Scholarly article on topic 'Experimental Stark broadening studies of the CI transition 3s 1 P 1o − 3p 1 S 0 at 833.5 nm'

Experimental Stark broadening studies of the CI transition 3s 1 P 1o − 3p 1 S 0 at 833.5 nm Academic research paper on "Physical sciences"

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Academic research paper on topic "Experimental Stark broadening studies of the CI transition 3s 1 P 1o − 3p 1 S 0 at 833.5 nm"

Cent. Eur. J. Phys. • 9(1) • 2011 • 131-137 DOI: 10.2478/s11534-010-0053-5

VERS ITA

Central European Journal of Physics

Experimental Stark broadening studies of the CI transition 3s p - 3p 1S0 at 833.5 nm

Research Article

Agnieszka Bartecka*, Adam Bactawski, Jozef Musielok

Institute of Physics, Opole University, ul. Oleska 48, 45-052 Opole, Poland

Received 21 March 2010; accepted 1 June 2010

Abstract:

Experimental Stark broadening studies of the infrared CI transition 3s1P1 — 3p1 So at 833.5 nm are reported for the first time. A high-current wall-stabilized arc, operated in a mixture of helium, argon, carbon dioxide and hydrogen, was applied as the plasma source. Radiation emitted from homogeneous and optically thin plasma layers was analyzed. Stark broadening studies of the selected CI transition and the hydrogen Balmer ft line were performed. As expected from theoretical considerations, the CI line width depends linearly on the electron density of the plasma. Applying theoretical Stark broadening data for the H^ line, the measured Stark widths of the CI line were calibrated for the purpose of electron density determination in low temperature plasmas.

PACS C200BJ: 32.70.Jz, 52.70.Kz

Keywords: Stark broadening • line asymmetry • neutral carbon spectrum

© Versita Sp. zo.o.

1. Introduction

Intensities and shapes of spectral lines emerging from plasmas provide very useful information concerning the main parameters of the plasma: the temperature and electron density. In cases of homogeneous plasmas or plasmas exhibiting axial symmetries, the interpretation of observed line intensities and their shapes is a rather simple task [1-3]. In particular, when the Stark effect dominates over other broadening mechanisms for a given spectral line, the electron density of the plasma can be easily deduced from measured line widths [4, 5]. From this point of view, hy-

*E-mail: bartecka@uni.opole.pl

drogen spectral lines of the Balmer series (H^ and Ha) play a special role [6-8]. These lines are subject to the linear Stark effect and thus their widths are particularly large. The broadening of non-hydrogenic lines, caused by the quadratic Stark effect, is also frequently used for the purpose of electron density determination [9-13]. In this paper we present a study devoted to the broadening of the well isolated singlet transition of neutral carbon CI 3s1P1 — 3p 1S0, appearing in the infrared part of the spectrum. The measured line widths (full widths at half maximum - FWHM) of this selected transition were calibrated against the corresponding widths of the H line applying a well diagnosed plasma source, the high-current wall-stabilized arc.

Springer

2. Experiment

The arc was operated at atmospheric pressure and currents of 39 and 54 A in a mixture of helium (gas flow rate 45 cm3/s), argon (3.4 cm3/s), carbon-dioxide (0.78 cm3/s), and hydrogen (0.51 cm3/s). The amount of CO2 and H2 was carefully adjusted in order to obtain optimal conditions for registration of (i) the hydrogen Hp line (for determination of electron density (ne)), (ii) some selected OI transitions (for determination of the temperature (T) of the plasma) and (iii) the studied CI line profile. Detailed description of the arc source and the operation conditions can be found elsewhere [14, 15]. The arc radiation emerging in end-on direction was measured applying an Ebert-type grating spectrometer (grating with 1300 grooves/mm) equipped with a CCD detector.

f=280 mm |

f=730 mm

Figure 1. The scheme of the experimental setup is shown: 1- wall-stabilized arc, 2- radiometric standard source, 3- and 4-concave mirrors, 5- swivel plane mirror, 6- Ebert-type grating spectrometer, 7- CCD detector, 8- computer, 9- spectral filter.

