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Astron. Astrophys. 363, 1177-1185 (2000)

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4. Plasma diagnostics

4.1. Spectra processing

Firstly, an average of the five records taken with retro-reflection in mirror M3, as well as an average of the five records taken without this mirror, has been made for each spectral interval registered and for each instant of the plasma life. The individual records differ from the corresponding average less than 5%, which indicates the good repeatability of this plasma source. The comparison of both averages by using the algorithms described by González (1999) gives a measurement of the plasma optical depth and therefore determines the self-absorption of each spectral line. Most of lines present no self-absorption or a value less than 15% in the peak intensity. With the mentioned algorithms is possible to obtain in a reliable way the unabsorbed emission profile in all cases.

After dividing the records by the transmittance functions of the spectroscopic channel, every spectra have been fitted to a sum of asymmetric Lorentzian functions plus a luminous background with linear dependence (Gigosos et al. 1994):


This fitting algorithm, valid since the Stark broadening component dominates over the rest, determines the central wavelength [FORMULA], the peak intensity i, the asymmetry a and the full width at half maximum [FORMULA] (FWHM), of each line profile. Deviations of the fitted spectrum relative to the experimental one are less or about 2% (see Fig. 2). Asymmetries remain below 5%, which suggest that the ionic contribution to the Stark broadening of SiIII lines in this plasma is not relevant.

[FIGURE] Fig. 2. An experimental spectrum of the SiIII 455.3-457.5 nm lines with its corresponding fit to Eq. (1) at the instant [FORMULA] µs of the plasma lifetime.

Other broadening mechanisms like instrumental function and Doppler have also been considered when obtaining the Stark width, [FORMULA], from [FORMULA]. Instrumental broadening has been estimated by introducing 632.8-nm laser radiation into the spectrometer and checking the FWHM of the entrance slit image. The result has been [FORMULA] OMA channels for the two orders of diffraction. Doppler width, [FORMULA], has been calculated by assuming a kinetic temperature for emitters around 19 000 K. As an example, Doppler width results [FORMULA] pm for helium and [FORMULA] pm for silicon when [FORMULA] nm. At this wavelength, instrumental width is [FORMULA] pm in the first and [FORMULA] pm in the second order of diffraction. Every fitted spectral line has been treated like a Voigt profile, and the Stark width has been extracted from [FORMULA] by using a deconvolution procedure (Davies & Vaughan 1963) represented by the polynomic expression:


where [FORMULA] is the fractional Gaussian line width and the Gaussian component of [FORMULA] has been calculated as [FORMULA].

Finally, Stark shift parameters, [FORMULA], have been directly determined from each line central wavelength value, [FORMULA], obtained from relation (1).

4.2. Electron density

Electron density, [FORMULA], has been determined by two-wavelength interferometry from the plasma refractivity changes due to free electrons only, because bound electron refractivity changes do not depend on the wavelength, at least for the 476-633 nm interval (de la Rosa et al. 1990).

The phase change evolution curve [FORMULA] has been obtained from every measured interferogram at each wavelength from very simple algorithms (Aparicio et al. 1998), and one average curve has been computed from tens of interferograms recorded at each experiment. This curve takes into account the whole plasma refractivity changes from [FORMULA] µs, the beginning of the discharge, to [FORMULA] µs, when the plasma is off. Mechanical vibrations are completely negligible in this temporal interval. The electron density evolution has been subsequently calculated from:


In Eq. (3) L represents the plasma column length, which has been assumed to be the lamp length, 210 mm. When comparing the [FORMULA] curves measured at different experiments the standard deviation results lower than 5%, and therefore no significant departures have taken place. Nevertheless, each Stark width has been compared with the electron density curve measured in the corresponding experiment.

A complementary spectroscopic determination of [FORMULA] has been obtained from the Stark broadening of the 501.6 nm and 728.1 nm HeI lines. Previous calibrations presented in Eqs. (5), performed in this laboratory with an analogous plasma source (Pérez et al. 1991 , 1995), electron densities between [FORMULA] and [FORMULA] m-3 and temperatures around 20 000 K, have been used:


These lines emit strongly and have a notable Stark width in the experimental conditions of this work. Also, they are almost very insensitive to the ion dynamics effects (Mijatovic et al. 1995) and so their Stark profiles correspond to the pure electron impact. The interferometric and HeI Stark width-based diagnostics of electron density are compared in Fig. 3. The curves in the figure follow the temporal shape of the high current pulse applied on the lamp closely, and this picture shows the good agreement between the interferometric and spectroscopic determinations of [FORMULA].

[FIGURE] Fig. 3. Comparison between interferometric electron density curve and spectroscopic one determined by Stark broadening of two HeI lines.

