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MUON COLLIDER DESIGN R. Palmer1'2, A. Sessler3, A. Skrinsky4, A. ToUestrup5, A. Baltz1, S. Caspi3, P. Chen2, W-H. Cheng3, Y. Cho6, D. Cline7, E. Courant1, R. Fernow1, J. Gallardo1, A. Garren3'7, H. Gordon1, M. Green3, R. Gupta1, A. Hershcovitch1, C. Johnstone5, S. Kahn1, H. Kirk1, T. Kycia1, Y. Lee1, D. Lissauer1, A. Luccio1, A. Mclnturfl3, F. Mills5, N. Mokhov5, G. Morgan1, D. Neuffer5'8, K-Y. Ng5, R. Noble5, J. Norem6, B. Norum9, K. Oide 10, Z. Parsa1, V. Polychronakos1, M. Popovic5, P. Rehak1, T. Roser1, R. Rossmanith11, R. Scanlan3, L. Schachinger3, G. Silvestrov4,1. Stumer1, D. Summers12, M. Syphers1, H. Takahashi1, Y. Torun1'13, D. Trbojevic1, W. Turner3, A. Van Ginneken5, T. Vsevolozhskaya4, R. Weggel14, E. Willen1, W. Willis1-15, D. Winn16, J. Wurtele17, Y. Zhao1
1. INTRODUCTION FERMILAB machines would also be possible (see second Ref.[4]). 1.1. Technical Considerations Hadron collider energies are limited by their The possibility of muon colliders was intro• size, and technical constraints on bending mag• duced by Skrinsky et al.[l], Neuffer[2], and others. netic fields. At very high energies it will More recently, several workshops and collabora• also become impractical to obtain the re• tion meetings have greatly increased the level of quired luminosities, which must rise as the en• discussion[3],[4]. In this paper we present scenar• ergy squared. e+e~colliders, because they un• ios for 4 TeV and 0.5 TeV colliders based on an dergo simple, single-particle interactions, can optimally designed proton source, and for a lower reach higher energy Anal states than an equiv• luminosity 0.5 TeV demonstration based on an alent hadron machine. However, extension of upgraded version of the AGS. It is assumed that e+e~ colliders to multi-TeV energies is severely a demonstration version based on upgrades of the performance-constrained by beamstrahlung, and cost-constrained because two full energy linacs 1Brookhaven National Laboratory, Upton, NY 11973- are required[6] to avoid the excessive synchrotron 5000, USA radiation that would occur in rings. Muons 2Stanford Linear Accelerator Center, Stanford, CA 94309, (2j£- = 207) have the same advantage in en• USA ergy reach as electrons, but have negligible beam• 'Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA strahlung, and can be accelerated and stored 4BINP, RU-630090 Novosibirsk, Russia in rings, making the possibility of high energy 5 Fermi National Accelerator Laboratory, Batavia, IL ft+H~ colliders attractive. There are however sev• 60510, USA eral major technical problems with /*'s: 'Argonne National Laboratory, Argonne, IL 60439-4815, USA 7 Center for Advanced Accelerators, UCLA, Los Angeles, 6 CA 90024-1547.USA • they decay with a lifetime of 2.2 x 10" *CEBAF, Newport News, VA 23606, USA s. This problem is partially overcome by 'University of Virginia, Charlottesville, VA 22901, USA rapidly increasing the energy of the muons, 10KEK, Tsukuba-shi, Ibaraki-Ken 305, Japan and thus benefitting from their relativistic UDESY, Hamburg, Germany ,2University of Mississippi, Oxford, MS 38677, USA 7 factor. At 2 TeV, for example, their life• 1SSUNY, Stony Brook, NY 11974, USA time is 0.044 s: sufficient for approximately 14 Francis Bitter National Magnet Laboratory, MIT, Cam• 1000 storage-ring collisions; bridge, MA 02139, USA "Columbia University, New York, NY 10027, USA 16Fairneld University, Fairfield, CT 06430-5195, USA • another consequence of the muon decays is ,TUC Berkeley, Berkeley, CA 94720-7300, USA that the decay products heat tlf|if£g:
DISTRIBUTION OF iniS DuAMtNT IS UNLIMITED * S 2
of the collidet ring and cieate backgrounds • It will be relatively hard to obtain both in the detector; high polarization and good luminosity in a ii+fi~ collider, whereas good polariza• • Since the muons axe created through pion tion of one beam can be obtained in an decay into a diffuse phase space, some e+e~ collider without any loss in luminosity. form of cooling is essential. Conventional One notes however that in the muon case, stochastic or synchrotron cooling is too slow moderate polarization could be obtained for to be effective before they decay. Ioniza• both beams. tion cooling, can be used, but the final emittance of the muon beams will remain • because of the decays of the muons, there larger than that possible for electrons in an will be a considerable background of pho• e+e~ collider. tons, muons and neutrons in the detec• tor. This background may be acceptable Despite these problems it appears possible that for some experiments, but it cannot be as + high energy muon colliders might have lumi• clean as in an e e~ collider. nosities comparable to or, at energies of several + 1.3. Discussion TeV, even higher than those in e e~colliders[5]. + We conclude that a muon collider has both And because the fi n~ machines would be much technical advantages and disadvantages when smaller[7], and require much lower precision (the compared with an e+e~ machine. Similarly it has final spots are about three orders of magnitude specific physics advantages and disadvantages. It larger), they may be significantly less expen• thus seems reasonable to consider fi+fi~ colliders sive. It must be remembered, however, that a + + as complementary to e e~ colliders, just as fi p~ collider remains a new and untried concept, e+e~ colliders are complementary to hadron ma• and its study has just begun; it cannot yet be chines. compared with the more mature designs for an + e e~ collider. 1.4. Overview of Components The basic components of the n+p~ collider are 1.2. Physics Considerations shown schematically in Fig.l. Tb.l shows pa• There are at least two physics advantages + rameters for the candidate designs. The normal• of a (t fi~ collider, when compared with an N + ized emittance e is defined as the rms transverse e e~ collider: phase space divided by ir. Notice that more pre• • Because of the lack of beamstrahlung, a cisely a factor of jr must appear in the dimensions ft+ti~ collider can be operated with an en• of emittance (i.e. Tmmmrad). A high intensity ergy spread of as little as 0.01 %. It is thus proton source is bunch compressed and focussed possible to use the fi+fi~ collider for preci• on a heavy metal target. The pions generated sion measurements of masses and widths, are captured by a high field solenoid and trans• that would be hard, if not impossible, with ferred to a solenoidal decay channel within a low an e+e~ collider. frequency linac. The linac serves to reduce, by phase rotation, the momentum spread of the pi• • The direct coupling of a lepton-lepton sys• ons, and of the muons into which they decay. Sub• tem to a Higgs boson has a cross section sequently, the muons are cooled by a sequence of that is proportional to the square of the ionization cooling stages. Each stage consists of mass of the lepton. As a result, the cross energy loss, acceleration, and emittance exchange section for direct Eiggs production from the by energy absorbing wedges in the presence of dis• fi+fi~ system is 40,000 times that from an persion. Once they are cooled the muons must be e+e~ system. rapidly accelerated to avoid decay. This can be done in recirculating accelerators (a la CEBAF) However, there are liabilities: or in fast pulsed synchrotrons. Collisions occur Table 1 Parameters of Collider Rings 4TeV .5TeV Demo. Beam energy TeV 2 .25 .25 Beam f 19,000 2,400 2,400 Repetition rate Hz 15 15 2.5 Muons per bunch 1012 2 4 4 Bunches of each sign 2 1 1 Normalized rms emittance eN nnm mrad 50 90 90 Bending Field T 9 9 8 Circumference Km 7 1.2 1.5 Average ring mag. field B T 6 5 4 • Effective turns before decay 900 800 750 /?* at intersection mm 3 8 8 rms beam size at I.P. fim 2.8 17 17 Luminosity cm~2s-1 1035 51033 6 1032
OVERVIEW intensity (2.5 x 1013 protons per pulse) 30 GeV proton synchrotron. The preferred cycling rate Proton Source would be 15 Hz, but for a demonstration machine using the AGS [8], the repetition rate would be limited to 2.5 Hz and to 24 GeV. For the lower Target Decay Channel energy machines, 2 final bunches are employed (one to make fi~'s and the other to make /*+'s). For the high energy collider, four are used (two ft Cooling bunches of each sign). Earlier studies had suggested that the driver could be a 10 GeV machine with the same charge
Acce leration per bunch, but a repetition rate of 30 Hz. This specification was almost identical to that stud• ied^] at ANL for a spallation neutron source. Studies at FNAL[10] have further established that such a specification is not unreasonable. But in order to reduce the cost of the muon phase ro• tation section and for minimizing the final muon
Figure 1. Schematic of a Muon Collider.
