- Email: [email protected]
Intrinsic ion transmission of RFQ ion guides in vacuum
Nuclear Instruments and Methods in Physics Research B 361 (2015) 183–188
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Intrinsic ion transmission of RFQ ion guides in vacuum X.-L. Zhao a,⇑, A.E. Litherland b a b
Department of Physics and A.E. Lalonde AMS Laboratory, University of Ottawa, 25 Templeton St., Ottawa, ON K1N 6N5, Canada Department of Physics and IsoTrace Laboratory, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada
a r t i c l e
i n f o
Article history: Received 28 November 2014 Received in revised form 23 February 2015 Accepted 5 March 2015 Available online 18 March 2015 Keywords: Isobar separator Ion transmission Radiofrequency quadrupole ion guides
a b s t r a c t As part of a recent detailed overview of linear radiofrequency ion guides for the conceptualization of their efficient additions into Accelerator Mass Spectrometry (AMS), the intrinsic ion transmission properties were studied further for RF quadrupoles (RFQs) of several electrode shapes, because these are at present the only type being actively considered for use together with AMS. RFQs using hyperbolic poles, cylindrical rods, cylindrical rods plus gradient bars, and 60–30° split cylinders were studied in this work. It is found that the abilities of the first two types for securing ion transmission in vacuum are among the best although the others are quite satisfactory in some applications. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The recent initiatives that use radiofrequency quadrupoles (RFQs) to facilitate on-line isobar separations, either by selective photodetachment of electrons from anions [1] or by element sensitive anion-gas reactions [2], have the potential to significantly extend the analytic scope of AMS, especially those systems using small tandem accelerators. Similar opportunities also exist for positive ions [3], thus providing the potential to extend the applicability of single-stage AMS or even tandem accelerators using Neutral Injection methods. However, the techniques for implementing these on-line isobar separation methods for the AMS of rare long-lived radioactive atoms are relatively complicated and undeveloped because of the very small isotope ratios involved (rare/abundant often < 1012). As AMS must use ion sources that produce micro-Amperes (>160 nA or >1012 ions per second) of beam currents extracted at tens of keV ion energies, the rare isotopes of such ion beams must be mass selected and then energy retarded by a factor of several hundreds to a thousand before they can be captured and controlled by an RFQ field. The abundant isotopes are not possible to control in RFQs without phase space sampling because of the space charge repulsion at such low energies. The captured ions in this case inevitably fill up a significant part of the radial volume of the RFQ ion guide of practical dimensions (the inscribed radius r0 6 10 mm). This introduces ion loss issues where the solutions for the
⇑ Corresponding author. E-mail address: [email protected] (X.-L. Zhao). http://dx.doi.org/10.1016/j.nimb.2015.03.007 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
complete elimination of the losses are not well known despite the long history of RFQ uses for ion confinement and analysis. To conceptualize on their efficient addition into AMS, ultimately for routine AMS, a comprehensive simulation study of linear RF ion guides in general has been completed recently [4]. The study aims to find theoretical solutions of avoiding the two major root causes for analyte losses, especially when the analyte is an anion: (1) The boundaries of a beam captured in a cylindrical electrode system by a radial RF field, i.e., the ranges of the ions’ radial trajectory position and radial speed, must match the maximum ability of the initial RF ion guide for 100% transmission in vacuum, and that match should ideally be maintained thereafter in collisions with gas atoms or molecules. (2) The ion-gas interactions must be carried out within the required safe range of impact energies throughout, to avoid electron detachment and/or molecular fragmentation to the analyte, aside from the expected losses due to chemical reactions of the analyte. To avoid all possible losses (other than those due to expected chemical reactions) it has been found necessary to consider taking advantages of linear RF ion guides of various types for AMS. The higher multipoles are shown to be better suited for guiding ions to enter the vacuum ion guide leading to the gaseous region, while RFQs operated under certain field conditions (Mathieu stability parameter q2 0.5) are shown to be best suited for preparing energy cooled ions for gas cell exit into the high vacuum re-acceleration region. These conclusions are at present only theoretical; so far only RFQs have been used experimentally for isobar
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X.-L. Zhao, A.E. Litherland / Nuclear Instruments and Methods in Physics Research B 361 (2015) 183–188
separation tests with AMS, as described in several papers in the recent past and in this 13th AMS conference. As RFQs for Isobar Separators prior to AMS are likely to remain as the practical choice for some time to come, further simulation studies are therefore still necessary for RFQs to cover various topics in detail. This paper discusses one of such topics, the effect of electrode shapes to the intrinsic ion transmission in vacuum. For gas filled RFQs, certain electrode arrangements are required to also perform some important secondary axial purposes in addition to providing RFQ field for radial ion confinement. One such secondary purpose is to produce a small axial drift gradient for sustaining the ions’ forward motion in gases as the ions are slowed down by collisions. Another potential secondary purpose is to use a special RF ion guide as an impedance of gas conductance, which can be advantageously used to replace small apertures for entering gas cell or gas region [4] and thereby increase the efficiency of transmission. These secondary purposes can be achieved in several ways, but they all inevitably alter the perfect RFQ field produced by precisely shaped hyperbolic electrodes, thus affecting the RFQ’s intrinsic ability for transmitting ions. The question is by how much? This work