Can magnetic field be used to reduce cosmic charged particles background to low energy particle detectors?
CCan magnetic field be used to reduce cosmic charged particlesbackground to low energy particle detectors?
Kolahal Bhattacharya
Manipal Centre for Natural SciencesCentre of ExcellenceManipal Academy of Higher Education, Manipal 576104. India ∗ [email protected] Abstract : The possibility to reduce the background due to cosmic ray charged particles by the use ofmagnetic field in the ground based low energy particle detectors is explored. The degree of reduction ofcosmic rays as a function of the magnetic field strength and its depth is quantified.
Keywords: cosmic ray background, muon
1. Introduction
Cosmic rays pose a serious background to a vast majority of the ground-based nuclear and particle physicsexperiments. For example, many current generation neutrino physics experiments attempt to observe muonsand electrons generated in the neutrino events to resolve the unknown questions in neutrino physics, e.g.CP violation, neutrino mass hierarchy, or existence of sterile neutrinos etc. Since a major component ofthe cosmic rays are muons, removal of the muon signature due to cosmic background is an absolute neces-sity for these experiments. For this reason, it is common to design experimental facilities in underground(e.g. DEAP-3600 in SNOlab [1], or ICECUBE in Antarctica [2]), or to use the plastic scintillator-basedveto method to effectively reduce the background (e.g. MicroBooNE [3] and mu2e [4] in Fermilab). Manyupcoming experiments (e.g. INO [5], and far detector of DUNE [6]) will also place their detectors deep un-derground to this end. However, building the underground laboratories from scratch is expensive. Therefore,many experiments in past (and present) were (are) conducted where mine was (is) already in existence, e.g.the ‘proton decay’ experiment in Kolar gold field (in India), or the SNOlab in Sudbury, Canada. On theother hand, the paddle scintillator-based veto method can be used effectively in conjunction with the beampulse window to reduce the cosmic background. This method can be very successful in accelerator-basedneutrino experiments where there is definite time window of events to occur. However, for a ground basednon-accelerator experiment, it is not a very practical method where timings of the events are not known.In this context, the question whether it is possible to reduce a significant fraction of the cosmic raybackground by deflecting them using magnetic field is addressed in this paper. This looks appealing, becausethis method may be able to reduce the charged particle component of the cosmic rays for both accelerator-based as well as non-accelerator based experiments. At the same time, it appears that this may require1 a r X i v : . [ phy s i c s . i n s - d e t ] J un xtremely high magnetic field to have any practical utility in any particle detectors. No quantified resultswere found in the scientific literature to address this question. Even if the method is not practical, due tothe requirement of very strong magnetic field over a large volume, that needs to be addressed. In this paper,the strength and volume of the field needed to achieve a given degree of reduction will be estimated. Also,the threshold of the momenta of the cosmic ray charged particles which cannot be deflected away will beinvestigated. These details can be used to decide whether magnetic field can be employed in specific futureexperiments. If it is possible, then one can try to figure out the way to accomplish that. For example, it maybe possible to achieve the experiment’s desired degree of reduction of cosmic ray charged particles by buildinga very shallow (50 m deep) underground detector and a magnet system constructed above the ground. Thepaper will also discuss the currently available technologies for generating necessary magnetic field and otherindirect benefits of the reduction of cosmic muons. To address these points, a thought experiment, describedin the next section 2, has been performed using GEANT4 [7] simulation program. The outcomes of thisexperiment, will hopefully throw some light on the topic.
2. Set up for thought experiment
The basic configuration of the thought experiment is shown in the following Figure 1a. The magnet systemto deflect the charge particle component of the cosmic rays must be placed over the particle detector. Thismay be able to reduce the background to the detector placed underneath. However, the cosmic muons canalso reach the detector from sides. Therefore, it may be helpful to use a magnet that spans a large area andto place it on top or over the particle detector, shown as a brown right rectangular parallelepiped in Figure1b. (a) (b)
Fig. 1: (a) Magnet system as a buffer between the down headed cosmic rays and the particle detector, (b)the system is shown as a green box lined with blue boundaries at the top and bottom surfaces. It isplaced on top of the particle detector (brown) placed underneath. The whole setup is placed below alarge reference plane with red boundary (upper plane of the magnet coincides with the referenceplane).
