1. Frictional Cooling TRIUMF Seminar July 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. R.Galea, Columbia University Triumf Seminar22/07/02 Outline Introduction & Motivation Frictional Cooling Simulation and Optimization Target and  capture Phase Rotation Cooling cell Nevis experimental work Results and Conclusions

3. R.Galea, Columbia University Triumf Seminar22/07/02 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. R.Galea, Columbia University Triumf Seminar22/07/02 Dimensions of Some Colliders under Discussion

5. R.Galea, Columbia University Triumf Seminar22/07/02 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

6. R.Galea, Columbia University Triumf Seminar22/07/02 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

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8. R.Galea, Columbia University Triumf Seminar22/07/02 HIGH ENERGY MUON COLLIDER PARAMETERS

9. R.Galea, Columbia University Triumf Seminar22/07/02 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

10. R.Galea, Columbia University Triumf Seminar22/07/02 Phase Space Reduction Simplified emittance estimate: At end of drift, rms x,y,z approx 0.05,0.05,10 m P x,P y,P z approx 50,50,100 MeV/c Normalized 6D emittance is product divided by (m  c) 3  drift 6D,N 1.7 10 -4 (  m) 3 Emittance needed for Muon Collider  collider 6D,N 1.7 10 -10 (  m) 3 This reduction of 6 orders of magnitude must be done with reasonable efficiency (luminosity calculation assumes typically few 10 12 muons per bunch, 1-4 bunches).

11. R.Galea, Columbia University Triumf Seminar22/07/02 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. R.Galea, Columbia University Triumf Seminar22/07/02 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. R.Galea, Columbia University Triumf Seminar22/07/02 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. R.Galea, Columbia University Triumf Seminar22/07/02 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. R.Galea, Columbia University Triumf Seminar22/07/02 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

16. R.Galea, Columbia University Triumf Seminar22/07/02 Frictional Cooling: particle trajectory ** Using continuous energy loss In 1   d  =10cm*sqrt{T(eV)} keep d small at low T reaccelerate quickly

17. R.Galea, Columbia University Triumf Seminar22/07/02 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

18. R.Galea, Columbia University Triumf Seminar22/07/02 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

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

20. R.Galea, Columbia University Triumf Seminar22/07/02 Target System cool  + &  - at the same time calculated new symmetric magnet with gap for target

21. R.Galea, Columbia University Triumf Seminar22/07/02 28m 0.4m  ’s in red  ’s in green View into beam

22. R.Galea, Columbia University Triumf Seminar22/07/02 Target & Drift Optimize yield Maximize drift length for  yield Some  ’s lost in Magnet aperture

23. R.Galea, Columbia University Triumf Seminar22/07/02 Phase Rotation First attempt simple form Vary t 1,t 2 & E max for maximum low energy yield

24. R.Galea, Columbia University Triumf Seminar22/07/02 Phase Rotation W Cu

25. R.Galea, Columbia University Triumf Seminar22/07/02 Frictional Cooling Channel

26. R.Galea, Columbia University Triumf Seminar22/07/02 Time sequence of events…

27. R.Galea, Columbia University Triumf Seminar22/07/02 Cell Magnetic Field Correction solenoid Main Ring Solenoid Extract & accelerate Realistic Solenoid fields in cooling ring

28. R.Galea, Columbia University Triumf Seminar22/07/02 Fringe fields produce Uniform B z =5T  B r =2% Uniform B z total field

29. R.Galea, Columbia University Triumf Seminar22/07/02 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 P z <50 MeV/c. Phase rotation is combined with cooling channel. He gas is used for  +, H 2 for  -. There is a nearly uniform 5T B z field everywhere, and E x =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. R.Galea, Columbia University Triumf Seminar22/07/02 Detailed Simulation - continued Barkas effect (reduced energy loss for  - relative to  + ) included  - 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. R.Galea, Columbia University Triumf Seminar22/07/02 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)

32. R.Galea, Columbia University Triumf Seminar22/07/02 Scattering Cross Sections Scan impact parameter  (b) to get d  /d  from which one can get mean free path Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) Simulate all scatters  >0.05 rad

33. R.Galea, Columbia University Triumf Seminar22/07/02 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

34. R.Galea, Columbia University Triumf Seminar22/07/02 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

35. R.Galea, Columbia University Triumf Seminar22/07/02 Motion in Transverse Plane Lorentz angle Assuming E x =constant

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64.  ct vs z for  + He on Cu

65.  ct vs z for  - H on W

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

67. P long vs P trans for  - H on W

68. R  vs z for  + He on CU

69. R  vs z for  - H on W

70. R.Galea, Columbia University Triumf Seminar22/07/02 Emittance Calculation After cooling cylindrical coordinates are more natural After drift cartesian coordinates More natural Beamlet uniform z distribution :

71. R.Galea, Columbia University Triumf Seminar22/07/02 Beamlet coordinates: X 100 beamlets

72. 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 

73. R.Galea, Columbia University Triumf Seminar22/07/02 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

74. R.Galea, Columbia University Triumf Seminar22/07/02 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

75. R.Galea, Columbia University Triumf Seminar22/07/02 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

76. R.Galea, Columbia University Triumf Seminar22/07/02 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

77. 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.