provides a quantitative analysis for the following four RFQ variations: (1) RFQ made of hyperbolic poles. An advantage using hyperbolic poles is that it also allows exact analytical descriptions of ion motion using Mathieu functions. It is included in this study to provide a base reference. (2) RFQ made of cylindrical rods with rod radius equal to 1.14511r0 [5]. This is the simplest RFQ form. It is not a perfect RFQ (n = 2) as it introduces higher multipole components, but the next higher multipoles n = 6 and n = 10 are very small (<103 of the n = 2), and equal in size but opposite in sign. The rods can be segmented to create a small axial drifting field [6]. (3) Same as above, but with the small axial drifting field created by the insertion of 4 wedged bars between the rods. This is probably the simplest method for creating an effective small axial drifting field, avoiding the much more complicated segmentation of the RF electrodes. However, the gradient bars introduce higher multipoles of increased magnitudes. This technique was initiated as T-shaped bars by ref. [7] and the almost identical plate-shaped bars were first used for transporting negative ions in a gas filled RFQ by ref. [8]. (4) RFQ made of 60–30° split cylinders with the 30° electrodes kept at the constant central potential of the RF [9]. Such a configuration has no n = 6 component and the nearly closed electrodes can be used as a natural gas impedance pipe, and the axial drifting field can be created by segmenting the 30° DC electrodes, also avoiding the segmentation of the RF electrodes. When the properties of these variations are compared to each other, the comparison is made under the same Mathieu stability parameter q2 as calculated below, even though they are not exactly comparable within the full radial volume for the RF fields produced: 2
q2 ¼ 4:8888 ½q V pp =½m f r 20 where q is the ion’s charge state number, Vpp is the RF peak-to-peak voltage in Volt, m is mass of the ion in AMU, f is the RF frequency in MHz, r0 is the inscribed radius in mm. The stability of ion motion in RFQs occur within 0 < q2 < 0.9, but for a captured AMS beam by RFQs, it is not possible to avoid strong ion energy modulation [4]. Due to electron detachment and/or molecular fragmentation, anion analyte losses are inevitable when anion-gas impact energies are large. This is the case for anions
filling a significant radial volume of an RFQ, especially when the RFQ is operated with a large q2. To reduce such losses, only a modest RF ion confinement strength, q2 = 0.2, should be considered for confining RF captured AMS beams, as in this work. 2. Simulation The intrinsic ion transmission of a linear RF ion guide refers to its ability to transmit an ion through an arbitrarily long distance in vacuum given the ion’s conditions at ‘birth’ inside the RF field, i.e., the RF phase, the radial position and radial velocity. For quadrupoles with hyperbolic poles, this subject has been investigated by Baranov [10] analytically, and in fact the acceptance of a hyperbolic electrode RFQ can be calculated exactly. The same concept was adapted and developed further to describe linear RF ion guides in general, with the numerical results derived more simply for a variety of electrode shapes from simulations using SIMION 8.1 [4]. The quantitative result of the ‘intrinsic ion transmission’ of a linear RF ion guide is best graphically displayed for a group of ions with their ‘birth’ conditions randomized, i.e., the RF phase randomized over an RF period, the directions of the radial position and radial velocity, corresponding to the ‘transverse’ energy E, randomized in the radial plane. These randomizations, or uniform distributions, over several ‘birth’ conditions do not necessarily present situations in which a realistic beam would result inside an RFQ. This is merely a choice of simulation convenience to describe an ‘intrinsic’ property of an RF ion guides, so that the ‘intrinsic’ transmission curves for an RFQ that is operated with a stability parameter q2, can be plotted as functions of a pair of _ calculated as (with E in eV): dimensionless parameters, (u, u),
u ¼ r=r 0 u_ ¼ 4:4218 ½E=m1=2 =½f r 0 Fig. 1 illustrates the setup of an approximation to an ideal (infinitely long) RFQ ion guide in SIMION 8.1 and the simulation method with which a transmission curve is obtained. The RFQs studied all have r0 = 10 mm and length = 500 mm; SIMION 8.1 simulations are set up all with 15 grid-units per mm and are all run with default parameters of the software. For each RFQ ion guide studied, transmission curves of q2 = 0.2 for 11 given u values are _ Each data point is derived from the simobtained by varying u. ulations of 10,000 ions (41CaF 3 ) that start on the circle of a u (r/ r0) and 20 mm from the left edge, with ‘axial’ energy Ez = 5 eV, and with starting time randomized in all phases of an RF period. The ‘transverse’ energy E is varied to correspond to an u_ value using the above formula, but with the ‘transverse’ momentum randomized in all directions in the x–y plane. The transmission is calculated as the fraction of the 10,000 randomized ions reaching the right edge of the simulation setup at 500 mm. As has been discussed in the overview study [4], these transmission curves describe an intrinsic property of a linear RF ion guide, which is independent of the RF frequency used as long as it is within the range to support the kind of ion motion that does not gain excessive instantaneous kinetic energy. Thus, only f = 2.5 MHz is used in this work. The quantitative results of the obtained transmissions are inevitably still overestimated somewhat, because 500 mm is not infinite, although it represents a good practical length. 3. Results _ curves for each studied RFQ ion guide A set of 11 u-transmission are summarized in Fig. 2 for convenient comparison. Also shown _ contour lines for transmissions from are the reconstructed 2D (u, u) 0% to 100% and the equipotential lines of the RF field. The electrode
X.-L. Zhao, A.E. Litherland / Nuclear Instruments and Methods in Physics Research B 361 (2015) 183–188
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Fig. 1. Illustration of (a) simulation setup in SIMION 8.1 and (b) transmission computation. (vm is the ion speed in the x–y plane, corresponding to the ion’s ‘transverse’ kinetic energy as E = ½mv2m.)
