Muon Colliders have unique technical and physics advantages and disadvantages
when compared with both hadrons and electron machines. They should be regarded
as complementary. Parameters are given of a 4 TeV high luminosity muon-muon
collider, and of a 0.5 TeV demonstration machine. We discuss the various
systems in such muon collider.Comment: LaTeX 5 pages 4 figure

Gallardo, J. C.

Palmer, R. B.

English

arXiv

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadrons and electron machines. They should be regarded as complementary. Parameters are given of a 4 TeV high luminosity muon-muon collider, and of a 0.5 TeV demonstration machine. We discuss the various systems in such muon collider

Palmer, R B

Gallardo, J C

CERN Document Server

HIGH LUMINOSITY MUON COLLIDER DESIGNRobert Palmer, Juan Gallardo,Brookhaven National LaboratoryUpton, NY 11973-5000, USAAbstractMuon Colliders have unique technical and physics advantagesand disadvantages when compared with both hadron and elec-tron machines. They should be regarded as complementary. Pa-rameters are given of 4 TeV high luminosity +−collider, andof a 0.5 TeV lower luminosity demonstration machine. We dis-cuss the various systems in such muon colliders.IntroductionThe possibility of muon colliders was introduced by Skrinsky etal.[1], Neuffer[2], and others. More recently, several workshopsand collaboration meetings have greatly increased the level ofdiscussion[3],[4]. A detailed Feasibility Study[5] was presentedat Snowmass 96.Technical QuestionsHadron collider energies are limited by their size, and techni-cal constraints on bending magnetic fields. Lepton (e+e−or+−) colliders, because they undergo simple, single-particleinteractions, can reach higher energy final states than an equiv-alent hadron machine. However, extension of e+e− collidersto multi-TeV energies is severely performance-constrained bybeamstrahlung, The luminosity L of a lepton collider can bewritten:L =14Enγ2roPbeamyncollisions (1)where y is the average vertical (assumed smaller) beam spotsize, E is the beam energy, Pbeam is the total beam power, is the electromagnetic constant, ro is the classical radius, andnγ is the number of photons emitted by one bunch as it passesthrough the opposite one. If this number is too large then thebeamstrahlung background of electron pairs and other productsbecomes unacceptable.As the energy rises, the luminosity, for the same event rate,must rise as the square of the energy. For an electron collider,ncollisions = 1, and, for a fixed background, we have the severerequirement:Pbeamy/ E3 (2)In a muon collider there are two significant changes: 1) Theclassical radius ro is now that for the muon and is 200 timessmaller; and 2) the number of collisions a bunch can makencollisions is no longer 1, but is now related to the average bend-ing field in the muon collider ring, For 6 T, it is 900.In addition, with muons, synchrotron radiation is negligible,and the collider is circular. In practice this means that it can bemuch smaller than a linear electron machine. The linacs for the0.5 TeV NLC will be 20 km long. The ring for a muon colliderof the same energy would be only about 1.2 km circumference.There are, of course, technical difficulties in making suffi-cient muons, cooling and accelerating them before they decayand dealing with the decay products in the collider ring. Despitethese difficulties, it appears possible that high energy muon col-liders might have luminosities comparable to or, at energies ofseveral TeV, even higher than those in e+e−colliders.ParametersThe basic parameters of a 4 TeV +−collider are shownschematically in Fig.1 and given in Tb.1 together with thosefor a 0.5 TeV demonstration machine based on the AGS as aninjector. It is assumed that a demonstration version based onupgrades of the FERMILAB machines would also be possible.C of m Energy TeV 4 .5Beam energy TeV 2 .25Beam γ 19,000 2,400Repetition rate Hz 15 2.5Muons per bunch 1012 2 4Bunches of each sign 2 1Norm. rms emit. N  mm mrad 50 90Bending Field T 9 9Circumference Km 7 1.2Ave. ring field B T 6 5Effective turns 900 800 at intersection