Issue 
Eur. Phys. J. Appl. Phys.
Volume 80, Number 3, December 2017
Plasma Sources and Plasma Processes (PSPP)



Article Number  30801  
Number of page(s)  5  
Section  Plasma, Discharges and Processes  
DOI  https://doi.org/10.1051/epjap/2017170228  
Published online  30 January 2018 
https://doi.org/10.1051/epjap/2017170228
Regular Article
Electronion recombination in low temperature hydrogen/deuterium plasma^{★}
^{1}
Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University,
18000
Prague, Czech Republic
^{2}
Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University,
12116
Prague, Czech Republic
^{*} email: juraj.glosik@mff.cuni.cz
Received:
28
June
2017
Received in final form:
16
October
2017
Accepted:
21
November
2017
Published online: 30 January 2018
The stationary afterglow with cavity ring down spectrometer (SACRDS) was used to study the recombination of H_{3}^{+}, H_{2}D^{+}, HD_{2}^{+} and D_{3}^{+} ions with electrons in low temperature (77–300 K) plasmas in He/Ar/H_{2}/D_{2} gas mixtures. By measuring effective recombination rate coefficients (α_{eff}) in plasma with mixtures of ions and their dependences on temperature and partial densities of He, H_{2} and D_{2}, α_{eff} (T, [He],[H_{2}],[D_{2}]), we determined binary (α_{binH3}, α_{binH2D}, α_{binHD2}, α_{binD3}) and ternary (K_{H3}, K_{H2D}, K_{HD2}, K_{D3}) recombination rate coefficients for H_{3}^{+}, H_{2}D^{+}, HD_{2}^{+} and D_{3}^{+} ions. For all four ions we observed very efficient He assisted ternary recombination which is comparable with binary recombination already at [He] =1 × 10^{17} cm^{−3}. The removal of excited particles in afterglow plasma was monitored to obtain the plasma thermalisation rate at given experimental conditions. The inferred deexcitation rates for reaction of helium metastable atoms with D_{2} are k_{D2} (300 K)=(2.1 ± 0.3) × 10^{−10} cm^{3} s^{−1} and k_{D2} (140 K)=(1.3 ± 0.3) × 10^{−10} cm^{3} s^{−1}.
© EDP Sciences, 2017
1 Introduction
The dissociative recombination of cation and its deuterated isotopologues and has been investigated for nearly six decades (see e.g. Refs. [1,2]). This extensive research is motivated by fundamental character of processes of recombination of these ions. Further motivation is in astrophysics, plasma physics and in technological applications of hydrogen and deuterium plasmas. Ions and have been detected many times in the interstellar medium [3,4]. All four isotopologues of are included in the current models of interstellar chemistry of molecular clouds [5–7]. The degree of deuteration of ions in H_{2}/D_{2} buffered plasmas depends on physical conditions such as the [D_{2}]/[H_{2}] ratio, temperature and overall pressure. Essential are also the rates of formation and destruction of these ions in actual plasmatic environments.
Having in mind low temperature plasmas and their technological applications, the present study focuses on binary and neutral assisted ternary electronion recombination processes [8–10] in plasmas containing both hydrogen and deuterium. The employed experimental technique (discussed in the next section) enables in situ probing of number densities of all four isotopologues of in afterglow plasma. A particular attention was given to the plasma thermalisation by monitoring the presence and rate of removal of excited particles in the afterglow and the kinetic and the rotational temperatures of the recombining ions.