shape in each case is apparent, but for the case that uses wedged bars, what is actually modeled in this study is a set of straight bars with the inner edges reaching 1.25r0. In each case studied, the u_ max for 100% transmission occurs when u = 0 at (a) 0.113, (b) 0.111, (c) 0.112, and (d) 0.098; the umax for 100% transmission occurs when u_ = 0 at (a) 0.495, (b) 0.489, (c) 0.490, and (d) 0.390. The different electrode shapes have the most impact on the RF field gradient distribution in the radial volume >50% r0, affecting mostly the transmission contour lines of <100%. 4. Discussion _ number density distribution of an AMS beam The actual (u, u) after been captured by a realistic RFQ or other multipole ion guides will be studied in follow-up works. The results of those would be beam and device dependant. Before the modeling of realistic (u, _ number density distributions the implications of the present u) results for practical work need to be evaluated carefully, and they are not obvious. However, the results can be discussed to relate to
several questions of practical concerns. First, can a typical energy retarded AMS beam be completely captured by an RFQ ion guide in vacuum, and what the dimension (r0) of such an RFQ ought to be? The results in Fig. 2 suggest that the very largest u_ max for 100% transmission is about 0.11 at q2 = 0.2. With r0 = 10 mm and f = 2.5 MHz, u_ max = 0.11 means that the maximum ‘transverse’ energy of the ions that can be accepted by the RFQ operated under 36 q2 = 0.2 is about 38 eV for 41CaF Cl . If the total 3 and 14 eV for retarded energy is 50 eV, this further means, that the maximum trajectory angle for anions starting on the axis that can be accepted 36 by the RFQ, is 61° for 41CaF Cl . If r0 = 5 mm is used 3 and 32° for for the above analysis, the maximum ‘transverse’ energy and angle for axial rays become 9.5 eV/26° for 41CaF 3 and 3.5 eV/15° for 36 Cl . If the original beam before deceleration has 35 keV energy and 1° trajectory angle, the final maximum angle for the energy retarded beam at 51.8 eV is roughly 26° because of phase space conservation. This means, r0 = 5 mm cannot be expected to achieve the full capture of a 36Cl beam, unless substantially greater RF
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_ Fig. 2. The u-transmission curves of different u values at q2 = 0.2 for the four quadrupole electrode configurations discussed in the text. Shown in the inserts are the _ contour plots for transmissions from 0% to 100% with every 10% increment, and also the 20 equipotential lines dividing equally from Vrf to +Vrf (the reconstructed 2D (u, u) 50% r0 circle is also marked).
frequency is used, which, however, could have adverse effects such as increasing the modulation of ion energies greatly [4]. The results in Fig. 2 also suggest that the very largest umax for 100% transmission is about 0.49 at q2 = 0.2, i.e., 650% r0 (for a uniformly randomized ion beam as described earlier). If the fully extended radius (half width) of an AMS beam before retardation is 2 mm at 35 keV, it is hard not to expect the fully extended beam radius to double or triple when the beam is energy retarded to 35 eV. The outcome of RF capturing of an originally several tens of keV beam cannot be described well without the fully integrated simulation of the entire system with all its DC and RF components working together. Many retardation/RFQ configurations were simulated for practice with typical AMS beam phase space areas, and the doubling or tripling of the waists (or widths) of the final RF captured beams was always observed. This also suggests that r0 = 5 mm cannot be expected to work well for capturing a thousand fold energy retarded AMS beam. Although the minimum requirement on r0 would to a large extent depend on the retarder and matching optics, the simple analysis based on the results shown in Fig. 2 already indicates that for their efficient uses in AMS, RFQ ion guides having larger dimensions, such as around of r0 = 10 mm, may be preferable. However, r0 = 10 mm is a more costly choice for RFQ ion guides as it requires larger Vpp to achieve a needed q2 value. Considerably
smaller r0 is often used, with which it is more difficult to achieve full acceptance of an energy retarded AMS beam. Even if a full _ RFQ acceptance in vacuum is achieved, i.e., the boundary of (u, u) _ beam, this for 100% transmission matches the boundary of (u, u) match is not expected to have large margins for captured AMS beams. Then, the second question is naturally: what happens when the RFQ contains gas? In our experience with transporting anions through RFQs so far, considerable extra losses were always observed when gases were used, although the light gases such as hydrogen and helium had not been tested by us due to the use of cryopumps. An example is shown in the Fig. 3 of [11] where the transmissions of a 37Cl beam in various gases are compared. It shows that the heavier the gas atom/molecule, the greater the loss. This is often simply referred to as losses induced by scattering (in addition to the losses by electron detachment and/or molecular fragmentation, etc.). _ description, this loss mechanism can be more Using the (u, u) _ beam boundary expansion induced clearly explained as the (u, u) by gas collisions, and the expansion is found further amplified by the RFQ field when Mgas/Mion is very large. _ beam expansion mechanism, the radial traTo illustrate this (u, u) jectories of Cl in three different gasses are compared in Fig. 3. These simulated results are done with the following arbitrarily chosen parameters: (1) 10 36Cl ions randomly start moving from
X.-L. Zhao, A.E. Litherland / Nuclear Instruments and Methods in Physics Research B 361 (2015) 183–188
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_ beam expansion in a gas filled RFQ for an original beam in vacuum of (u, u) _ beam = (0, 0). Fig. 3. An illustration of (u, u)