In Figure 1 the scheme of the experimental setup is shown. The registered spectra were calibrated against signals measured from the tungsten strip standard source. The spatial resolution of the optical imaging system allows for selecting the radiation originating from nearly homogeneous plasma layers, of a length of 80 mm along the arc axis and a size (height/width) of 0.1 mm measured perpendicular to the arc axis.

The CCD detector area was divided into 64 tracks, each consisting of four pixels in the direction perpendicular to the arc axis and 1024 pixels along the direction of the spectrometer's dispersion. The distance between the centers of neighboring tracks is 0.1 mm and precisely matches the spatial resolution of the optical imaging system. In

this manner, each detected spectrum directly yields the radial intensity distribution in the arc plasma for the selected spectral interval. The concave mirror (3) was applied for performing self-absorption checks. By reflecting the radiation reaching this mirror back into the arc and comparing the measured signals, with and without back reflection, conclusions about possible self-absorption effects in the arc plasma could be drawn [16, 17]. For our plasma conditions, these checks demonstrated negligible self-absorption in all studied spectral intervals (the investigated CI line, the OI "thermometric" lines as well as the Hp transition). Details of the data acquisition and evaluation of the registered spectra can be found e.g. in [18].

3. Plasma diagnostics

The plasma temperature was determined from measured OI line intensities, using transition probabilities from the NIST data base1 and applying the standard Boltz-mann plot method [19]. For this purpose, intensities of three OI transitions (at wavelengths 777.337, 926.387 and 882.043 nm), originating from upper levels with excitation energies ranging from 10.741 to 14.134 eV, have been measured. The temperature obtained in this way is the so-called excitation temperature. At electron densities and temperatures of our experiment (ne X 1016 cirT3, T X 12500 K), the collision frequency between electrons and atoms (ions) is sufficient for establishing partial Local Thermal Equilibrium (pLTE) conditions in the plasma, leading to a Boltzmann population among excited atomic levels with principal quantum numbers n ^ 3 [20]. At pLTE conditions one can assume that the determined excitation temperature and the temperature characterizing the kinetic energy distribution of electrons (Maxwell distribution) are the same.

In the case of arc plasmas at atmospheric pressure (d.c. discharges), the large collision frequency between electrons and atoms (ions) leads also to "thermalization" of the heavy components of the plasma, i.e., to a balance between kinetic energies of the electrons and heavy particles. Thus, the so-called gas temperature in arc plasmas at atmospheric pressure is only somewhat smaller than the electron temperature [19].

The main parameter, determining the Stark broadening of spectral lines, is the electron density (ne) of the plasma. This crucial parameter was determined from measured

1 NIST Atomic Spectra Database (http://physics.nist.gov/PhysRefData/ASD/index.html)

FWHM of the hydrogen Hp transition. For this purpose, we applied the theoretical broadening results of Gigosos and Cardenoso [8]. These calculations include the contribution to the observed line widths arising from ion dynamic effects. Other broadening mechanisms, such as in_I

strumental and Doppler broadening, have been taken into account while determining the pure Stark FWHM of the Hft line. In Figure 2 the radial distributions of the plasma temperature and the electron density are shown for two arc currents of 39 and 54 A.

Figure 2. The radial distributions of the temperature (left graph) and the electron density of the plasma (right graph) are shown.