To exclusively study the effect of magnetic field, the field is assumed to operate in vacuum, so that energyloss and generation of secondary particles do not occur when cosmic rays traverse through the magnet.Practically, the magnet system can be composed of iron, or neodymium magnets or the superconducting2agnets and must be assembled within a box made of shielding material (e.g. Mu-metal, iron) to ensurethat the magnetic field lines do not penetrate the detector placed underneath. The field lines should returnfrom the far north pole to the far south pole through the wall of this shielding box.A typical ground based particle detector can be placed in an underground pit, and the magnet system maybe placed on top of it, supporting on the surrounding ground level. The field should point in the horizontaldirection, because a component parallel to the vertical direction is not helpful to deflect the muons comingvertically down. We have used the CRY [8] cosmic ray generator to simulate the cosmic ray shower (muons µ ± , electrons e ± , pions π ± , kaons and protons) on top of the reference plane of Figure 1b, lined with redboundary. This results in contribution of cosmic rays from the sides as well, in addition to the usual verticalflux. The dimension of this reference plane is taken as 100 m ×
100 m and the dimension of particle detectoris taken as ∆ x =5 m, ∆ y =5 m and ∆ z = 2.5 m (vertical direction). The size of the magnet system (shownas the green box in Figure 1b) is (∆ x mag , ∆ y mag , ∆ z mag ). These variables will be varied to find out theresidual flux leaked into the particle detector (brown) placed underneath. If ∆ x mag = ∆ y mag = ∆ z mag = 10m, then the boundaries of the reference plane subtends a zenith angle of tan − . ≈ o . If ∆ z mag is less, the zenith angle coverage will be higher. If θ denotes the zenith angle, then the cosmic muon fluxapproximately drops as cos θ [9]. At larger θ , the flux reduces significantly and majority of the cosmic muonflux is contained in lower θ . So, these dimensions should be good enough to represent realistic muon fluxleaking into the detector. Generation of 3 million events in CRY at ground level (i.e. zero altitude) results in a shower of about 3 . ×
100 m wide reference plane (additional tracks are generated whencosmic rays collide with the atmosphere and multiple daughter particles are produced) in ∼ Table 1:
Out of about 3 million charged cosmic ray particles simulated by CRY, about 10 thousand muonsenter the particle detector from all directions in about 2.379 seconds. Pions and kaons are almostnegligible in number.
In fact, the number of cosmic ray charged particles entering the detector is roughly proportional to thefraction of the effective area of the detector to the aperture of the reference plane, i.e. × × ∼ . z coordinate of the tracks entering the detector for a magnetsystem of depth 1 meter. From table 1, it is seen that the main background comes from muons and electrons.3 ntries 13943Std Dev 70.9 - - - - N o . o f c o s m i c r a ys l ea k i ng i n t o t he de t e c t o r Entries 13943Std Dev 70.9 (a) -
10 1 10Kinetic energy (GeV) - - -
10 110 ) - G e V - s - ( m F – m muon, – electron, e (b) Fig. 2: (a) Cosmic ray tracks are killed as they enter the particle detector from top or from sides. For 1meter deep magnet, the height of the magnet and detector system is ∼ (1+2.5) m ∼ ∼ (2.5 m - 1.75 m) ∼ Spectra of these particles at the point of entering the particle detector in absence of magnetic field are shownin the figure 2b.
The following study assumes uniform magnetic field and without any loss of generality, its direction is takenas the positive y direction. The degee of reduction of the flux with the use of magnetic field will be quantifiednext. It is clear that there are several parameters in this problem:(a) depth ∆ z mag of the magnet system; a higher depth might allow deflection of a higher fraction of muons.(b) strength of magnetic field.(c) the transverse area of the magnet system; how much more area compared to the aperture of the detectoris needed?(d) energy spectrum and composition of the particles (i.e. the relative fraction of different particles, e.g.muon, electrons etc.) leaking into the detector.(e) material of the magnet system and its effect on the above parameters.All these details will be useful to throw light on different aspects of the problem and may give hintstowards future building of experiments. Below these parameters are investigated in details.GEANT4 simulation was performed for 10 m ×
10 m wide magnet systems of different strengths (1-5tesla) and depths (1-10 m). The following figure 3a shows the energy spectrum of muons, electrons andprotons when 1.5 tesla field is applied through a magnet of depth 1 meter. Muons dominate the spectrum,specifically at higher energy. However, in comparison with the no magnetic field case (figure 2b), the chargedparticle background is seen to be suppressed at the lower energy bins.4 -
10 1 10Kinetic energy (GeV) - - -
10 110 ) - G e V - s - ( m F – m muon, – electron, eproton (a) Depth (m) Field (T) Total protons e ± µ ± (b) Fig. 3: (a) Energy spectra of muons, electrons and protons leaking into the detector for 1.5 tesla fieldoperating at 1 meter depth. (b) Effect of varying depth and magnetic field on the composition ofcosmic ray spectrum leaking into the detector.