mm 3 8rms I.P. beam size m 2.8 17Luminosity cm−2s−1 1035 1033Table 1: Parameters of Collider RingsComponentsProton DriverThe proton driver is a high-intensity (four bunches of 2:51013protons per pulse) 30 GeV proton synchrotron, operating at arepetition rate of 15 Hz. Two of the bunches are used to make+’s and two to make −’s. Prior to targeting the bunches arecompressed to an rms length of 1 ns.For a demonstration machine using the AGS[6], two bunchesof 5  1013 at a repetition rate of 2.5 Hz at 24 GeV could beused.Figure 1: Schematic of a Muon Collider.TargetPredictions of nuclear Monte-Carlo programs[7][8][9] suggestthat  production is maximized by the use of heavy target mate-rials, and that the production is peaked at a relatively low pionenergy ( 100 MeV), substantially independent of the initialproton energy.Cooling requirements dictate that the target be liquid: liq-uid lead and gallium are under consideration. In order to avoidshock damage to a container, the liquid could be in the form ofa jet.Pion CapturePions are captured from the target by a high-field (20 T, 15 cmaperture) hybrid magnet: superconducting on the outside, anda water cooled Bitter solenoid on the inside. A preliminarydesign[10] has a Bitter magnet with an inside coil diameter of24 cm (space is allowed for a 4 cm heavy metal shield inside thecoil) and an outside diameter of 60 cm; it provides half (10T) ofthe total field, and would consume approximately 8 MW. Thesuperconducting magnet has a set of three coils, all with insidediameters of 70 cm and is designed to give 10 T at the targetand provide the required tapered field to match into the decaychannel.Decay Channel and Phase Rotation LinacThe decay channel consists of a periodic superconductingsolenoidal (5 T and radius = 15 cm). A linac is introduced alongthe decay channel, with frequencies and phases chosen to deac-celerate the fast particles and accelerate the slow ones; i.e. tophase rotate the muon bunch.Fig. 2 shows the energy vs ct at the end of the decay channel.Figure 2: Energy vs ct of muons at end of decay channel withphase rotation; muons with polarization P> 13 , −13 < P <13 ,and P< − 13 are marked by the symbols ‘+’, ‘.’ and ‘-’ respec-tively.The selected muons have a mean energy 150 MeV, rmsbunch length 1:7 m, and rms momentum spread 20 % (95 %,L = 3:2 eVs). The number of muons per initial proton in thisselected bunch is  0.3.Polarization SelectionIf nothing is done then the average muon polarization is about0.19. If higher polarization is desired, some selection of muonsfrom forward pion decays (cos d ! 1) is required. This can bedone by momentum selecting the muons at the end of the decayand phase rotation channel. A snake[11] is used to generate therequired dispersion. Varying the selected minimum momentumof the muons yields polarization as a function of luminosity lossas shown in Fig.3. Dilutions introduced in the cooling havebeen calculated[12] and are included. A siberian snake is alsorequired in the final collider ring.Figure 3: Polarization vs Floss of muons accepted; the dashedline shows polarization as selected before cooling; the solid linegives polarization after cooling.Ionization CoolingFor the required collider luminosity, the phase-space volumemust be greatly reduced; and this must be done within the  life-time. Cooling by synchrotron radiation, conventional stochas-tic cooling and conventional electron cooling are all too slow.Optical stochastic cooling[13], electron cooling in a plasmadischarge[14] and cooling in a crystal lattice[15] are being stud-ied, but appear very difficult. Ionization cooling[16] of muonsseems relatively straightforward.In ionization cooling, the beam loses both transverse and lon-gitudinal momentum as it passes through a material medium.Subsequently, the longitudinal momentum can be restored bycoherent reacceleration, leaving a net loss of transverse momen-tum.The equation for transverse cooling (with energies in GeV)is:dnds= −dEdsnE+?