MICE STEP I: FIRST MEASUREMENT OF EMITTANCEWITH PARTICLE PHYSICS DETECTORS

R. Asfandiyarov∗, DPNC, University of Geneva, SwitzerlandOn Behalf of the MICE Collaboration

Abstract

The muon ionization cooling experiment (MICE) is astrategic R&D project intending to demonstrate the onlypractical solution to prepare high brilliance beams nec-essary for a neutrino factory or muon colliders. MICEis under development at the Rutherford Appleton Labora-tory (UK). It comprises a dedicated beam line to gener-ate a range of input emittance and momentum, with time-of-flight and Cherenkov detectors to ensure a pure muonbeam. The emittance of the incoming beam is measuredin the upstream magnetic spectrometer with a scintillatingfiber tracker. A cooling cell will then follow, alternatingenergy loss in liquid hydrogen absorbers and RF accelera-tion. A second spectrometer identical to the first and a sec-ond muon identification system measure the outgoing emit-tance. In the 2010 run the beam and most detectors havebeen fully commissioned and a first measurement of theemittance of a beam with particle physics (time-of-flight)detectors has been performed. The analysis of these datais presented here. The next steps of more precise measure-ments, of emittance and emittance reduction (cooling), thatwill follow in 2011 and later, are also outlined.

INTRODUCTION

The Muon Ionization Cooling Experiment (MICE) col-laboration is building a lattice cell of the cooling chan-nel [1] of Neutrino Factory of Neutrino Factory FeasibilityStudy-II [2] at a muon beam line at the ISIS proton accel-erator at the Rutherford Appleton Laboratory in the UK.In order to demonstrate cooling over a range of emittancesand momenta, the beam line must generate several matchedbeams with different optical parameters at TOF1.

The normalized root mean square (RMS) emittance in 6dimensions is defined as

εrms =1

mµ

√|V |,

|V | is the determinant of the 6× 6 covariance matrix of thephase space vector �U = (�x, �p), where �x = (x, y, t) and�p = (px, py, E). All these 6 variables will be measuredin spectrometers before and after cooling cell on a particle-by-particle basis and then bunched to up to 106 particlesfor emittance calculation. The beam before colling channelcan be measured by timing detectors. Data from TOF0 andT0F1 were used already to analyze the performance of theexisting MICE muon beam line.

∗ ruslan.asfandiyarov@unige.ch

Technique

Data from timing detectors TOF0 and T0F1 are usedto analyze the performance of the MICE muon beam line(Figure 1). Both detectors are composed of two orthogo-nally oriented planes of scintillator slabs read out at eachend by photomultiplier tubes, and measure time. with reso-

suring the time of flight between TOF0 and TOF1. Lon-gitudinal momentum may then be reconstructed using aniterative method.

Figure 1: The MICE time of flight system.

The average momentum between the TOFs is given by

p(s, t) =m0s/t√

1− s2/(ct)2,

where the path length s = L + δ is reconstructed by track-ing (Figure 2) the particle’s trace-space vectors (x, dx/dz)and (y, dt/dz) through the beam line, and integrating thepath length through each section. The initial trace spacevector at TOF0 can be transported to TOF1 by a trans-fer matrix (x1, x

′1) = M(x0, x

′0) defined by quadrupole

parameters. Since the TOFs provide a measurement of(x0, x1) and that det M = 1 for linear transformation, itis possible to find the angles x′ = dx/dz and y′ = dy/dzneeded for path length calculation:(

x′0x′1

)=

1M12

(−M11 1−1 M22

) (x0

x1

)A set of beam line optics configurations have been gener-

ated and corresponding beam parameter measured by TOFsystem. All variables measured in data have been comparedwith simulation.

lution st = 50 ps [3]. Particle species is determined by mea-

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Figure 2: Particle reconstruction technique.

MEASURED OPTICAL BEAMPARAMETERS

A sample time of flight spectrum for a base line μ− beamis shown in Figure 3. An electron peak is clearly distin-guishable at 25.7 ns. As the electrons have E∼m, this isused to calibrate the time of flight of the muons. The broadpeak at 28.3 ns is mainly made up of muons. This is borneout by the Monte Carlo simulation results plotted on thesame graph, which indicate a pion contamination ¡ 1%. Thesimulated beams were generated by G4Beamline, a beamline simulation program which models particle interactionsin matter in detail [4].

Figure 3: A comparison of the simulation and data.(top)The time of flight between TOF0 and TOF1. (bottom) Thelongitudinal momentum at TOF1.

The discrepancy between data and reconstructed simula-tion at the low-pz edge is ascribed to model sensitivity tothe size of the magnet apertures given the significant hor-izontal dispersion, and the fast variation in M(pz) at lowmomenta. This anomaly is not a concern for MICE as thisportion of the momentum spectrum is not optimized fortransmission in the subsequent cooling channel.