The relative percentage of different particles, i.e. composition of the residual cosmic ray charged particleflux does not change significantly if the strength and/or the depth of the magnet are varied. This is shownin table 3b. However, overall decrease in number is observed with the increase in field strength. The trendis shown for 3 tesla and 5 tesla field operating at 1 m depth in figure 4a. -
10 1 10Kinetic energy (GeV) - - -
10 110 ) - G e V - s - ( m F – m muon, 3 T, 1m – electron, eproton 3 T, 1m 5 T, 1m – m muon, 5 T, 1m – electron, eproton 5 T, 1m (a) -
10 1 10Kinetic energy (GeV) - -
10 110 ) - G e V - s - ( m F – m muon, 1.5 T, 3m – electron, eproton 1.5 T, 3m 1.5 T, 5m – m muon, 1.5 T, 5m – electron, eproton 1.5 T, 5m (b) Fig. 4:
Effect of increase in (a) magnetic field and (b) depth on the cosmic ray charged particle spectrum.
Figure 4b, on the other hand, shows the spectra of these particles if depth of the magnet is increasedwithout changing the field strength. The reduction can be understood in the following way: the depth ofthe magnet system is the effective ‘clearance distance’ the charged particles have before they bend away.Evidently, the low energy muons will be deflected away at a lower depth whereas high energy muons willneed higher depth, if both pass through a system of the same magnetic field.5 .3. Relative reduction with respect to no magnetic field case
One way to quantify the degree of reduction of the cosmic ray muons due to magnetic field is to take theratio of the number of all the cosmic ray muons leaking into the detector in the presence of the magneticfield to the number of those in the absence of magnetic field. However, this is a function of the strengthof magnetic field as well as the depth of the magnet system. In the following figure 5a, the dependence onthe magnetic field is shown for all depth values used in the analysis. A monotonic decrease in the relativefraction of cosmic rays leaking into the detector is observed as the field is increased. For a fixed value offield, higher depth corresponds to the higher degree of removal of cosmic rays. Similar trend is observed forelectrons. This is shown in the adjacent plot 5b. R e l a t i v e r edu c t i on Depth (m)1m2m3m4m5m6m7m8m9m10m (a) R e l a t i v e r edu c t i on Depth (m)1m2m3m4m5m6m7m8m9m10m (b)
Fig. 5: (a) Effect of depth field strength on the relative reduction (ratio of number of muons which leaksinto the detector in the presence and absence of magnetic field) of cosmic ray muons for variousdepth values (b) corresponding plot for electrons.
Figure 5 depicts the relative reduction in the total number of muons and electrons, without any referenceto their energies. It does not reveal the energy bins which are more (or less) depleted when magnetic fieldis applied. However, this is an important parameter to consider while designing an experiment specificallywhen the signal region may be lying in in sub-GeV range. This is shown in the following figure 6a.
The preceding discussion quantifies the degree of reduction of cosmic ray charged particles possible throughthe use of magnetic field. As expected, a stronger field ensures less deep magnet with less volume. In adetector equipped with such a magnet overburden, if an observed event is reconstructed as a low energyevent, it is much less probable to have come from cosmic rays. This conclusion is true whether or not theexperiment is accelerator based.The use of magnetic field shifts the residual cosmic muon spectrum to the higher energy end. From theperspective of the experimenter, the important parameters to consider are the mean and the mode (theenergy bin where the events are populated the most) of the distribution. In the following figure 6b, thegradual increase of the mean (red) and the mode (blue) of the muon residual spectrum are presented byputting all the events below 20 GeV in 100 bins of equal width (so, each bin corresponds to 200 MeV). The6 R e l a t i v e r edu c t i on (a) S h i ft ( G e V ) mag z D (b) Fig. 6: (a) Energy bin representation of relative reduction for two magnetic fields operating at 1 m depth;(b) systematic shift of mean of muon spectrum. increase in mean can be fitted with a polynomial of 5 th order. The increase in mode with the increase inmagnetic field is somewhat obscure due to the effect of the binning. But the overall trend is understandable.