the middle of the simulation setup as shown in Fig. 1, on and along the axis to the right with an initial energy of 1 meV. Thus they have no initial ‘transverse’ energy, and also have little initial ‘axial’ energy that can be converted into ‘transverse’ energy upon gas collisions. This is a beam which begins as completely ‘cooled’ and _ beam = (0, 0). (2) The hard sphere collision (HSC) model with (u, u) that comes with SIMION 8.1 is used to model the collision dynamics at room temperature. The mass of He atom used is 4 AMU, and its HSC collision cross section with 36Cl is assumed to be 2.5 1019 m2; the ‘effective’ mass of NO2 used is 32 AMU (which is more appropriate according to the experimental results shown in the Fig. 3 of [11]), and its HSC collision cross section with 36 Cl is assumed to be 5 1019 m2. This is by no means intended to be an accurate simulation, but _ beam boundary must inevitably the point is well made that the (u, u) expand upon interactions with gases, especially relatively heavy gases. It can be expected that in relatively light buffer gases, the initial expansion could be modest, and as ion energies are collision_ beam must eventually contract ally cooled, the boundary of (u, u) towards an equilibrium distribution (ufinal, u_ final )beam, where u_ final can ultimately approach the buffer gas temperature, but ufinal may or may not approach zero (on and along axis) as it is also dependant on the q2 used [4]. In cases when Mgas/Mion >0.7, how_ beam contraction does not necessarily occur ever, the eventual (u, u) to all ions as might be expected if neutron thermalization is used as an analogy for collisional cooling. For charged particles in an RFQ field, such an analogy can only be approximately correct if the mass of the ion is substantially heavier than the mass of the gas atom/molecule. Transporting 36Cl through NO2 alone cannot be expected to be efficient. In this case, the additional use of the lightest common buffer gas He can dampen down the severity of the (u, _ beam expansion. u) It is becoming rather apparent from the discussion above that for transporting an energy retarded AMS beam through a gas filled _ RFQ for 100% transmission and the RFQ, the matching between (u, u) _ beam is likely to be probmaximum expanded boundary of (u, u) lematical, if in fact they can be matched at all. Therefore, the RFQs of perfect hyperbolic poles or cylindrical rods without the gradient bars can be expected to be most efficient when operated under the same q2, because their contour lines for all percentage _ ‘RF phase space’, transmissions cover the most extent in the (u, u) as shown in Fig. 2. To create axial drift gradient using these electrodes, they have to be segmented into sufficiently short lengths. To use them for gas impedance pipes, their gaps have to be sealed up with insulators. These are certainly more complicated and more costly in practice. The uses of the gradient bars and the 60–30° split cylinders can be more straightforward for providing these secondary functions, but their efficient uses for ion confinement are more demanding because, as the results in Fig. 2 imply, if they
are to be efficiently used, their transmissions must in fact be near 100%, or they may risk somewhat more rapid decline as boundary _ beam expands. of (u, u) _ efficient RFQs An attempt was made to search for more (u, u) made of electrode shapes other than the perfect hyperbolic poles. Various arrangements were modeled, including a 32-wire RF cage with multiple RF voltages. Nothing more efficient has been found so far, so it will be interesting to determine whether or not this situation persists.
5. Conclusions Four differently shaped RFQ ion guides have been studied by simulation using SIMION 8.1 and their intrinsic ion transmission _ have been compared. This work is an abilities in terms of (u, u) extension of the recently completed more general study on linear RF ion guides [4]. The implications for the efficient uses of RFQs for transporting an energy retarded AMS beam cannot be simply stated. It in fact emphasizes the need for more in depth studies on these topics, with emphasis on inserting electrically retarded ion beams from suitable AMS ion sources into vacuum ion guides first. Once that can be done it can be seen that whether the ion guides can transport and control the ions in vacuum forever, and their ability to transport and control the ions through gases can then be evaluated. Acknowledgements We acknowledge the support from NSERC Canada, and the University of Ottawa for the continued operation of IsoTrace Laboratory at its original location in Toronto until the end of 2013. We are grateful to our former and current colleagues Drs. J. Eliades and C. Charles, Profs. W. E. Kieser, J. Cornett and I. Clark, for their active and timely support and discussions. References [1] Y. Liu, J.R. Beene, C.C. Havener, J.-F. Liang, Isobar suppression by photodetachment in a gas-filled rf quadrupole ion guide, Appl. Phys. Lett. 87 (2005) 113504 (1–4). [2] A.E. Litherland, I. Tomski, X.-L. Zhao, L.M. Cousins, J.P. Doupe, G. Javahery, W.E. Kieser, Isobar separation at very low energy, Nucl. Instr. Meth. B259 (2007) 230–235. [3] D.R. Bandura, V.I. Brannov, A.E. Litherland, S.D. Tanner, Gas-phase ion– molecule reactions for resolution of atomic isobars: AMS and ICP-MS perspectives, Int. J. Mass Spect. 255256 (2006) 312327. [4] X.-L. Zhao and A.E. Litherland, A simulation study of linear RF ion guides for AMS, submitted to Nucl. Instr. Meth. B (2014). [5] C.M. Niculae, M. Niculae, Numerical method for calculating of potential distribution in non-ideal multipole ion guides, Optoelectron. Adv. Mater. Rapid Commun. 3 (10) (2009) 1073–1075.
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[6] G. Javahery, B. Thomson, A segmented radiofrequency-only quadrupole collision cell for measurements of ion collision cross section on a triple quadrupole mass spectrometer, J. Am. Soc. Mass Spectrom. 8 (1997) 697–702. [7] A. Laboda, A. Krutchinsky, O. Loboda, J. McNabb, V. Spicer, W. Ens, K. Standing, Novel Linac II electrode geometry for creating an axial field in a multipole ion guide, Eur. J. Mass Spectrom. 6 (2000) 531–536. [8] Y. Liu, J.-F. Liang, G.D. Alton, J.R. Beene, Z. Zhou, H. Wollnik, Collisional cooling of negative-ion beams, Nucl. Intr. Meth. B187 (2002) 117–131.
