c Allerton Press, Inc., 2016. ISSN 1068-3356, Bulletin of the Lebedev Physics Institute, 2016, Vol. 43, No. 6, pp. 195–198. ° c A.V. Bernatskiy, V.N. Ochkin, R.N. Bafoev, 2016, published in Kratkie Soobshcheniya po Fizike, 2016, Vol. 43, No. 6, pp. 18–23. Original Russian Text °
Effect of the Electron Energy Distribution on the Measurement of the Atom Concentration by Optical Actinometry A. V. Bernatskiya , V. N. Ochkina , and R. N. Bafoevb a
Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia; e-mail:
[email protected] b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700 Russia Received March 29, 2016
Abstract—The oxygen and hydrogen atom concentrations in the hollow cathode discharge with water vapor additives are determined using small argon and xenon additives as optical actinometers. The problem of the rejection of measurements of the electron plasma component parameters is discussed. DOI: 10.3103/S1068335616060038
Keywords: actinometry, low-temperature plasma, atom concentration content. The optical actinometry method can be used for measuring atom and molecule concentrations in plasma [1]. It is based on a comparison of the concentration X of analyzed particles with the known concentration A of actinometer particles added in controlled amounts when comparing the particle luminosity intensities I. If we neglect emitting state quenching by collisions under conditions of lowpressure plasma, this relation is given by NX = NA ·
IX λX CA kA · · · . IA λA CX kX
(1)
Here NX,A is the X, A particle concentrations in electronic ground states (it is assumed that they are almost identical to total concentrations), kX,A are the rate constants of excitation from ground states to upper levels of transitions, CX,A are the coefficients defined by optical device geometry and transmittance and the spectral sensitivity of detection, and λX,A are the emission wavelengths of corresponding particles. Assuming that emitting states are excited by electrons with the energy distribution function (EEDF) f (ε), the constants kX,A are defined as Z √ K = σ(ε) · f (ε) · ε · dε, (2) where σ(ε) is the excitation cross section. The method is attractive by the fact that the determination of the sought concentration does not require measurements of absolute intensities and electron concentrations. In this case, generally speaking, the EEDF knowledge necessity remains. In this work, we study by specific examples how much would the distribution shape be critical. In this case, the problem of the selection of actinometric pairs appears important. A. Excitation thresholds εt and cross section shapes σX (ε) and σA (ε) differ. Then, according to (1) and (2), it is necessary to measure EEDF f (ε), intensities IX , IA in relative units and to find the desired concentration NX from (1). B. Excitation thresholds εt are identical, while cross section shapes σX (ε) and σA (ε) are similar, i.e., σX (ε) = Γ · σA (ε). 195
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Fig. 1. Cross sections of excitation by electrons of (1) Xe [8], (2) O [9], (3) H [10], and (4) Ar [11] atoms. (5) EEDF according to probe measurements; (6, 7, 8, 9) Maxwellian EEDFs with average energies hεi = 6, 8, 10, and 12 eV, respectively.
The similarity of the cross section shapes at close thresholds εt is not something accidental, since they are related to the oscillator strength fgu of the optically allowed transition between the ground and excited states in the Born approximation as [1] µ ¶ µ ¶ Ry 2 εt ε σ(ε) = 4 · π · a20 · · fgu , (4) · · ln εt ε εt where Ry is the hydrogen atomic ionization potential and a0 is the Bohr radius. For excitations at optically forbidden transitions, the cross section maxima are grouped near the values ε/εt ≈ 1.2 − 1.6 and the cross section shapes are also close [1]. If condition (3) is satisfied exactly, measurements of the concentration NX become significantly simpler, kA /kX is replaced by the ratio of cross sections and the results calculated by formula (1) are independent of the EEDF. The values of Γ can be determined, e.g., by maxima of cross sections or by their average (integral) values. Thus, when selecting actinometric pairs, one should where possible to focus on the lines in the spectra of particles with close excitation thresholds. Then, relation (1) takes the form IX λX CA · · · Γ−1 · (1 + δX ), (5) NX = NA · IA λA CX where δX is the correction removing the differences between (1) and (5) associated with approximateness of (3). In the present work, we study how much are such corrections significant by the example of measurements of concentrations of oxygen and hydrogen atoms produced during water molecule decomposition in the gas discharge containing water vapor. This problem arises in connection with the development of new and operation of existing high-power electrovacuum installations for which purity maintenance of plasma-forming gases is one of the central problems. Among such problems is the exclusion of water vapor penetration into the working chamber from wall cooling loops [2, 3]. Such events are monitored, in particular, by optical methods [4–6]. In the recent study [7], it was proposed to apply the actinometry method to monitor the O atom content as a possible indication of water vapor penetration into plasma. The Xe atom was used as an actinometer, and the EEDF was measured. In the present study, we use simultaneously two actinometers (Xe, Ar), which increases the measurement reliability, extends the list of analyzed particles, combinations of actinometric pairs, and makes it possible to estimate the applicability of only spectral measurements without probe measurements, which significantly simplifies the practical monitoring technique. The experimental setup includes a stainless steel vacuum chamber 22 l in volume with a discharge unit shaped as a metal–ceramic hollow cathode. The chamber is equipped with optical windows for BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 43 No. 6
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Fig. 2. Time behavior of the oxygen atom concentration after discharge turn-on: (a) data processing without and (b) with regard to the experimental EEDF; (1, 2) correspond to Xe and Ar actinometers, respectively. Solid curve is the approximation by a polynomial of the values averaged for Xe and Ar.
