A Demonstrator For Muon Ionisation Cooling

: The muon collider is an excellent prospect as a multi-TeV lepton collider, with the pos-1


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The muon collider is an excellent candidate for an energy frontier collider [1]. Unlike 13 protons, muons are fundamental particles so that all of the collision energy is available to 14 form products enabling access to relatively high energy physics processes. The relatively 15 high muon mass compared to electrons means that muons do not emit much synchrotron ra-16 diation so that they can be accelerated in rings, enabling a compact facility to be constructed 17 compared to an electron-positron collider at the same energy. 18 In existing facilities muons are created as products of proton collisions on a target. The 19 muons produced have a large beam emittance and must be cooled. Muons have a short 20 lifetime, approximately 2.2 µs, and the cooling must be achieved before decays reduce the 21 beam intensity prohibitively.

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A cooling system has been proposed as part of the Muon Accelerator Programme using 23 ionisation cooling [2]. In ionisation cooling, muons are passed through energy absorbing 24 material [3]. The muons ionise the absorber material reducing the total momentum of the 25 beam. The muons are subsequently reaccelerated in RF cavities, restoring the longitudinal 26 momentum of the beam. Overall the transverse beam emittance is reduced.

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Multiple Coulomb Scattering of muons off the atomic nuclei spoils the ionisation 28 cooling effect. Absorbers having low atomic number tend to remove more energy relative 29 to the amount of scattering and so perform better. A tight focus on the absorber increases 30 the transverse momentum of the beam, so that the relative impact of the scattering is 31 reduced.

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Longitudinal emittance can be removed by introducing a position-energy correlation 33 (dispersion) into the beam using dipoles. Suitably arranged wedge-shaped absorbers can 34 be placed so that the higher energy part of the beam passes through the thicker part of the 35 wedge. The position-energy correlation is cancelled by the wedge. This process effectively 36 moves emittance from longitudinal phase space to transverse phase space, where the 37 ionisation cooling process outlined above removes the emittance.

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Muon ionisation cooling was demonstrated by the Muon Ionisation Cooling Exper-39 iment (MICE) [4]. MICE demonstrated cooling in a single absorber at relatively high 40 emittances and in transverse phase space only.

RF Solenoid Absorber
Upstream Instrumentation and Matching Downstream Instrumentation

Target Collimation and phase rotation
High-intensity high-energy pion source  In this paper a Demonstrator for muon cooling is studied that will reduce the emit-42 tance of a muon beam in all 6 phase space dimensions, operating at low emittances and 43 demonstrating staging of many cooling cells. The preparation of a beam having suitable lon-44 gitudinal and transverse parameters are investigated and the potential facility performance 45 is studied.

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An overall schematic of the facility is shown in Fig. 1. Protons are passed onto a target. 48 An initial dipole selects muons in a momentum range between around 190 and 210 MeV/c. 49 The resultant beam is prepared in a series of RF cavities that rotate the beam in phase-50 energy space. Collimators remove the high emittance muons at the edge of the beam. A 51 further dipole and collimator removes muons that do not have the correct energy, resulting 52 in a beam that has the relatively low emittance and short bunch structure required for the 53 Demonstrator.

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The beam is passed through a short section of uniform field where the beam is charac-55 terised. Matching dipoles and solenoids are used to match the beam to the cooling beam 56 line. The cooling line itself comprises a number of dipoles, solenoids, RF cavities and 57 absorbers. A further characterisation of the beam is performed following the ionisation 58 cooling line.

Beam preparation 60
The muon beam for the Demonstrator is likely to be produced by firing protons onto a 61 horn-type target. A beam produced in such a way occupies a large volume in phase space. 62 For a Demonstrator it is not practicable to build a full cooling system. In order to create 63 the rather low emittance beams required as input to the Demonstrator it is necessary to 64 collimate the resultant muon beam in the beam preparation system.

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The beam preparation system comprises a dipole to select a narrow momentum bite 66 from the initial beam followed by a number of 0.5 T solenoids that provide transverse 67 focusing. The relatively low solenoid field enables collimation to the low emittances 68 required for the cooling demonstration. High gradient RF cavities rotate the beam in 69 phase-energy space. Momentum collimation is performed by a further 45 • dipole. Overall 70 a beam having low emittance in short bunches is produced.

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The resultant beam following the beam preparation system is shown in Fig. 2, sim-72 ulated in G4Beamline [5]. A short proton bunch, only a few ns long, was assumed as 73 input to the target. Such a bunch can be achieved for example in the CERN PS or SPS. The 74 parameters of the beam preparation system are listed in Table 1 75

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The muon cooling system comprises a sequence of high field solenoids to yield a tight 77 focus at the absorber, with additional dipole coils on each solenoid to deliver sufficient 78 dispersion. Adjacent solenoids have opposite polarity, so that absorbers are at a focus 79 of the lattice. Significant dispersion is excited when dipole polarity is swapped in every 80 other dipole. While β is periodic between 2 adjacent absorbers the dispersion flips on each 81 absorber so the overall cell length is 2 m, which is the distance between three consecutive 82 absorbers.

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The optical β at each absorber is roughly 0.13 m at the central momentum of 0.2 GeV/c. 84 The phase advance in each 2 m cell ranges between π at 226 MeV/c and 3π at 145 MeV/c. 85 The 2π stop band at 167 MeV/c is suppressed by the symmetry of the cell and further 86 damped by the cooling apparatus, but tolerance studies should be performed to verify 87 that it does not become detrimental to the cell performance in the event of field errors 88 and misalignments. The dispersion at the absorber is 63 mm, which is sufficient to induce 89 significant longitudinal emittance reduction even with a modest wedge angle of 5 • .

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Overall, the cooling lattice achieves a 98 % transmission over a 48 m distance, ne-91 glecting decays and assuming perfect matching. Decays would reduce the transmission 92 by a further 4 %. The transverse emittance is reduced from 1.95 mm to 1.57 mm and the 93 longitudinal emittance, calculated in ct-energy space, is reduced from 3.61 mm to 2.99 mm. 94 The 6D emittance is reduced from 12.7 mm 3 to 6.3 mm 3 , more than a factor two reduction 95 in emittance. The facility requires access to a suitable proton beam. Two sites have been identified at 98 CERN and discussions are ongoing with other laboratories. It may be particularly beneficial 99 to share the proton transfer line and target area with an experiment like nuSTORM [6]. 100 nuSTORM in turn would be the first demonstration of storage of a muon beam at high 101 energy and with muon flux approaching that required for the muon collider.

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Integration of magnet, RF and absorber hardware is a subject of study. The solenoid 103 field is rather moderate compared to existing magnets, but consideration must be made 104 for a suitable integration of RF equipment which may require large apertures. The over-105 lapping solenoid and RF fields can induce breakdown in the cavities; past experiments 106 have demonstrated configurations that mitigate this effect, but construction of production 107 cavities and testing in the design solenoid field is required. Space for bellows and beam 108 instrumentation must also be considered and is challenging to fit in such a compact lattice. 109 Further optimisation of the lattice is under consideration. Tighter focusing and more 110 cooling is possible, potentially at the cost of smaller dynamic aperture and some losses.