WDS'15 Proceedings of Contributed Papers — Physics, 155–161, 2015. ISBN 978-80-7378-311-2 © MATFYZPRESS

Source of Atomic Hydrogen for Ion Trap Experiments: Review and Basic Properties

A. Kovalenko, Š Roučka, S. Rednyk, T. D. Tran, D. Mulin, R. Plašil, J. Glosík Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.

Abstract. The H-atom source was used to produce atomic hydrogen for study of ion-molecule reactions relevant to astrochemistry at low temperatures. H atoms were cooled and formed into an effusive beam, passing through a 22-pole ion trap. Here we present the basic operating principles of the H-atom source and give a review of this apparatus with some calculations of vacuum conditions and parameters of the produced H-atom beam.

Introduction Hydrogen is the most abundant element in the Universe [Field et al., 1966]. It is the main component of stars, giant planets and interstellar clouds. Reactions with atomic or molecular hydrogen are important for understanding the processes which occur in the interstellar medium and during the formation of the new stars. There are three isotopes of hydrogen: protium, deuterium and tritium. The reactions of ions with H atoms have to be studied for better understanding of formation and destruction of more complex ions and molecules observed in interstellar medium. There are regions in space called H I and H II regions where hydrogen is mostly neutral in H I regions, rather than ionized or molecular in the H II regions. The atomic hydrogen plays fundamental role in many astrophysical contexts especially in formation H2 molecules [Habart et al., 2005; Sternberg et al., 2014]. There are only a few numbers of measurements of reaction rate coefficient for reactions with H atoms at temperature lower than 100 K. It makes them unique and demanded for the astrochemistry and plasma physic. In our laboratory we study reactions with atomic hydrogen at temperature lower than 100 K because such kind of temperature (even lower) corresponds to the temperature of nebulas and ion clouds in interstellar space. A by-product of the H atom source is molecular hydrogen, which can penetrate into the trap volume and react with the studied ions via unwanted parasitic reactions. For example, the D+ ions can react with both H atoms and + H2 molecules and produce the same ion, H . Therefore the rate of reaction with H atoms cannot be determined until we know the rate of reaction with molecular hydrogen in the chamber. Calculation of number density of molecular hydrogen can help us to design a more efficient pumping system and to estimate the rate of reaction with H2, which will improve the accuracy of our measurements.

Experimental technique Our experimental setup is based on a 22-pole RF ion trap [Gerlich, 1992a; Gerlich et al., 1992b; Gerlich, 1995] and an effusive beam source of atomic hydrogen (AB) [Borodi, 2008] which has been designed and constructed in Chemnitz in laboratory of prof. Gerlich and then it has been moved to Charles University in Prague. Using this apparatus we have studied reactions with atomic hydrogen. For example, there have been studied reactions with hydrogen anion [Gerlich et al., 2012], deuterium anion [Roučka et al., 2015] and CH+ ion [Plašil et al., 2011]. H atoms are produced by disassociation of H2 molecules in an inductively coupled RF discharge (22 MHz, 20 W). The mixture of H atoms and H2 molecules flows through the cooled nozzle in accommodator which is ® covered with a polytetrafluoroethylene (Teflon ) film for minimizing the association of H back to H2 because of exceptionally low atomic recombination coefficient [Collins et al., 1964]. The H-atom beam is formed in the nozzle, whereupon the beam penetrates to 22-pole RF ion trap. The temperature of the H-beam (TACC) and 22-pole trap (T22PT) can be set in the range of 6–300 K and 10–300 K, respectively. The trapped ions are thermalized in collisions with H2 or He buffer gas [Roučka, 2012]. A schematic view of an atomic beam-22 pole trap apparatus (AB-22PT) and a scheme of the three-stages pumping system are shown in Figure 1. The temperatures of neutral particles atoms (TACC) and ions in the trap (T22PT) are different. It is the interaction temperature which defines as TACC+ T22PT T = . (1) kin + 푚1 푚2 where m1 and m2 are masses of neutral particle and ion. 푚1 푚2 In case of hydrogen ion mass ( H ) and neutral mass ( H) of interacting particles

