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  capture Phase Rotation Cooling cell Nevis experimental work Results and Conclusions

3. Physics at a Muon Collider Stopped  physics physics Higgs Factory Higher Energy Frontier Muon Collider Complex: Proton Driver 2-16GeV; 1-4MW leading to 10 22 p/year  production target & Strong Field Capture COOLING resultant  beam  acceleration Storage & collisions

4. Cooling Motivation  s not occur naturally so produce them from p on target –  beam – decay to   &  beam occupy diffuse phase space Unlike e & p beams only have limited time (   =2.2  s) to cool and form beams Neutrino Factory/Muon Collider Collaboration are pursuing a scheme whereby they cool  s 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 10 6 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    has the problem of Muonium formation  dominates over e-stripping  in all gases except He    has the problem of Atomic capture  calculated up to 80 eV not measured below ~1KeV Cool  ’s extracted from gas cell T=1  s so a scheme for reacceleration must be developed

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

8. 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

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

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

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

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

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

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

15. Phase Rotation W Cu

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 B z =5T  B r =2% Uniform B z total field

20. Simulations Improvements 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)

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

22. 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

23. Frictional Cooling: Particle Trajectory 50cm long solenoid 10cm long cooling cells  gas for  + 0.7atm &  - 0.3atm E x =5MV/m B z =5T realistic field configuration  - use Hydrogen Smaller Z help in  capture Lower r fewer scatters BUT at higher equilibrium energy

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

25.  ct vs z for  + He on Cu

26.  ct vs z for  - H on W

27. P long vs P trans for  + He on CU

28. P long vs P trans for  - H on W

29. R  vs z for  + He on CU

30. R  vs z for  - H on W

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

32. Beamlet coordinates: X 100 beamlets

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 & recombine beamlets for injection into storage ring The   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 Cooling factors  6D /  ’ 6D Yield (  /p)  trans  long   D (1x10 6 )  + He on Cu 0.00511239201222  - He on Cu 0.0024031560.06  - H on Cu 0.00319704060.8  + He on W 0.0069533194018  - He on W 0.003401149.06  - H on W 0.00417183470.6

35. Conclusions Frictional cooling shows promise with potential cooling factors of O(10 5 -10 6 ) –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