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AN ASYMMETRIC - COLLIDER: LUMINOSITY CONSIDERATION V.D. Shiltsev FNAL, MS 221, P.O. Box 500, Batavia, Illinois 60510

Abstract mrad]. The last relation assumes limiting factors for pro- ton beam population are low-energy space charge effects at An asymmetric muon-proton collider is proposed as an in- injector stages and intrabeam scattering. strument for possible structure search. Energy of Transverse sizes σ ,σ of the beams at the µ−p collider proton beam is supposed to be some 5-6 times of muon µ p interaction point should be approximately the same, thus, energy. Estimated luminosity of the collider with two rings under the condition on beta-functions β ∼ β ∼ σz we – the Tevatron accelerator and µ-ring – is found to be of the µ p 33 −1 −2 have following relation between transverse emittances: order of 10 s cm .  γ β   = p µ  , np nµ (1) 1 INTRODUCTION γµ βp Several proposals of µ+−µ− and µ−p colliders were made here γp ≈ 1000 and γµ ≈ 2000 denote relativistic factors in recent years (the past and present status of these ideas of . can be found, e.g., in Ref. [1]). Here we discuss a mod- Taking for definiteness βp =2βµ = σz =15cm, we ification of existing plans of muon facilities which would q σ =  β/γ ≈ 40 µ  =12.5 · fit to the requirements of a search for quark structure. This obtain IP nµ µ µ mand np could be an asymmetric muon-proton collider in which the 10−6 m. Consequently, the expected maximum number of 12 momenta of colliding and are roughly the is Np =1.25 · 10 . same in value but opposite. This condition will ease the Now we can estimate the luminosity of the muon-proton observation of the events with large transverse momentum collider as: transfer which involve destruction of quarks or where quark f n N N M L = L s µ p ≈ 1.3 · 1033 s−1cm−2. structure may manifest itself. As an example, one can con- 4πσ2 (2) sider 1000 GeV protons of the Tevatron facilities which IP confine quarks with broad momentum spectra around the As protons are supposed to live for a long time in the mean value of some 160 GeV/c. Therefore, an appropriate ring, one should consider beam-beam effects. With the pa- muon momentum should be about 100-200 GeV/c. This rameters mentioned above, the proton tune shift due to op- paper is devoted to brief consideration of the possibilities posite muon beam is: of such a collider, beam parameters and luminosity of the machine, and comparison with other probable competitive Nµrp ξp = ≈ 0.02, (3) accelerator schemes. 4πnp −18 that seems acceptable (here rp =1.53 · 10 m is the pro- 2 BEAM PARAMETERS AND COLLIDER ton classical radius). The decay of muons leads to changing LUMINOSITY (reduction) of the shift within characteristic time of 2000 Let us consider possible scheme of the µ−p collider which turns, therefore some external stabilization of the proton consists of two rings. Parameters of the ∼200 GeV muon ring tune probably would be useful. ring are taken from[2] where it is assumed that muon pro- Beam-beam tune shift for muons is equal to duction and acceleration systems can provide M =2 12 Nprµ bunches of Nµ =2· 10 particles within transverse nor- ξµ = ≈ 0.026, (4) 4πnµ malized rms emittance of nµ=50 mm · mrad with a rate of fL=30 Hz. These muons decay in the ring after a charac- −17 again far away of limiting values (rµ =1.36 · 10 m). n = 300 · B[T ] teristic number of turns of s in the bending Concluding this section, we would note that the key pa- B B ∼ 6T field of in Tesla. Here we will consider and, rameters for the µ − p collider luminosity are the muon n ∼ 2000 therefore, s . production rate and the muon emittance. As these param- A good candidate to deliver the beam of protons could eters are presently under detailed study, somewhat “pes- be Tevatron. In the upgraded regime of “TeV33”[3] the simistic” variant II[1] with smaller Nµ, smaller repetition length of the bunch of Ep=1000 GeV protons will be about rate of µ production fL, and larger emittance nµ is con- σ z=15 cm, while the number of protons depends on the sidered and put into summarizing Table 1, while high µ- N ' 1011 ·  [mm · transverse normalized emittance as p np production option is marked as variant I in the Table. For ∗ Operated by Universities Research Association, Inc., under contract proton beam-beam tune shift estimations with smaller rep- with the U.S. Department of Energy etition rate fL, the ‘duty factor’ of collisions was taken into

