Frictional Cooling

1. Frictional Cooling 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 • Taget and p capture • Phase Rotation • Cooling cell • Nevis experimental work • Results and Conclusions

3. 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

4. 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

5. 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

6. 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

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

8. 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

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

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

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

12. 0.4m 28m p’s in red m’s in green View into beam

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

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

15. Phase Rotation Cu W

16. Frictional Cooling Channel

17. Time sequence of events…

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

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

20. 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)

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

22. 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

23. 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

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

25. bct vs z for m+He on Cu

26. bct vs z for m-H on W

27. Plong vs Ptrans for m+He on CU

28. Plong vs Ptrans for m-H on W

29. Rf vs z for m+He on CU

30. Rf vs z for m-H on W

31. Emittance Calulation After cooling cylindrical coordinates are more natural After drift cartesian coordinates More natural Beamlet uniform z distribution:

32. X 100 beamlets Beamlet coordinates:

33. Problems/Things to investigate… • Extraction of ms through window in gas cell • Must be very thin to pass low energy ms • 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 & recombine beamlets for injection into storage ring • The m- capture cross section depends very sensitively on kinetic energy & fall off sharply for kinetic energies greater than e- binding energy. NO DATA – simulations use calculation • Critical path item intend to make measurement

34. Conclusions

35. Conclusions • Frictional cooling shows promise with potential cooling factors of O(105-106) • Simulations contain realistic magnet field configurations and detailed particle tracking • Built up a lab at Nevis to test technical difficulties • There is room for improvement • Phase rotation and extraction field concepts very simple • Need to evaluate a reacceleration scheme