2 Characterisation of afterglow plasma in He/Ar/H_{2}/D_{2} gas mixture
For measurements of recombination rate coefficients we use a standard stationary afterglow (SA) experiment with cavity ring down absorption spectrometer (for details see [8] and references therein). In afterglow experiments time evolutions of electron and ion number densities are monitored during the decay of the recombination dominated afterglow plasma. In the present experiments a plasma is formed by microwave discharge in a He/Ar/H_{2}/D_{2} gas mixture with typical number densities of 5 × 10^{17}/10^{14}/10^{14}/10^{14}cm^{−3}, respectively. The flows of helium buffer gas and reactants are monitored by MKS mass flow meters and controllers and the pressure in the discharge tube is measured by MKS Baratron Type 622 and by PTUFAC332AH piezo pressure transducer enabling us to determine the corresponding partial number densities. If the desired reactant flow is lower than achievable by the flow controller, we create mixture of the reactant with helium in a reservoir equipped with absolute MKS Baratron Type 122A. In such way number densities down to 10^{11}cm^{−3} are achievable. During the discharge and in the very early afterglow the plasma contains electrons, ions and , and some highly excited particles. The temperature of the electrons (T_{e}) during the discharge is on the order of ∼2 eV. After switching off the discharge (microwaves) electrons are cooled in collisions with He, assuming that they are not heated in collisions with highly excited metastable Ar or He particles [11]. The electron temperature in the afterglow can be determined by monitoring losses of charged particles due to the ambipolar diffusion [12].
The determination of plasma parameters during the active discharge and during the afterglow is obviously a first step in the experiment. Important parameters are those that characterise thermalisation of afterglow plasmas. For example the equality within the error of measurement between the kinetic (T_{kin}) and the rotational (T_{rot}) temperature of ions, the temperature of the buffer gas (T_{He}), and the wall temperature of the discharge tube (T_{wall}) needs to be experimentally verified. By measuring the corresponding absorption line profiles T_{rot}, T_{kin} and ion densities can be determined for all four ions. Examples of absorption lines profiles measured for ions at T_{wall} = 80 K are shown in Figure 1. From the obtained Boltzmann plots (examples are shown in the insert) T_{rot} are evaluated during the discharge and during the early afterglow. The kinetic temperature is evaluated from the Doppler broadening of the measured absorption lines. As the T_{kin} and T_{rot} of H_{2}D^{+} and ions are very close to each other and to the T_{wall} and the same also applies for and ions [8,9], in the following text we will use only single temperature T with numerical value of T_{wall} if not stated otherwise.
To confirm thermalisation of electrons within the very early afterglow we have monitored the time decay of the densities of the (N = 9, J = 10) excited state of He_{2} and the , J = 2 excited state of argon that indirectly hint on the presence of helium metastable atoms [11]. The corresponding transitions are listed in Table 1. and in reference [11]. The present measurements were carried out in pure He, He/Ar, He/Ar/H_{2} and in He/Ar/H_{2}/D_{2} mixtures in order to characterise the time constant τ for deexcitation in collisions with Ar, H_{2} and D_{2}. The examples of measured dependences of inverse time constants (1/τ) of the decays of the density of excited and on [D_{2}] and [H_{2}] are plotted in Figure 2. The slope of the linear fit to the data in Figure 2 gives effective rate coefficients of deexcitation for metastable helium atoms in collisions with D_{2} or H_{2} (see discussion and explanation in Ref. [11]): k_{D2} (300 K) = (2.1 ± 0.3) × 10^{−10}cm^{3}s^{−1} and k_{D2} (140 K)=(1.3 ± 0.3) × 10^{−10}cm^{3}s^{−1}. These values are approximately 30% lower than the corresponding rates obtained for H_{2} reactant gas [11]. Under conditions for which the data plotted in Figure 1 were measured and which are typical for current experiments, the plasma (ions and electrons) is thermalised in time shorter than 100 μs.
Fig. 1
The absorption line profiles obtained for ions at T_{wall} = 80 K in a mixture of He/Ar/H_{2}/D_{2} with [He]=4.0 × 10^{17}cm^{−3}, [Ar] =2.1 × 10^{14}cm^{−3}, [H_{2}] = [D_{2}] =9 × 10^{13}cm^{−3}. The particular transitions are shown at the top of each plot and denoted by corresponding vibrational (v_{1}, v_{2}, v_{3}) and rotational J_{KaKc} quantum numbers, for details see reference [13]. The insert shows Boltzmann plots obtained for (T_{wall} = 80 K) at two different pressures of He buffer gas. The filled symbols (A and B) denote values obtained in the discharge while the values indicated by open symbols (C) were measured 100 s after switching off the discharge. The obtained rotational temperatures are: T_{rotA} = (87 ± 10) K, T_{rotB} = (96 ± 10) K and T_{rotC} = (98 ± 15) K while the kinetic temperature evaluated from the Doppler broadening of the plotted absorption lines is T_{kin} = (96 ± 10) K. 
