The international Muon Ionization Cooling Experiment (MICE), under construction atRAL, will test a prototype cooling channel for a future Neutrino Factory or Muon Collider.The cooling channel aims to achieve, using liquid hydrogen absorbers, a 10% reduction intransverse emittance. The change in 4D emittance will be determined with an accuracy of 1%by measuring muons individually. Step IV of MICE will make the first preciseemittance-reduction measurements of the experiment. Simulation studies using G4MICE, basedon GEANT4, find a significant difference in multiple scattering in low Z materials,compared with the standard expression quoted by the Particle Data Group. Direct measurementof multiple scattering using the scintillating-fibre trackers is found to be possible, butrequires the measurement resolution to be unfolded from the data. Copyright © 2012 byIEEE

/Fermilab

Carlisle, T.

Cobb, J.

Neuffer, D.

U., /Oxford

The international Muon Ionization Cooling Experiment (MICE), under construction at RAL, will test a prototype cooling channel for a future Neutrino Factory or Muon Collider. The cooling channel aims to achieve, using liquid hydrogen absorbers, a 10% reduction in transverse emittance. The change in 4D emittance will be determined with an accuracy of 1% by measuring muons individually. Step IV of MICE will make the first precise emittance-reduction measurements of the experiment. Simulation studies using G4MICE, based on GEANT4, find a significant difference in multiple scattering in low Z materials, compared with the standard expression quoted by the Particle Data Group. Direct measurement of multiple scattering using the scintillating-fibre trackers is found to be possible, but requires the measurement resolution to be unfolded from the data