[9] J.D. Prestage, R.L. Tjoelker, L. Maleki, Radio frequency measurements of cloud size in a linear ion trap, 1997 IEEE International Frequency Control Symposium, 1997, pp. 225–227. [10] V.I. Barannov, Analytical approach for description of ion motion in quadrupole mass spectrometer, J. Am. Soc. Mass Spectrom. 14 (2003) 818–824. [11] W.E. Kieser, J. Eliades, A.E. Litherland, X.-L. Zhao, L. Cousins, S.J. Ye, The low energy isobar separator for anions: progress report, Radiocarbon 52 (2010) 236–242.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Intrinsic ion transmission of RFQ ion guides in vacuum X.-L. Zhao a,⇑, A.E. Litherland b a b
Department of Physics and A.E. Lalonde AMS Laboratory, University of Ottawa, 25 Templeton St., Ottawa, ON K1N 6N5, Canada Department of Physics and IsoTrace Laboratory, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada
a r t i c l e
i n f o
Article history: Received 28 November 2014 Received in revised form 23 February 2015 Accepted 5 March 2015 Available online 18 March 2015 Keywords: Isobar separator Ion transmission Radiofrequency quadrupole ion guides
a b s t r a c t As part of a recent detailed overview of linear radiofrequency ion guides for the conceptualization of their efficient additions into Accelerator Mass Spectrometry (AMS), the intrinsic ion transmission properties were studied further for RF quadrupoles (RFQs) of several electrode shapes, because these are at present the only type being actively considered for use together with AMS. RFQs using hyperbolic poles, cylindrical rods, cylindrical rods plus gradient bars, and 60–30° split cylinders were studied in this work. It is found that the abilities of the first two types for securing ion transmission in vacuum are among the best although the others are quite satisfactory in some applications. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The recent initiatives that use radiofrequency quadrupoles (RFQs) to facilitate on-line isobar separations, either by selective photodetachment of electrons from anions [1] or by element sensitive anion-gas reactions [2], have the potential to significantly extend the analytic scope of AMS, especially those systems using small tandem accelerators. Similar opportunities also exist for positive ions [3], thus providing the potential to extend the applicability of single-stage AMS or even tandem accelerators using Neutral Injection methods. However, the techniques for implementing these on-line isobar separation methods for the AMS of rare long-lived radioactive atoms are relatively complicated and undeveloped because of the very small isotope ratios involved (rare/abundant often < 1012). As AMS must use ion sources that produce micro-Amperes (>160 nA or >1012 ions per second) of beam currents extracted at tens of keV ion energies, the rare isotopes of such ion beams must be mass selected and then energy retarded by a factor of several hundreds to a thousand before they can be captured and controlled by an RFQ field. The abundant isotopes are not possible to control in RFQs without phase space sampling because of the space charge repulsion at such low energies. The captured ions in this case inevitably fill up a significant part of the radial volume of the RFQ ion guide of practical dimensions (the inscribed radius r0 6 10 mm). This introduces ion loss issues where the solutions for the
⇑ Corresponding author. E-mail address: [email protected] (X.-L. Zhao). http://dx.doi.org/10.1016/j.nimb.2015.03.007 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
complete elimination of the losses are not well known despite the long history of RFQ uses for ion confinement and analysis. To conceptualize on their efficient addition into AMS, ultimately for routine AMS, a comprehensive simulation study of linear RF ion guides in general has been completed recently [4]. The study aims to find theoretical solutions of avoiding the two major root causes for analyte losses, especially when the analyte is an anion: (1) The boundaries of a beam captured in a cylindrical electrode system by a radial RF field, i.e., the ranges of the ions’ radial trajectory position and radial speed, must match the maximum ability of the initial RF ion guide for 100% transmission in vacuum, and that match should ideally be maintained thereafter in collisions with gas atoms or molecules. (2) The ion-gas interactions must be carried out within the required safe range of impact energies throughout, to avoid electron detachment and/or molecular fragmentation to the analyte, aside from the expected losses due to chemical reactions of the analyte. To avoid all possible losses (other than those due to expected chemical reactions) it has been found necessary to consider taking advantages of linear RF ion guides of various types for AMS. The higher multipoles are shown to be better suited for guiding ions to enter the vacuum ion guide leading to the gaseous region, while RFQs operated under certain field conditions (Mathieu stability parameter q2 0.5) are shown to be best suited for preparing energy cooled ions for gas cell exit into the high vacuum re-acceleration region. These conclusions are at present only theoretical; so far only RFQs have been used experimentally for isobar
184
X.-L. Zhao, A.E. Litherland / Nuclear Instruments and Methods in Physics Research B 361 (2015) 183–188
separation tests with AMS, as described in several papers in the recent past and in this 13th AMS conference. As RFQs for Isobar Separators prior to AMS are likely to remain as the practical choice for some time to come, further simulation studies are therefore still necessary for RFQs to cover various topics in detail. This paper discusses one of such topics, the effect of electrode shapes to the intrinsic ion transmission in vacuum. For gas filled RFQs, certain electrode arrangements are required to also perform some important secondary axial purposes in addition to providing RFQ field for radial ion confinement. One such secondary purpose is to produce a small axial drift gradient for sustaining the ions’ forward motion in gases as the ions are slowed down by collisions. Another potential secondary purpose is to use a special RF ion guide as an impedance of gas conductance, which can be advantageously used to replace small apertures for entering gas cell or gas region [4] and thereby increase the efficiency of transmission. These secondary purposes can be achieved in several ways, but