A Complete Scheme for a Muon Collider
Robert B. Palmer, J. Scott Berg, Richard C. Fernow, Juan Carlos Gallardo, Harold G. Kirk, ; Yuri Alexahin, David Neuffer, ; Stephen Alan Kahn, ; Don J. Summers
aa r X i v : . [ phy s i c s . acc - ph ] S e p A COMPLETE SCHEME FOR A MUON COLLIDER ∗ Robert B. Palmer, J. Scott Berg, Richard C. Fernow, Juan Carlos Gallardo, Harold G. Kirk(BNL, Upton, NY); Yuri Alexahin, David Neuffer (Fermilab, Batavia, IL); Stephen Alan Kahn(Muons Inc, Batavia, IL); Don J. Summers (University of Mississippi, Oxford, MS)
Abstract
A complete scheme for production, cooling, accelera-tion, and ring for a 1.5 TeV center of mass muon collideris presented, together with parameters for two higher en-ergy machines. The schemes starts with the front end of aproposed neutrino factory that yields bunch trains of bothmuon signs. Six dimensional cooling in long-period heli-cal lattices reduces the longitudinal emittance until it be-comes possible to merge the trains into single bunches, oneof each sign. Further cooling in all dimensions is appliedto the single bunches in further helical lattices. Final trans-verse cooling to the required parameters is achieved in 50 Tsolenoids.Table 1: Parameters of three muon colliders. Note 1: Depthis relative to any nearby low land, e.g. Fox river at FNAL.Note 2: Survival is from the end of phase rotation to thecollider ring. E c . m . s (TeV) 1.5 4 8 L ( cm sec − ) 1 4 8Beam-beam ∆ ν µ /bunch ( ) 2 2 2 < B ring > (T) 5.2 5.2 10.4 β ∗ = σ z (mm) 10 3 3rms dp/p (%) 0.09 0.12 0.06Depth for ν rad (m) 13 135 540Muon Survival ≈ ≈ ≈ P driver (MW) ≈ ≈ ≈ ǫ ⊥ ( π mm mrad) 25 25 25 ǫ k ( π mm rad) 72 72 72 INTRODUCTION
Muon colliders were first proposed by Budker in1969 [1], and later discussed by others [3]. A more de-tailed study was done for Snowmass 96 [4], but in none ofthese was a complete scheme defined for the manipulationand cooling of the required muons.Muon colliders would allow the high energy study ofpoint-like collisions of leptons without some of the diffi-culties associated with high energy electrons; e.g. the syn-chrotron radiation requiring their acceleration to be essen- ∗ This work was presented by A. Sessler at the workshop. Thiswork was supported by US Department of Energy under contracts AC02-98CH10886 and DE-AC02-76CH03000
Figure 1: (Color) Schematic of the components of a MuonCollider.tially linear, and as a result, long. Muons can be accel-erated in smaller rings and offer other advantages, but theyare produced only diffusely and they decay rapidly, makingthe detailed design of such machines difficult. In this paper,we outline a complete scheme for capture, phase manipula-tion and cooling of the muons, every component of whichhas been simulated at some level.The work in this paper was performed as part of theNFMCC collaboration [5], the recently formed MCTF [6],and Muons Inc. [7].
COLLIDER PARAMETERS
Table 1 gives parameters for muon colliders at three en-ergies. Those at 1.5 TeV correspond to a recent colliderring design [9]. The 4 TeV example is taken from the 96–study [4]. The 8 TeV is an extrapolation assuming higherbending fields and more challenging interaction point pa-rameters. All three use the same muon intensities and emit-tances, although the repetition rates for the higher energyigure 2: (Color) Transverse vs. longitudinal emittancesbefore and after each stage. The nine stages are indicatedwith the numeral 1–9.machines are reduced to control neutrino radiation.
PROPOSED SYSTEM
Figure 1 shows a schematic of the components of thesystem. Figure 2 shows a plot of the longitudinal and trans-verse emittances of the muons as they progress from pro-duction to the specified requirements for the colliders. Thesubsystems used to manipulate and cool the beams to meetthese requirements are indicated by the numerals 1–9 onthe figures.