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Multiple Scattering Measurements in the MICE ExperimentT. Carlisle, J. Cobb, Department of Physics, Oxford University, Oxford, UK.∗D. Neuffer, Fermilab, USA.AbstractThe international Muon Ionization Cooling Experiment(MICE), under construction at RAL, will test a prototypecooling channel for a future Neutrino Factory or Muon Col-lider. The cooling channel aims to achieve, using liquidhydrogen absorbers, a 10% reduction in transverse emit-tance. The change in 4D emittance will be determined withan accuracy of 1% by measuring muons individually. StepIV of MICE will make the first precise emittance-reductionmeasurements of the experiment. Simulation studies us-ing G4MICE, based on GEANT4, find a significant differ-ence in multiple scattering in low Z materials, comparedwith the standard expression quoted by the Particle DataGroup. Direct measurement of multiple scattering usingthe scintillating-fibre trackers is found to be possible, butrequires the measurement resolution to be unfolded fromthe data.INTRODUCTIONThe Muon Ionization Cooling Experiment (MICE) [1] isa test of a prototype muon cooling channel, shown in Fig-ure 1. It is an integral part of the worldwide research efforttowards a Neutrino Factory or Muon Collider. MICE usesthree, 35 cm, liquid-hydrogen (LH2) absorbers to achievea 10% reduction in emittance, and is based on US Study2 [2]. Eight 201 MHz RF cavities, positioned between theabsorbers, re-accelerate the muon beam.Scintillating-fibre trackers within 4 T super-conductingsolenoids make single particle measurements at each endof the cooling channel. Each tracker consists of fivescintillating-fibre stations, shown in Figure 2, with an ac-tive diameter of 30 cm. Each station is composed of threedoublet-layers of 350µm scintillating-fibre. The trackersare designed to measurex, y, px, py, the transverse coordi-nates to the beam andE the muon energy. A pair of match-ing coils in each spectrometer tune the magnetic optics tomatch the muon beam into and out of the cooling lattice.STEP IVStep IV of MICE, shown in Figure 3, is due to start in2013. It will make the first ionization cooling measure-ments of the MICE programme, with solid LiH (∆z =63 mm) and LH2 (∆z = 35 cm) absorbers. Absorberthicknesses were selected to extract 10 MeV of energy fromthe beam.Step IV contains one absorber focus coil (AFC) module,with spectrometer solenoids at each end to study the beam∗on behalf of the MICE CollaborationFigure 1: CAD Drawing of MICE.Figure 2: The MICE scintillating-fibre tracker.Figure 3: Step IV configuration of the MICE Experiment.at input and output. The AFC module will house the ab-sorber, the cryogenic system to cool the LH2, and a pairof coils to bring the beam to a tight focus. In addition,two pairs of thin aluminium safety windows are present,one pair to maintain the vacuum and a second to provideredundancy.The cooling performance of Step IV has been studiedpreviously [3] using G4MICE software [4], which is basedon GEANT4.9.2. Muon multiple scattering was also inves-tigated, the results of which found significant disagreementwith the standard Particle Data Group (PDG) formalism.The PDG supply a straightforward expression to calculatemultiple scattering, based on work by V. Highland [5]. Itgives the projected angular distribution as:FERMILAB-CONF-12-171-APCTable 1: Tracker resolution in phase-space coordinatesui.ui σ(ui)x [mm] 0.54y [mm] 0.44px [MeV/c] 2.05py [MeV/c] 1.52pz[MeV/c] 4.58Figure 4: Simulation of Step IV in G4MICE software.θplanerms =13.6 MeVβcp√∆z/X0[1 + 0.038 ln(∆z/X0)], (1)said to be accurate to 11 % or better for10−3 < ∆z/X0 < 100. θplanerms = θspacerms /√2.Note that the logarithmic term is ignored in the standardcooling formula fordǫn/dz, quoted in [3].MULTIPLE SCATTERINGMEASUREMENTSA procedure was developed to investigate the ability ofthe trackers to measure multiple scattering with individualmuons, in addition to beam emittance. In order to simulatethe track reconstruction a Gaussian smear was applied tothe coordinates of each muon, where the resolution for eachphase-space variable is listed in Table 1, found in [6].Four Step IV configurations were simulated in G4MICE:an empty channel, an AFC module (incl. Al windows, to-talling ∆z = 0.7 mm) without an absorber, an AFC with35 cm LH2 and an AFC containing 63 mm of LiH. Phys-ical material in the spectrometer solenoids was removedfrom the simulation geometry. Muon beams were injectedinto a constant field region in the upstream spectrometersolenoid, matched according to the conditionβκ = 1,given in Penn [8], whereκ is the focusing strength. Step IVwas simulated using beams of 10,000 muons (µ−), withinitial pz = 207 MeV/c andσpz = 1 MeV/c. Energy losseswere turned off.For each configuration, the procedure followed was:1. The beam was tracked through the Step IV geome-try, and the coordinates of each muon recorded at theposition of the innermost scintillating-fibre plane, ineach of the trackers (z = −4.65 m,−0.85 m). Thisproduced an upstream and a downstream set of muonvectors.2. The upstream muon vectors were re-injected into anempty Step IV geometry, and tracked to the down-stream edge of the absorber.Figure 5: Muons tracked upstream (red) and downstream(blue) to the downstream face of the absorber.3. The particle sign (µ− → µ+) and momenta ofthe downstream muon vectors were flipped, and themuons tracked upstream to the absorber.4. The 3D space angle between the upstream (~p) anddownstream (~q) vectors was calculated at the down-stream absorber face, using:cos θspacerms =~p.