+ TACC+T22PT 푚 T = 푚 . (2) kin 2

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Figure 1. Schematic view of the AB-22PT apparatus and scheme of the two-stage pumping system. H-atom source part (chamber 1) consists of discharge tube, cold head and accommodator (ACC). After H-atom source there are the chambers 2, 3 (with variable aperture) and 4 (with shutter and reacting chamber (22 Pole Trap)). The chambers are pumped by turbomolecular pumps mTP and oTP (magnetic-levitation and oil vacuum- pumping, respectively). To reduce the ultimate pressure we use the second-stage turbomolecular and turbodrag pumps (TDP). The scroll pumps (SP) and rotary pump (RP) are used as fore-vacuum pumps. The respective calculated values of pressure are also depicted.

+ The reaction of CO2 ions with hydrogen atoms in the H-atom beam is used to calibrate the number density of the H atoms in the beam [Borodi, 2008]. An advantage of these reactions is that it gives different products in reaction with H and H2:

+ + CO2 + H → HCO + O (3) + + CO2 + H2 → HCO2 + H (4)

Using the shutter we can block the H beam. We measure the rate of HCO+ production with and without H- atom beam and thus we can determine the number density of H atoms. Accuracy of our calibration is limited by + 40% uncertainty of the reaction rate coefficient of CO2 + H [Borodi, 2008]. To improve the accuracy in the planned experiments, we consider to calibrate density of H atoms by using the D+ + H charge exchange reaction. The rate coefficient of this reaction has already been reliably calculated in [Savin, 2002].

Calculation of the number density of H2 inside the chambers In the most cases, molecules of hydrogen are formed by recombination of H atoms on the chamber walls and the mechanism in details has been studied and described in [Borodi, 2008]. The same process occurs in accommodator. In our calculations, we assume that the molecular hydrogen is contained in the chambers and thermalized by collisions with chamber walls. The temperatures of accommodator and ion trap are 300 K. We also suppose that the H-atom beam consists of entirely hydrogen atoms. To calculate appropriate values of number density in the chambers we used parameters of the pumps and some geometrical specification of the chambers which are presented in a Table 1.

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Table 1. The parameters of the pumps and some geometrical specifications. Diameter of the Length of an accommodator Parameters of the pumps orifices, [cm] tube, [cm]

Pumping speed for Compression ratio d1 0.2 1.55 H2, [ℓ/s] for H2 d2 0.4 Diameter of an accommodator S 340 CR 2,500 d 0.3 mTP1 mTP1 3 tube, [cm]

SmTP2 480 CRmTP2 200,000 Radius of 22PT 0.25 STDP1 3.7 CRTDP1 300 orifice, [cm]

SSP1 1.5 — 0.25 Typical pressure of H2 in the SSP2 1.5 — Distance from the chamber 1, [Pa] S 340 CR 2,500 skimmer to 22PT, [cm] mTP3 mTP3 0.001 STP1 48 CRmTP1 140,000 78

The total flow through the orifice between chamber 1 and 2 in molecular regime can be determined as

1 Ф = = ( ), (5) 4 12

1 2 1 2 where Ф1 is flow and Ф2 is backflowФ throughФ − Ф the chambersА 푛 〈1푣 and〉 − 푛2, 〈n푣1〉, n2, are the gas number densities in the respective chambers, A12 is the cross sectional area of the chamber orifice and = 8 / is the average velocity of the particles with the temperature of the chamber walls , where k is the Boltzmann B B wall constant and m is the particle mass. The temperature is the same for all chambers.〈푣〉 �Therefore푘 푇 we휋� can wall conclude that the velocity of molecules is also the same. Expressing the gas 푇number density in terms of the wall partial pressure of H2 inside chamber 1 and chamber 2 as 푇p1 and p2, respectively, we obtain

1 = ( ) . (6) 4 B

Ф 퐴12〈푣〉 푝1 − 푝2 The total flow through the orifice Ф is equal푘 푇 to , where S is the pumping speed of the pump connected to the chamber 2. Expressing it in terms of the pressure, we finally obtain 푚푚푚1 2 푆 ∙ 푛 = . (7) B2