The electron density has also been obtained by measuring the temporal evolution of the [FORMULA] Stark broadening, which is achievable due to the small amount of hydrogen present in silane. The HeI and the [FORMULA] profile records have been inserted between the SiIII ones and have been performed with 3 µs exposures. They have been corrected from self-absorption, the maximum value being 10% for HeI lines and 15% for [FORMULA] line, and the Stark width of HeI profiles has been obtained as described in the previous paragraph. However, with the experimental conditions of this work, the [FORMULA] line is sensitive to ion dynamics effects (Gigosos & Cardeñoso 1987) and it does not present a pure electron impact profile. Consequently, its Stark width can not be obtained from a simple deconvolution procedure and the FWHM does not define the electron density completely. It is possible to make an electron density diagnostic by comparing the [FORMULA] FWHM from the measured profiles and those calculated by simulation techniques developed in this laboratory (Gigosos & Cardeñoso 1987 , 1996) based on the µ-ion model. The reduced mass corresponding to the plasma of this work is [FORMULA] since hydrogen emitters are almost completely rounded by helium perturbers. The interferometric and [FORMULA] Stark FWHM-based diagnostics of electron density are compared in Fig. 4. A very good agreement between interferometric and spectroscopic [FORMULA] determinations of [FORMULA] exists from [FORMULA] µs on. However, in the earliest instants of the plasma life the calculated profile widths corresponding to interferometric-based values of electron density are greater than measured ones. Therefore, the electron density seems to be notably smaller than that predicted by the interferometric diagnostic. Taking into account the previous good results illustrated in Fig. 3 it may be possible to reject this possibility. A reasonable explanation for this effect can be obtained assuming that ionic kinetic temperature is lower than the electronic one (González 1999). Comparison of the experimental [FORMULA] profile shapes with those calculated taking into account this hypothesis, which can be achieved in a equivalent scheme where the ions have a reduced mass greater than [FORMULA], shows that ionic temperature is about 0.2 times the electron temperature ([FORMULA]) until [FORMULA] µs; around this instant a rapid thermalisation process of both species begins, ending the kinetic decoupling about [FORMULA] µs. This result shows that the plasma probably has a 2-T behaviour (van der Mullen 1990) at the initial instants, when the rise flank of the high current pulse applied on the lamp "drives" the plasma. At these instants the applied external electric field heats more the electrons than ions; later, the collisionnal processes in the plasma prevail and the kinetic energy is redistributed.

[FIGURE] Fig. 4. Comparison between interferometric electron density curve and spectroscopic one determined by Stark FWHM of the [FORMULA] line.

The good agreement found between the independent interferometric and spectroscopic determinations of [FORMULA](t) reinforces the assumption made for L as the lamp length and therefore the negligible influence of possible inhomogeneous boundary layers. We conclude that in this work the electron density, which ranges between 0.2 and [FORMULA] m-3, has been determined with uncertainties lower than 10% and from now on we will take the interferometric determination of [FORMULA] as a reference for other comparisons and calculations.

4.3. Temperature

The relevant temperature parameter in Stark broadening and shift of spectral lines of multiply-charged ions is the kinetic electron temperature, [FORMULA]. It is very usual in these kinds of collision-dominated plasmas to assume that [FORMULA] is very similar to the ion excitation temperature (van der Mullen 1990). In this work the SiIII excitation temperature has been calculated from the SiIII /SiII intensities ratio assuming total LTE. This calculation has been performed with the multiplet (2) of SiIII ([FORMULA]455.3, 456.8 and 457.5 nm lines) and the multiplet (5) of SiII ([FORMULA]504.1 and 505.6 nm lines). The silicon excitation temperature has also been calculated from a SiII Boltzmann-plot assuming pLTE. This plot involves the SiII lines of the five most prominent visible low-excitation multiplets. Their upper energy levels cover an energy interval of about 3 eV (between 10.067 and 12.839 eV). Additional determinations of T have been obtained from the absolute emission intensity measurements of HeI lines, assuming total LTE, and from the HeI excitation temperature by using a HeI Boltzmann-plot and assuming partial LTE. The HeI lines used for this calculations were 471.3, 501.6, 706.5 and 728.1 nm, whose upper energy levels cover only an energy interval of about 1 eV (between 22.719 and 23.594 eV). The statistical errors corresponding to the diverse determinations are: around 10% for SiIII /SiII intensities ratio method, around 14% for SiII Boltzmann-plot method, around 18% for HeI Boltzmann-plot method, and around 7% for absolute emission of HeI method. The temperature curves are shown in Fig. 5. In this figure has also been depicted an average of the four previous determinations with an error band around 20%. This average curve does not have any physical meaning since the various methods to calculate the plasma temperature are not comparable in a simple way. However, this curve can be considered as a reasonable working estimation of the kinetic electron temperature, [FORMULA]. A more profound analysis of the plasma temperature is given by González (1999) but, summarizing, it can be pointed out that there is evidence that for HeI the plasma has an ionizing (van der Mullen 1990) behaviour while for SiIII the plasma has a recombining (van der Mullen 1990) behaviour. This fact is reflected in Fig. 5 since the excitation temperature for HeI is less than [FORMULA] and the opposite occurs for SiIII .

[FIGURE] Fig. 5. Electron temperature estimation from Boltzmann-plot methods, from consecutive silicon ion intensities ratio and from absolute HeI emission measurements.

The final estimation for [FORMULA] ranges from 17 500 to 21 000 K with a statistical uncertainty of about 20%. This result is reasonably satisfactory if the high uncertainty of the SiII and SiIII probability transitions (about 25%) and the small difference between the HeI energy levels used in the Boltzmann-plot methods are taken into account. In this experiment there are no direct measurements available to determine the kinetic temperature of the emitters, which creates an ambiguity in relation to the estimation of the Doppler contribution to the total linewidth. The results obtained in Sect. 4.2 in relation to an ionic temperature about 0.2 times lower than the electronic one in the first instants of the plasma life, seem to indicate than SiIII emitters could have a kinetic temperature of about 4000 K during these instants. Processing of line profiles with this temperature generates a discrepancy with respect to those processed with the reference temperature of 19 000 K, not higher than 10% in the narrowest SiIII lines at [FORMULA] m-3.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000