Measured transitions (ν_{exp}) belonging to the (1–0) vibrational band of the He_{2} − system compared to the calculated values (ν_{calc}). For details on the calculations see reference [11]. The estimated error of the measurement is 5 × 10^{−4} cm^{−1}. The calculated Einstein coefficients of spontaneous emission A are also listed. The transitions are labeled with the corresponding quantum numbers , where F = 1 for J = N + 1, F = 2 for J = N, and F = 3 for J = N  1 and the prime and double prime denote the upper and lower state, respectively.
Fig. 2
Dependences of the reciprocal time constants of exponential decays of and number densities on [D_{2}] measured in the afterglow at 300 K (upper panel) and at 140 K (lower panel). The values obtained in a He/Ar/D_{2} gas mixture (open circles for and open triangles for ) are compared to those previously measured in a He/Ar/H_{2} gas mixture (filled circles and filled triangles for and , respectively) [11]. In the present experiment the helium buffer gas pressure was 900 Pa and [Ar]=5 × 10^{12}cm^{−3} at 300 K and [Ar] =7 × 10^{12}cm^{−3} at 140 K. The dashed lines are linear fits to the data. 
3 Electron–ion recombination in He/Ar/H_{2}/D_{2} gas mixtures
In this section we will summarise the complications connected with evaluation of recombination rate coefficients in plasmas containing both H_{2} and D_{2}. The ions and formed in discharge in He/Ar/H_{2}/D_{2} gas mixtures are during the decay of an afterglow plasma removed by recombination with electrons and by ambipolar diffusion. In description of such plasmas we have to consider several recombination processes, e.g. for H_{2}D^{+} ions: (1) (2) where α_{binH2D} and K_{H2D} are binary and ternary (He assisted) recombination rate coefficients. Ions and recombine similarly with rate coefficients α_{binH3}, α_{binHD2}, α_{binD3}, K_{H3}, K_{HD2} and K_{D3}. In agreement with present results and results of previous experimental studies, we assume that binary and threebody recombination processes add linearly, i.e. that an “effective” rate coefficient can be defined as α_{effion} = α_{binion} + K_{ion} [He]. The linear combination is known to become invalid at high He densities due to saturation (high pressure limit) [14]. For recombination dominated quasineutral afterglow plasma the balance equation for electron density is: (3)
The term n_{e}/τ_{RD} describes losses due to ambipolar diffusion and due to possible conversion to other ion species (for more detailed description of kinetics of processes see Refs. [14–16]). By using the fractions f_{H3}, f_{H2D}, f_{HD2} and f_{D3} for all ions (f_{ionX} = [X^{+}]/n_{e}) instead of the ion number densities the balance equation (3) can then be written in the simple form: (4) where the overall effective recom(f_{ionX} = [X^{+}]/n_{e})bination rate coefficient α_{effS} is equal to the sum: α_{effS∑} = α_{effH3}f_{H3} + α_{effH2D}f_{H2D} + α_{effHD2}f_{HD2} + α_{effD3}f_{D3}. The ionic composition at constant temperature and constant [He] is given by the relative densities of D_{2} and H_{2}, which can be characterised e.g. by relative D_{2} density, F_{D2} = [D_{2}]/([H_{2}] + [D_{2}]). It is obvious that if α_{effS} is measured for several ionic compositions of plasma then the values of particular effective recombination rate coefficients α_{effion} (T, [He]) can be obtained. From the dependence of α_{effion} (T, [He]) on [He] the binary (α_{binion}) and ternary (K_{ion}) recombination rate coefficient can be obtained. The example of the dependence of α_{effS} on [He] measured at T = 80 K and F_{D2} = 0.49 is shown in upper panel of Figure 3. The examples of dependences of α_{effion} on [He] for and measured at T = 125 K are shown in lower panel of Figure 3. The dependences α_{effion} (T, [He]) were determined over broad range of temperatures and He densities. We need to consider several limiting factors in order to obtain reliable binary and ternary recombination rate coefficients. In plasma in He/Ar/H_{2} or He/Ar/D_{2} gas mixture the recombination rate coefficients for or can be measured relatively simply, because just one type of ions is present in the afterglow. In He/Ar/H_{2}/D_{2} gas mixture the situation is more complicated, because at least 8 processes (rate coefficients) are influencing the plasma decay and actual α_{effS} depends on T, [He], [H_{2}], [D_{2}] and F_{D2}.