푚푚푚1 푝 Expression the appropriate pressure p2 fromФ eq.푆 (6) and (7), we obtain 푘 푇 1 12 = 4 . 1 (8) А+ 〈푣〉12 2 4 1 푝 푝 푚푚푚1 Analogous equations can be also written for푆 p2, p3 andА p3,〈 푣p〉4. The typical value of p1 in our experiments is −3 −6 −7 −9 10 Pa. The obtained results for all chambers are p2 = 8.8·10 Pa, p3 = 1.7·10 Pa, p4 = 1.6·10 Pa. For our −6 −7 AB-22PT apparatus the pressure for the chambers are p2exp = 4.0·10 Pa, p3exp = 1.3·10 Pa and for the chamber 4 it is lower than 10–8 Pa. In case of our pumping system we also have to calculate the lowest possible value of pressure (ultimate pressure). The obtained results are compared with calculated value for chambers 2, 3 and 4. For the further calculations we need to derive the appropriate pressures for the fore-vacuum system. To get pressure between pumps links, we multiply pressure of upper stage by the pump speed ratio. For the chambers 2 and 3 this pressure p21 and p31, respectively, can be calculated as

= , = . (9) mTP1 mTP2 푆 푆 푝21 푝2 ∙ 푝31 푝3 ∙ As it can be seen from Figure 1, the links 푆afterTDP1 the pumps of these푆TDP1 chambers are combined into one. Thus the total pressure p231 for these links can be expressed as

( + ) = . (10) 2 mTP1 3 mTP2 푝 ∙ 푆 푝 ∙ 푆 푝231 푆TDP1

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Using the value of compression ratio as maximum pressure ratio between pressure above the pump and pressure below it we obtain the ultimate pressure that we can reach. In general, combining the fore vacuum of chambers 2 and 3 can lead to the back flow of H2 into the chamber with lower pressure. However, in our case the compression ratio (CR) (the pressure ratio between pressure above the pump and pressure below) CRmTP2 is 80 times higher than CRmTP1. Thus the ultimate pressure in chamber 3 is 80 times lower than in chamber 2. The pressure in the link above the scroll pump (SP1) is obtained like in the previous formula (9). The calculations for the chamber 4 are analogous. 232 Using the푝 value of compression ratio of appropriate pumps, we obtain the ultimate pressure that we can reach. The ultimate pressure for the link between SP1 and TDP ( ) is given by the ultimate pressure of the scroll pump, and the compression ratio can be expressed as 푝232ult = . (11) 232ult 푝 퐶퐶 231ult) Then, after getting pressure for combined link ( 푝 , we can calculate the pressure for chamber 2 and chamber 3 ( and p , respectively) in the same way, knowing the compression ratio of these pumps. The 231ult calculation results of the vacuum system and all pressures푝 were written in Tables 2 and 3. 푝2ult 3ult Table 2. Table of pressures inside chambers 1, 2, 3, 4 and in fore-vacuum system. Pressure in the Total pressure for the Pressure inside Pressure in the pumping pumping connection between p chambers, [Pa] 21 stage two, [Pa] stage two, [Pa] and p31, [Pa] −3 p1 1·10 — — — −6 −4 p2 8.8·10 p21 8.1·10 −4 −3 −7 −5 p231 8.3·10 p232 2.1·10 p3 1.7·10 p31 2.2·10 −9 −7 −6 p4 1.6·10 p41 1.1·10 — p42 3.5·10

