comparison with theoretical results shown in
Figure 3, that an increase in the pressure has the same effect on the spectral profile as an increase in the electronic density. The PPP calculations provide reasonable qualitative agreement with the experimental data.
In the following, we have considered that the experimental spectra result from three different broadening mechanisms: Stark broadening, van der Waals broadening, and instrumental broadening. For a gas temperature of 300 K, the Doppler width is 1 × 10−3 nm for the H-β line and 7 × 10−4 nm for the He I 492 nm line, leading to negligible effects on these line profiles compared to overall broadenings. Thus, the combination of these different broadening mechanisms results in complex spectral line profiles showing an inhomogeneous structure, i.e., a set of Stark components due to ionic Stark effect, where each component is homogeneously broadened by electronic collisions, van der Waals effects, and instrumental artifacts.
The van der Waals broadening mechanism, together with the resonance (which is not taken into account in this work) and electronic impact broadening, contributes to the width of the Lorentzian part of the line shape. The corresponding widths for the H-β line and for the He I 492.2 nm lines emitted in a helium plasma are determined by formulas given in column 2 of
Table 1 and
Table 2, respectively [
24].
In these formulas, the units of pressure and temperature are Pa and K, respectively. In the present study, it is assumed that van der Waals broadening can be taken into account by considering the same equation for three radiative lines in both the H-β and He I 492.2 nm spectra. The result of this assumption has been proved with a modified version of the PPP code, and it was found that it is negligible in the present conditions. The theoretical values of the van der Waals (VDW) widths for the H-β and He I 492.2 nm spectral lines are shown in
Table 3 and
Table 4, respectively.
The opacity effects have also been estimated for both lines in the conditions of the present study. In this experiment, the corona discharge occurs in gaseous helium at 300 K at different gas pressures in the test cell, at 0.1 MPa, 0.2 MPa, and 0.3 MPa. The helium gas is not perfectly pure and contains impurities, in particular ~0.1 ppm of hydrogen. By using the helium density given by nhe = P/kT, where k is the Boltzmann constant, and the hydrogen density by 0.1 × 10−6 nhe, it is possible to estimate the line center opacity assuming a spatially uniform plasma of given geometrical path length, ℓ, at local thermodynamic equilibrium. For a geometrical path length ℓ = 100 μm, the line center opacities are of the order of a few 10−6 for the helium line and of a few 10−8 for the hydrogen line (for these three pressure values). Thus, in the following analysis, it is assumed that both lines are optically thin.
The comparisons between line shapes synthesized by the PPP code in the conditions determined by the GA analysis and the H-β and He I 492 nm experimental lines are shown in
Figure 6 for each pressure value.
The plasma parameters ne and Te are determined with the GA procedure, together with the potential additional broadening of spectral lines corresponding to the full (Lorentzian) width at half maximum (FWHM) for van der Waals broadening, and the full (Gaussian) width at half maximum (FWHM) for instrumental broadening. The latter has been measured in the range between 0.08 nm and 0.09 nm which has been set in the GA procedure in order to determine the Gaussian width.
The four parameters obtained by the GA analysis, i.e., the electron density n
e, the electron temperature T
e, the van der Waals width
, and the additional Gaussian width Δλ
ins, are given in
Table 5 for the H-β line and in
Table 6 for the He I 492 nm line.
It can be seen that the electronic densities obtained by individual fitting of the hydrogen and helium lines are significantly different. The densities obtained using the helium line are in accordance with the densities obtained previously by analyzing the peak distances. However, these values are completely incompatible with a suitable fit of the H-β experimental spectra. The H-β line is much more difficult to fit with the synthetic spectral line profile than the He I 492.2 nm, in particular because of a bump in the blue wing which is not explained by the models. In other words, if the experimental spectral lines include specific structures which cannot be reproduced by the models (e.g., impurity emission lines), the GA will produce the best fit between the synthesized and experimental profiles, including the given structures, at the expense of the rest of the spectra. In the present work, to avoid the problem caused by the bump in the blue wing of the Balmer-β line, the fitting procedure has been restricted to the center of the line, as neither the Stark broadening models nor the van der Waals modeling could predict this bump in the He I 492.2 nm line.
Nevertheless, it appears that it is impossible to fit both lines with the same plasma parameters. The parameters obtained by analyzing the Balmer line do not permit to correctly reproduce the distance between the allowed and the forbidden components of the helium line. This distance depends on the electronic density only; however, the synthetic profiles obtained by analyzing the helium line provide densities leading to a too strong Stark effect to fit the Balmer line. One explanation could be that the emitting plasma is not uniform and that, even though these two spectra are recorded simultaneously, the spectroscopic measurements being not local, they are not emitted in the same part of the plasma and thus correspond to different plasma parameters.
Furthermore, the experimental spectral profiles of both lines at 0.1 MPa have been also compared to theoretical profiles obtained by the simulation method described in [
25,
26]. Density values of ~1.8 × 10
15 cm
−3 and ~10
15 cm
−3 have been obtained for the He I and for the H-β lines, respectively. In these preliminary works, the authors do not consider either van der Waals or instrumental broadening. Thus, it is difficult to compare the results of these papers [
25,
26] with the results obtained in the present paper, as both broadening mechanisms are not negligible. However, there is no contradiction between these papers [
25,
26] and the present study, as in articles [
25,
26] the authors obtained higher electronic densities to compensate the omission of additional broadening mechanisms.
The values of van der Waals broadening obtained from the best-fit procedure are close to those calculated by the formula given in
Table 4 for the He I line. However, for the H-β line, the results of the GA analysis are not so straightforward to interpret; the obtained values of van der Waals broadening are 2–3 times greater than the theoretical values. Again, it can be assumed that the observed non-symmetrical profile of the spectral line can be a reason for such mismatch. Calculations have been performed using the PPP code by considering the van der Waals effect according to the theoretical values given in
Table 3. In this case, the density values obtained by fitting the synthetic profiles to the experimental data are 1 × 10
14, 1.19 × 10
15, and 2.5 × 10
15 cm
−3 for 0.1, 0.2, and 0.3 MPa, respectively. However, these values are still below the density values obtained by analyzing the helium line.