they all inevitably alter the perfect RFQ field produced by precisely shaped hyperbolic electrodes, thus affecting the RFQ’s intrinsic ability for transmitting ions. The question is by how much? This work provides a quantitative analysis for the following four RFQ variations: (1) RFQ made of hyperbolic poles. An advantage using hyperbolic poles is that it also allows exact analytical descriptions of ion motion using Mathieu functions. It is included in this study to provide a base reference. (2) RFQ made of cylindrical rods with rod radius equal to 1.14511r0 [5]. This is the simplest RFQ form. It is not a perfect RFQ (n = 2) as it introduces higher multipole components, but the next higher multipoles n = 6 and n = 10 are very small (<103 of the n = 2), and equal in size but opposite in sign. The rods can be segmented to create a small axial drifting field [6]. (3) Same as above, but with the small axial drifting field created by the insertion of 4 wedged bars between the rods. This is probably the simplest method for creating an effective small axial drifting field, avoiding the much more complicated segmentation of the RF electrodes. However, the gradient bars introduce higher multipoles of increased magnitudes. This technique was initiated as T-shaped bars by ref. [7] and the almost identical plate-shaped bars were first used for transporting negative ions in a gas filled RFQ by ref. [8]. (4) RFQ made of 60–30° split cylinders with the 30° electrodes kept at the constant central potential of the RF [9]. Such a configuration has no n = 6 component and the nearly closed electrodes can be used as a natural gas impedance pipe, and the axial drifting field can be created by segmenting the 30° DC electrodes, also avoiding the segmentation of the RF electrodes. When the properties of these variations are compared to each other, the comparison is made under the same Mathieu stability parameter q2 as calculated below, even though they are not exactly comparable within the full radial volume for the RF fields produced: 2
q2 ¼ 4:8888 ½q V pp =½m f r 20 where q is the ion’s charge state number, Vpp is the RF peak-to-peak voltage in Volt, m is mass of the ion in AMU, f is the RF frequency in MHz, r0 is the inscribed radius in mm. The stability of ion motion in RFQs occur within 0 < q2 < 0.9, but for a captured AMS beam by RFQs, it is not possible to avoid strong ion energy modulation [4]. Due to electron detachment and/or molecular fragmentation, anion analyte losses are inevitable when anion-gas impact energies are large. This is the case for anions
filling a significant radial volume of an RFQ, especially when the RFQ is operated with a large q2. To reduce such losses, only a modest RF ion confinement strength, q2 = 0.2, should be considered for confining RF captured AMS beams, as in this work. 2. Simulation The intrinsic ion transmission of a linear RF ion guide refers to its ability to transmit an ion through an arbitrarily long distance in vacuum given the ion’s conditions at ‘birth’ inside the RF field, i.e., the RF phase, the radial position and radial velocity. For quadrupoles with hyperbolic poles, this subject has been investigated by Baranov [10] analytically, and in fact the acceptance of a hyperbolic electrode RFQ can be calculated exactly. The same concept was adapted and developed further to describe linear RF ion guides in general, with the numerical results derived more simply for a variety of electrode shapes from simulations using SIMION 8.1 [4]. The quantitative result of the ‘intrinsic ion transmission’ of a linear RF ion guide is best graphically displayed for a group of ions with their ‘birth’ conditions randomized, i.e., the RF phase randomized over an RF period, the directions of the radial position and radial velocity, corresponding to the ‘transverse’ energy E, randomized in the radial plane. These randomizations, or uniform distributions, over several ‘birth’ conditions do not necessarily present situations in which a realistic beam would result inside an RFQ. This is merely a choice of simulation convenience to describe an ‘intrinsic’ property of an RF ion guides, so that the ‘intrinsic’ transmission curves for an RFQ that is operated with a stability parameter q2, can be plotted as functions of a pair of _ calculated as (with E in eV): dimensionless parameters, (u, u),
u ¼ r=r 0 u_ ¼ 4:4218 ½E=m1=2 =½f r 0 Fig. 1 illustrates the setup of an approximation to an ideal (infinitely long) RFQ ion guide in SIMION 8.1 and the simulation method with which a transmission curve is obtained. The RFQs studied all have r0 = 10 mm and length = 500 mm; SIMION 8.1 simulations are set up all with 15 grid-units per mm and are all run with default parameters of the software. For each RFQ ion guide studied, transmission curves of q2 = 0.2 for 11 given u values are _ Each data point is derived from the simobtained by varying u. ulations of 10,000 ions (41CaF 3 ) that start on the circle of a u (r/ r0) and 20 mm from the left edge, with ‘axial’ energy Ez = 5 eV, and with starting time randomized in all phases of an RF period. The ‘transverse’ energy E is varied to correspond to an u_ value using the above formula, but with the ‘transverse’ momentum randomized in all directions in the x–y plane. The transmission is calculated as the fraction of the 10,000 randomized ions reaching the right edge of the simulation setup at 500 mm. As has been discussed in the overview study [4], these transmission curves describe an intrinsic property of a linear RF ion guide, which is independent of the RF frequency used as long as it is within the range to support the kind of ion motion that does not gain excessive instantaneous kinetic energy. Thus, only f = 2.5 MHz is used in this work. The quantitative results of the obtained transmissions are inevitably still overestimated somewhat, because 500 mm is not infinite, although it represents a good practical length. 3. Results _ curves for each studied RFQ ion guide A set of 11 u-transmission are summarized in Fig. 2 for convenient comparison. Also shown _ contour lines for transmissions from are the reconstructed 2D (u, u) 0% to 100% and the equipotential lines of the RF field. The electrode
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Fig. 1. Illustration of (a) simulation setup in SIMION 8.1 and (b) transmission computation. (vm is the ion speed in the x–y plane, corresponding to the ion’s ‘transverse’ kinetic energy as E = ½mv2m.)