For over ten years we have been studying electronion recombination of the cation and its deuterated isotopologues and using flowing and stationary afterglow techniques. Essential result in these studies was the discovery that there exists a very efficient ternary neutral assisted recombination process, which is at 300 K already at few thousands pascal of He comparable with binary recombination [2,10]. Ternary recombination assisted by molecular hydrogen is by another three orders of magnitude more efficient [14]. The ternary recombination rate coefficients for and ions measured by our group so far are summarised in Figure 4 (see also Refs. [9,16]). For comparison some data for ternary recombination of Ar^{+} and other ions are also included in the figure.
Fig. 3
The dependence of α_{effS} on [He] obtained at 80 K for F_{D2} = 0.49. The dashed lines denoted and are linear fits to the α_{effH3} and α_{effD3} taken from reference [10]. Lower panel: The dependence of α_{effH2D} and α_{effHD2} on [He] measured at 125 K. The full lines are linear fits to the data used to obtain the recombination rate coefficients α_{binH2D}, α_{binHD2}, K_{H2D} and K_{HD2}. The dashed lines denoted and are linear fits to the α_{effH3} and α_{effD3} [10]. The arrows indicate the theoretical values of α_{binH2D} and α_{binHD2} [17]. The stars denote the values measured for in SACRDS experiment (see also Ref. [8]). 
Fig. 4
Temperature dependences of the ternary recombination rate coefficients of helium assisted recombinations measured for [9], [10], H_{2}D^{+} and [15], [16] ions. The values of ternary recombination rate coefficient obtained for Ar^{+} ions in helium [18] and for a mixture of atmospheric ions in helium [19] are plotted for comparison. The dashed line denotes the classical theoretical prediction by Bates and Khare [20] scaled for Ar^{+} ion in helium by reduced mass. Note the substantial difference between the values of ternary recombination rate coefficients obtained for in helium and those measured in H_{2} buffer gas [14]. 
4 Summary and conclusion
The recombination of and ions with electrons have been recently studied at temperatures ranging from 50 K up to 340 K in He buffered afterglow plasma. In the studies the flowing afterglow (CRYOFALP) and the stationary afterglow with CRDS spectrometer (SACRDS) were used to measure effective recombination rate coefficients (α_{eff}) of mixtures of ions and their dependences on temperature, He buffer gas density ([He] = 10^{16} − 10^{18}cm^{−3}) and on densities of H_{2} and D_{2}. From measured dependences α_{eff} = α_{eff} (T, [He],[H_{2}] , [D_{2}]) over broad range of plasma parameters we were able to determine binary (α_{binH3}, α_{binH2D}, α_{binHD2}, α_{binD3}) and ternary (K_{H3}, K_{H2D}, K_{HD2}, K_{D3}) recombination rate coefficients for and ions (see also Refs. [10,16]). For all four ions we observed very strong He assisted ternary recombination which is comparable with binary recombination already at He densities of [He] =1 × 10^{17}cm^{−3}. We have studied plasma thermalisation during the afterglow in He/Ar/H_{2}/D_{2} gas mixtures. The results confirm that at conditions used in present recombination studies the afterglow plasma is thermalised and the excited particles are effectively removed. Our results provide more detailed picture of recombination processes in hydrogen and deuterium containing low temperature plasmas, for instance those used in spectroscopy and in technological applications.
Acknowledgements
This work was partly supported by Czech Science Foundation projects GACR 1515077S, GACR 1708803S, GACR 1718067S, and Charles University Grant Agency project GAUK 1583517.
