rus
Issue #5/2017
A.R.Gildina, P.A.Mikheyev, A.K.Chernyshov, N.I.Ufimtsev, V.N.Azyazov
Pressure Broadening Coefficients for Argon and Krypton Lines in Low-Temperature Plasma
Pressure Broadening Coefficients for Argon and Krypton Lines in Low-Temperature Plasma
Pressure broadening coefficients of ( n + 1 ) s [ 3 / 2 ]2 → ( n + 1 ) p [ 5 / 2 ]3 transition for argon and krypton lines with rare gases as pressure partners were measured in a low temperature RF glow discharge plasma. This data is necessary for diagnostics of the active medium of the promising optically pumped rare-gas lasers.
Теги: diode-laser spectroscopy inert gases pressure broadening rf glow discharge вч-разряд диодно-лазерная спектроскопия инертные газы столкновительное уширение
INTRODUCTION
One of the topical problems of laser physics is the development of a continuous high-power laser with a high quality of output radiation. Diode-pumped alkali laser is an example, but its operation is associated with chemical risks caused by the high reactivity of alkali metals [1]. Optically pumped rare-gas laser (OPRGL) [2] uses meta-stable rare gas atoms produced in a gas discharge to generate laser radiation, and its experimental realization is an important step in the development of new types of high-power lasers [3]. OPRGL kinetics is similar to the alkali laser kinetics, but the gas medium is chemically inert [4]. The advantage of this laser is the ability to generate hundreds of watts of laser power in a continuous mode from the cubic centimeter of the active medium. This requires number density of meta-stable atoms of 1012–1013 cm–3 at atmospheric pressure.
To measure the concentration of meta-stable atoms and gas temperature in gas discharge plasma, the methods of diode-laser spectroscopy require a set of coefficients for pressure broadening of rare gas lines for different gas mixtures. However, a reference analysis has shown that these coefficients in mixtures that are of interest to OPRGL, such as mixtures of argon, krypton, xenon in neon, helium, and among themselves, need to be clarified. For example, the values of these coefficients for the broadening of 811.3 nm krypton line in krypton and in helium were measured only once [5], and information on pressure broadening coefficients by other rare gases is not available. In our previous papers, the pressure broadening coefficients for mixtures of argon and helium, krypton and helium, and coefficients in the parent gases for argon and krypton have already been determined [6]. The purpose of the work was to measure these coefficients for 811.5 nm argon line in neon, and 811.3 nm krypton line mixed with neon and argon. In contrast to the experiment [5], where enriched 86Kr was used, in our work we used a natural mixture of isotopes and a specially designed form factor for absorption line, taking into account the contribution of all krypton isotopes. The method for determining the coefficients will be described below.
EXPERIMENTAL SET-UP
Figure 1 shows the scheme of the experimental set-up for spectroscopic measurements. Meta-stable atoms of argon and krypton were produced in the discharge chamber in a pressure range, where pressure and Doppler broadening were of the same order. This made it possible to take into account the temperature changing in the course of the experiment in the discharge chamber due to the determination of the Gaussian component of the Voigt absorption profile. The discharge chamber [6, 7] for a continuous RF glow discharge with a frequency of 40 MHz was made out of a quartz tube with an internal diameter of 15 mm and a wall thickness of 1.5 mm, and four wire electrodes attached to its wall. Laboratory-made RF generator and the matching device provided up to 20 watts of power loaded into the discharge, which corresponded to ~1 W cm‑3 of power density in the plasma. Gas flow through the discharge tube was measured using Bronkhorst flowmeters, partial gas pressures were determined based on the measured flow and total pressure.
The measurements were conducted with the help of L808P030 (Thorlabs) diode laser with original short external resonator, described in [8, 9]. Laser power was supplied from current and temperature controller ITC4001 (Thorlabs). Output laser power in the collimated beam was 5 mW. Continuous spectral tuning of the laser was achieved by saw-tooth pumping current modulation, and was controlled using Fabry-Perot interferometer. The range of continuous laser frequency tuning reached 36 GHz, and the width of the laser line did not exceed 50 MHz. These parameters were estimated from the number and width of the observed resonances of Fabry-Perot interferometer.