4 TeV .5 TeV Demo Proton energy (GeV) 30 30 24 in a separate high field collider storage ring with Repetition rate (Hz) 15 15 2.5 a single very low beta insertion. 13 Protons per bunch (10 ) 2.5 2.5 2.5 Bunches 4 2 2 2. MUON PRODUCTION CL/bunch (eV s) 4.5 4.5 4.5
2.1. Proton Driver rms (Tz (ns) 1 1 1 The specifications of the proton drivers are Table 2 given in Tb.2. In the examples, it is a high- Proton Driver Specifications 4
24 GeV/c protons on Hg
S. s a. 1
0.4 06 Pion Kinolc Enargr (GeV| SO 1S.0 B«am Momentum [ GttV/c )
Figure 2. ARC forward »r+ production vs proton Figure 3. v+ energy distribution for 24 GeV pro• energy and target material. tons on Hg.
longitudinal phase space, it appears now that the final proton bunch length should be 1 ns (or even dent of the initial proton energy. Fig.2 shows the less). This appears difficult to achieve at 10 GeV, forward TT+ production as a function of proton but possible at 30 GeV. energy and target material; the jr~ distributions A 1 ns rms bunch at 30 GeV with a phase space are similar. per bunch of 6TT tTt
4MARS13 ADPMJET2 -ABC
04 06 Ron Kkwlc Energy (G«V|
Figure 4. x energy distribution for 24 GeV pro• Figure 5. Schematic of a hybrid magnet solenoid tons on Hg. system for ir capture and matching.
and 7T_ for 24 GeV protons on Hg; the distribu• 2.3. Use of Both Signs tions for Cu are similar. Protons on the target produce pions of both Pions are captured from the target by a high- signs, and a solenoid will capture both, but the field (20 T, 15 cm inside diameter) hybrid mag• required subsequent phase rotation rf systems will net: superconducting on the outside, and a water have opposite effects on each. One solution is to cooled Bitter solenoid on the inside. A prelim• break the proton bunch into two, aim them on the inary design[16] (see Fig.5) has an inner Bitter same target one after the other, and adjust the rf magnet with an inside diameter of 24 cm (space phases such as to act correctly on one sign of the is allowed for a 4 cm heavy metal shield inside first bunch and on the other sign of the second. the coil) and an outside diameter of 60 cm; it pro• This is the solution assumed in the parameters of vides half (10T) of the total field, and would con• this paper. sume approximately 8 MW. The superconduct• A second possibility would be to: 1) to sepa• ing magnet has a set of three coils, all with in• rate the charges into two channels, 2) delay the side diameters of 70 cm and is designed to give particles of one charge by introducing a chikane 10 T at the target and provide the required ta• in one of the channels, 3) recombine the two chan• pered field[17] (see Fig.6) to match into the pe• nels so that the particles of the two charges are in riodic superconducting solenoidal decay channel line, but separated longitudinally (i.e. box cared). (5T and radius = 15 cm). Monte Carlo studies Both charges can now be phase rotated by a sin• indicate a yield of 0.4-0.6 muons, of each sign, gle linac with appropriate phases of if. per initial proton, captured in the decay channel. A third solution is to separate the pions of each Surprisingly, this conclusion seems relatively in• charge prior to the use of rf, and feed the beams dependent of whether the system is optimised for of each charge into different channels. energies of 50 to 500 MeV (using ARC), or 200 After the target, and prior to the use of any to 2000 MeV (using MARS). rf or cooling, the beams have very large emit- 6
to a straight solenoid is about 25 % (due to the loss of very low and very high mo• - total mentum pions), but this must be weighed • 1st coil » 2nd coil against the fact that both charge signs are « 3rd coil captured for each proton on target. * 4th coil - 5th coil • The system of bend, separate, and return • 6th coil bend will require significant length and must occur prior to the start of phase ro• tation (see below). Unfortunately, it ap• pears that the cost of the phase rotation rf is strongly dependent on keeping this distance 5 - as short as possible. On the other hand a bent solenoid would separate the remnant
O f:tiijti««f . .,. • proton beam and other charged debris exit• -0.50.0 0.5 1.0 1.5 2.0 2.5 3.0 ing the target before the rf cavities. z (m) Clearly, compromises will be involved, and more study of this concept is required.
Figure 6. Total and individual component field 2.4. Phase Rotation Linac profiles of hybrid magnet solenoid. The pions, and the muons into which they de• cay, have an energy spread from about 0-3 GeV, with an rms/mean of ss 100%, and with a peak tances and energy spread. Conventional charge at about 100 MeV. It would be difficult to handle separation using a dipole is not practical. But such a wide spread in any subsequent system. A if a solenoidal channel is bent, then the particles linac is thus introduced along the decay channel, trapped within that channel will drift[18] in a di• with frequencies and phases chosen to deacceler- rection perpendicular to the bend. With our pa• ate the fast particles and accelerate the slow ones; rameters this drift is dominated by a term (cur• i.e. to phase rotate the muon bunch. Tb.3 gives vature drift) that is linear with the forward mo• an example of parameters of such a linac. It is mentum of the particles, and has a direction that seen that the lowest frequency is 30 MHz, a low depends on the sign of the charges. If sufficient but not impossible frequency for a conventional bend is employed [15], the two charges could then structure. be separated by a septum and captured into two separate channels. When these separate channels are bent back to the same forward direction, the Linac Length Frequency Gradient momentum dispersion is separately removed in m MHz MeV/m each new channel. 1 3 60 5 Although this idea is very attractive, it has 2 29 30 4 some problems: 3 5 60 4 4 5 37 4 • If the initial beam has a radius r=0.15m, Table 3 and if the momentum range to be accepted Parameters of Phase Rotation Linacs is F = £s^ = 3, then the required height of the solenoid just prior to separation is 2(l+j7)r=1.2m. Use of a lesser height will result in particle loss. Typically, the reduc• A design of a reentrant 30 MHz cavity is shown tion in yield for a curved solenoid compared in Fig.7. Its parameters are given in Tb.4. The 7
parameters of a 30 MHz cavity are given in Tb.4. It has a diameter of approximately 2 m, only
Cavity Radius cm 101 Cavity Length cm 120 Beam Pipe Radius cm 15 Accelerating Gap cm 24 Q 18200 < AccelerationGradient > MV/m 3 Peak rf Power MW 6.3 < Power > (15 Hz) KW 18.2 Stored Energy J 609 Table 4 Parameters of 30 MHz rf Cavity
about one third of that of a conventional pill• BEAM AXIS box cavity. To keep its cost down, it would be Figure 7. 30 MHz cavity for use in phase rotation made of Al. Mtiltipactoring would probably be and early stages of cooling. suppressed by stray fields from the 5 T focusing coils, but could also be controlled by an internal coating of titanium nitride. Figs.8 and 9 show the energy vs ct at the end all too slow. Optical stochastic cooling[19], elec• of the decay channel with and without phase ro• tron cooling in a plasma discharge[20] and cool• tation. Note that the c t scales are very different: ing in a crystal lattice[21] are being studied, but the rotation both compacts the energy spread and appear very difficult. Ionization cooling[22] of limits the growth of the bunch length. muons seems relatively straightforward. After this phase rotation, a bunch can be se• 3.1. Ionization Cooling Theory lected with mean energy 150 MeV, rms bunch In ionization cooling, the beam loses both length 1.7 m, and rms momentum spread 20% transverse and longitudinal momentum as it (95%, «L = 3.2 eVs). The number of muons per passes through a material medium. Subsequently, initial proton in this selected bunch is 0.2-0.3, the longitudinal momentum can be restored by about half the total number of pions initially cap• coherent reacceleration, leaving a net loss of tured. As noted above, since the linacs cannot transverse momentum. Ionization cooling is not phase rotate both signs in the same bunch, we practical for protons and electrons because of nu• need two bunches: the phases are set to rotate + clear interactions (p's) and bremsstrahlung (e's), the (t 's of one bunch and the (t~'s of the other. but is practical for /i's because of their low nuclear Prior to cooling, the bunch is accelerated to 300 cross section and relatively low bremsstrahlung. MeV, in order to reduce the momentum spread The equation for transverse cooling (with ener• to 10 %. gies in GeV) is:
