Frictional Cooling TRIUMF Seminar July 22, 2002

1. Frictional CoolingTRIUMF SeminarJuly 22, 2002 Studies at Columbia University &Nevis Labs Raphael Galea Allen Caldwell Stefan Schlenstedt (DESY/Zeuthen) Halina Abramowitz (Tel Aviv University) Summer Students: Christos Georgiou Daniel Greenwald Yujin Ning Inna Shpiro Will Serber

2. Outline • Introduction & Motivation • Frictional Cooling • Simulation and Optimization • Target and p capture • Phase Rotation • Cooling cell • Nevis experimental work • Results and Conclusions

3. 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

4. Dimensions of Some Colliders under Discussion

5. Physics at a Muon Collider • Muon Collider Complex: • Proton Driver 2-16GeV; 1-4MW leading to 1022p/year • p production target & Strong Field Capture • COOLING resultant m beam • m acceleration • Storage & collisions • Stopped m physics • n physics • Higgs Factory • Higher Energy Frontier

6. 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

8. HIGH ENERGY MUON COLLIDER PARAMETERS

9. Cooling Motivation • ms not occur naturally so produce them from p on target – p beam – decay to m • p & m beam occupy diffuse phase space • Unlike e & p beams only have limited time (tm=2.2ms) to cool and form beams • Neutrino Factory/Muon Collider Collaboration are pursuing a scheme whereby they cool ms by directing particles through a low Z absorber material in a strong focusing magnetic channel and restoring the longitudinal momentum • IONIZATION COOLING COOL ENERGIES O(200MeV) • Cooling factors of 106 are considered to be required for a Muon Collider and so far factors of 10-100 have been theoretically achieved through IONIZATION COOLING CHANNELS

10. Phase Space Reduction Simplified emittance estimate: At end of drift, rms x,y,z approx 0.05,0.05,10 m Px,Py,Pz approx 50,50,100 MeV/c Normalized 6D emittance is product divided by (mmc)3 drift6D,N 1.7 10-4 (pm)3 Emittance needed for Muon Collider collider6D,N 1.7 10-10(pm)3 This reduction of 6 orders of magnitude must be done with reasonable efficiency (luminosity calculation assumes typically few 1012 muons per bunch, 1-4 bunches).

11. 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.

12. 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

13. 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

14. Frictional Cooling • Bring muons to a kinetic energy (T) range where dE/dx increases with T • Constant E-field applied to muons resulting in equilibrium energy

15. Problems/Comments: • large dE/dx @ low kinetic energy • low average density • Apply to get below the dE/dx peak • m+has the problem of Muonium formation • s(Mm) dominates over e-stripping s in all gases except He • m-has the problem of Atomic capture • s calculated up to 80 eV not measured below ~1KeV • Cool m’s extracted from gas cell T=1ms so a scheme for reacceleration must be developed

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

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

18. Cooling scheme • Phase rotation is E(t) field to bring as many m’s to 0 Kinetic energy as possible • Put Phase rotation into the ring

19. Target Study Cu & W, Ep=2GeV, target 0.5cm thick

20. Target System • cool m+ & m- at the same time • calculated new symmetric magnet with gap for target

21. 0.4m 28m p’s in red m’s in green View into beam

22. Target & Drift Optimize yield • Maximize drift length for m yield • Some p’s lost in Magnet aperture

23. Phase Rotation • First attempt simple form • Vary t1,t2 & Emax for maximum low energy yield

24. Phase Rotation Cu W

25. Frictional Cooling Channel

26. Time sequence of events…

27. Cell Magnetic Field Correction solenoid Main Ring Solenoid Extract & accelerate • Realistic Solenoid fields in cooling ring

28. Fringe fields produce Uniform Bz=5T DBr=2% Uniform Bz total field

29. 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 Pz<50 MeV/c. Phase rotation is combined with cooling channel. • He gas is used for m+,H2 for m-. There is a nearly uniform 5T Bz field everywhere, and Ex =5 MeV/m in gas cell region. • Electronic energy loss treated as continuous, individual nuclear scattering taken into account since these yield large angles.

30. Detailed Simulation - continued • Barkas effect (reduced energy loss for m- relative tom+) included • m- 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.

31. Simulations Improvements • Incorporate scattering cross sections into the cooling program • Born Approx. for T>2KeV • Classical Scattering T<2KeV • Include m- capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)

32. Scattering Cross Sections • Scan impact parameter q(b) to get ds/dq from which one can get lmean free path • Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) • Simulate all scatters q>0.05 rad

33. Barkas Effect • Difference in m+ & m- 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

34. Frictional Cooling: Particle Trajectory • m- use Hydrogen • Smaller Z help in scapture • Lower r fewer scatters • BUT at higher equilibrium energy • 50cm long solenoid • 10cm long cooling cells • rgas for m+ 0.7atm & m- 0.3atm • Ex=5MV/m • Bz=5T realistic field configuration

35. Motion in Transverse Plane • Assuming Ex=constant Lorentz angle