The experimental signal was in form of dependence of the laser power transmitted through the plasma on time. For further processing, the time scale should be converted to a frequency scale, which was achieved with the help of signal peaks from Fabry-Perot interferometer.
The subsequent processing included subtracting the zero signal, calculating the logarithm of ratio of reference and signal channel signals, and fitting the experimentally obtained absorption line to Voigt profile using the Levenberg-Marquardt algorithm.
RESULTS AND ANALYSIS
The method for measuring the pressure broadening coefficients is described in our papers [6, 7] and is based on the simultaneous determination of the Gaussian (WG) and Lorentz (WL) Voigt profile components. Voigt contour is a convolution of Gaussian and Lorentz functions. The explicit form of Voigt profile is determined by formula 1:
. (1)
Figure 2 shows Gaussian, Lorentz, and Voigt functions with parameters WG=WL=WF=1, the area under the curves A=1. In this case, in order to make the half-maximum width values for Voigt profile (WF) equal 1, we can assume WG=WL=0.61. WG and WL parameters are the width values at half-height of Gaussian and Lorentz functions responsible for thermal and pressure parts of the spectral line broadening. The approximation of the absorption lines by Voigt profile can be performed, for example, using Origin software package.
Our experiments have shown that if the values of WG, WL are commensurable, it becomes possible to determine them by approximating the experimentally obtained absorption line shape by Voigt profile.
In the experiments, in order to make thermal and pressure broadening of the same order, the range of gas pressures in the discharge was chosen from 20 to 70 Torr. For each pressure value, Gauss and Lorentz components were obtained. For 811.5 nm line of argon at 300 K WG=0.72 GHz, therefore:
, (2)
where p is pressure (Torr). Now, knowing WG, WL parameters and using ratio (2), we can determine the value of the pressure broadening coefficient. At constant pressure, the right-hand part of expression (2) depends only on the pressure measured in the experiment, and is temperature independent [6].
For 811.3 nm line of krypton at 300 K: WG=0.5 GHz and T=300Ч(WG/0.5)2:
. (3)
To make sure that the resulting line shape is correct, it is reasonable to assume that WG and WL parameters of Voigt contour, obtained by approximating line profile, should not depend on the number of experimental points included in the approximation. To verify this assumption, we first found the coordinate of the center of the absorption line Xc and the line width at half-height WF, taking into account the expression from [10].
Then, the coordinates Xc ± ns, e. g., for values n=[2 … 6] were calculated, and Voigt contour was approximated by n data samples within these boundaries. The values obtained for Gaussian WG and Lorentz WL components made it possible to estimate the error in their determination.
The value of the width parameters at half-height of WG and WL, determined in this way, usually remained unchanged at values n=[3 … 6], which allows us to assume high quality of the data obtained. The error of WG and WL, as a rule, did not exceed 5%.
Appreciable longitudinal temperature gradient was observed in the experiment. Gas heating in the discharge was determined from the value of WG parameter (T=300Ч(WG/0.72)2), and did not exceed 300 K.
The optical path in the discharge plasma included areas with different temperatures, estimated to be from 300 to 600 K. To estimate the error due to the temperature gradient, the absorption line profile was modeled by the sum of several weighted Voigt profiles at different temperatures and with the corresponding frequency shifts [11]. The evaluation of the systematic error in the measurement of the coefficients thus obtained showed that the error does not exceed +3%.
The results of measurement of pressure broadening coefficients for argon in neon are given in Fig. 3. Argon pressure in the experiment was from 2.9 to 3.2 Torr. The coefficient value, determined from the slope of linear approximation of the experimental points, was ξArNe=(1.3±0.1)Ч10–10 s–1 cm‑3. The error in ξAr-Ne value was estimated as three standard deviations where the experimental data were approximated by linear function.