4. Results and discussion

For line shape studies of the CI transition only the spectra originating from nearly homogeneous plasma layers have been applied. In Figure 3 two CI line shapes (after radiance calibration) measured at two different arc currents and selected plasma layers are presented. The measured line shapes reveal a noticeable asymmetry: the red line wings are clearly enhanced. Therefore, for the purpose of determining the Stark broadening parameters, the electron impact width (w) and the asymmetry parameter (A), the measured shapes were corrected on account of two other broadening mechanisms: the Doppler and instrumental broadening. The instrumental FWHM was determined on the basis of measured spectra originating from a low pressure Plucker-type discharge in xenon. It turns out that the instrumental width could be well approximated by a Gaussian with a FWHM of 0.010 nm. Knowing the temperatures corresponding to individual plasma layers, the Doppler widths could be calculated. These widths range from 0.017 to 0.020 nm for temperatures in the interval 11500 —13500 K, respectively. Both broadening mechanisms, Doppler and instrumental, obviously lead

to Gaussian profiles with widths from 0.020 to 0.022 nm. The Stark broadening parameters corresponding to the selected CI spectrum (originating from an individual plasma layer) were obtained in the following way:

1. The Griem-type profile j(x) (converted to wavelength units) was generated [21],

jA,R M — jm

Hr (ß)

where jmax is the line intensity maximum, w is the electron impact broadening parameter (full half width),

A is the asymmetry parameter, R = D0 is the so-called screening parameter (r0 =

t 4nnB I 3

and D Is the Debye radius),

ß = F Is the reduced field strength (F0 Is the normal field strength depending on electron density ne), and HR(ß) is the ion microfield distribution function at the (neutral) emitter position taken

from2.

2. This jAsR(A) profile was numerically convoluted with the corresponding Gaussian representing the "sum" of the instrumental and Doppler broadening.

3. To this final profile a background continuum in the form C = aA + b was added and the resulting spectrum was fitted to the measured line shape.

Figure 3. Two CI line profiles originating from two selected homogeneous plasma layers corresponding to two operating conditions of the arc: 39 and 54 A.

The fitting parameters were the wavelength position A0, the maximum line intensity jmax, the electron impact broadening parameter w, the asymmetry parameter A, and the coefficients a and b, determining the course of the background continuum.

In Figure 4, as an example, we present the results of our fitting procedure corresponding to the plasma layer with nt = 9.41015 cm-3 and T = 12200 K. In the lower part of this figure, the quantity

D = (Itxpt - Ifit)

(given in %) characterizing the quality of the fit is shown versus the wavelength. As can be seen, the fit in the central part of the profile (within the full half width of the line) is almost perfect: the D values (relative errors) do not exceed 3%. Nevertheless, the fitting procedure slightly

2 J. Halenka, The microfield probability distribution function Wr(b)

(http://draco.uni.opole.pl/~halenka/microfield_hal.htm)

Figure 4. The measured line profile (circles) and the result of the fitting procedure (solid line) are shown. In the lower part the quantity D = (Itxpt - Iftt)HBxpt is shown versus the wavelength.

enhances the red line wing and thus the determined asymmetry parameter A is somewhat overestimated. On the left hand side of Figure 5, the electron impact widths (w is full half widths) are shown as a function of electron density of the plasma, while on the right hand side the widths (w*), normalized to the standard electron density value of 1016 cm-3, are presented as a function of temperature.

The obtained normalized w* values slightly decrease with increasing temperature and are about a factor of 1.3 larger than those calculated by Griem [7]. In addition, the temperature course obtained experimentally does not agree with Griem's calculations: according to the calculations [7], the electron impact width increases somewhat with rising temperature.

In Figure 6 the results for the dimensionless asymmetry

parameter (A) are presented: on the left hand side, the

asymmetry parameter A is shown versus the quantity nt, while on the right hand side, the normalized asymmetry parameter (A*) is presented as a function of the temperature T. The obtained asymmetry parameters substantially disagree with those calculated by Griem [7]. Our normalized asymmetry parameter A* exceeds the theoretical value by about a factor of 4.