3. COOLING dEr g±(0.014)a (1) ds ds + 2 EftTtlp LR For collider intensities, the phase-space volume % must be reduced within the ft lifetime. Cooling where e„ is the normalized emittance, f3± is the by synchrotron radiation, conventional stochas• betatron function at the absorber, dEp/ds is the tic cooling and conventional electron cooling are energy loss, and LR is the radiation length of 8
QQ» • • • I I I I I I I I • 1 • I I I I I I I I I I I I I I I 0 10 20 30 40 SO ' 0 2 4 S 8 10 12 ct (m) ct (m)
Figure 8. Energy vs ct of Muons at End of Decay Figure 9. Energy vs ct of Muons at End of Decay Channel without Phase Rotation. Channel with Phase Rotation. the material. The first term in this equation is tly, giving some cooling, but not sufficient for our the coherent cooling term, and the second is the application. heating due to multiple scattering. This heating Energy spread can also be reduced by artifi• term is minimized if/3j_ is small (strong-focusing) cially increasing * dg *< by placing a transverse and LR is large (a low-Z absorber). From Eq.l variation in absorber density or thickness at a lo• we find a limit to transverse cooling, which oc• cation where position is energy dependent, i.e. curs when heating due to multiple scattering bal• where there is dispersion. The use of such wedges ances cooling due to energy loss. The limits are can reduce energy spread, but it simultaneously -2 2 en « 0.6 10 0± for Li, and c„ « 0.8 10" /3± increases transverse emittance in the direction of for Be. the dispersion. Six dimensional phase space is not The equation for energy spread (longitudinal reduced, but it does allow the exchange of emit• emittance) is: tance between the longitudinal and transverse di• rections. In the long-path-length Gaussian-distribution limit, the heating term (energy straggling) is ''(^i;>)?l,.,.B., f ) 2 given by[23] where the first term is the cooling (or heating) d(AJ? ag8 in8 2 2 due to energy loss, and the second term is the 'd7 ' =^(remec ) JV0f p heating due to straggling. x 2 (l - £) , (3) Cooling requires that did^fd') > o. But at en• 7 ergies below about 200 MeV, the energy loss func• where N0 is Avogadro's number and p is the den• tion for muons, dE^/ds, is decreasing with energy sity. Since the energy straggling increases as f2, and there is thus heating of the beam. Above and the cooling system size scales as 7, cooling at 400 MeV the energy loss function increases gen- low energies is desired. 9
3.2. Cooling System is hoped[25] that liquid lithium columns, can be We require a reduction of the normalized trans• used to raise the surface field to 20 T and improve verse emittance by almost three orders of mag• the resultant cooling. nitude (from 1 x 10-2 to 5 x 10""5m-rad), and It would be desirable, though not necessarily a reduction of the longitudinal emittance by one practicable, to economize on linac sections by order of magnitude. This cooling is obtained in forming groups of stages into recirculating loops. a series of cooling stages. In general, each stage consists of three components with matching sec• 3.3. Example tions between them: A model example has been generated that uses no lithium rods and no recirculating loops. It is 1. a FOFO lattice consisting of spaced axial assumed here that each charge is cooled in a sep• solenoids with alternating field directions arate channel, although it might be possible to and lithium hydride absorbers placed at the design a system with both charges in the same centers of the spaces between them, where channel. Individual components of the lattices the f3± 's are minimum. have been defined, but a complete lattice has not yet been specified, and no Monte Carlo study of 2. a lattice consisting of more widely separated its performance has yet been performed. Spher• alternating solenoids, and bending magnets ical aberration due to solenoid end effects, wake between them to generate dispersion. At fields, and second order rf effects have not yet the location of maximum dispersion, wedges been included. of lithium hydride are introduced to inter• The phase advance in each cell of the lattice is change longitudinal and transverse emit• made as close to x as possible in order to mini• tance. mize the /3's at the location of the absorber, but 3. a linac to restore the energy lost in the ab• it is kept somewhat less than this value so that sorbers. the phase advance per cell should never exceed x. The following effects are included: the maximum At the end of a sequence of such cooling stages, space charge transverse defocusing; a 3 cr fluctua• the transverse emittance can be reduced to about tion of momentum; a 3 6i—i—l—i—i—I—i—i—i—i—I—i—i—i—l—i—i—l—i—r 10 JH , , -n 1 1 h O 5 10 15 20 25 30 length / call lenqth stage No. Figure 10. Beta function(solid) and Phase Ad- Figure 11. ex, ^g-r and E^ [GeV] vs stage num• vance(dashed) vs z in FOFO cells. ber in the cooling sequence. tating permanent magnets interspersed with high are again exchanged, but in the opposite direc• field fixed magnets. tion: lowering the transverse and raising the lon• gitudinal. During this exchange the energy is al• 4.1. Recirculating Acceleration lowed to fall to 10 MeV in order to minimize the Tb.5 gives an example of a possible sequence 0, and thus limit the emittance dilution. of recirculating accelerators. After initial linacs, The total length of the system is 500 m, and the there are two conventional rf recirculating accel• total acceleration used is 3.3 GeV. The fraction of erators taking the muons up to 75 GeV, then two muons remaining at the end of the cooling system superconducting recirculators going up to 2000 is calculated to be 58 %. GeV. Criteria that must be considered in picking the parameters of such accelerators are: 4. ACCELERATION • The wavelengths of rf should be chosen to Following cooling and initial bunch compres• limit the loading, JJ, (it is restricted to below sion the beams must be rapidly accelerated to 4 % in this example) to avoid excessive lon• full energy (2 TeV, or 250 GeV). A sequence of gitudinal wakenelds and the resultant emit• linacs would work, but would be expensive. Con• tance growth. ventional synchrotrons cannot be used because • The wavelength should also be sufficiently the muons would decay before reaching the re• large compared to the bunch length to avoid quired energy. The conservative solution is to use second order effects (in this example: 10 a sequence of recirculating accelerators (similar to times). that used at CEBAF). A more economical solu• tion would be to use fast rise time pulsed magnets • For power efficiency, the cavity fill time in synchrotrons, or synchrotrons with rapidly ro- should be long compared to the accelera- 11 Linac #1 #2 #3 #4 initial energy GeV 0.20 1 8 75 250 final energy GeV 1- 8 75 250 2000 nloop 1 12 18 18 18 freq. MHz 100 100 400 1300 2000 linac V GV 0.80 0.58 3.72 9.72 97.20 grad 5 5 10 15 20 dp/p initial % 12 2.70 1.50 1 1 dp/p final % 2.70 1.50 1 1 0.20 crz initial mm 341 333 82.52 14.52 4.79 tion time. When conventional cavities can• giving a