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3 Calculations and plasma diagnostics

All the spectra were fitted to sums of Lorentzian functions plus a luminous background with a linear dependence, as explained in Gigosos et al. (1994). Differences between the experimental spectra and the fits were usually lower than 1%. These fitting algorithms allow simultaneous determination of the center, asymmetry, linewidth and area of each profile. While dependent on the chosen line, asymmetries remain below 5%, which suggests that the ionic contribution to the Stark broadening of OII lines in these plasma conditions is not relevant. Every fitted spectral line was treated as a Voigt profile. From the whole experimental width $w_{\rm exp}$ the Lorentzian or Stark component $w_{\rm S}$ (FWHM) was extracted by using a deconvolution procedure which can be expressed in the following polynomical form:

 
(1)

where $x = w_{\rm G}/w_{\rm exp}$ is the ratio between the Gaussian component and the whole experimental width. This Gaussian component $w_{\rm G}$ has been calculated from Doppler broadening $w_{\rm D}$ and instrumental width $w_{\rm i}$ as $w_{\rm G}=(w_{\rm D}^2+w_{\rm i}^2)^{1/2}$. In this experiment the instrumental profile has a gaussian shape for which FWHM is fundamentally determined by the entrance slit width of the spectrometer, and the measured value results in $w_{\rm i}=2.6$ OMA channels. For the Doppler width $w_{\rm D}$ calculation the emitters kinetic temperature was assumed to be close to the OII and NeII excitation temperatures. Taking into account the low gas pressure and the high degree ionisation reached in this experiment, which can be estimated according to Saha law (even greater than 50%) another broadening mechanisms like neutral pressure or natural width result completely negligible.

Finally, H$_\alpha $ profiles were processed according to the same procedure.

The electron density $N_{\rm e}$ was determined interferometrically and spectroscopically. In the experiment 156 interferometric registers (1 ms long) were made, the half corresponding to 457.9 nm and the rest to the 514.0 nm transition of an argon ion laser. Although these are the most separated available transitions of the laser, in this case, the small difference in wavelength between them does not actually allow double-wavelength interferometry. The differences between the electron density curves obtained from 457.9 nm one-wavelength interferometry and those corresponding to 514.0 nm are always lower than 4% (Fig. 3); hence, we take the mean value of the two curves in all cases.

From each one of the interferograms taken during the experiment, phase evolution was extracted (Aparicio el al. 1998; de la Rosa et al. 1990) by assuming that the plasma column fills the lamp and that refractivity changes are mostly due to free electrons. Both hypotheses have been proved in many works made in this laboratory in recent years (Gigosos et al. 1994; Aparicio et al. 1998; del Val et al. 1997; del Val 1997; de la Rosa et al. 1990). Electron density was also calculated from the hydrogen Balmer-alpha Stark width (Fig. 3). This has been calibrated as a function of electron density and temperature in a simulation (Gigosos et al. 1996). In Fig. 3 interferometric and spectroscopic results are compared. As shown in this figure very good agreement between both methods is observed, which seems to confirm the negligible contribution of the bound electrons to refractivity changes and that the effective length of the plasma column is the same as the lamp length. We conclude that 10% is a good estimation of the electron density uncertainty.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{fig3.ps}\end{figure} Figure 3: Electron density evolution measured from interferometry and from H$_\alpha $-Stark broadening

Considering pressure broadening theories and taking into account the electron density and temperature ranges, the OII line profiles are primarily determined by electron impact broadening, so Stark widths are closely related to free electron density and kinetic electron temperature. Moreover, in collision-dominated plasmas like the one generated in this experiment, it is a common hypothesis that excitation temperature and kinetic electron temperature take similar values (Van der Mullen 1990). In this work for each instant of the plasma lifetime we determined OII excitation temperature from the slope of a Boltzmann-plot calculated with the intensities of a select set of 14 OII lines, whose transition probabilities can be taken from the literature. The same procedure has been followed with 13 selected NeII lines, so that NeII excitation temperature was also determined. Both temperatures are in good agreement, as it is shown in Fig. 4, although the greater one (OII) was taken as electronic temperature, with an estimated uncertainty around 15%.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{fig4.ps}\end{figure} Figure 4: Electron temperature evolution measured from the Boltzmann-plots of NeII and OII lines

Due to the narrow features of the OII lines measured in this work we must discuss the influence of the kinetic emitters temperature in the final Stark widths. Although beyond the scope of this work to demonstrate this point, probably a two-temperature (2-T) model for these collision-dominated plasmas could be considered, as already was pointed out by Van der Mullen (1990). If kinetic emitters temperature were lower than kinetic electron temperature, then the Stark width results would increase. Simple calculations prove that, for ion kinetic temperatures of 40000 K or 20000 K, the resulting Stark widths at $N_{\rm e}=10^{23}\,{\rm m}^{-3}$ can differ even up to 30% for the narrowest OII lines. This will be reflected in the uncertainties assigned to these lines. Table 1 shows an example of the full calculations made to obtain the Stark widths $w_{\rm S}$ from the experimental linewidth $w_{\rm exp}$ (following the deconvolution procedure already described in Eq. (1)), for the line 407.216 nm at the plasma life instant 40 $\mu $s. Data obtained considering 42000 K and 20000 K as kinetic emitter temperature are compared. As a whole, the best agreement between our OII $w_{\rm S}$ data and the literature is achieved when considering the kinetic emitters temperature very similar to NeII or OII excitation temperatures.


   
Table 1: Different FWHM values (in pm) for the 407.216 nm OII line emitted at the instant $t=40~\mu$s. To show the influence of the value taken as emitter kinetic temperature in deconvolution procedure, temperatures of T=42000 K and T=20000 K are considered. At this instant $N_{\rm e}=7.45\ 10^{22}\,{\rm m}^{-3}$. $w_{\rm D} =$ Doppler width, $w_{\rm i}$ = instrumental width, $w_{\rm G}$ = Gaussian component, $w_{\rm S}$ = Lorentzian Stark width
$T({\rm K})$ $w_{\rm exp}$ $w_{\rm D}$ $w_{\rm i}$ $w_{\rm G}$ $w_{\rm S}$
42000 30.15 13.30 15.11 20.13 16.20
20000 30.15 9.18 15.11 17.68 19.31


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