Table 3. Ultimate value for chambers 2, 3, 4 and between pumps. Ultimate pressure for the links Ultimate pressure for the links and and chambers 2 and 3, [Pa] chamber 4, [Pa] −6 p2ult 8.8·10 −8 −7 p4ult 1.9·10 p3ult 1.1·10 −2 −5 p231ult 2.2·10 p41ult 4.7·10

pSPult 6.6 pSPult 6.6

For the chamber 2 we took the ultimate pressure, because the previous calculated pressure inside the chamber was lower than ultimate, thus we could not reach it. The pressure inside the chamber 3 is higher than ultimate. For the chamber 4, the ultimate pressure is 12 times higher than the calculated. Therefore the H2 molecules can leak back because of the high ultimate pressure of H2 in the fore-vacuum system. Another source of H2 can be the hydrogen from the outside. A permeation of hydrogen through the stainless steel walls of vacuum chamber have to be also taken into account. The flow of H2 due to permeation is

= , (12)

퐶 perm H2 where = 0.01 Pa is the typical pressure ofФ air-born∙ 퐾 hydrogen,�푝 b = 2 mm is the wall thickness, C ≈ 0.4 m2 is 푏 area of the chamber walls and K at 300 K is given by [Louthan, 1975] as H2 perm 푝 = 1.61 10 Pa l s m . (13) 1 −10 2 −1 −1 After evaluating the flow from퐾perm formula (12∙) and dividing∙ ∙by the∙ pumping speed SmTP3 we obtain that the partial pressure of H2 due to the permeation is by two orders of magnitude lower than calculated for chamber 4. We can neglect permeation in comparison with the flow from the H-atom source. To solve the problem with back flow of H2 inside the 22PT chamber, we need to add the gas with higher compression ratio than for hydrogen. We present nitrogen as a carrier gas and put the balloon with it between the scroll pump and turbomolecular pump. Because the compression ratio of our pumping system for nitrogen is more than five orders of magnitude higher than for hydrogen, replacing the hydrogen in fore-vacuum with nitrogen will reduce the ultimate pressure in the 22PT (chamber 4). The nitrogen does not have a significant influence on our trap experiments, because of the high compression ratio for this gas. It has more than twenty orders of magnitude for our pumping system.

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The total pressure of two gas components can be expressed by Dalton's law. In our case, for H2 and N2, we have

= + . (14) sp sp sp 2 2 Here is given by the term = ( +푃 푃)/H 푃.N The typical value of N2 flow in the AB-22PT experiment is 1.67 Pa·l/s. The H flow we can get from the calculation of pressure for this chamber as sp 2 sp H2 N2 sp 5.3·10−7 Pa·l/s.푃 The pumping speed of푃 the scrollФ pumpФ is 1.5푆 l/s. The partial pressures of H2 and N2 above the SP are proportional to the flows of these gases, that means

sp = . (15) 푃H2 H2 sp Ф 2 After solving the system of eq. (14) and (15),푃 Nwe2 obtainФN

= /(1 + ). (16) sp N2 Ф H2 sp 푃 푃 2 The obtained result is six orders of magnitude better thanH without added N2. Therefore, the pressure p4 will −9 Ф not be limited by its ultimate value, i.e., p4 = 1.6·10 Pa.

Calculation of the number density of H atoms inside the 22PT One of the disadvantages of an effusion beam source is the low intensity maximum restricted by low number density due to the molecular flow condition. In this case, in terms of mean free path, the probability of collision between molecules is lower than the probability of molecule–wall collision. Another one is the poor H directivity [Borodi,푛 2008]. The last problem can be improved if a simple orifice is replaced by a long channel with a circular cross section. To compare the number density of H2 molecules and H atoms in the trap, we need to derive the intensity maximum of the H atoms flying into the 22PT. The maximum number density of H atoms for the molecular flow condition Kn ≥ 0.5 in the accommodator tube can be derived from the formula for the Knudsen number. It is a dimensionless number defined as

= , (17) 휆 where λ is a mean free path and L is representative퐾푛 physical length scale, which in our case is accommodator nozzle diameter (2.5 mm). For a ideal gas, the mean free path퐿 may be calculated as 4 = , (18) 2 푛H where, is the collision cross section, is maximum퐾푛 number density in the accommodator. For the molecular √ 휎� 19 −3 flow Kn ≥ 0.5 and all data we obtained the number density as = 1.6·10 cm . H The휎 total flow rate Фt through the 푛tube can be calculated using the Clausing formula [Clausing, 1930] 푛H 1 = , (19) 4

t 0 0 where the geometrical factor = 4D/3LACC is Фthe Clausing휉퐴 푛 factor〈푣〉 with D and LACC the diameter and the length of the tube. The maximum intensity on axis I can be expressed from [Giordmaine et al., 1960] as 휉