(0:014)22 Em LR; (3)where n is the normalized emittance, ? is the betatron func-tion at the absorber, dE=ds is the energy loss, and LR is theradiation length of the material. The first term in this equationis the coherent cooling term, and the second is the heating dueto multiple scattering. This heating term is minimized if ? issmall (strong-focusing) and LR is large (a low-Z absorber).Energy spread is reduced by placing a transverse variationin absorber density or thickness at a location where position isenergy dependent, i.e. where there is dispersion. The use ofsuch wedges can reduce energy spread, but it simultaneouslyincreases transverse emittance in the direction of the dispersion.It thus allows the exchange of emittance between the longitudi-nal and transverse directions.Cooling System The cooling is obtained in a series of cool-ing stages. In general, each stage consists of three componentswith matching sections between them:1. a FOFO lattice consisting of spaced axial solenoids withalternating field directions and lithium hydride absorbersplaced at the centers of the spaces between them, wherethe ?’s are minimum.2. a lattice consisting of more widely separated alternatingsolenoids, and bending magnets between them to gener-ate dispersion. At the location of maximum dispersion,wedges of lithium hydride are introduced to interchangelongitudinal and transverse emittance.3. a linac to restore the energy lost in the absorbers.In a few of the later stages, current carrying lithium rods re-place item (1) above. In this case the rod serves simultaneouslyto maintain the low ?, and attenuate the beam momenta. Sim-ilar lithium rods, with surface fields of 10 T , were developed atNovosibirsk and have been used as focusing elements at FNALand CERN[17].The emittances, transverse and longitudinal, as a function ofstage number, are shown in Fig.4. In the first 10 stages, rela-tively strong wedges are used to rapidly reduce the longitudinalemittance, while the transverse emittance is reduced relativelyslowly. The object is to reduce the bunch length, thus allow-ing the use of higher frequency and higher gradient rf in thereacceleration linacs. In the next 7 stages, the emittances arereduced close to their asymptotic limits. In the last 3 stages, us-ing lithium rods, there are no wedges and the energy is allowedto fall to about 15 MeV. Transverse cooling continues, and themomentum spread is allowed to rise. The total length of thesystem is 750 m, and the total acceleration used is 5 GeV. Thefraction of muons remaining at the end of the cooling system iscalculated to be 55 %.AccelerationFollowing cooling and initial bunch compression the beamsmust be rapidly accelerated to full energy (2 TeV, or 250 GeV).A sequence of recirculating accelerators (similar to that usedat CEBAF)could be used but would be relatively expensive. Amore economical solution would be to use fast pulsed magnetsin synchrotrons with rf systems consisting of significant lengthsof superconducting linac.For the final acceleration to 2 TeV in the high energy ma-chine, the power consumed by a ring using only pulsed magnetswould be excessive and alternating pulsed and superconductingmagnets[18] are used instead.Collider Storage RingAfter acceleration, the + and − bunches are injected intoa separate storage ring. The highest possible average bendingfield is desirable to maximize the number of revolutions beforedecay, and thus maximize the luminosity. Collisions occur inone, or perhaps two, very low- interaction areas.Bending Magnet Design The magnet design is compli-cated by the fact that the ’s decay within the rings (− !e−e), producing electrons whose mean energy is approxi-mately 0.35 that of the muons. These electrons travel towardthe inside of the ring dipoles, radiating a fraction of their energyas synchrotron radiation towards the outside of the ring, anddepositing the rest on the inside. The total average power de-posited, in the ring, in the 4 TeV machine is 13 MW. The beammust thus be surrounded by a  6 cm thick warm shield[19],which is located inside a large aperture conventional supercon-ducting magnet.The quadrupoles can use warm iron poles placed as closeto the beam as practical, with coils either superconducting orwarm, as dictated by cost