wall power consumption for the rf in this not satisfy this condition, superconducting ring of 108 MW. cavities are required. A recent study[26] tracked particles through a similar sequence of recirculating accelerators and • In order to minimize muon decay dur• found a dilution of longitudinal phase space of the ing acceleration (in this example 73% of order of 15% and negligible particle loss. the muons are accelerated without decay), the number of recirculations at each stage should be kept low, and the rf acceleration voltage correspondingly high. But for mini• 4.2. Pulsed Magnets mum cost, the number of recirculations ap• An alternative to recirculating accelerators for pears to be of the order of 20 - a relatively stages #2 and #3 would be to use pulsed mag• high number. In order to avoid a large num• net synchrotrons. The cross section of a pulsed ber of separate magnets, multiple aperture magnet for this purpose is shown in Fig.13. If magnets can be designed (see Fig. 12). desired, the number of recirculations could be higher in this case, and the needed rf voltage cor• Note that the linacs see two bunches of oppo• respondingly lower, but the loss of particles from site signs, passing through in opposite directions. decay would be somewhat more. The cost for a In the final accelerator in the 2 TeV case, each pulsed magnet system appears to be significantly bunch passes through the linac 18 times. The less than that of a multi-hole recirculating mag• total loading is then 4 x 18 x ij = 288%. With net system, and the power consumption is mod• this loading, assuming 60% klystron efficiencies erate for energies up to 250 GeV. Unfortunately, and reasonable cryogenic loads, one could prob• the power consumption is impractical at energies ably achieve 35% wall to beam power efficiency, above about 500 GeV. 12 Figure 13. Cross section of pulsed magnet for use in the acceleration to 250 GeV. Figure 12. A cross section of a 9 aperture sc mag• net. from 0.5 - 1 TeV, and the other from 1-2 TeV. 4.3. Pulsed and Superconducting Hybrid Each would employ 8 T superconducting fixed For the final acceleration to 2 TeV in the high magnets alternating now with pairs of counter- energy machine, the power consumed by a ring rotating permanent magnets[27]. Fields as high using only pulsed magnets would be excessive. A as 2 T should be possible in magnets of outside recirculating accelerator is still usable, but a hy• diameter less than 20 cm. brid ring with alternating pulsed warm magnets If, for example, the superconducting magnets and fixed superconducting magnets might be a are 1.5 times the lengths of the two rotating mag• cheaper alternative. nets, then as the rotating magnets turn, the av• For instance: A sequence of two such hybrid g erage field will swing from ' ' 3 g ~ ' = 2.3 T accelerators could be used. One from 0.25-1 TeV, (1-5 2+2) and the other from 1-2 TeV. Each would employ to *3t = 4.6; varying by a factor of 2. 10 T superconducting fixed magnets alternating For the final stage (1 to 2 TeV): with accelera• with pulsed warm magnets whose fields would tion in 20 turns, and a ring, circumference of 20 swing from -1.5 T to + 1.5 T. The power con• km, the acceleration time would be 1.3 msec, re• sumption of such a system would be large, but quiring a rotation rate of about 15,000 rpm. For the capital cost probably far less than that of a the penultimate stage (0.5 to 1 TeV): again with recirculating accelerator. acceleration in 20 turns, and a ring circumfer• ence of 10 km, the acceleration time would be 0.7 4.4. Rotating and Superconducting Hy• msec, requiring a rotation rate of about 30,000 brid rpm. If 30,000 rpm is too high, 40 turn accelera• Pulsed magnets would be used up to the high• tion could be used in this stage and the rotation est possible energy; say 0.5 TeV. A sequence of rate kept at 15,000 rpm. This should be practical, two hybrid accelerators could then be used: one and the power consumption would be negligible. 13 However, many technical questions remain to be Cos Theta Oipole 75 answered. 5. COLLIDER STORAGE RING 50 After acceleration, the /*+ and pT bunches are 25 - injected into a separate storage ring. The high• est possible average bending field is desirable, to maximize the number of revolutions before de• cay, and thus maximize the luminosity. Collisions would occur in one, or perhaps two, very low-/?* -25- interaction areas. Parameters of the ring were given earlier in Tb.l. -50 5.1. Bending Magnet Design The magnet design is complicated by the fact 7S' ' ' ' I ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ~5 -50 -25 0 25 50 75 that the fi's decay within the rings (fi~ —• x tun) e"vlv^), producing electrons whose mean en• ergy is approximately 0.35 that of the muons. These electrons travel toward the inside of the ring dipoles, radiating a fraction of their energy Figure 14. Cos Theta Arc Bending Magnet as synchrotron radiation towards the outside of the ring, and depositing the rest on the inside. The total average power deposited, in the ring, could be either superconducting or warm, as dic• in the 4 TeV machine is 13 MW, yet the max• tated by cost considerations. If an elliptical vac• imum power that can reasonably be taken from uum chamber were used, and the poles were at 1 the magnet coils at 4 K is only of the order of cm radius, then gradients of 150 T/m should be 40 KW. The power deposited could be reduced if possible. the beams are kicked out of the ring prior to their their complete decay. Since the luminosity goes 5.1.2. 'C Magnets as the square of the number of muons, a signifi• An alternative is to use 'C magnets facing in• cant power reduction can be obtained for a small ward, with a broad vacuum pipe extending out luminosity loss. But still the power level is high. of the gaps (see Fig. 16). The decay electrons will Two promising approaches are discussed below. spiral inward, out of the gap of the magnet, and can be absorbed in a separate warm dump. Some 5.1.1. Large Cosine-Theta Magnet The beam is surrounded by a thick warm shield, located inside a large aperture conven• tional cosine-theta magnet (see Fig. 14). Fig. 15 2TeV 0.5 TeV Demo shows the attenuation of the heating produced as Unshielded P (MW) 13 1.6 .26 a function of the thickness of a warm tungsten Liner inside rad (cm) 2 2 2 liner[28]. If conventional superconductor is used, Liner thickness (cm) 6 4 2 then the thicknesses required in the three cases Coil inside rad (cm) 9 7 5 would be as given in Tb.6. If high Tc super• Attenuation 400 80 12 conductors could be used, then these thicknesses P leakage (KW) 32 20 20 could probably be halved. Pwa„for4Jir(MW) 26 16 16 If this approach were taken, then the Table 6 quadrupoles would best use warm iron poles Thickness of Shielding for Cos Theta Collider placed as close to the beam as practical. The coils Magnets. 14 5.1.3. Discussion The 'C magnet designs would require about 2/3 of the superconductor needed for the cos theta magnets, but their overall size would not be much smaller. The simple pancake coils of the 'C magnets could be easier to wind than the cos theta type, but the support of the coils would be a new challenge. It is not yet known whether the thermal load would be greater or less in a 'C magnet design. Clearly, more study is needed to determine which approach is best. 12 3 4 Radial thickness of Tungsten icm] Figure 15. Energy attenuation vs the thickness of a tungsten liner. of the synchrotron radiation will still strike the inner wall of the vacuum chamber and a more limited dump is required there. With NbsSn conductors, there appear no theo• retical problems in achieving 10 T fields with very Figure 16. 'C Arc Bending Magnet. good field quality (dB/B < 10-5 for x < 1cm). The problems would be in supporting the coils . ' 1 " and maintaining the required position accuracy. ..I. . ' " 1 ' 1 - If this approach were chosen, then the quadrupoles could also be made as 'C magnets . 