1. Frictional Cooling NUFACT02 Studies at Columbia University & Nevis Labs Raphael Galea Allen Caldwell Stefan Schlenstedt (DESY/Zeuthen) Halina Abramowitz (Tel Aviv University) Summer 2001 Students: Christos Georgiou Daniel Greenwald Yujin Ning Inna Shpiro Will Serber

2. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

3. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

4. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

5. Raphael Galea, Columbia University NUFACT02 : Imperial College London Frictional Cooling: particle trajectory ** Using continuous energy loss In 1   d  =10cm*sqrt{T(eV)} keep d small at low T reaccelerate quickly

6. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

7. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

8. Raphael Galea, Columbia University NUFACT02 : Imperial College London Target System cool  + &  - at the same time calculated new symmetric magnet with gap for target

9. Raphael Galea, Columbia University NUFACT02 : Imperial College London 28m 0.4m  ’s in red  ’s in green View into beam

10. Raphael Galea, Columbia University NUFACT02 : Imperial College London Target & Drift Optimize yield Maximize drift length for  yield Some  ’s lost in Magnet aperture

11. Raphael Galea, Columbia University NUFACT02 : Imperial College London Phase Rotation First attempt simple form Vary t 1,t 2 & E max for maximum low energy yield

12. Raphael Galea, Columbia University NUFACT02 : Imperial College London Frictional Cooling Channel

13. Raphael Galea, Columbia University NUFACT02 : Imperial College London Cell Magnetic Field Correction solenoid Main Ring Solenoid Extract & accelerate Realistic Solenoid fields in cooling ring

14. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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)

15. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

16. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

17. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

18. Raphael Galea, Columbia University NUFACT02 : Imperial College London Motion in Transverse Plane Lorentz angle Assuming E x =constant

19. Raphael Galea, Columbia University NUFACT02 : Imperial College London Emittance Calulation After cooling cylindrical coordinates are more natural After drift cartesian coordinates More natural Beamlet uniform z distribution :

20. Raphael Galea, Columbia University NUFACT02 : Imperial College London Beamlet coordinates: X 100 beamlets

21.  ct vs z for  + He on Cu

22.  ct vs z for  - H on W

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

24. P long vs P trans for  - H on W

25. R  vs z for  + He on CU

26. R  vs z for  - H on W

27. 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 For cooled 

28. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

29. Raphael Galea, Columbia University NUFACT02 : Imperial College London MCP frontMCP sideAccelerating Grid Multi-Wire Proportional Chamber Work at NEVIS labs Want to measure the energy loss,  -  capture, test cooling principle Developing Microchannel Plate & MWPC detectors

30. Raphael Galea, Columbia University NUFACT02 : Imperial College London A simpler approach Avoid difficulties of kickers & multiple windows Without optimization initial attempts have 60% survival & cooling factor 10 5 Still need to bunch the beam in time

31. Raphael Galea, Columbia University NUFACT02 : Imperial College London 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

32. Summary of Frictional Cooling Nevis Labs work on  -  capture Works below the Ionization Peak Possibility to capture both signs Cooling factors O(10 6 ) or more? Still unanswered questions being worked on but work is encouraging.