Because of these rather large discrepancies between the measured and calculated values (w,A), particularly in case of the asymmetry parameter A, we evaluated these parameters according to the procedure described by Griem [7] and included in our calculations the contribution to the electron impact width, originating from levels disturbing the lower level involved in the transition (3s 1P1°). The

evaluated w value was found to be (in agreement with our measurements) indeed 1.37 times larger than those quoted in [7]. However, in the evaluation of the asymmetry parameter A, the contribution arising from disturbances of the level (3s 1P1°) leads to an even smaller A value (by a factor of 2), than those listed in [7]. In our opinion, the disagreement between the calculated and measured asymmetry parameter may arise from violation of the LS coupling rule in CI. In the calculations, the LS coupling

rule is assumed and thus, only levels having the same multiplicity as the quantum states involved in the transition are taken into account as disturbing levels. However, radiative triplet - singlet transitions in CI have been observed and are listed in [22, 23]. Also, measured line strengths for intersystem transitions for the next member of the carbon isoelectronic sequence (NII) are found to be rather strong [24].

1.0 1.2 n (10'6 cm3)

11500 12000 12500 13000 13500 14000 T(K)

Figure 5. On the left hand side the determined electron impact widths (w -full half widths) of the CI transition at wavelength 833.5 nm are shown as a function of electron density of the plasma. The results for lower ne correspond to plasma layers with lower temperatures. On the right hand side the widths (w*) normalized to the standard electron density value of 1016 cm-3 are presented as a function of temperature.

Figure 6. On the left hand side the obtained asymmetry parameters (A) are shown as a function of ne4. The results for lower ne values correspond

to plasma layers with lower temperatures. On the right hand side the parameters (A*), normalized to the standard electron density value

of 1016 cm-3, are presented as a function of temperature.

Figure 7. The measured line profile (circles) and the result of the modyfied fitting procedure (fixed asymmetry parameter) are shown. Below the quantity D = (Itxpt - Ifitt)IItxpt is shown as a function of wavelength.

the relation [25]

AÀS1tark = wM0-17ne(1 + 1.75^10-M*n! • q),

(ne In cm-3, AAStark In nm),

q = 1 - 0.068 nt T-1 (n In cm-3, T In K). (3)

On the basis of the Stark broadening parameters w* and A* determined in this work for the CI transition 3s 1P1° - 3p 1S0, the following simple formula, suitable for electron density determination of low temperature plasmas, can be derived:

= 24.4-1016-AASf

As mentioned above, the results shown in Figure 4 indicate that our fitting procedure yields asymmetry parameters that are too large. In order to check how this fitting uncertainty influences the determination of the asymmetry parameter A, we modified the fitting procedure keeping the asymmetry parameter constant. In Figure 7, the results for the same plasma layer as presented in Figure 4 are shown, assuming A = 0.10, i.e., 2.3 times larger than those quoted by Griem and 1.7 times smaller than the experimentally-determined values. As can be seen, the quality of the fit is substantially worse. Particularly, the discrepancies in the blue line wing are significantly larger compared to the fitting results presented in Figure 4. The determined electron impact width, however, is only 10% larger than obtained from fitting with the free asymmetry parameter. Nevertheless, the results may be regarded as indicating the limit of possible systematic uncertainty of the determined asymmetry parameter. Concluding this question, the error bars shown in Figure 6 have to be regarded as statistical errors;an additional systematic uncertainty of at most 0.07 (towards smaller A values) should be included. Fortunately, the possible systematic uncertainties in the determination of w and A (smaller asymmetry parameters A bring about larger electron impact widths w - see the results shown in Figures 4 and 7) do not significantly influence the calculated total line widths. The total line width (FWHM) AA1 resulting from the Stark effect in the plasma (including contributions from both electron and ion broadening), is given by

It must be emphasized that the line widths measured directly have to be released from other broadening mechanisms such as Doppler and instrumental broadening.

When the AAStark is given in nm, the electron density

nt is obtained in cm-3. The formula is reliable for measured AAStark widths exceeding 0.03 nm, i.e., for electron

densities larger than 81015 cm-3, and may be applied to plasmas with temperatures typically associated with the appearance of the CI spectrum, i.e., from 9000 to 15000 K.

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