considerations.Lattice In order to maintain a bunch with rms length 3 mm,without excessive rf, an isochronous lattice, of the dispersionwave type[20] is used. For the 3 mm beta at the intersectionpoint, the maximum beta’s in both x and y are of the order of400 km (14 km in the 0.5 TeV machine). Local chromatic cor-rection is essential. Two lattices have been generated[21][22],Figure 4: Normalized transverse and longitudinal emittances asa function of section number in the model cooling systemone of which[22], after the application of octupole and decapolecorrectors, has been shown to have an adequate calculated dy-namic aperture.Studies of the resistive wall impedance instabilities indi-cate that the required muon bunches would be unstable if un-corrected. In any case, the rf requirements to maintain suchbunches would be excessive. BNS[23] damping, applied by rfquadrupoles[24], is one possible solution, but needs more care-ful study.Muon Decay BackgroundMonte Carlo study[25],[19] indicated that the background,though serious, should not be impossible. Further reductionsare expected as the shielding is optimized, and it should be pos-sible to design detectors that are less sensitive to the neutronsand photons present.There would also be a background from the presence of a haloof near full energy muons in the circulating beam. The beamwill need careful preparation before injection into the collider,and a collimation system will have to be designed to be locatedon the opposite side of the ring from the detector.There is a small background from incoherent (i.e. +−!e+e−) pair production in the 4 TeV Collider case. The crosssection is estimated to be 10 mb, which would give rise to abackground of  3 104 electron pairs per bunch crossing. Ap-proximately 90 % of these, will be trapped inside the tungstennose cone, but those with energy between 30 and 100 MeV willenter the detector region.Conclusion Considerable progress has been made on a scenario for a 2+ 2 TeV, high luminosity collider. Much work remains tobe done, but no obvious show stopper has yet been found. The two areas that could present serious problems are: 1)unforeseen losses during the 25 stages of cooling (a 3%loss per stage would be very serious); and 2) the excessivedetector background from muon beam halo. Many technical components require development: a largehigh field solenoid for capture, low frequency rf linacs,multi-beam pulsed and/or rotating magnets for accelera-tion, warm bore shielding inside high field dipoles for thecollider, muon collimators and background shields, etc.but: None of the required components may be described as ex-otic, and their specifications are not far beyond what hasbeen demonstrated. If the components can be developed and the problems over-come, then a muon-muon collider could be a useful com-plement to e+e−colliders, and, at higher energies could bea viable alternative.AcknowledgmentThis research was supported by the U.S. Department of Energyunder Contract No. DE-ACO2-76-CH00016 and DE-AC03-76SF00515.References[1] E. A. Perevedentsev and A. N. Skrinsky, Proc. 12th Int. Conf. onHigh Energy Accelerators, F. T. Cole and R. Donaldson, Eds.,(1983) 485; Early Concepts for +− Colliders and High En-ergy  Storage Rings, Physics Potential & Development of +−Colliders. 2nd Workshop, Sausalito, CA, Ed. D. Cline, AIP Press,Woodbury, New York, (1995).[2] D. Neuffer, IEEE Trans. NS-28, (1981) 2034.[3] Proceedings of the Mini-Workshop on +− Colliders: Parti-cle Physics and Design, Napa CA, Nucl Inst. and Meth., A350(1994) ; Proceedings of the Muon Collider Workshop, February22, 1993, Los Alamos National Laboratory Report LA- UR-93-866 (1993) and Physics Potential & Development of +− Col-liders 2nd Workshop, Sausalito, CA, Ed. D. Cline, AIP Press,Woodbury, New York, (1995).[4] Transparencies at the 2 + 2 TeV +− Collider CollaborationMeeting, Feb 6-8, 1995, BNL, compiled by Juan C. Gallardo;transparencies at the 2 + 2 TeV +− Collider CollaborationMeeting, July 11-13, 1995, FERMILAB, compiled by RobertNoble; Proceedings of the 9th Advanced ICFA Beam DynamicsWorkshop, Ed. J. C. Gallardo, AIP Press, Conference Proceed-ings 372 (1996).