3. Transverse dimension (width) of magnet system
In earlier study, the transverse dimension of the magnet system was taken as 10 m ×
10 m. Does thisparameter has a significant effect on the rate of charged particle cosmic background? To see this, GEANT4simulation of 3 million events was performed for three different transverse dimensions of the magnet: (1)one whose width is the same as the particle detector, i.e. 5 m, (2) one whose width is 1.5 times that of thedetector, i.e. 7.5 m and (3) one whose width is double, i.e. 10 m. The outcome of the experiment is shownin the following table 2: depth width 5 m 7.5 m 10 m1 m 11315 10493 102992 m 10455 9229 8893
Table 2:
Effect of transverse dimension of the magnet on the residual flux of cosmic rays into the particledetector. The field strength is 1.5 tesla.
So, increasing the width of the magnet system helps to reduce the rate of cosmic rays seen by the detector,as less number of particles can enter the detector from the side walls. However, the order of magnitude ofthe reduction is not very significant. Specifically, the reduction is about 1.8% × depth (in meter) if themagnet transverse dimension is increased from 1.5 times to 2 times of the detector width.7 . Magnet system It is known that many particle physics experiments are engineering strong magnets [10, 11] etc. Can similarmagnets be utilized to achieve this goal? Perhaps yes, but currently, these magnets do not enclose very largevolumes and are not ideal for reducing the cosmic muon background. But the study presented in this papergives a hint how the future magnets can be designed to achieve a desired degree of the reduction in residualcosmic muons. It is not only the strength that matters, the depth of the magnet is also a very importantparameter.The studies were presented mostly using a nominal field strength of 1.5 T which is attainable by an iron-core electromagnet or by rare-earth neodymium magnet. Use of iron or neodymium as the material of themagnet would lead to additional energy loss and multiple scattering of the charged particles of cosmic rays,apart from their desired deflection. This would make the role of magnetic field on the reduction in the cosmicrays obscure. This is why the preceding discussion assumed the field to be operating in vacuum. The effectof using the solid materials as magnet has been studied as well and is presented in the next subsection 4.1.The superconducting magnets are scientifically the best options, as expected, since the field strength canbe made very high (5-10 T, or even more). But with the current technology, the construction of a largevolume superconducting magnet (even of a size comparable to the dimension of the detector) may be quitecostly. But this cost must be compared with the total cost of construction and operation of the undergroundfacilities and the physics output. This cost-benefit ratio will be discussed in section 6.
The cheapest option is perhaps to use a DC-based electromagnet with iron core. Another option is to usepermanent neodymium bar magnets. One must keep in mind that the system must be supported on thesurrounding ground due to their weight. Simulation of three million CRY cosmic ray events through 1 meterdeep and 10 m ×
10 m wide magnet system (for 1.5 T magnetic field) in 2.379 seconds produces a lot ofsecondary particles 3:material particles µ e γ ν e ν µ nIron 7240 1052 10677 1103 1860 599Neodymium 7893 1218 12040 870 1519 1349 Table 3:
Effect of using solid ferromagnetic material to construct the magnet system.
