3 Measurements and plasma diagnostics

The experiment consists of end-on measurements of the NII lines emitted by the plasma in the region 380-700 nm, and also the NI lines 742.36, 744.23 and 746.83 nm. Each spectral interval has been recorded at 15 different instants of the plasma lifetime. For each instant, we have made six runs, three of them with the mirror M 3 and the other three ones without it, in order to test for self-absorption in all measurements. The averages of the 3 registers made without mirror M 3 differed from the measured spectra less than 4%, which indicates the great repeatability of this plasma source. By comparing the average of registers with the mirror with the average of the registers without it and using the algorithms described in (González 1999) self-absorption only appeared in less than 2% of the whole spectral profiles. Even more, in less than 10% of these cases, the original profiles which can be reconstructed had peak intensity greater than 1.2 times that measured without mirror M 3. In these cases, the profile was rejected for further calculations. An example of a spectrum recorded with several NII lines at 50 $\mu$s of the plasma life is shown in Fig. 2.

Figure 2: An example of experimental spectrum showing several NII lines at the instant 50 $\mu$s of the plasma lifetime

It has also been possible to make measurements of the HeI 471.3 nm profiles, whose well-known Stark broadening has allowed us to determine the electron density spectroscopically. All the lines here considered were registered in first order of diffraction of the spectrometer, the most efficient. As a whole around 10000 discharges were made.

In relation to interferometric registers, 450 interferograms for both wavelengths were taken at the beginning, in the middle and at the end of the whole experiment. Besides, at regular intervals of 1.5 hours, 15 interferograms were registered, all of them 500 $\mu$s long. They have been used to determine the electron density evolution curve and to detect possible drifts in such a long experiment. When comparing the different curves, differences were always lower than 5%, which shows that no significant drifts occurred. This has also been shown when comparing temperature curves obtained from different groups of lines by means of Boltzmann-plots, each group corresponding to regular time intervals around 2 hours within the whole experiment. In fact, differences between temperature curves are also less than 5%. Anyway we have taken in each case for further calculations its corresponding temperature and density curve.

After dividing the spectra by the spectrometer transmittance functions, all the spectra were fitted to sums of Lorentzian functions plus a luminous background with a linear dependence, as explained in reference (Gigosos et al. 1994). Differences between the experimental spectra and the fits were usually lower than 1% (see Fig. 2). This fitting algorithm allows to determine simultaneously the center, asymmetry, linewidth and area of each profile.

Figure 3 shows the electron density $N_{\rm e}$, determined interferometrically and spectroscopically. As it is shown in this figure, very good agreement between both methods is observed. Uncertainty in this plasma parameter is lower than 10%.

Figure 3: Comparison between interferometric and spectroscopic electron density values. The uncertainty for this plasma parameter are below 10%

In collision-dominated plasmas like the one generated in this experiment, it is a common hypothesis to assume that excitation temperature, Saha temperature and kinetic electron temperature take similar values (Van der Mullen 1990). In this work excitation temperature has been calculated from NII Boltzmann-plots. As Fig. 4 shows, these plots involve NII lines whose upper energy levels cover a very broad range (from 20.64 to 30.36 eV). Here, for temperature determination, we introduce a fairly large number of lines, that is, of A_ki values taken from literature (the last data tabulated by NIST), which in fact will determine the absolute scale of this work A_ki data. In this way, the accuracy of this work results comes both from the great number of literature collected data as the great number of measurements taken into account in the temperature calculation. Additional determination of temperature was obtained from the NII/NI intensities ratio by combining different NII and the NI measured lines. The statistical error of temperature calculated from Boltzmann-plot is less than 5% (with the exception of the three last instants of plasma life, which is 7%). In the case of the temperature calculated from the intensity ratios this error does not exceed 3%. When combining intensities of consecutive species to calculate temperatures, total LTE is assumed and the measured electron density is used. As it can be seen in Fig. 5, the two methods employed in this experiment give rise to temperatures which cannot be distinguished into a very reasonable error band around 10%. Therefore, the assumption of a partial LTE model in the NII energy levels range considered can be perfectly made.

Figure 4: An example of NII Boltzmann-plot corresponding to the plasmalife instant 50 $\mu$s. The good point distribution along the straight line shows that excitation temperature follows the Boltzmann law for these energy levels

Figure 5: NII excitation temperature evolution obtained from Boltzmann-plot and temperature curve obtained from NII/NI intensities ratio assuming total LTE. Although the statistical errors are below 5% in both methods, we give error bars up to 10% in order to include also the uncertainties coming from the set of Aki data taken as reference from NIST critical compilation