shape in each case is apparent, but for the case that uses wedged bars, what is actually modeled in this study is a set of straight bars with the inner edges reaching 1.25r0. In each case studied, the u_ max for 100% transmission occurs when u = 0 at (a) 0.113, (b) 0.111, (c) 0.112, and (d) 0.098; the umax for 100% transmission occurs when u_ = 0 at (a) 0.495, (b) 0.489, (c) 0.490, and (d) 0.390. The different electrode shapes have the most impact on the RF field gradient distribution in the radial volume >50% r0, affecting mostly the transmission contour lines of <100%. 4. Discussion _ number density distribution of an AMS beam The actual (u, u) after been captured by a realistic RFQ or other multipole ion guides will be studied in follow-up works. The results of those would be beam and device dependant. Before the modeling of realistic (u, _ number density distributions the implications of the present u) results for practical work need to be evaluated carefully, and they are not obvious. However, the results can be discussed to relate to
several questions of practical concerns. First, can a typical energy retarded AMS beam be completely captured by an RFQ ion guide in vacuum, and what the dimension (r0) of such an RFQ ought to be? The results in Fig. 2 suggest that the very largest u_ max for 100% transmission is about 0.11 at q2 = 0.2. With r0 = 10 mm and f = 2.5 MHz, u_ max = 0.11 means that the maximum ‘transverse’ energy of the ions that can be accepted by the RFQ operated under 36 q2 = 0.2 is about 38 eV for 41CaF Cl . If the total 3 and 14 eV for retarded energy is 50 eV, this further means, that the maximum trajectory angle for anions starting on the axis that can be accepted 36 by the RFQ, is 61° for 41CaF Cl . If r0 = 5 mm is used 3 and 32° for for the above analysis, the maximum ‘transverse’ energy and angle for axial rays become 9.5 eV/26° for 41CaF 3 and 3.5 eV/15° for 36 Cl . If the original beam before deceleration has 35 keV energy and 1° trajectory angle, the final maximum angle for the energy retarded beam at 51.8 eV is roughly 26° because of phase space conservation. This means, r0 = 5 mm cannot be expected to achieve the full capture of a 36Cl beam, unless substantially greater RF
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_ Fig. 2. The u-transmission curves of different u values at q2 = 0.2 for the four quadrupole electrode configurations discussed in the text. Shown in the inserts are the _ contour plots for transmissions from 0% to 100% with every 10% increment, and also the 20 equipotential lines dividing equally from Vrf to +Vrf (the reconstructed 2D (u, u) 50% r0 circle is also marked).
frequency is used, which, however, could have adverse effects such as increasing the modulation of ion energies greatly [4]. The results in Fig. 2 also suggest that the very largest umax for 100% transmission is about 0.49 at q2 = 0.2, i.e., 650% r0 (for a uniformly randomized ion beam as described earlier). If the fully extended radius (half width) of an AMS beam before retardation is 2 mm at 35 keV, it is hard not to expect the fully extended beam radius to double or triple when the beam is energy retarded to 35 eV. The outcome of RF capturing of an originally several tens of keV beam cannot be described well without the fully integrated simulation of the entire system with all its DC and RF components working together. Many retardation/RFQ configurations were simulated for practice with typical AMS beam phase space areas, and the doubling or tripling of the waists (or widths) of the final RF captured beams was always observed. This also suggests that r0 = 5 mm cannot be expected to work well for capturing a thousand fold energy retarded AMS beam. Although the minimum requirement on r0 would to a large extent depend on the retarder and matching optics, the simple analysis based on the results shown in Fig. 2 already indicates that for their efficient uses in AMS, RFQ ion guides having larger dimensions, such as around of r0 = 10 mm, may be preferable. However, r0 = 10 mm is a more costly choice for RFQ ion guides as it requires larger Vpp to achieve a needed q2 value. Considerably
smaller r0 is often used, with which it is more difficult to achieve full acceptance of an energy retarded AMS beam. Even if a full _ RFQ acceptance in vacuum is achieved, i.e., the boundary of (u, u) _ beam, this for 100% transmission matches the boundary of (u, u) match is not expected to have large margins for captured AMS beams. Then, the second question is naturally: what happens when the RFQ contains gas? In our experience with transporting anions through RFQs so far, considerable extra losses were always observed when gases were used, although the light gases such as hydrogen and helium had not been tested by us due to the use of cryopumps. An example is shown in the Fig. 3 of [11] where the transmissions of a 37Cl beam in various gases are compared. It shows that the heavier the gas atom/molecule, the greater the loss. This is often simply referred to as losses induced by scattering (in addition to the losses by electron detachment and/or molecular fragmentation, etc.). _ description, this loss mechanism can be more Using the (u, u) _ beam boundary expansion induced clearly explained as the (u, u) by gas collisions, and the expansion is found further amplified by the RFQ field when Mgas/Mion is very large. _ beam expansion mechanism, the radial traTo illustrate this (u, u) jectories of Cl in three different gasses are compared in Fig. 3. These simulated results are done with the following arbitrarily chosen parameters: (1) 10 36Cl ions randomly start moving from
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_ beam expansion in a gas filled RFQ for an original beam in vacuum of (u, u) _ beam = (0, 0). Fig. 3. An illustration of (u, u)