~q|p||q| . (2)5. Steps 2-4 were repeated, applying the Gaussian smearto represent the measured 6D muon vectors.Figure 5 shows a visualization of the method, with theblueµ− beam tracked to the downstream edge of the ab-sorber, and the red,µ+ beam tracked upstream to meet it.RESULTSFigure 6 shows the rms space angle distributions for theAl windows in the AFC, and the LH2 and LiH absorbers(incl. Al windows), with and without the tracker smearing.Table 2 lists the rms space angle predictions for the fourconfigurations, from G4MICE simulations and the PDGformula. The empty channel run shows the accuracy ofthe tracking within GEANT4 (θspacerms = 0.06 mrad), andthe effect of the smearing, which limited the resolution toθspacerms = 23.37 mrad.G4MICE simulations predicted scattering of9.87 mradin the AFC (Al windows), which was larger than the PDGvalue, including the 11 % error. G4MICE scattering pre-dictions with LiH and LH2 absorbers however were sig-nificantly less than the PDG value. These findings wereconsistent with previous work [3], which found a strongZ dependency (particularly at low Z) in the PDG expres-sion when compared with GEANT4. The Al windows ofthe AFC were included in the PDG prediction forθrmsplaneTable 2: rms multiple scattering space angle predictions,from theory and G4MICE.Configurationθspacerms [mrad]PDG theory No Smear Smearempty channel n/a 0.06 23.37Al windows 7.78 9.87 25.61Al windows + LH2 20.41 16.26 28.26Al windows + LiH 25.74 21.55 32.82(a)(b)(c)Figure 6: Space angle distributions for beams of 10,000muons in G4MICE, at the downstream face of the absorberposition, for (a) Al windows only (AFC), (b) 35 cm LH2and (c) 63 mm LiH. The black line represents Monte Carlotruth, and red the tracker reconstructed distribution.in LH2 and LiH, calculatingx/X0 for the combined scat-terer (absorber + Al), as given in Lynch & Dahl’s paper[7]. The Monte Carlo prediction for the multiple scatter-ing in LH2 wasθspacerms = 16.26 mrad, 20 % less than thePDG value. In LiHθspacerms = 21.55 mrad, 16 % less thanthe PDG prediction. The data were unfolded by subtractingthe smear errors in quadrature. Whilst the scattering in theAl windows was apparent in the Monte Carlo (when com-pared with the empty geometry), the scattering appearedtoo small to measure. Unfolding the LH2 and LiH datasetshowever provided sufficient resolution to observe the dif-ference between the Monte Carlo and PDG scattering pre-dictions. As a result the trackers were considered able todirectly measure multiple scattering in the LH2 and LiHabsorbers.CONCLUSIONStep IV of MICE will make the first measurements ofionization cooling, and is due to begin operation in 2013.It will measure cooling in 35 cm LH2 and 63 mm LiH ab-sorber materials, along with plastic and Al. Scintillating-fibre trackers will make precision measurements of thetransverse emittance of the muon beam.Simulations in G4MICE (Monte Carlo) indicated 20 %less multiple scattering than predicted by the PDG expres-sion. A procedure was developed to ascertain whetherStep IV of MICE could shed light on this discrepancy. AGaussian smear was added to the muon positions and mo-menta recorded in the tracker, to imitate the tracker reso-lution. In an empty channel, with no scattering material,the smear resulted in an error of 23.37 mrad. As a resultit will be necessary to unfold the smeared data to achievesufficient resolution to address the difference between theMonte Carlo and PDG predictions. Step IV therefore pro-vides an opportunity to directly measure multiple scatter-ing.REFERENCES[1] G. Gregoire et al., MICE Proposal, RAL (2004);http://www.mice.iit.edu/.[2] S. Ozaki et al., BNL-52623, June 2001; M.M. Alsharo’a etal., Phys. Rev. ST Accel. Beams 6, 081001 (2003).[3] T. Carlisle & J. H. Cobb, Ionization Cooling in MICE StepIV. IPAC 2011, Sans Sebastián, September 2011, p. 877.[4] Documentation on the G4MICE software suite is to be foundat: http://mice.iit.edu/software/software.html.[5] V. Highland, Some Practical Remarks On Multiple Scatter-ing, Nucl. Instr. and Meth, I29 (1975) 497-499.[6] A. Khan et al., MICE Scintillating Fibre Tracker Prototype.MICE Note 90, 24/1/2005.[7] G. Lynch & O. Dahl, Approximations to multiple Coulombscattering, Nucl. Instr. and Meth B, 58, I1, 2 May 1991, 6-10.[8] G. Penn, Beam Envelope Equations in a Solenoidal Field,MuCool Note 71, January 2000.

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