Comparison with table 3b shows that indeed the rate of muon flux decreases by ∼ ∼ · cm /gm × ×
100 cm ∼ -
10 1 10Kinetic energy (GeV) - - -
10 110 ) - G e V - s - ( m F IronNeodymium (a) -
10 1 10Kinetic energy (GeV) - -
10 110 ) - G e V - s - ( m F IronNeodymium (b)
Fig. 7:
Spectrum of (a) muons and (b) gamma which arise when cosmic rays are attempted to be blockedand deflected by 1 m deep iron/neodymium plates. many neutrino experiments detect neutrino signature by observing Cherenkov or scintillation light fromneutrino events. The gamma rays coming from the magnetized block (placed above to deflect cosmic rays)would give rise to secondary backgrounds from gammas of energy up to 1 GeV. Not only that, the methodalso produces ν µ and ν e s which can also act as additional background to a low-medium energy neutrinoexperiment. Spectra of such neutrinos are shown in the following figure: 9. The spike in the ν µ plot at < -
10 1 10Kinetic energy (GeV) - -
10 110 ) - G e V - s - ( m F IronNeodymium (a) -
10 1 10Kinetic energy (GeV) - -
10 110 ) - G e V - s - ( m F IronNeodymium (b)
Fig. 8:
Spectrum of (a) ν µ and (b) ν e which arise when cosmic rays are attempted to be blocked anddeflected by 1 m deep iron/neodymium plates. MeV bin is due to the decay of stopped pions which is monochromatic with 29.8 MeV energy. Althoughthere is negligible number of pions in the cosmic rays at the ground level, the protons present in the cosmicray produce large number of pions as they hit the block. The neutrinos with energy higher than >
100 MeVare coincident with the lower side of standard atmospheric neutrinos.9 .2. Conclusion
A ferromagnetic material-based magnet will suppress the overall cosmic muon background, but not in anenergy specific manner. It can be unambiguously stated, though, that a vacuum-core magnet can be usedto reduce the cosmic muon and electron background significantly for a low energy ( <
100 MeV) nuclear orparticle physics detector whose signals may come from particles with zero to tens of MeV of energy. Theperfect examples of this kind of experiments are the reactor neutrino experiments and the current generationexperiments (e.g. COHERENT) that intend to observe the “coherent elastic neutrino nucleus scattering”(CE ν NS) and neutrinos coming from Supernovae (with tens of MeV of energy). The COHERENT detectorcan achieve background rejection with timing of the neutrino pulse. But this is not possible while trying toobserve neutrinos coming from Supernovae. The use of a magnet system can be fruitful to achieve very highdegree of cosmic ray reduction. It may even present the possibility of performing event by event analysis atlow energy bins.
5. Comparison with standard rock overburden
The discussion remains incomplete until we compare the preceding observation with the usual situation wherea detector is constructed in an underground laboratory. Even a shallow underground laboratory receivesmuch less number of muons [12]. However, along with the muons, other particles are also generated like thecase of iron or neodymium. These include muon induced spallation neutrons which is a major issue for thedirect dark matter detection experiments. The following table 4 shows the number of different particles asthe depth of rock overburden of a shallow underground detector is increased.depth particles µ e γ ν e ν µ n10 m 5074 1086 6747 1045 1460 5620 m 4620 1024 6709 1014 1265 7330 m 4560 1004 6669 1040 1230 5940 m 4239 874 5730 982 1246 3950 m 3884 814 5727 981 1203 55 Table 4:
Number and composition of background cosmic rays to a 5 m × Comparison with table 3 shows that 10 m depth of rock overburden reduces muons by almost 30% withrespect to 1 m deep iron. The background of neutrons are also suppressed significantly. This shows why allthe direct dark matter detectors are constructed underground. The spectrum of the muons as a function ofshallow underground depth is shown in the following figure 9a. The adjacent figure 9b shows the comparisonof the spectra of residual muons to a ground-based detector for 1.5 tesla field operating in 1 m deep magnetsystem in vacuum and in iron with 50 m and 800 feet deep (Homestake shallow level) underground detectors.The interesting point to see is the dip at low energy bins ( ∼
100 MeV) for the vacuum core magnet system.There is an overall suppression of cosmic muon background for iron/rock overburden (the deeper undergroundthat laboratory is situated, the better). But there is no dip in these cases which reflects an overall down10 -
10 1 10Kinetic energy (GeV) -
10 110 ) - G e V - s - ( m F
10 m Standard rock30 m Standard rock50 m Standard rock (a) -
10 1 10Kinetic energy (GeV) - - -
10 110 ) - G e V - s - ( m F Iron, 1.5 T 1 m depth50 m Standard rockVacuum 1.5 T 1 m depth243.84 m Standard rock (b)
Fig. 9: (a) Spectrum of residual cosmic muons to an underground detector as a function of standard rockdepth; rock density is taken as 2.65 g/cm . (b) comparison of the muon spectra for 1 m deepmagnetic field in vacuum (purple), iron (red) with 50 m deep rock (blue) and 243.84 m (800 ft) deeprock (green). shift of the kinetic energy of all the cosmic rays. In comparison, it is seen that at ∼
100 MeV energy, thevacuum core magnetic field (purple) is almost as effective in reducing the cosmic muon background as a 800ft. deep underground laboratory (green). In the case of the latter, the high energy tail is also suppressed asexpected. If a stronger magnetic field can be constructed by deploying the superconducting magnet systems,it may be possible to reduce the cosmic muon background even further, extending to higher energy range.