the middle of the simulation setup as shown in Fig. 1, on and along the axis to the right with an initial energy of 1 meV. Thus they have no initial ‘transverse’ energy, and also have little initial ‘axial’ energy that can be converted into ‘transverse’ energy upon gas collisions. This is a beam which begins as completely ‘cooled’ and _ beam = (0, 0). (2) The hard sphere collision (HSC) model with (u, u) that comes with SIMION 8.1 is used to model the collision dynamics at room temperature. The mass of He atom used is 4 AMU, and its HSC collision cross section with 36Cl is assumed to be 2.5 1019 m2; the ‘effective’ mass of NO2 used is 32 AMU (which is more appropriate according to the experimental results shown in the Fig. 3 of [11]), and its HSC collision cross section with 36 Cl is assumed to be 5 1019 m2. This is by no means intended to be an accurate simulation, but _ beam boundary must inevitably the point is well made that the (u, u) expand upon interactions with gases, especially relatively heavy gases. It can be expected that in relatively light buffer gases, the initial expansion could be modest, and as ion energies are collision_ beam must eventually contract ally cooled, the boundary of (u, u) towards an equilibrium distribution (ufinal, u_ final )beam, where u_ final can ultimately approach the buffer gas temperature, but ufinal may or may not approach zero (on and along axis) as it is also dependant on the q2 used [4]. In cases when Mgas/Mion >0.7, how_ beam contraction does not necessarily occur ever, the eventual (u, u) to all ions as might be expected if neutron thermalization is used as an analogy for collisional cooling. For charged particles in an RFQ field, such an analogy can only be approximately correct if the mass of the ion is substantially heavier than the mass of the gas atom/molecule. Transporting 36Cl through NO2 alone cannot be expected to be efficient. In this case, the additional use of the lightest common buffer gas He can dampen down the severity of the (u, _ beam expansion. u) It is becoming rather apparent from the discussion above that for transporting an energy retarded AMS beam through a gas filled _ RFQ for 100% transmission and the RFQ, the matching between (u, u) _ beam is likely to be probmaximum expanded boundary of (u, u) lematical, if in fact they can be matched at all. Therefore, the RFQs of perfect hyperbolic poles or cylindrical rods without the gradient bars can be expected to be most efficient when operated under the same q2, because their contour lines for all percentage _ ‘RF phase space’, transmissions cover the most extent in the (u, u) as shown in Fig. 2. To create axial drift gradient using these electrodes, they have to be segmented into sufficiently short lengths. To use them for gas impedance pipes, their gaps have to be sealed up with insulators. These are certainly more complicated and more costly in practice. The uses of the gradient bars and the 60–30° split cylinders can be more straightforward for providing these secondary functions, but their efficient uses for ion confinement are more demanding because, as the results in Fig. 2 imply, if they
are to be efficiently used, their transmissions must in fact be near 100%, or they may risk somewhat more rapid decline as boundary _ beam expands. of (u, u) _ efficient RFQs An attempt was made to search for more (u, u) made of electrode shapes other than the perfect hyperbolic poles. Various arrangements were modeled, including a 32-wire RF cage with multiple RF voltages. Nothing more efficient has been found so far, so it will be interesting to determine whether or not this situation persists.
5. Conclusions Four differently shaped RFQ ion guides have been studied by simulation using SIMION 8.1 and their intrinsic ion transmission _ have been compared. This work is an abilities in terms of (u, u) extension of the recently completed more general study on linear RF ion guides [4]. The implications for the efficient uses of RFQs for transporting an energy retarded AMS beam cannot be simply stated. It in fact emphasizes the need for more in depth studies on these topics, with emphasis on inserting electrically retarded ion beams from suitable AMS ion sources into vacuum ion guides first. Once that can be done it can be seen that whether the ion guides can transport and control the ions in vacuum forever, and their ability to transport and control the ions through gases can then be evaluated. Acknowledgements We acknowledge the support from NSERC Canada, and the University of Ottawa for the continued operation of IsoTrace Laboratory at its original location in Toronto until the end of 2013. We are grateful to our former and current colleagues Drs. J. Eliades and C. Charles, Profs. W. E. Kieser, J. Cornett and I. Clark, for their active and timely support and discussions. References [1] Y. Liu, J.R. Beene, C.C. Havener, J.-F. Liang, Isobar suppression by photodetachment in a gas-filled rf quadrupole ion guide, Appl. Phys. Lett. 87 (2005) 113504 (1–4). [2] A.E. Litherland, I. Tomski, X.-L. Zhao, L.M. Cousins, J.P. Doupe, G. Javahery, W.E. Kieser, Isobar separation at very low energy, Nucl. Instr. Meth. B259 (2007) 230–235. [3] D.R. Bandura, V.I. Brannov, A.E. Litherland, S.D. Tanner, Gas-phase ion– molecule reactions for resolution of atomic isobars: AMS and ICP-MS perspectives, Int. J. Mass Spect. 255256 (2006) 312327. [4] X.-L. Zhao and A.E. Litherland, A simulation study of linear RF ion guides for AMS, submitted to Nucl. Instr. Meth. B (2014). [5] C.M. Niculae, M. Niculae, Numerical method for calculating of potential distribution in non-ideal multipole ion guides, Optoelectron. Adv. Mater. Rapid Commun. 3 (10) (2009) 1073–1075.
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