References
 M. Larsson, A.E. Orel, Dissociative recombination of molecular ions (Cambridge University Press, Cambridge, 2008) [CrossRef] [Google Scholar]
 J. Glosík, R. Plašil, T. Kotrík, P. Dohnal, J. Varju, M. Hejduk, I. Korolov, Š. Roučka, V. Kokoouline, Mol. Phys. 108, 2253 (2010) [CrossRef] [Google Scholar]
 B. Parise, A. Belloche, F. Du, R. Güsten, K.M. Menten, Astron. Astrophys. 526, A31 (2011) [CrossRef] [EDP Sciences] [Google Scholar]
 T.J. Millar, Astron. Geophys. 46, 2.29 (2005) [CrossRef] [Google Scholar]
 A. Das, L. Majumdar, S.K. Chakrabarti, D. Sahu, New Astron. 35, 53 (2015) [Google Scholar]
 T. Albertsson, D.A. Semenov, A.I. Vasyunin, T. Henning, E. Herbst, Astrophys. J., Suppl. Ser. 207, 27 (2013) [Google Scholar]
 O. Sipilä, P. Caselli, J. Harju, Astron. Astrophys. 554, A92 (2013) [Google Scholar]
 P. Dohnal, M. Hejduk, P. Rubovič, J. Varju, Š. Roučka, R. Plašil, J. Glosík, J. Chem. Phys. 137, 194320 (2012) [CrossRef] [PubMed] [Google Scholar]
 M. Hejduk, P. Dohnal, P. Rubovič, Á. Kálosi, R. Plašil, R. Johnsen, J. Glosík, J. Chem. Phys. 143, 044303 (2015) [CrossRef] [PubMed] [Google Scholar]
 R. Johnsen, P. Rubovič, P. Dohnal, M. Hejduk, R. Plašil, J. Glosík, J. Phys. Chem. A 117, 9477 (2013) [CrossRef] [PubMed] [Google Scholar]
 Á. Kálosi, P. Dohnal, L. Augustovičová, Š. Roučka, R. Plašil, J. Glosík, Eur. Phys. J.: Appl. Phys. 75, 24707 (2016) [CrossRef] [EDP Sciences] [Google Scholar]
 T. Kotrík, P. Dohnal, Š. Roučka, P. Jusko, R. Plašil, J. Glosík, R. Johnsen, Phys. Rev. A 83, 032720 (2011) [CrossRef] [Google Scholar]
 O. Asvany, E. Hugo, F. Müller, F. Kühnemann, S. Schiller, J. Tennyson, S. Schlemmer, J. Chem. Phys. 127, 154317 (2007) [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
 J. Glosík, P. Dohnal, P. Rubovič, Á. Kálosi, R. Plašil, Š. Roučka, R. Johnsen, Plasma Sources Sci. Technol. 24, 065017 (2015) [CrossRef] [Google Scholar]
 P. Dohnal, Á. Kálosi, R. Plašil, Š. Roučka, A. Kovalenko, S. Rednyk, R. Johnsen, J. Glosík, Phys. Chem. Chem. Phys. 18, 23549 (2016) [CrossRef] [PubMed] [Google Scholar]
 R. Plašil, P. Dohnal, Á. Kálosi, Š. Roučka, R. Johnsen, J. Glosík, Plasma Sources Sci. Technol. 26, 035006 (2017) [CrossRef] [Google Scholar]
 L. Pagani, C. Vastel, E. Hugo, V. Kokoouline, C.H. Greene, A. Bacmann, E. Bayet, C. Ceccarelli, R. Peng, S. Schlemmer, Astron. Astrophys. 494, 623 (2009) [Google Scholar]
 P. Dohnal, P. Rubovič, T. Kotrík, M. Hejduk, R. Plašil, R. Johnsen, J. Glosík, Phys. Rev. A 87, 052716 (2013) [CrossRef] [Google Scholar]
 Y.S. Cao, R. Johnsen, J. Chem. Phys. 94, 5443 (1991) [CrossRef] [Google Scholar]
 D.R. Bates, S.P. Khare, Proc. Phys. Soc. 85, 231 (1965) [CrossRef] [Google Scholar]
Cite this article as: Juraj Glosík, Petr Dohnal, Ábel Kálosi, Lucie D. Augustovičová, Dmytro Shapko, Štěpán Roučka, Radek Plašil, Electronion recombination in low temperature hydrogen/deuterium plasma, Eur. Phys. J. Appl. Phys. 80, 30801 (2017)
All Tables
Measured transitions (ν_{exp}) belonging to the (1–0) vibrational band of the He_{2} − system compared to the calculated values (ν_{calc}). For details on the calculations see reference [11]. The estimated error of the measurement is 5 × 10^{−4} cm^{−1}. The calculated Einstein coefficients of spontaneous emission A are also listed. The transitions are labeled with the corresponding quantum numbers , where F = 1 for J = N + 1, F = 2 for J = N, and F = 3 for J = N  1 and the prime and double prime denote the upper and lower state, respectively.