1 ... " (see Fig. 17). In such magnets there would be two 20 pancake coils above and two below the vacuum chamber, with the current directions, in the two ','ff f ' i11 \« 1 1 coils, opposite. This arrangement would generate a downward field to the left of the beam and an upward field to the right with a linear gradient, ) i.e. quadrupole field, in the center (see Fig. 18) Again there appear no theoretical problems in . . 1 . 1 • defining coil blocks that achieve good field qual• -50 0 50 ity, and gradients of about 230 T/m seem practi• « [an) cal with NbaSn conductors. Again, the problems would be in supporting the coils and maintaining the required conductor position accuracy. Figure 17. 'C Arc Quadrupole. 15 5.2. Lattice Design isochronous design. It has, however, been pointed 5.2.1. Arcs out [30] that if chromaticity is corrected in the In a conventional 2 TeV superconducting ring ring, then amplitude dependent anisochronisity is the tune would be of the order of 200 and the automatically removed. momentum compaction a around* 2 x 10~3. In this case, in order to maintain a bunch with rms 5.2.2. Low /3 Insertion length 3 mm, 45 GeV of S-band rf would be re• In order to obtain the desired luminosity we re• quired. This would be excessive. It is thus pro• quire a very low beta at the intersection point: posed to use an approximately isochronous lattice P* = 3 mm for 4 TeV, 0* - 8 mm for the .5 of the dispersion wave type[29]. Ideally one would 7 TeV design. A possible final focusing quadru• like an a of the order of 10~ . In this case no rf plet design is shown in Fig. 19. The parameters would be needed to maintain the bunch and the of the quadrupoles for this quadruplet are given machine would behave more like a linear beam in Tb.7. The maximum fields at 4 sigma have transport. In practice it appears easy to set the been assumed to be 6.4 T. This would allow a ra• zero'th order slip factor TJO to zero, but if noth• diation shield of the order of 5 cm, while keeping ing is done, there is a relatively large first order the peak fields at the conductors less than 10 T, slip factor -q\ yielding a maximum a of the order -5 which should be possible using NbaSn conductor. of 10 . The use of sextupoles appears able to correct this tji yielding a maximum a of the or• With these elements, the maximum beta's in der of 10-6. With octupoles it may be possible both x and y are of the order of 400 km in to correct 7j2i but this remains to be seen. the 4 TeV case, and 14 km in the 0.5 TeV ma• chine. The chromaticities (l/4ir f /3dk) are ap• It had been feared that amplitude depen• proximately 6000 for the 4 TeV case, and 600 for dent anisochronisity generated in the insertion the .5 TeV machine. Such chromaticities are too would cause bunch growth in an otherwise purely large to correct within the rest of a conventional ring and therefore require local correctional]. A preliminary model design[32] of local chro• i i i i I i i i i I i i i i I i i i i I i i i i I i i i r matic correction has been generated for the 4 TeV 10- ^ case, and has been incorporated into a dispersion wave lattice[33]. Fig.20 shows the tune shift as a function of momentum. It is seen that this design has a momentum acceptance of ±0.35 %. The sec• ond order amplitude dependent tune shifts shown in Fig.21 are less than 0.03 at one sigma (0.27 at P \ / \ 3 sigma in amplitude), which may be too large, of \ / V even for only 1000 turns. In addition, this de• sign used some bending fields that are unrealis• tic. It is expected that these limitations will soon be overcome, and that more sophisticated de• signs^] should achieve a momentum acceptance of ±0.6 % for use with a clipped rms momentum -10 - ^ spread of 0.2 %. i »< i I i i i i I • i i i I i i i i I i i i i I i i i i -10 -5 0 5 10 % ICIDJ 5.3. Instabilities Studies[35] of the resistive wall impedance instabilities indicate that the required muon Figure 18. Vertical field as function of horizontal bunches (eg for 2 TeV: 4MeV 0.5 MeV field (T) L(m) R(cm) L(m) R(cm) drift 6.5 1.99 focus 6 6.43 6 1.969 5.625 drift 4.0 1.2247 -. defocus 6.4 13.144 12 4.025 11.25 drift 4.0 1.2247 focus 6.4 11.458 12 3.508 11.25 drift 4.0 1.2247 defocus 6.348 4.575 10 1.400 9.375 drift 80 24.48 Table 7 Final Focus Quadrupoles; L and R are the length and the radius respectively. Q.Q4i i i i i i i i i i 1 i i i i i i i i i t t i i i i i i i t Tune Q vs <5p/p I I I I I I L 0.03- 0.00 T 1 i 1 1 1 r 25 50 75 100 125 -3—2-10 1 2 3 4 5 length [ml 1OO0 <5p/p Figure 19. rms radius of the beam at the last four Figure 20. The tune shift as a function of Ap/p. quadrupoles of the final focus. In any case, the rf requirements to maintain such minum beam pipe of radius b = 2.5 cm, the resis• bunches would be excessive. tive wall effect will cause the tail amplitude of the If one can obtain momentum-compaction fac• bunch to double in about 500 turns. For a broad• tor a < 10-7, then the synchrotron oscillation band impedance of Q — 1 and Z\\/n = 1 Ohm, period is longer than the effective storage time, the doubling time in the same beam pipe is only and the beam dynamics in the collider behave about 130 turns; which is clearly unacceptable. like that in a linear beam transport[36][37]. In But both these instabilities can easily be stabi• this case, beam breakup instabilities are the most lized using BNS[38] damping. For instance, to important collective effects. Even with an alu• stabilize the resistive wall instability, the required 17 8 10- dQ/de vs 6p/p parameters. The impedance of the ring is domi• 0.6 -H-1 1 ' ' ' ' nated by the rf cavities, and the microwave insta• bility is well beyond threshold. Two approaches are being considered to control these instabilities: 1) BNS damping applied by rf quadrupoles as suggested by Chao[39]; and 2) applying an oscil• lating perturbation on the chromaticity[40]. When the ring is nearly isochronous, a longitu• dinal head-tail (LHT) instability may occur be• cause the nonlinear slip factor T}\ becomes more important than the first order rjo [3]. The growth time for the rf impedance when t\ ~ 10-5 is about 0.1256rjo/'7i SI where b is the pipe radius in cm. This would be longer than the storage time of ~ 41 ms if i}\ ~ 7jo- However, if rj\ ~ Tfo/6, with 6 ~ 10~3, then the growth time is about 0.1256 ms, which is much shorter than the stor• age time. More study is needed. Figure 21. Amplitude dependent tune shift -j*- as 6. COLLIDER PERFORMANCE a functions of Ap/p. 6.1. Luminosity vs Energy and Momentum Spread The bunch populations decay exponentially, tune spread, calculated[36] using the two particle yielding an integrated luminosity equal to its ini• model approximation, is (for Al pipe) tial value multiplied by an effective number of turns neffective = 150 B, where B is the mean 4 A f 1.5810- 6= 1.0 cm bending field in T. 5 —— =< 1.0710- 6 =2.5 cm (4) The luminosity is given by: Vfi \ 1.26 10-6 b= 5.0 cm c H A D But this application of the BNS damping to - i^ < ' > « a quasi-isochronous ring, where there are other head-tail instabilities due to the chromaticities £ where A = o-2//3*, and TJI, needs more careful study. If it is not possible to obtain an a less than -7 f limated to ± 4 x o-g0 (where agB is the AE/E rms divergence of the beam) by a cone lead• C = 2C0 (8) (AE/E)0' ing down towards the vertex. 2) The detec• tor could not see any surface directly illu• There may, however, be beam-beam tune shift minated by these initial electrons, whether emittance growth problems in this case. seen in the forward or backward (albedo) 6.2. Detector Background directions. 3) The detector could not see any surface that is illuminated by secondary There will be backgrounds from the decay of electrons if the secondary scattering angle is muons in the ring, from muon halo around the forward. 