6. Cost comparison
The next obvious point to consider is whether the use of a suitable magnet system is cost-worthy in com-parison with the construction of an underground detector. This comparison is somewhat difficult, becausethe available information on the cost of underground facilities reflect both the underground depths as wellas the scales of the experiments. Not only that, the type of backgrounds received and their spectra atdeep underground laboratories are very different from the composition and spectra of residual backgroundin a detector placed under the magnet system. Nevertheless, a comparison may give some idea about thepracticality of the use of the magnet systems. In the following table 5, the range of costs of various un-derground research laboratories is shown (as found in [13] and [14]). It would be nice to compare with thecorresponding numbers for the shallow underground laboratories (e.g. Felenskeller laboratory at 47 m depthand the shallow underground laboratory at Pacific Northwest National Laboratory at 11.3 m depth). Butnumbers representing the cost were not found from reliable resources.The cost of superconducting magnet as a function of the field volume times the field strength has beendiscussed in the literature [15]. From the figures and the formulae given in these papers, we see that thecost of the superconducting magnet of volume-strength 150 Tm will be about 15-25 M $ in accordance with2008 valuation. This is an order of magnitude less than the costs of the major underground laboratories.11xperiment location depth (m) facility cost annual operating costDM+DBD Homestake 2255 290-530 20DM+DBD SNOlab 2070 60 n/aLBNE w/LAr-DM+DBD Homestake 1480 978-1137 18-23Study 155 millionyear old clay rock Bure (France) 450-500 315 67.65 Table 5:
Costs (2011 M $ ) of construction and operation of the underground research laboratories at variousdepths. The acronyms DM, DBD and LAr in the above table correspond to dark matter, double β decay and Liquid Argon. The cost at SNOlab is substantially less, presumably due to existinginfrastructure. The cost for Bure URL has been converted from Euro to US $ .
7. Indirect implication of the method for WIMP dark matter detectors
The detectors for the direct search of dark matter are usually placed underground for reducing cosmicray background to as minimum as possible. They look for Weakly Interacting Massive Particles (WIMPs)that are hypothesized to be electrically neutral particles only responding to weak interaction apart fromgravity. For such detectors, perhaps neutrons are the most problematic backgrounds, as they lead to nuclearrecoil events exactly the same way as could be done by the WIMPs. A magnet system cannot deflect awayelectrically neutral neutrons of the cosmic rays. So, it is not directly helpful for such detectors. However, oneof the sources of background neutrons in the underground dark matter detectors is the spallation of cosmicmuons and the other charged particles in the earth’s crust. This continues to be a background, even if thedetector is buried deep in the underground. Multiple levels of veto (e.g. water shielding) and reconstructionare needed to take care of the neutron background. A reduction in the residual cosmic muon rays at theground level which can be achieved by the magnet system, can partially reduce the neutron background dueto the spallation neutrons to an underground dark matter detector. This is because, a less fraction of muonswill lead to a less fraction of spallation neutrons. Detectors that intends to observe solar neutrinos or diffuseSupernova neutrino background (DSNB) signals [16] may also benefit from this technique. In this case, itmay be helpful to bury the detector deep in the underground with the magnet resting on top of the ground.
8. Summary
In this work, it has been shown that a ground based magnet system may be scientifically useful to cut downthe background due to the cosmic ray charged particles. With currently available technology, it is possibleto reduce the cosmic background to low energy neutrino detectors. A significant reduction of the higherenergy cosmic muons will require a stronger superconducting magnet. The technique can also indirectlyhelp in reducing the background of spallation neutrons at deep underground detectors. It will be a sheerengineering challenge to build a large superconducting magnet and to make sure that the field does not leak,but it will save the cost of constructing an underground detector and danger associated with it.12 . Acknowledgement
Manipal Centre for Natural Sciences, Manipal Academy of Higher Education,Manipal is acknowledged forthe encouragement and facilities to carry out this work.
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