Proton Driver
The proton driver requirements depend on the muon sur-vival estimates that will be discussed in a later section. Wefurther assume, from the neutrino factory studies, that pionproduction in the 21 best bunches, at the end of phase ro-tation, is 1.7% per proton per GeV. The resulting requiredproton bunches, for different energies, are given in Tb. 2.For efficiency in the following phase rotation, an rms bunchlength of 3 ns is required. The space charge tune shift andrequired longitudinal phase space densities are challengingat the lower proton energies, but easier at the higher ener-gies.Table 2: Proton bunch intensity for three different protonenergies E (GeV) 8 24 60N p (10 ) 21 7 2.8 Production, Phase Rotation, and Initial Cooling
The muons are generated by the decay of pions producedby proton bunches interacting in a mercury jet target [8].These pions are captured by a 20 T solenoid surroundingthe target, followed by an adiabatic lowering of the field to3 T in a decay channel. Figure 3: Phase spaces during phase rotation a) beforebunching, b) after bunching, c) after rotation.The first manipulation (
D Cooling Before Merge
The next stage (
Bunch Merge
Since collider luminosity is proportional to the square ofthe number of muons per bunch, it is important to use rela-tively few bunches with many muons per bunch. Capturingthe initial muon phase space directly into single bunchesrequires low frequency ( ≈
30 MHz) rf, and thus low gra-dients, resulting in slow initial cooling. It is thus advanta-geous to capture initially into multiple bunches at 201 MHz Figure 6: (Color) 1D Simulation of merge (
6D Cooling After Merge
After the bunch merging, the longitudinal emittance ofthe single bunch is now similar to that at the start of cool-ing. It can thus be taken through the same, or similar,cooling systems as (
Final Transverse Cooling in High FieldSolenoids
To attain the required final transverse emittance, thecooling needs stronger focusing than is achievable in the6D cooling lattices used in the earlier stages. It can be ob-tained in liquid hydrogen in strong solenoids, if the mo-mentum is allowed to fall sufficiently low. But at thelower momenta the momentum spread, and thus longitu-dinal emittance, rises relatively rapidly. However, as wesee from Fig. 2, the longitudinal emittance after (
Acceleration
Sufficiently rapid acceleration is straightforward inlinacs and recirculating linear accelerators (RLAs). Lowercost solutions might use fixed field alternating gradient(FFAG) accelerators, rapidly pulsed magnet synchrotrons,and/or hybrid SC and pulsed magnet synchrotrons[18].
Muon Losses
The estimate of muon losses is very preliminary. Thesimulations assumed Gaussian initial distributions andwere not very well matched into each lattice, leading tolarger initial losses. And no tapering of the focus param-eters as function of length was included, leading to largerlosses as the emittances approached their equilibrium. As aresult, the losses observed were larger than those deducedusing the performances in the mid range of each simula-tion. Table 3 shows the result of an attempt to estimaterealistic losses, but this remains very preliminary. Sinceit is this estimate that was used to determine the requiredproton driver specifications used above, these too must beconsidered very preliminary.Table 3: Calculated transmission tune shifts at differentstages in the system. Transmission CumulativeLinear transverse pre-cooling 0.7 0.7Pre-merge RFOFO cooling ≈ ≈ Collider Ring
For the 1.5 TeV c.m.s, a lattice has been developed [9].The parameters as given in Tb. 1 were achieved with ade-quate momentum acceptance but with dynamic transverseacceptance of only at little over σ for the specified finalemittance. We note however that since luminosity is de-pendent on the square of the bunch densities, there wouldbe little luminosity loss if the larger amplitudes were colli-mated prior to injection into the ring. pace Charge Tune Shifts For bunches with Gaussian distributions in all dimen-sions: ∆ νν cell = (cid:18) N µ ǫ ⊥ (cid:19) β ⊥ ave r µ √ πσ z β v γ where β ⊥ ave = (cid:16) L cell π ν cell (cid:17) and r µ = 1 .
35 10 − m Then at the the ends of a number of stages in this system,one obtains the tune shifts given in Tb. 4.Table 4: Calculated maximum space charge tune shifts atdifferent stages in the system. N µ β ⊥ ave σ z ǫ ⊥ p ∆ ν/ν mm mm π µ m MeV/c %( ) 6 222 27 400 100 26.1( ) 3 93 354 25 42 20.0 Note that N µ is larger at earlier cooling stages to allowfor losses. The first order shifts can be corrected by increas-ing the focus strength, but tune spreads of half the shiftscannot be corrected.Before the merge, the shifts are small because the num-bers of muons per bunch are small. The only 6D coolingstage with significant tune shift is the last ( ∆ ν/ν ≈ . which is 5 times the calculated max-imum full tune spread of ± β ⊥ s corresponding to 3 T focusing fields. The design ofthese lattices to accept such tune shifts appears possible,although we are clearly nearing the limit. ONGOING STUDIES
There is a serious question as to whether the specifiedgradients of rf cavities operating under vacuum would op-erate in the specified magnetic fields. This is under studyby NFMCC collaboration [5] and alternative designs usinghigh pressure hydrogen gas, or open cell rf with solenoidsin the irises, are being considered. The bunching and phaserotation will be optimized for the muon collider, instead ofbeing copied from a neutrino factory. Instead of the slowhelices, a planar wiggler lattice is being studied that wouldcool both muon signs simultaneously, thus greatly simpli-fying the system. The use of more, but lower field (e.g.,35 T) final cooling solenoids is also under study. Experi-ments are underway to demonstrate two of the new tech-nologies: mercury target [8], ionization cooling [19]. Fur-ther experimental studies are needed.
CONCLUSION
Although much work remains to be done, the scenariooutlined here appears to be a plausible solution to the prob-lems of capturing, manipulating, and cooling muons to thespecifications for muon colliders with useful luminositiesand energies, even up to 8 TeV in the center of mass.
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