4) The minimum distance through beam, and from the interactions themselves. the collimator from the detector to any pri• 6.2.1. Muon Decay Background marily illuminated surface was more than A first Monte Carlo study[44] of the muon 100 mm, and from any secondarily illumi• decay background was done with the MARS95 nated surface, 30 mm. code[13], based on a preliminary insertion lattice. A tungsten shielding nose was introduced, ex• • It was assumed that a collimator placed at tending to within 15 cm of the intersection point. a focus 130 m from the intersection point It was found that: would be able to effectively shield all syn• chrotron photons from the bending magnets • a large part of the electromagnetic back• beyond that point. The rms beam size at ground came from synchrotron radiation, this focus is only 10 /*m so a very effective from the bending magnets in the chromatic collimation should be possible. correction section. This study indicated that the dominant back• • As many as 500 hits per cm2 were expected ground was no longer from synchrotron photons, in a vertex detector, falling off to the order but from (i decay electrons. The average momen• of 2 hits per cm2 in an outer tracker. tum of these photons was only 1 MeV. Tb.8 gives 19 only is its density lower, but the small deposi• tions of ionization from low energy photons and neutrons could not be mistaken for real tracks. This study also found a relatively modest flux of muons from /x pair production in electromag• netic showers: about 50 such tracks pass through the detector per bunch crossing. The general conclusion of the two studies are not inconsistent. The background, though seri• ous, is not apparently impossible. Further reduc• tions are expected as the shielding is optimized, and, as mentioned above, it should be possible to design detectors that are less sensitive to the neutrons and photons present. 6.2.2. Muon Halo Background There would be a very serious background from the presence of even a very small halo of near full energy muons in the circulating beam. The beam Figure 22. Schematic of the detector nose. will need careful preparation before injection into the collider, and a collimation system will have to be designed to be located on the opposite side of the ring from the detector. Detector vertex tracker Radius 5 cm 1 m b b 6.2.3. Electron Pair Background Number of photons 50 10 15 10 + Number of hits 150,000 15,000 In e e~machines there is a significant problem Detector Area 863 cm2 34 m2 from beamstrahlung photons (synchrotron radia• Pixel size 20 x 20 /tm 1 mm x 1 cm tion from beam particles in the coherent field of Sensitivity 0.3 % 0.1 % the oncoming bunch), and an additional problem Occupancy .07 % 0.4% from pair production by these photons. With muons, there is negligible beamstrahlung, Table 8 and thus negligible pair production from them. P. Detector Backgrounds from ft decay Chen[48] has further shown that beamstrahlung of electrons from the nearby decay of muons does not pose a problem. the total numbers of photons, the total number There is, however, significant incoherent (i.e. of hits, possible pixel sizes, and the hits per pixel, H+(i~~> e+e~) pair production in the 4 TeV Col• for a) a vertex detector placed at a 5 cm radius, lider case. The cross section is estimated to be and b) a gas detector placed at a 1 m radius. In 10mb[49], which would give rise to a background all cases the numbers are given per bunch cross• of sa 3104 electron pairs per bunch crossing. Most ing. The sensitivities given here are for a silicon of these, approximately 90 %, will be trapped in• strip detector (.3%) at the small radius, and a side the tungsten nose cone, but those with en• pad readout gas chamber (.1%) at the larger ra• ergy between 30 and 100 MeV will enter the de• dius. Both sensitivities could be reduced. Silicon tector region. strip detectors could be developed with less thick• There remains some question about the coher• ness, and a time projection chamber (TPC) could ent pair production generated by the virtual pho• be used at the larger radii. The use of the TPC tons interacting with the coherent electromag• would be particularly advantageous because, not netic fields of the entire oncoming bunch. A sim- 20 pie Weizsacker-Williams calculation[50] yields a If higher polarization is required some selection background so disastrous that it would consume of muons from forward (cos 8d —+ 1) is required. the entire beam at a rate comparable with its de• This could be done by selecting pions within a cay. However, I. Ginzburg[51] and others have narrow energy range and then selecting only those argued that the integration must be cut off due muons with energy close to that of the selected to the finite size of the final electrons. If this is pions. But such a procedure would collect a very true, then the background becomes negligible. A small fraction of all possible muons and would more detailed study of this problem is now un• yield a very small luminosity. Instead we wish, derway [52]. as in the unpolarized case, to capture pions over If the coherent pair production problem is con• a wide energy range, allow them to decay, and to firmed, then there are two possible solutions: use rf to phase rotate the resulting distribution. 1) one could design a two ring, four beam ma• Consider the distributions in velocity vs time at chine (a fi+ and a fi~ bunch coming from each the end of a decay channel. If the source bunch side of the collision region, at the same time). of protons is very short and if the pions were gen• In this case the coherent electromagnetic fields at erated forward, then the pions, if they did not the intersection are canceled and the pair produc• decay, would all be found on a single curved line. tion becomes negligible. Muons from forward decays would have gained 2) Plasma could be introduced at the inter• velocity and would lie above that line. Muons section point to cancel the beam electromagnetic from backward decay would have lost velocity and fields[53]. would fall below the line. The real distribution would be diluted by the width of the proton bunch 6.3. Polarization and the finite pion angles. In order to reduce the 6.3.1. Polarized Muon Production latter, it is found desirable to lower the solenoid The generation of polarized muons has not yet field in the decay channel from 5 to 3 Tesla. When received enough attention and the specifications this is done one obtains the distribution shown in and components described above have not been Fig.23. designed or optimized for polarization. Neverthe• After phase rotation with rf the correlation is less, simple manipulations of parameters and/or preserved: see Fig.24. the addition of simple components would allow If a selection is made on the minimum energy some polarization with relatively modest loss of of the muons, then net polarization is obtained. luminosity. The tighter the cut on energy, the higher the po• In the center of mass of a decaying pion, the larization, but the less the fraction Fp of muons out coming muon is fully polarized (-1 for fi+ and that are selected. Fig.25 gives the results of a +1 for (JL~ ). In the lab system the polarization de- Monte Carlo study. pends[42] on the decay angle Bd and initial pion The loss, about 30%, from the use of the lower energy. For pion kinetic energy larger than the solenoid field, is included in the fractions Fp plot• pion mass, the dependence on pion energy be• ted. comes negligible and the polarization is given ap• proximately by: 6.3.2. Polarization Preservation A recent paper[43] has discussed this problem 2 in some detail. During the ionization cooling pro• P,,- ss cos 9d + 0.28(1 - cos Bd) (9) cess the muons lose energy in material and have The average value of this is about 0.19. At lower a spin flip probability V, where pion energies the polarization is higher, and has a value of the order of 0.5 at a kinetic energy of 10 MeV. If nothing is done, the polarization of the muons captured and phase rotated by the where (3V is the muon velocity divided by c, and proposed system is approximately 20 %. dE/E is the fractional loss of energy due to ion- 21 0.5 0.20 ! 