All Figures
Fig. 1
The absorption line profiles obtained for ions at T_{wall} = 80 K in a mixture of He/Ar/H_{2}/D_{2} with [He]=4.0 × 10^{17}cm^{−3}, [Ar] =2.1 × 10^{14}cm^{−3}, [H_{2}] = [D_{2}] =9 × 10^{13}cm^{−3}. The particular transitions are shown at the top of each plot and denoted by corresponding vibrational (v_{1}, v_{2}, v_{3}) and rotational J_{KaKc} quantum numbers, for details see reference [13]. The insert shows Boltzmann plots obtained for (T_{wall} = 80 K) at two different pressures of He buffer gas. The filled symbols (A and B) denote values obtained in the discharge while the values indicated by open symbols (C) were measured 100 s after switching off the discharge. The obtained rotational temperatures are: T_{rotA} = (87 ± 10) K, T_{rotB} = (96 ± 10) K and T_{rotC} = (98 ± 15) K while the kinetic temperature evaluated from the Doppler broadening of the plotted absorption lines is T_{kin} = (96 ± 10) K. 

In the text 
Fig. 2
Dependences of the reciprocal time constants of exponential decays of and number densities on [D_{2}] measured in the afterglow at 300 K (upper panel) and at 140 K (lower panel). The values obtained in a He/Ar/D_{2} gas mixture (open circles for and open triangles for ) are compared to those previously measured in a He/Ar/H_{2} gas mixture (filled circles and filled triangles for and , respectively) [11]. In the present experiment the helium buffer gas pressure was 900 Pa and [Ar]=5 × 10^{12}cm^{−3} at 300 K and [Ar] =7 × 10^{12}cm^{−3} at 140 K. The dashed lines are linear fits to the data. 

In the text 
Fig. 3
The dependence of α_{effS} on [He] obtained at 80 K for F_{D2} = 0.49. The dashed lines denoted and are linear fits to the α_{effH3} and α_{effD3} taken from reference [10]. Lower panel: The dependence of α_{effH2D} and α_{effHD2} on [He] measured at 125 K. The full lines are linear fits to the data used to obtain the recombination rate coefficients α_{binH2D}, α_{binHD2}, K_{H2D} and K_{HD2}. The dashed lines denoted and are linear fits to the α_{effH3} and α_{effD3} [10]. The arrows indicate the theoretical values of α_{binH2D} and α_{binHD2} [17]. The stars denote the values measured for in SACRDS experiment (see also Ref. [8]). 

In the text 
Fig. 4
Temperature dependences of the ternary recombination rate coefficients of helium assisted recombinations measured for [9], [10], H_{2}D^{+} and [15], [16] ions. The values of ternary recombination rate coefficient obtained for Ar^{+} ions in helium [18] and for a mixture of atmospheric ions in helium [19] are plotted for comparison. The dashed line denotes the classical theoretical prediction by Bates and Khare [20] scaled for Ar^{+} ion in helium by reduced mass. Note the substantial difference between the values of ternary recombination rate coefficients obtained for in helium and those measured in H_{2} buffer gas [14]. 

In the text 
Current usage metrics show cumulative count of Article Views (fulltext article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 4896 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.