In the experiment with krypton it was necessary to take into account isotope shifts and the presence of lines of the hyperfine structure of 83Kr isotope. As our experiments have shown, despite a relatively small contribution of 83Kr (11.55% isotope content), if the hyperfine line structure was neglected, it was impossible to obtain a qualitative approximation of absorption line shape. Natural krypton is a mixture of the five most common isotopes: 80Kr (2.25%), 82Kr (11.56%), 83Kr (11.55%), 84Kr (56.9%) and 86Kr (17.37%). The centers of the absorption lines in 80Kr, 82Kr, and 86Kr isotopes are shifted by several tens of MHz relative to the most abundant 84Kr isotope. As for 83Kr isotope with a nuclear spin of I=9/2, its fifteen hyperfine lines at a wavelength of 811.3 nm overlap the range of about 3 GHz. Therefore, the absorption line profile in natural krypton is the sum of Voigt profiles for fifteen hyperfine lines of 83Kr and for the remaining four isotopes multiplied by weighting factors and shifted relative to each other. The weight coefficients for isotope lines are proportional to their abundance in nature, and for 83Kr lines also to their absorption forces calculated by the quantum mechanical method [12].
Figure 4 shows the form factors of krypton line constructed for natural isotope mixture, as compared with Voigt form factor at a temperature of 340 K and a pressure of 29 Torr (Figure 4a), as well as an absorption line obtained in the experiment (Fig. 4b). As can be seen from the figure, form factor of krypton line differs from Voigt profile, and adequately describes the results of the experimental measurements.
The results of the measurement of pressure broadening coefficients of 811.3 nm krypton line in neon are given in Fig. 5. The krypton partial pressure was 2.5 to 6 Torr. The values of the coefficients of the pressure broadening of krypton line of 811.3 nm at 300 K: ξKr-Ne=(1.50±0.05)Ч10–10 s‑1 cm‑3 in neon and ξKr-Ar=(3.5±0.3)Ч10–10 s‑1 cm‑3 in argon.
CONCLUSIONS
Table presents all pressure broadening coefficients for 811.5 nm argon and 811.3 nm krypton lines, measured by us up to date. The simultaneous determination of Gaussian (WG) and Lorentz (WL) components of Voigt profile made it possible to determine pressure broadening coefficients with accuracy better than 10% for the first time. Please note that there is a noticeable difference between the values of pressure broadening coefficients in neon compared to others. This pattern is characteristic when neon acts as a collisional partner. The values of this coefficient in a mixture of xenon with neon for the xenon line of 1.73 µm [13] were about half of those in mixtures with argon and helium. The measured values of pressure broadening coefficients can be applied in the tasks of optical diagnostics of low-temperature rare gas plasma.
The research was carried out under support of the Ministry of Education and Science of the Russian Federation within the framework of the State Order under Projects 3.5624.2017/8.9, 3.5708.2017/6.7.
One of the topical problems of laser physics is the development of a continuous high-power laser with a high quality of output radiation. Diode-pumped alkali laser is an example, but its operation is associated with chemical risks caused by the high reactivity of alkali metals [1]. Optically pumped rare-gas laser (OPRGL) [2] uses meta-stable rare gas atoms produced in a gas discharge to generate laser radiation, and its experimental realization is an important step in the development of new types of high-power lasers [3]. OPRGL kinetics is similar to the alkali laser kinetics, but the gas medium is chemically inert [4]. The advantage of this laser is the ability to generate hundreds of watts of laser power in a continuous mode from the cubic centimeter of the active medium. This requires number density of meta-stable atoms of 1012–1013 cm–3 at atmospheric pressure.
To measure the concentration of meta-stable atoms and gas temperature in gas discharge plasma, the methods of diode-laser spectroscopy require a set of coefficients for pressure broadening of rare gas lines for different gas mixtures. However, a reference analysis has shown that these coefficients in mixtures that are of interest to OPRGL, such as mixtures of argon, krypton, xenon in neon, helium, and among themselves, need to be clarified. For example, the values of these coefficients for the broadening of 811.3 nm krypton line in krypton and in helium were measured only once [5], and information on pressure broadening coefficients by other rare gases is not available. In our previous papers, the pressure broadening coefficients for mixtures of argon and helium, krypton and helium, and coefficients in the parent gases for argon and krypton have already been determined [6]. The purpose of the work was to measure these coefficients for 811.5 nm argon line in neon, and 811.3 nm krypton line mixed with neon and argon. In contrast to the experiment [5], where enriched 86Kr was used, in our work we used a natural mixture of isotopes and a specially designed form factor for absorption line, taking into account the contribution of all krypton isotopes. The method for determining the coefficients will be described below.