[5] +− Collider: A Feasibility Study, BNL-52503, FermiLab-Conf.-96/092, LBNL-38946, Proceedings of the SnowmassWorkshop 96, to be published.[6] T. Roser, AGS Performance and Upgrades: A Possible ProtonDriver for a Muon Collider, Proceedings of the 9th AdvancedICFA Beam Dynamics Workshop, Ed. J. C. Gallardo, AIP Press,Conference Proceedings 372 (1996).[7] D. Kahana, et al., Proceedings of Heavy Ion Physics at the AGS-HIPAGS ’93, Ed. G. S. Stephans, S. G. Steadman and W. E. Ke-hoe (1993); D. Kahana and Y. Torun, Analysis of Pion ProductionData from E-802 at 14.6 GeV/c using ARC, BNL Report # 61983(1995).[8] N. V. Mokhov, The MARS Code System User’s Guide, version13(95), Fermilab-FN-628 (1995).[9] J. Ranft, DPMJET Code System (1995).[10] R. Weggel, private communication; Physics Today, pp. 21-22,Dec. (1994).[11] F. Chen, Introduction to Plasma Physics, Plenum, New York, pp.23-26 (9174); T. Tajima, Computational Plasma Physics: WithApplications to Fusion and Astrophysics, Addison-Wesley Pub-lishing Co., New York, pp. 281-282 (1989).[12] B. Norum and R. Rossmanith, Polarized Beams in a Muon Col-lider, in Physics Potential & Development of +− Colliders,Proc., 3rd Int. Conf., San Francisco, Dec. 1995, Elsevier, in press.[13] A. A. Mikhailichenko and M. S. Zolotorev, Phys. Rev. Lett. 71,(1993) 4146; M. S. Zolotorev and A. A. Zholents, SLAC-PUB-6476 (1994).[14] A. Hershcovitch, Brookhaven National Report AGS/AD/Tech.Note No. 413 (1995).[15] Z. Huang, P. Chen and R. Ruth, SLAC-PUB-6745, Proc. Work-shop on Advanced Accelerator Concepts, Lake Geneva, WI ,June (1994); P. Sandler, A. Bogacz and D. Cline, Muon Cool-ing and Acceleration Experiment Using Muon Sources at Triumf,Physics Potential & Development of +− Colliders 2nd Work-shop, Sausalito, CA, Ed. D. Cline, AIP Press, Woodbury, NewYork, pp. 146 (1995).[16] A. N. Skrinsky and V.V. Parkhomchuk, Sov. J. of Nucl. Physics12, (1981) 3; D. Neuffer, Particle Accelerators, 14, (1983) 75; D.Neuffer, Proc. 12th Int. Conf. on High Energy Accelerators, F.T. Cole and R. Donaldson, Eds., 481 (1983); D. Neuffer, in Ad-vanced Accelerator Concepts, AIP Conf. Proc. 156, 201 (1987).[17] G. Silvestrov, Proceedings of the Muon Collider Workshop,February 22, 1993, Los Alamos National Laboratory ReportLA-UR-93-866 (1993); B. Bayanov, J. Petrov, G. Silvestrov, J.MacLachlan, and G. Nicholls, Nucl. Inst. and Meth. 190, (1981)9; Colin D. Johnson, Hyperfine Interactions, 44 (1988) 21; M. D.Church and J. P. Marriner, Annu. Rev. Nucl. Sci. 43 (1993) 253.[18] D. Summers, presentation at the 9th Advanced ICFA Beam Dy-namics Workshop, unpublished.[19] I. Stumer, presentation at the BNL-LBL-FNAL CollaborationMeeting, Feb 1996, BNL, unpublished.[20] S.Y. Lee, K.-Y. Ng and D. Trbojevic, FNAL Report FN595(1992); Phys. Rev. E48, (1993) 3040; D. Trbojevic, et al., Designof the Muon Collider Isochronous Storage Ring Lattice, Micro-Bunches Workshop, BNL Oct. (1995), to be published.[21] A. Garren, et al., Design of the Muon Collider Lattice: PresentStatus, in Physics Potential & Development of +− Colliders,Proc., 3rd Int. Conf., San Francisco, Dec. 1995, Elsevier, in press.[22] K. Oide, private communication.[23] V. Balakin, A. Novokhatski and V. Smirnov, Proc. 12th Int. Conf.on High Energy Accel., Batavia, IL, 1983, ed. F.T. Cole, Batavia:Fermi Natl. Accel. Lab. (1983), p. 119.[24] A. Chao, Physics of Collective Beam Instabilities in High EnergyAccelerators, John Wiley & Sons, Inc, New York (1993).[25] G. W. Foster and N. V. Mokhov, Backgrounds and Detector Per-formance at 2 + 2 TeV +− Collider, Physics Potential & De-velopment of +− Colliders 2nd Workshop, Sausalito, CA, Ed.D. Cline, AIP Press, Woodbury, New York, pp. 178 (1995). pre-sentation at the unpublished.

High Luminosity Muon Collider Design

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should be regarded as complementary. Parameters are given of 4 TeV high luminosity {mu}{sup +}{mu}{sup {minus}} collider, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders

High Luminosity Muon Collider Design

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