1 I I I I 1 I I I I I I I i i»#ri i-r i I-, !... T._..y-T— 11.111 • •.*$** + + + --•f 0.4 7 + .+ + ,H+ 0.15 *AX • >4 * -.4 • 0.3 ' "-*&••• • > 0.10 .*•?*" (9 + • •••*&>* -•+ •* 0.2- '-=*• thA * * • • iJvt +• + 0.05 0.1 11 ) * 0.0 i t.i x 1 J._I, J i 1 i~i t i J i t ) _i_l 1 J....L-J- 0.00 l l I l l ' ' ' • I • I 15 20 25 30 7 Ct («) c tin) Figure 23. Energy vs c time of muons at end of Figure 24. Energy vs c time of muons at end of decay channel without phase rotation; polariza• decay channel with phase rotation; polarization tion P> g, —i < P < |, and P< ^ are marked p> h ir < p < h and p< ^ are marked bv by the symbols '+', '.' and '-' respectively. the symbols '+','•' and '-' respectively. • Bending can be performed with vertical ization loss. In our case the integrated energy loss spin, and the spin rotated into the longitu• is approximately 3 GeV and the typical energy is dinal direction only for the interaction re• ISO MeV, so the integrated spin flip probability gion. The design of such spin rotator ap• is close to 10%. The change in polarization dP/P pears relatively straightforward. The exam• is twice the spin flip probability, so the reduction ple given in the above reference would only in polarization is approximately 20 %. add 120 m of additional arc length, but no During circulation in any ring, the muon spins, design has yet been incorporated into the if initially longitudinal, will precess by (g-2)/2 7 lattice. turns per revolution in the ring; where (g-2)/2 -3 is 1.166 10 . A given energy spread d-y/j will • The alternative is to install a 120 m 10 introduce variations in these precessions and di• T solenoid (Siberian Snake) at a location lution of the polarization. But if the particles exactly opposite to the intersection point. remain in the ring for an exact integer of syn• Such a solenoid reverses the sign of the hor• chrotron oscillations then their individual average izontal polarization and generates a cancel• 7's will be the same and no dilution will occur. It lation of the precession in the two halves of appears reasonable to use this "synchrotron spin the ring. matching" [43] to avoid dilution during accelera• tion. Provision must also be made to allow changes In the collider, however, the synchrotron fre• in the relative spins of the two opposing bunches. quency will probably be too slow to use "syn• This could be done, prior to acceleration, by chrotron spin matching" so one of two methods switching one of the two beams into one or the must be used. other of two alternative injection lines. 22 1.0 larization. If, for instance, the driver repetition rate were increased from 15 to 30 Hz, the fractions Fft set at 0.5, and the number of bunches reduced to one, then the full luminosity of 1035 (cm~2s~1) wonld be maintained with polarization of both beams of 35%. 0.6 The numbers given in this section are pre• liminary. Optimization of the systems may im• prove the polarizations obtained, but other dilu• 0.4 tion mechanisms may reduce them. 7. CONCLUSION 0.2 j- polarization at source (solid line) -s polarization after ccolinq (dashed line) • Considerable progress has been made on a scenario for a 2 + 2 TeV, high luminosity J_ _J 1 ' I ' ' • •4 01 0.02 0.05 040 0.20 0.50 1.00 collider. Much work remains to be done, LunanosWf loss f»«or F, but no obvious show stopper has yet been found. • The two areas that could present serious Figure 25. Polarization vs the fraction -Fp of problems are: 1) unforseen losses during the muons accepted; solid line is the polarization at 25 stages of cooling (a 3% loss per stage source; dashed line after cooling would be very serious); and 2) the excessive detector background from muon beam halo. • Many technical components require devel• 6.3.3. Luminosity loss with polarization opment: a large high field solenoid for cap• If both muon beams are polarized, then natu• ture, low frequency rf linacs, multi-beam rally the luminosity would drop as the square of pulsed and/or rotating magnets for acceler• the fraction Fp of selected fi's shown in Fig.25, ation, warm bore shielding inside high field but the loss need not be so great. In the un- dipoles for the collider, muon collimators polarized case of the 5 TeV collider, there were and background shields, etc. but: two bunches of each sign. If the Fp chosen for polarization is less than 0.5 then this number of • None of the required components may be bunches could be reduced to one, without intro• described as exotic, and their specifications ducing excessive beam-beam tune shift. A factor are not far beyond what has been demon• of two in luminosity is then restored. If, for in• strated. stance, the Fp is taken as 0.5 for both signs, and • If the components can be developed and if the number of bunches is reduced to one of each the problems overcome, then a muon-muon sign, then the luminosity is reduced by a factor collider should be a viable tool for the study of only 0.5 and not 0.25. of high energy phenomena, complementary One also notes that the luminosity could be to e+e~and hadron colliders. maintained at the full unpolarized value if the proton source intensity could be increased. Such 8. ACKNOWLEDGMENTS an increase in proton source intensity in the un• polarized case would be impractical because of We acknowledge important contributions from the resultant excessive high energy muon beam our colleagues, especially W. Barletta, A. Chao, power, but this restriction does not apply if the J. Irwin, H. Padamsee, C. Pellegrini and A. Rug- increase is used to offset losses in generating po• giero. 23 This research was supported by the U.S. De• Tigner, in Advanced Accelerator Concepts, partment of Energy under Contract No. DE- Port Jefferson, NY 1992, AIP Conf. Proc. ACO2-76-CH00016 and DE-AC03-76SF00515. 279,1(1993). 7. R. B. Palmer et al., Monte Carlo Simula• tions of Muon Production, Physics Potential REFERENCES & Development offi+fi' Colliders 2nd Work• 1. E. A. Perevedentsev and A. N. Skrinsky, Proc. shop, Sausalito, CA, Ed. D. Cline, AIP Press, 12th Int. Conf. on High Energy Accelerators, Woodbury, New York, pp. 108 (1995). F. T. Cole and R. Donaldson, Eds., (1983) 8. T. Roser, AGS Performance and Upgrades: A 485; A. N. Skrinsky and V.V. Parkhomchuk, Possible Proton Driver for a Muon Collider, Sov. J. of Nucl. Physics 12, (1981) 3; Early Proceedings of the 9th Advanced ICFA Beam Concepts for M+M~ Colliders and High En• Dynamics Workshop, Ed. J. C. Gallardo, AIP ergy n Storage Rings, Physics Potential & Press, to be published. Development of fi+n~ Colliders. 2nd Work• 9. Y. Cho, et al., A 10-GeV, 5-MeV Proton shop, Sausalito, CA, Ed. D. Cline, AIP Press, Source for a Pulsed Spallation Source, Proc. Woodbury, New York, (1995). of the 13th Meeting of the Int'l Collaboration 2. D. Neuffer, Colliding Muon Beams at 90 on Advanced Neutron Sources, PSI Villigen, GeV, Fermilab Physics Note FN-319 (1979), Oct. 11-14 (1995); Y. Cho, et al., A 10-GeV, unpublished; D. Neuffer, Particle Accelera• S-Me V Proton Source for a Muon-Muon Col• tors, 14, (1983) 75; D. Neuffer, Proc. 12th lider, Proceedings of the 9th Advanced ICFA Int. Conf. on High Energy Accelerators, F. T. Beam Dynamics Workshop, Ed. J. C. Gal• Cole and R. Donaldson, Eds., 481 (1983). lardo, AIP Press, to be published. 