EXPERIMENTAL SET-UP
Figure 1 shows the scheme of the experimental set-up for spectroscopic measurements. Meta-stable atoms of argon and krypton were produced in the discharge chamber in a pressure range, where pressure and Doppler broadening were of the same order. This made it possible to take into account the temperature changing in the course of the experiment in the discharge chamber due to the determination of the Gaussian component of the Voigt absorption profile. The discharge chamber [6, 7] for a continuous RF glow discharge with a frequency of 40 MHz was made out of a quartz tube with an internal diameter of 15 mm and a wall thickness of 1.5 mm, and four wire electrodes attached to its wall. Laboratory-made RF generator and the matching device provided up to 20 watts of power loaded into the discharge, which corresponded to ~1 W cm‑3 of power density in the plasma. Gas flow through the discharge tube was measured using Bronkhorst flowmeters, partial gas pressures were determined based on the measured flow and total pressure.
The measurements were conducted with the help of L808P030 (Thorlabs) diode laser with original short external resonator, described in [8, 9]. Laser power was supplied from current and temperature controller ITC4001 (Thorlabs). Output laser power in the collimated beam was 5 mW. Continuous spectral tuning of the laser was achieved by saw-tooth pumping current modulation, and was controlled using Fabry-Perot interferometer. The range of continuous laser frequency tuning reached 36 GHz, and the width of the laser line did not exceed 50 MHz. These parameters were estimated from the number and width of the observed resonances of Fabry-Perot interferometer.
The experimental signal was in form of dependence of the laser power transmitted through the plasma on time. For further processing, the time scale should be converted to a frequency scale, which was achieved with the help of signal peaks from Fabry-Perot interferometer.
The subsequent processing included subtracting the zero signal, calculating the logarithm of ratio of reference and signal channel signals, and fitting the experimentally obtained absorption line to Voigt profile using the Levenberg-Marquardt algorithm.
RESULTS AND ANALYSIS
The method for measuring the pressure broadening coefficients is described in our papers [6, 7] and is based on the simultaneous determination of the Gaussian (WG) and Lorentz (WL) Voigt profile components. Voigt contour is a convolution of Gaussian and Lorentz functions. The explicit form of Voigt profile is determined by formula 1:
. (1)
Figure 2 shows Gaussian, Lorentz, and Voigt functions with parameters WG=WL=WF=1, the area under the curves A=1. In this case, in order to make the half-maximum width values for Voigt profile (WF) equal 1, we can assume WG=WL=0.61. WG and WL parameters are the width values at half-height of Gaussian and Lorentz functions responsible for thermal and pressure parts of the spectral line broadening. The approximation of the absorption lines by Voigt profile can be performed, for example, using Origin software package.
Our experiments have shown that if the values of WG, WL are commensurable, it becomes possible to determine them by approximating the experimentally obtained absorption line shape by Voigt profile.
In the experiments, in order to make thermal and pressure broadening of the same order, the range of gas pressures in the discharge was chosen from 20 to 70 Torr. For each pressure value, Gauss and Lorentz components were obtained. For 811.5 nm line of argon at 300 K WG=0.72 GHz, therefore:
, (2)
where p is pressure (Torr). Now, knowing WG, WL parameters and using ratio (2), we can determine the value of the pressure broadening coefficient. At constant pressure, the right-hand part of expression (2) depends only on the pressure measured in the experiment, and is temperature independent [6].
For 811.3 nm line of krypton at 300 K: WG=0.5 GHz and T=300Ч(WG/0.5)2:
. (3)
To make sure that the resulting line shape is correct, it is reasonable to assume that WG and WL parameters of Voigt contour, obtained by approximating line profile, should not depend on the number of experimental points included in the approximation. To verify this assumption, we first found the coordinate of the center of the absorption line Xc and the line width at half-height WF, taking into account the expression from [10].
Then, the coordinates Xc ± ns, e. g., for values n=[2 … 6] were calculated, and Voigt contour was approximated by n data samples within these boundaries. The values obtained for Gaussian WG and Lorentz WL components made it possible to estimate the error in their determination.
