1. 1 Muon Collider/Higgs Factory A. Caldwell Columbia University Motivation Difficulties Focus on Cooling (frictional cooling)

2. 2 Why a Muon Collider ? No synchrotron radiation problem (cf electron) Muons are point particles (cf proton) We therefore dream of building a high energy collider. Parameter sets available up to 100 TeV+100 TeV. At lower energies, Higgs factory (40000 higher production cross section than electron collider). Very fine energy scans possible since limited radiation from muons. Neutrinos from target, muon decay allow wide range of physics Low energy muons allow many important condensed matter, atomic physics experiments

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4. 4 Dimensions of Some Colliders under Discussion

5. 5 Muon Collider as Higgs Factory Small beam energy spread allows a precision measurement of the Higgs mass (few hundred KeV) The width can also be measured to about 1 MeV

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7. 7 HIGH ENERGY MUON COLLIDER PARAMETERS

8. 8 Phase Space Reduction Simplified emittance estimate: At end of drift, rms x,y,z approx 0.05,0.05,10 m P x,P y,P z approx 50,50,100 MeV/c Normalized 6D emittance is product divided by (m c) 3  drift 6D,N 1.7 10 -4 (  m) 3 Emittance needed for Muon Collider  collider 6D,N 1.7 10 -10 (  m) 3 This reduction of 6 orders of magnitude must be done with reasonable efficiency (luminosity calculation assumes typically few 10 12 muons per bunch, 1-4 bunches).

9. 9 Some Difficulties Muons decay, so are not readily available – need multi MW source. Large starting cost. Muons decay, so time available for cooling, bunching, acceleration is very limited. Need to develop new techniques, technologies. Large experimental backgrounds from muon decays (for a collider). Not the usual clean electron collider environment. High energy colliders with high muon flux will face critical limitation from neutrino radiation.

10. 10 Muon Cooling Muon Cooling is the signature challenge of a Muon Collider Cooler beams would allow fewer muons for a given luminosity, Thereby Reducing the experimental background Reducing the radiation from muon decays Allowing for smaller apertures in machine elements, and so driving the cost down

11. 11 Cooling Ideas The standard approach (Skrinsky, Neuffer, Palmer, …) considered to date is ionization cooling, where muons are maintained at ca. 200 MeV while passed successively through an energy loss medium followed by an acceleration stage. Transverse cooling of order x20 seems feasible (see feasibility studies 1-2). Longitudinal cooling is more difficult, and remains an unsolved problem. There are significant developments in achieving 6D phase space via ionization cooling (see R. Palmer talk). Here, I focus on an alternative called ‘frictional cooling’. First studied by Kottmann et al., PSI. See talk by R. Galea.

12. 12 Frictional Cooling Bring muons to a kinetic energy (T) where dE/dx increases with T Constant E-field applied to muons resulting in equilibrium energy Big issue – how to maintain efficiency

13. 13 Problems/Comments: large dE/dx @ low kinetic energy low average density Apply to get below the dE/dx peak    has the problem of Muonium formation  dominates over e-stripping  in all gases except He    has the problem of Atomic capture  small below electron binding energy, but not known Slow muons don’t go far before decaying

14. 14 Frictional Cooling: particle trajectory ** Using continuous energy loss In 1   d  =10cm*sqrt{T(eV)} keep d small at low T reaccelerate quickly

15. 15 Frictional Cooling: stop the  Start with low initial muon momenta High energy  ’s travel a long distance to stop High energy  ’s take a long time to stop

16. 16 Cooling scheme Phase rotation is E(t) field to bring as many  ’s to 0 Kinetic energy as possible (performed in cooling ring.

17. 17 Detailed Simulation Full MARS target simulation, optimized for low energy muon yield: 2 GeV protons on Cu with proton beam transverse to solenoids (capture low energy pion cloud). Optimized drift length (28m). Simple phase rotation parameters, optimized to bring muons to P z <50 MeV/c. Phase rotation is combined with cooling channel. He gas is used for +, H 2 for -. There is a nearly uniform 5T B z field everywhere, and E x =5 MeV/m in gas cell region. Electronic energy loss treated as continuous, individual nuclear scattering taken into account since these yield large angles.

18. 18 Detailed Simulation - continued Barkas effect (reduced energy loss for - relative to + ) included - capture cross section included Windows for gas cells NOT included so far Time window for accepting muons into cooling channel consistent with rotation time Muons(pions) are tracked from the target through to the edge of the gas cell.

19. 19 Target System cool  + &  - at the same time calculated new symmetric magnet with gap for target

20. 20 28m 0.4m  ’s in red  ’s in green View into beam

21. 21 Target & Drift Optimize yield Maximize drift length for  yield Some  ’s lost in Magnet aperture

22. 22 Cooling Cell & Phase Rotation simplified version Drift region Cooling cell Phase Rotation Transverse view of cooling cell region. Cooling cell is 20 cm radius cylinder embedded in 11m solenoid with B z =5T. E x =5 MV/v in |y|<0.7 m, and E z =100 kV/m for 0.3<|y|<0.5 m.

23. 23 Phase Rotation First attempt simple form Vary t 1,t 2 & E max for maximum low energy yield

24. 24 Scattering Cross Section Individual nuclear scatters are simulated – crucial in determining final phase space, survival probability. Incorporate scattering cross sections into the cooling program Born Approx. for T>2KeV Classical Scattering T<2KeV Include  - capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)

25. 25 Scattering Cross Sections Scan impact parameter and calculate  (b), d  /d  from which one can get mean free path Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) Simulate all scatters  >0.05 rad

26. 26 Barkas Effect Difference in  + &  - energy loss rates at dE/dx peak Due to extra processes charge exchange Barkas Effect parameterized data from Agnello et. al. (Phys. Rev. Lett. 74 (1995) 371) Only used for the electronic part of dE/dx

27. 27 Energy Fluctuations around Equilibrium

28. 28 Motion in Transverse Plane Lorentz angle Assuming E x =constant

29. 29 Longitudinal profile for  + At cooling cell boundary Flat in Z rms  ct 1m

30. 30 P long vs P trans for  + rms 50-60 KeV

31. 31 R  vs z for  +

32. 32 Yields & Emittance Look at muons coming out of 11m cooling cell region after initial reacceleration. Yield: approx 0.002 per 2GeV proton after cooling cell. Need to improve yield by factor 3 or more. Emittance: rms x = 0.015 m y = 0.036 m z = 30 m ( actually  ct) P x = 0.18 MeV P y = 0.18 MeV P z = 4.0 MeV  6D,N = 5.7 10 -11 (  m) 3

33. 33 Problems/Things to investigate… Extraction of  s through window in gas cell Must be very thin to pass low energy  s Must be gas tight and sustain pressures O(0.1-1)atm Can we applied high electric fields in small gas cell without breakdown? Reacceleration & bunch compression for injection into storage ring The   capture cross section depends very sensitively on kinetic energy & falls off sharply for kinetic energies greater than e - binding energy. NO DATA – simulations use theoretical calculation Critical path items - intend to make measurement on all these.

34. 34 Conclusions Muon Collider complex would be a boon for physics We need to solve the muon cooling problem Different schemes should be investigated