0-7803-4376-/98/$10.00  1998 IEEE 420 It seems reasonable to consider the proposed µ − p ma- Table 1: Two Options of µ − p Collider chine as the first step toward a large scale 4 TeV c.m. Parameter I II energy µ+µ− collider. With respect to the full-scale set Muon Energy, Eµ,GeV 200 200 up such a testing facility does not require production of Proton Energy, Ep,GeV 1000 1000 both charge muons, allows large longitudinal emittance of 12 11 µ Intensity, Nµ/bunch 2 · 10 5 · 10 µ-beam and, therefore, gives some freedom in obtaining −6 µ Emittance, nµ, 10 m 50 200 lower transverse emittance (see in Refs. [1, 2]). Due to µ Storage turns, ns ∼2000 ∼2000 ability to operate with bunches as long as proton ones, µ Pulse rate, fL 30 10 one expects no troubles with single bunch instabilities in N bunches (p, µ), M 2 2 the muon ring, and at the same time it could substantially simplify focusing optics of the ring and the interaction re- Beta at IP βµ,cm 7.5 7.5 gion. βp ,cm 15 15 Further increase of the µ − p collider luminosity can be Waist size σIP , µm ∼40 ∼90 −6 obtained with larger number of bunches M, or with im- p Emittance np, 10 m 12.5 50 12 12 plementation of “traveling focus” regime [4] in order to de- p Intensity, Np/bunch 1.25 · 10 5 · 10 crease effective beam sizes at interaction point while bunch Beam-beam shift ξp 0.02 0.0005 length is larger than the value of beta function. Formally ξµ 0.026 0.026 speaking, quark-muon luminosity is some 3 times the ob- L, s−1cm−2 1.3 · 1033 1.1 · 1032 Luminosity tained value, because number of quarks is triple number of protons we used in our estimations. account: <ξp >≈ ξp(fLns/f0) where f0 ' 47 kHz 4 CONCLUSIONS is the Tevatron revolution , and ξp is given by Eq. (3). Let us remark also, that inasmuch as beta functions The asymmetric µ − p collider with energies of 200 GeV at the interaction point are of the order of bunch length, in muon beam and 1 TeV for protons is considered as a the “hour-glass” effect can slightly decrease luminosity (by tool for quark structure search. The option with intersect- some dozen percents). ing Tevatron accelerator and µ-ring allows to obtain lu- minosity of the order of 1033 s−1 cm−2. The key issues 3 DISCUSSION for high luminosity are large number and small transverse emittance of muons, while the muon bunch length can be It is interesting to compare the proposed proton-muon col- as large as proton one’s. The beam-beam effects are found lider with other - machines presently under to give no severe constraints on beam intensities. It was e − p study, namely, possible facilities of LEP+LHC at also shown that the proposed scheme has some advantages CERN and TESLA+HERA-p at DESY(Hamburg). Table 2 with respect to other possible lepton-hadron colliders, such demonstrates main features of these machines: momenta of as LEP+LHC and TESLA+HERA. The muon-proton col- p ∼ E /6c p quarks ( q √p ) and l, maximum momenta lider at FNAL seems to be also a perfect candidate as the Q ' 2 p p transfer q l (all momenta in GeV/c), and lumi- first stage of high-energy µ+µ− facility. nosity in s−1cm−2. 5 ACKNOWLEDGMENTS Table 2: Quark-Lepton Collider Projects I acknowledge valuable comments and corrections done by 31 Project Q pl pq L, 10 Dan Green and David Neuffer. Discussions with Rein- TESLA+HERA-p 350 250 140 ∼1.0 hard Brinkmann, Joerg Rossbach, Gus Voss (DESY), and LEP+LHC 700 90 1300 1–10 Pat Colestock encouraged me to pursue the topic. µ−ring+Tevatron 350 200 160 10–100 6 REFERENCES [1] AIP Conference Proceedings 352, “Physics Potential and De- The TESLA+HERA-p project[4] with use of super- velopment of µ+µ− Colliders”, 2nd Workshop, Sausalito, conducting linear accelerator of can provide CA (Nov. 1994). momenta-symmetric quark-lepton collisions, but its lumi- [2] . Palmer et al, “Beam Dynamics Problems in a Muon Col- nosity is limited by power of beam. The lumi- lider”, BNL - 61580 (March, 1995). nosity of the LEP+LHC is somewhat higher and limited by beam-beam instabilities into both beams of electrons [3] G. Jackson, ed., “Recycler Ring Conceptual Design Study”, -TM-1936 (July, 1995). and protons, but momenta asymmetry of the order of 15 is not convenient for the experiment. As it is mentioned in [4] R. Brinkmann and M. Dohlus, “A Method to Overcome the β∗ the Table 2, the luminosity of the muon-proton collider at Bunch Length Limitation on p for Electron-Proton Collid- FNAL could be the highest one, depending mostly on the ers”, Internal Report DESY M-95-11 (Sept. 1995). µ−production and cooling.

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