measuring emission spectra, high-voltage inputs for the discharge, and an electrical probe for measuring electronic component parameters. The setup is described in more detail in [5, 6]. The chamber was filled with a He:H2 O:Xe:Ar (99:33:1:1) gas mixture with total pressure p0 = 1 mbar. Actinometric line pairs O (777.19 nm)–Xe (823.16 nm), O (777.19 nm)–Ar (751.46 nm), H(656.28 nm)–Xe(823.16 nm), and H(656.28 nm)–Ar (751.46 nm) were used. Figure 1 shows the energy dependences of the cross sections σ(ε) of excitation of O, N, He, Ar atoms by electrons and the measured EEDF f (ε). There are also shown Maxwellian EEDFs fM (ε) with various average energies hεi. Figure 2(a) shows the results of measurements of the dependence of the oxygen atom concentration on the discharge duration when processing the intensities of actinometric pair lines by simplified relation (5). The values of Γ correspond to the ratio of the excitation cross section areas in the range of 0– 70 eV (characteristic range of significant values of the EEDF). Figure 2(b) shows the same taking into account the measured EEDF using formulas (1) and (2). We can see that the results of Figs. 2(a) and 2(b) are close within experimental error, if Xe is used as an actinometer. If Ar is used as an actinometer, the oxygen concentrations appear higher by a factor from 1.5 to 2. The fact that the difference of the measurement results taking into account the EEDF is larger in the latter case is probably caused by
Fig. 3. Time behavior of the hydrogen atom concentration after discharge turn-on: (a) data processing without regard to the EEDF and (b) with regard to the experimental EEDF; (1, 2) correspond to Xe and Ar actinometers, respectively. BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 43
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Fig. 4. Corrections δX for considering the effect of Maxwellian EEDFs with various average energies for actinometric pairs (1) O–Xe, (2) О–Ar, (3) N–He, and (4) Н–Ar.
larger differences in the excitation thresholds of lines of the particle under study and Ar actinometer (Fig. 1). The similar results are also obtained in the measurements of hydrogen atom concentrations shown in Figs. 3(a) and 3(b). Thus, the use of several actinometric pairs leads to well consistent results. Surely, in practice, it is much easier to perform only optical measurements, not involving probe measurements of the EEDF. The correction δX in formula (5) can be taken as a measure of associated errors. To estimate them, we calculated δX for a number of Maxwellian EEDFs with various average energies hεi as applied to the considered cases of oxygen and hydrogen atom measurements. The results are shown in Fig. 4. The corrections decrease with increasing hεi and decreasing differences between excitation thresholds of actinometric spectral line pairs. In the range from 12 eV to 6 eV, they do not exceed 60%. They can be approximately introduced if the average electron energy is estimated from the values of the given electric fields strengths E/N [12]. ACKNOWLEDGMENTS This study was supported by the Russian Science Foundation, project no. 14-12-00784. REFERENCES 1. V. N. Ochkin, Spectroscopy of Low-temperature Plasma (Wiley-VCH, Wienheim, 2009; Fizmatlit, Moscow, 2010). 2. ITER Final Design Report No. G 31 DDD 14 01.07.19 W 0.1, Section 3.1: Vacuum Pumping and Fuelling Systems (IAEA, Vienna, 2001). 3. Au. Durocher, A. Bruno, M. Chantant, et al., Fusion Eng. Des. 88, 1390 (2013); doi: 10.1016/j.fusengdes.2013.02.078. 4. A. B. Antipenkov, O. N. Afonin, V. N. Ochkin, et al., Fiz. Plazmy 38(3), 221 (2012) [Plasma Phys. Rep. 38, 197 (2012); doi: 10.1134/S1063780X12020018]. 5. A. B. Antipenkov, O. N. Afonin, A. V. Bernatskiy, and V. N. Ochkin, Yad. Fiz. Inzh. 5, 644 (2014); doi: 10.1134/S2079562914070021. 6. A. V. Bernatskiy, V. N. Ochkin, O. N. Afonin, and A. B. Antipenkov, Fiz. Plazmy 41, 767 (2015); doi: 10.7868/S0367292115090036 [Plasma Phys. Rep. 41, 705 (2015); doi: 10.1134/S1063780X15090032]. 7. A. V. Bernatskiy and V. N. Ochkin, Kratkie Soobshcheniya po Fizike FIAN 42(9), 30 (2015) [Bulletin of the Lebedev Physics Institute 42, 273 (2015)]; doi: 10.3103/S1068335615090055]. 8. Biagi-v8.9 (Magboltz version 8.9) database, www.lxcat.net, retrieved on June 10, 2015. 9. R. R. Laher and F. R. Gilmore, J. Phys. Chem. Ref. Data 19, 277 (1990). 10. H. W. Drawin, Collision and Transport Cross-Sections (EUR-CEA-FC report 383, 1966). 11. A. Yanguas-Gil, J. Cotrino, and L. L. Alves, J. Phys. D: Appl. Phys. 38, 1588 (2005). 12. Yu. P. Raizer, Gas Discharge Physics (Nauka, Moscow, 1987) [in Russian]. BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 43 No. 6 2016