3. Proceedings of the Mini-Workshop on /u+A*_ 10. F. Mills, et al., presentation at the 9th Ad• Colliders: Particle Physics and Design, Napa vanced ICFA Beam Dynamics Workshop, un• CA, Nucl Inst, and Meth., A350 (1994) ; published; see also second reference in [4j. Proceedings of the Muon Collider Workshop, 11. T, Roser and J. Norem, private communica• February 22,1993, Los Alamos National Lab• tion. oratory Report LA- UR-93-866 (1993) and 12. D. Kahana, et al., Proceedings of Heavy Ion Physics Potential & Development of /J+/J~ Physics at the AGS-HIPAGS '93, Ed. G. S. Colliders 2nd Workshop, Sausalito, CA, Ed. Stephans, S. G. Steadman and W. E. Ke- D. Cline, AIP Press, Woodbury, New York, hoe (1993); D. Kahana and Y. Torun, Anal• (1995). ysis of Pion Production Data from E-802 at 4. Transparencies at the 2 + 2 TeV (t+fi~ Col• 14.6 GeV/c using ARC, BNL Report # 61983 lider Collaboration Meeting, Feb 6-8, 1995, (1995). BNL, compiled by Juan C. Gallardo; trans• 13. N. V. Mokhov, The MARS Code System parencies at the 2 -f- 2 TeV (i+ft~ Col• User's Guide, version 13(95), Fermilab-FN- lider Collaboration Meeting, July 11-13, 1995, 628 (1995). FERMILAB, compiled by Robert Noble; Pro• 14. J. Ranft, DPMJET Code System (1995). ceedings of the 9th Advanced ICFA Beam Dy• 15. N. Mokhov, R. Noble and A. Van Ginneken, namics Workshop, Ed. J. C. Gallardo, AIP Target and Collection Optimization for Muon Press, to be published. Colliders, Proceedings of the 9th Advanced 5. Overall Parameters and Construction Tech• ICFA Beam Dynamics Workshop, Ed. J. C. niques Working Group report, Proceedings of Gallardo, AIP Press, to be published. the Fifth International Workshop on Next- 16. R. Weggel, private communication; Physics Generation Linear Colliders, Oct 13-21,1993, Today, pp. 21-22, Dec. (1994). Slac-436, pp.428. 17. R. Chehab, J. Math. Phys. 5, (1978) 19. 6. D. V. Neuffer and R. B. Palmer, Proc. Euro• 18. F. Chen, Introduction to Plasma Physics, pean Particle Ace. Conf., London (1994); M. Plenum, New York, pp. 23-26 (9174); 24 T. Tajima, Computational Plasma Physics: 29. S.Y. Lee, K.-Y. Ng and D. Trbojevic, FNAL With Applications to Fusion and Astro• Report FN595 (1992); Phys. Rev. E48, physics, Addison-Wesley Publishing Co., New (1993) 3040; D. Trbojevic, et al., Design of York, pp. 281-282 (1989). the Muon Collider Isochronous Storage Ring 19. A. A. Mikhailichenko and M. S. Zolotorev, Lattice, Micro-Bunches Workshop, BNL Oct. Phys. Rev. Lett. 71, (1993) 4146; M. S. Zolo• (1995), to be published. torev and A. A. Zholents, SLAC-PUB-6476 30. K. Oide, private communication. (1994). 31. K. L. Brown and J. Spencer, SLAC-PUB- 20. A. Hershcovitch, Brookhaven National Re• 2678 (1981) presented at the Particle Accel• port AGS/AD/Tech. Note No. 413 (1995). erator Conf., Washington, (1981) and K.L. 21. Z. Huang, P. Chen and R. Ruth, SLAC-PUB- Brown, SLAC-PUB-4811 (1988), Proc. Capri 6745, Proc. Workshop on Advanced Accelera• Workshop, June 1988 and J.J. Murray, K. L. tor Concepts, Lake Geneva, WI, June (1994); Brown and T.H. Fieguth, Particle Accelerator P. Sandler, A. Bogacz and D. Cline, Muon Conf., Washington, 1987; Bruce Dunham and Cooling and Acceleration Experiment Using Olivier Napoly, FFADA, Final Focus. Auto• Muon Sources at Triumf, Physics Potential matic Design and Analysis, CERN Report & Development offi+fi~ Colliders 2nd Work• CLIC Note 222, (1994); Olivier Napoly, it shop, Sausalito, CA, Ed. D. Cline, AIP Press, CLIC Final Focus System: Upgraded Version Woodbury, New York, pp. 146 (1995). with Increased Bandwidth ans Error Analy• 22. Initial speculations on ionization cooling sis, CERN Report CLIC Note 227, (1994). have been variously attributed to G. O'Neill 32. J. C. Gallardo and R. B. Palmer, Final Focus and/or G. Budker see D. Neuffer in [2]; D. System for a Muon Collider: A Test Model, Neuffer, in Advanced Accelerator Concepts, BNL #, CAP 138-MUON-96R (1996), this AIP Conf. Proc. 156, 201 (1987); see also [1]. proceedings. 23. U. Fano, Ann. Rev. Nucl. Sci. 13, 1 (1963). 33. A. Garren, et al., Design of the Muon Collider 24. G. Silvestrov, Proceedings of the Muon Col• Lattice: Present Status, this proceedings. lider Workshop, February 22, 1993, Los 34. K. Oide, SLAC-PUB-4953 (1989); J. Ir• Alamos National Laboratory Report LA-UR- win, SLAC-PUB-6197 and LBL-33276, Parti• 93-866 (1993); B. Bayanov, J. Petrov, G. cle Accelerator Conf.,Washington, DC, May Silvestrov, J. MacLachlan, and G. Nicholls, (1993); R. Brinkmann, Optimization of a Fi• Nucl. Inst, and Meth. 190, (1981) 9; Colin D. nal Focus System for Large Momentum Band• Johnson, Hyperfine Interactions, 44 (1988) width, DESY-M-90/14 (1990). 21; M. D. Church and J. P. Marriner, Annu. 35. M. Syphers, private communication; K.- Rev. Nucl. Sci. 43 (1993) 253. Y. Ng, Beam Stability Issues in a Quasi- 25. G. Silvestrov, Lithium Lenses for Muon Col• Isochronous Muon Collider, Proceedings of liders, Proceedings of the 9th Advanced ICFA the 9th Advanced ICFA Beam Dynamics Beam Dynamics Workshop, Ed. J. C. Gal- Workshop, Ed. J. C. Gallardo, AIP Press, to lardo, AIP Press, to be published. be published. 26. D. Neuffer, Acceleration to Collisions for the 36. K.Y. Ng, Beam Stability Issues in a Quasi- H+ft~ Collider, Proceedings of the 9th Ad• Isochronous Muon Collider, Proceedings of vanced ICFA Beam Dynamics Workshop, Ed. the 9th Advanced ICFA Beam Dynamics J. C. Gallardo, AIP Press, to be published. Workshop, Ed. J. C. Gallardo, AIP Press, to 27. D. Summers, presentation at the 9th Ad• be published. vanced ICFA Beam Dynamics Workshop, un• 37. W.-H. Cheng, A.M. Sessler, and J.S. Wurtele, published. Studies of Collective Instabilities, in Muon 28. I. Stumer, presentation at the BNL-LBL- Collider Rings, Proceedings of the 9th Ad• FNAL Collaboration Meeting, Feb 1996, vanced ICFA Beam Dynamics Workshop, Ed. BNL, unpublished. J. C. Gallardo, AIP Press, to be published. 25 38. V. Balakin, A. Novokhatski and V. Smirnov, 53. G. V. Stupakov and P. Chen, Plasma Sup• Proc. 12th Int. Conf. on High Energy Accel., pression of Beam-Beam Interaction in Circu• Batavia, IL, 1983, ed. F.T. Cole, Batavia: lar Colliders, SLAC Report: SLAC-PUB-95- Fermi Natl. Accel. Lab. (1983), p. 119. 7084 (1995) 39. A. Chao, Physics of Collective Beam Instabil- •* Hies in High Energy Accelerators, John Wiley & Sons, Inc, New York (1993). 40. W.-H. Cheng, private communication. 41. P. Chen and K. Yokoya, Phys. Rev. D38 987 (1988); P. Chen., SLAC-PUB-4823 (1987); Proc. Part. Accel. School, Batavia, IL, 1987; AIP Conf. Proc. 184: 633 (1987). 42. K. Assamagan, et al., Phys Lett. B335, 231 (1994); E. P. Wigner, Ann. Math. 40, 194 (1939) and Rev. Mod. Phys., 29, 255 (1957). 43. B. Norum and R. Rossmanith, Polarized Beams in a Muon Collider, this proceedings. 44. G. W. Foster and N. V. Mokhov, Back• grounds and Detector Performance at £ -j- 2 TeV n+p~ Collider, Physics Potential & Development of n+fi~ Colliders 2nd Work• shop, Sausalito, CA, Ed. D. Cline, AIP Press, Woodbury, New York, pp. 178 (1995). 45. I. Stumer, private communication and presen• tation at the BNL-LBL-FNAL Collaboration Meeting, Feb. 1996, unpublished. 46. Geant Manual, Cern Program Library V. 3.21, Geneva, Switzerland, 1993. 47. N. V. Mokhov and S. I. Striganov, Simula• tion of Background in Detectors and Energy Diposition in Superconducting Magnets at fi+fi- Colliders, Fermilab-Conf-96/011, Pro• ceedings of the 9th Advanced ICFA Beam Dy• namics Workshop, Ed. J. C. Gallardo, AIP Press, to be published. 48. P. Chen, presentation at the 9th Advanced ICFA Beam Dynamics Workshop and this conference, unpublished. 49. L. D. Landau and E. M. Lifshitz, Phys. Zs. Sowjetunion 6, 244 (1934); V. M. Budnev, I. F. Ginzburg, G. V. Medelin and V. G. Serbo, Phys Rep., 15C, 181 (1975). 50. P. Chen, presentation at the 9th Advanced ICFA Beam Dynamics Workshop and this conference, unpublished. 51. I. Ginzburg, private communication and this proceedings. 52. P. Chen and N. Kroll, private communication.