The value of the width parameters at half-height of WG and WL, determined in this way, usually remained unchanged at values n=[3 … 6], which allows us to assume high quality of the data obtained. The error of WG and WL, as a rule, did not exceed 5%.
Appreciable longitudinal temperature gradient was observed in the experiment. Gas heating in the discharge was determined from the value of WG parameter (T=300Ч(WG/0.72)2), and did not exceed 300 K.
The optical path in the discharge plasma included areas with different temperatures, estimated to be from 300 to 600 K. To estimate the error due to the temperature gradient, the absorption line profile was modeled by the sum of several weighted Voigt profiles at different temperatures and with the corresponding frequency shifts [11]. The evaluation of the systematic error in the measurement of the coefficients thus obtained showed that the error does not exceed +3%.
The results of measurement of pressure broadening coefficients for argon in neon are given in Fig. 3. Argon pressure in the experiment was from 2.9 to 3.2 Torr. The coefficient value, determined from the slope of linear approximation of the experimental points, was ξArNe=(1.3±0.1)Ч10–10 s–1 cm‑3. The error in ξAr-Ne value was estimated as three standard deviations where the experimental data were approximated by linear function.
In the experiment with krypton it was necessary to take into account isotope shifts and the presence of lines of the hyperfine structure of 83Kr isotope. As our experiments have shown, despite a relatively small contribution of 83Kr (11.55% isotope content), if the hyperfine line structure was neglected, it was impossible to obtain a qualitative approximation of absorption line shape. Natural krypton is a mixture of the five most common isotopes: 80Kr (2.25%), 82Kr (11.56%), 83Kr (11.55%), 84Kr (56.9%) and 86Kr (17.37%). The centers of the absorption lines in 80Kr, 82Kr, and 86Kr isotopes are shifted by several tens of MHz relative to the most abundant 84Kr isotope. As for 83Kr isotope with a nuclear spin of I=9/2, its fifteen hyperfine lines at a wavelength of 811.3 nm overlap the range of about 3 GHz. Therefore, the absorption line profile in natural krypton is the sum of Voigt profiles for fifteen hyperfine lines of 83Kr and for the remaining four isotopes multiplied by weighting factors and shifted relative to each other. The weight coefficients for isotope lines are proportional to their abundance in nature, and for 83Kr lines also to their absorption forces calculated by the quantum mechanical method [12].
Figure 4 shows the form factors of krypton line constructed for natural isotope mixture, as compared with Voigt form factor at a temperature of 340 K and a pressure of 29 Torr (Figure 4a), as well as an absorption line obtained in the experiment (Fig. 4b). As can be seen from the figure, form factor of krypton line differs from Voigt profile, and adequately describes the results of the experimental measurements.
The results of the measurement of pressure broadening coefficients of 811.3 nm krypton line in neon are given in Fig. 5. The krypton partial pressure was 2.5 to 6 Torr. The values of the coefficients of the pressure broadening of krypton line of 811.3 nm at 300 K: ξKr-Ne=(1.50±0.05)Ч10–10 s‑1 cm‑3 in neon and ξKr-Ar=(3.5±0.3)Ч10–10 s‑1 cm‑3 in argon.
CONCLUSIONS
Table presents all pressure broadening coefficients for 811.5 nm argon and 811.3 nm krypton lines, measured by us up to date. The simultaneous determination of Gaussian (WG) and Lorentz (WL) components of Voigt profile made it possible to determine pressure broadening coefficients with accuracy better than 10% for the first time. Please note that there is a noticeable difference between the values of pressure broadening coefficients in neon compared to others. This pattern is characteristic when neon acts as a collisional partner. The values of this coefficient in a mixture of xenon with neon for the xenon line of 1.73 µm [13] were about half of those in mixtures with argon and helium. The measured values of pressure broadening coefficients can be applied in the tasks of optical diagnostics of low-temperature rare gas plasma.
The research was carried out under support of the Ministry of Education and Science of the Russian Federation within the framework of the State Order under Projects 3.5624.2017/8.9, 3.5708.2017/6.7.
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