The distribution of the baseline beam in trace spacethereby deduced is shown in Figure 4. The transverse tracespace distribution of the base line beam is reconstructedwith resolution∼10 mrad arising from the position resolu-tion and the effects of multiple scattering in equal part. The

orientation of the trace ellipse varies as a function of pz , re-sulting in the visible skew. The reconstruction procedure isshown to skew the true distribution predominantly in thefringes of the distribution, where nonlinear effects are notnegligible.

Figure 4: The reconstructed transverse trace space of thebaseline beam at TOF1.

As the beam size in a plane is uniquely determined bythe emittance and betatron function, contours of constantbeam size are drawn in Figure 5. In both horizontal and ver-tical phase space, we note that all beams have RMS beamsizes between 5 and 7 cm. This illustrates further that thisbeam line is dominated by scraping in the quadrupoles, asdemonstrated in simulations, where ∼60% of muons arescraped in quadrupole 7. As a result of the constancy ofσx and σy , the betatron function is determined by the emit-tance to first order. Trends may also be observed in polarityand momentum. In both planes, μ+ beams tend to have ahigher emittance than μ− beams. This is a result of the in-clusion of a proton absorber in the μ+ beams which heatsthe beams slightly. We also observe that low-pz beams havea higher emittance. This is because the focusing strengthof a quadrupole is proportional to 1/pz . As the 140 MeV/cbeams are focused more powerfully by the magnets, theyhave a higher amplitude acceptance, and therefore a higheremittance.

Beams designed to have every combination of εn = (3, 6,10) mm upstream of the first liquid hydrogen absorber, andpz = (140, 200, 240) MeV/c in the center of each absorber.Muon beams of both polarities were generated and key op-tics parameter measured at TOF1. The transverse normal-ized emittance is related to the measured values of εx andεy as εn ≈ (pz/m)√εxεy . The emittance of the incomingbeam, measured by TOF0, TOF1 is much smaller than thatof the beam that will go through the cooling channel. Inorder to generate the desired large emittance the beam goesthrough a high Z diffuser of adjustable thickness situatedinside the first solenoid (Figure 6).

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Figure 5: The betatron function and RMS trace emittancefor all of the matched beams in both the horizontal and ver-tical planes, as measured just before the TOF1 detector.

Figure 6: Diffuser matching.

SIMULATION OF THE MEASUREDBEAM

A beam, starting at TOF1, with the transverse distribu-tions characteristic of the measured beam was simulated infull MICE cooling channel. The simulated beam was gen-erated according to the measured covariance matrix of thefour transverse phase space coordinates and therefore hadthe emittance and optical parameters of the real beam (Fig-ure 7). Dashed line is the reference particle traveling alongthe axis.

The evolution of the transverse beta function along theMICE cooling channel of the real beam has been also sim-ulated (Figure 8). The optics of the beam are seen to besimilar to the ideal optics (red line) derived from a numeri-cal solution to betatron equation:

2β⊥β′′⊥ − (β′⊥)2 + 4β2⊥κ2 − 4 = 0

where κ is the focusing strength.Figure 9 shows the evolution of the emittance of the sim-

ulated real beam. The emittance of the simulated real beam

Figure 7: Measured beam simulation.

Figure 8: Beam envelope.

is slightly higher than the nominal 6 mm but decreases asexpected at the absorbers. The initial overinflation of theemittance to 8 instead of 6 mm may be corrected by the useof a thinner lead diffuser disc. Despite no transverse selec-tion or re-weighting having taken place, the optics of thebeam behave tolerably well and the simulated real beam isseen to be cooled. It is anticipated that only a small re-weighting of the measured beam will be required.

CONCLUSIONS

The MICE collaboration intends to use beams with cen-tral momenta ranging from 140 MeV/c to 240 MeV/c,and normalized emittances between 3 and 10 mm. Sev-eral beams designed to have appropriate optical parame-ters were generated in a successful data taking campaign in2010. Timing detectors of ∼50 ps resolution confirm thegeneration of beams dominated by muons at the requiredmomenta.

Distributions of the trace space vectors of individualmuons have been reconstructed for the various beams, andpromising agreement is observed with Geant4 simulations.

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Figure 9: The baseline beam distribution measured in 2010evolved through the final MICE lattice.

The evolution through MICE of the optical parameters of ameasured baseline beam has then been simulated; the beamis relatively well matched, and tuning magnet currents anddiffuser thickness should be sufficient to generate a wellmatched beam.

REFERENCES

[1] R.Asfandiyarov, Progress in the Construction of the MICECooling Channel, this proceedings.

[2] S. Ozaki, R. Palmer, M. Zisman, and J. Gal-lardo (eds.), Feasibility Study-II of a Muon-BasedNeutrino Source, Tech. Rept. BNL-52623 (2001).http://www.cap.bnl.gov/mumu/studyii/FS2-report.

html

[3] R. Bertoni et al., The Design and Commission-ing of the MICE Upstream Time-of-Flight Sys-tem, Nucl. Instrum. Meth. A, 615 (2010) pp. 1426.http://arxiv.org/abs/1001.4426v2

[4] T. Roberts. A Swiss army knife forGeant4, optimized for simulating beam lines:http://www.muonsinc.com/tiki-index.php

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