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. 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 have been theoretically achieved through IONIZATION COOLING CHANNELS
Raphael Galea, Columbia University
NUFACT02 : Imperial College London

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

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

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

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

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

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

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

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

11. Phase Rotation First attempt simple form
Vary t1,t2 & Emax for maximum low energy yield
Raphael Galea, Columbia University
NUFACT02 : Imperial College London

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

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

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

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

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

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

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

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

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

21. bct vs z for m+He on Cu

22. bct vs z for m-H on W

23. Plong vs Ptrans for m+He on CU

24. Plong vs Ptrans for m-H on W

25. Rf vs z for m+He on CU

26. Rf vs z for m-H on W

27. Conclusions Cooling factors e6D/e’6D Yield (m/p) etrans elong e6D
(1x106)
m+He on Cu
0.005
11239
2012 22
m-He on Cu
0.002
403
156
0.06
m-H on Cu
0.003
1970
406
0.8
m+He on W
0.006
9533
1940 18
m-He on W
401
149
.06
m-H on W
0.004
1718
347
0.6
For cooled m

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

29. Work at NEVIS labs MCP front MCP side Accelerating Grid
Want to measure the energy loss, m- scapture, test cooling principle
Developing Microchannel Plate & MWPC detectors
Raphael Galea, Columbia University
NUFACT02 : Imperial College London
Multi-Wire Proportional Chamber

30. A simpler approach Avoid difficulties of kickers & multiple windows
Without optimization initial attempts have 60% survival & cooling factor 105
Still need to bunch the beam in time
Raphael Galea, Columbia University
NUFACT02 : Imperial College London

31. Conclusions
Frictional cooling shows promise with potential cooling factors of O( )
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
Raphael Galea, Columbia University
NUFACT02 : Imperial College London

32. Summary of Frictional Cooling
Works below the Ionization Peak
Possibility to capture both signs
Cooling factors O(106) or more?
Still unanswered questions being worked on but work is encouraging.
Nevis Labs work on m- scapture