= , [s sr ]. (20) t Ф −1 −1 퐼 ∙ Thus the axial intensity is proportional to휋 the휉 total flow rate through the tube. In this case, the gas flow in forward direction, compared to the total rate of flow, is superior to the one obtained by a simple orifice. Calculated peak intensity is equal to 1.7·1018 s−1sr−1. To know the flux through the entrance of the 22PT, we need to multiply the derived results by l/r, where l is the distance between the nozzle and the 22PT and r is the area of the 22PT entrance. The resulting number density of H atoms for the two and one stage vacuum systems 9 −3 9 −3 are 1.5·10 cm and 3·10 cm , respectively. The number densities of H2 corresponding to p4 calculated in the previous section are 3.8·105 cm−3 and 9.1·106 cm−3 for the two and one stage vacuum systems, respectively. From the calculations we can say that number density of the H atoms in the 22PT is bigger than number density of H2 molecules inside chamber with 22 pole trap more than 4·103 times. For the previous one stages system we get 3.3·102. Adding the differential pumping stage improves the ratio approximately by 12 times.

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Experimental results. H beam calibration + We used chemical probing with CO2 to measure the number densities of H2 and H in two configurations of + the vacuum system − with two and one stages of differential pumping. The CO2 ions have been produced by electron bombardment and stocked in the ion source. Then they are mass filtered and injected into the 22PT where they are cooled to above 10 K after collisions with buffer gas (He). The time evolutions for the reaction of + CO2 with H2 and H atoms are shown in Figure 2. Ratio between the number densities of H atoms and H2 molecules in the trap can be compared to the previous ratio for one-stage. We have found out that the ratio [H]/[H2] is 69 times higher in the two-stage system. This result is different from the calculations and there are several reasons to explain such a big discrepancy, such as geometry of the vacuum system and association on the surface of the accommodator or inside chambers. Furthermore, at low temperatures, the number density of H2 is increased by a factor / due to thermal transpiration. On the other hand, the number density of H atoms scales with

푐ℎ푎�푎푎푎/ 푡𝑡 푡 at constant flux due to change of velocity of the atoms. �푇 푇 푐ℎ푎�푎푎푎 퐻 푎�푎� 푠�푠𝑠� �Conclusion푇 푇 In the paper we described the H-atom source that can be used in combination with the 22-pole ion trap to study ion-molecule reactions. Descriptions, working principles and some parameters were also given. Using H- atom source the rate coefficient can be measured for the reactions of ions with atomic hydrogen. The added chamber 3 can improve [H]:[H2] ratio and it can be seen from calculations and measurements. We calculated that the two-stage of differential pumping is 12 times better than the previous system with one differential pumping stage. The results for the experiments indicate that two-stages are 69 times more efficient than one-stage. Calculations showed that we could lower the number density of H2 in the 22PT chamber by adding extra N2 after Scroll Pump (SP2). We managed to improve the ratio [H]:[H2] = 1:1 which is sufficient for studying reaction with rate coefficient higher than 10−11 cm3s−1 such as eq . D + H. + Acknowledgments. We thank Dieter Gerlich, the Technical University of Chemnitz, for the help and the DFG for lending us the 22-pole trap instrument. This work is partly supported by GACR P209/12/0233, by GACR 14-14715P, by GAUK 572214.

+ + + Figure 2. The measured and fitted time evolution of numbers of CO2 (■), HCO (▼), HCO2 (▲) for the + reaction of CO2 with H2 and H. The full and open symbols denote the measurements with the H beam ON and OFF. The graph (a) represents results obtained with one-stage vacuum system, the graph (b) are results obtained with two-stage vacuum system. [H2]on indicates the number density with H-atom beam ON.

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