1. Frictional Cooling 2004 Workshop on Muon Collider Simulation Columbia University & the Max-Planck-Institute R. Galea, A. Caldwell, S.Schlenstedt, H. Abramowicz What is Frictional Cooling (FC)? Simulation of the frontend of a Muon Collider based on FC Targetry & Capture Magnet Drift Region Phase Rotation Cooling section Reacceleration Physics covered by simulations Energy loss mechanisms, Nuclear & electronic Muonium Formation  - capture Experimental results & plans Future studies

2. Bring muons into a kinetic energy range where the dT/ds increases with kinetic energy (T) What is Frictional Cooling? Nuclear scattering, atomic excitation, charge exchange… muon too slow to ionize 1/  2 from ionization At high energy end change is only logarithmic whereas it is roughly proportional to speed at low energies

3. A constant accelerating force (an Electric field (E)) can be applied to the muons resulting in an equilibrium kinetic energy Same as freefall and reaching terminal velocity Gravity opposing friction

4. A strong solenoidal field (B) is needed to guide the muons until they are cooled, so apply E  B to get below the dT/ds peak

5. Oscillations around equilibrium limits final emittance

6. Yield is a critical issue: In this regime dT/ds extremely large Slow  s don’t go far before decaying d = 10 cm sqrt(T) T in eV  + forms Muonium  - is captued by Atom Low average density (gas) Make Gas cell long as you want but transverse dimension (extraction) small.  dominates over e- stripping  in all gases except He  small above electron binding energy, but not known. Keep T as high as possible

7. Simulation of Muon Collider based on FC:

8. 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).

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

10. Target & Drift Optimize yield Optimize drift length for  yield Some  ’s lost in Magnet aperture Only Muons at the end of 28m were tracked through the rest of the system

11. 28m 0.4m  ’s in red  ’s in green View into beam GEANT3.21 simulation

12. Attempt simple form Vary t 1,t 2 & E max for maximum low energy yield Phase Rotation: E max =5MV/m t 1 =100ns t 2 =439ns

13. Simulation of the cooling cell: Field extends outside cooling cell but is damped exponentially Smoothly alternate field in order to compensate ExB drift Length=11m, Radius=0.2m He density 1.25x10 -4 g/cm 3 Assume uniform Bz=5T Muons hitting the cell walls before reaching equil. T are considered lost

14. Simulation of the cooling cell: Initial longitudinal reacceleration to get beamlets out of cooling section E

15. Scattering Cross Sections Scan impact parameter and calculate  (b), 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 Simulation accurately reproduces ICRU tables

16. Difference in  + &  - energy loss rates at dE/dx peak Partly Due to charge exchange for  + parameterized data from Agnello et. al. (Phys. Rev. Lett. 74 (1995) 371) Only used for the electronic part of dE/dx

17. Muonium Formation Simulate the effect of muonium formation in the tracking, an effective charge as given by  I /(  F +  I ) was used

18. For  - the capture cross sections were parameterized and included in the simulation using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1) Although earlier studies showed promising results for  - this scheme has not been fully investigated for this flavor.

19. Out of the Cooling Cell: At z=11m

20. Beam Characterization

21. Muon Acceleration: Standalone study take the beam as described and accelerate to a final beam momentum of 147 MeV/c at 30% survival probability RMS 1  s to 3ns RMS 1.2MeV/c to 5MeV/c

22. Results: 1.7x10 -10 (  m) 3 Simulation of previous scheme yielded final beam emittances of 2-6x10 -11 (  m) 3 At yields of 0.001-0.003  + /GeV proton. Yield could be better yet emittance is better than ”required” Cooler beams smaller beam elements less background lower potential radiation hazard from neutrinos

23. RAdiological Research Accelerator Facility Perform TOF measurements with protons 2 detectors START/STOP Thin entrance/exit windows for a gas cell Some density of He gas Electric field to establish equilibrium energy NO B field so low acceptance  Look for a bunching in time Can we cool protons ? Nevis Experiment already reported at NuFact03 R.Galea, A.Caldwell, L.Newburgh, Nucl.Instrum.Meth.A524, 27-38 (2004) arXiv: physics/0311059

24. Results of RARAF experiment Various energies/gas pressures/electric field strengths indicated no cooled protons Lines are fits to MC & main peaks correspond to protons above the ionization peak Low acceptance but thicker windows was the culprit Experiment showed that MC could reproduce data under various conditions. Simulations of Frictional Cooling is promising. Exp. Confirmation still desired.

25. Frictional Cooling Demonstration at MPI Munich Repeat demonstration experiment with protons with IMPROVEMENTS: No windows 5T Superconducting Solenoid for high acceptance Silicon detector to measure energy directly Cryostat housing 5T solenoid.

26. Status of Experiment FWHM=250eV Silicon Drift Detector gives excellent resolution Thus far Fe55 X-rays Cryostat & Magnet commissioned Grid constructed & tested. Maintained 98KV in vacuum Source & support structures constructed Electronics & detectors available

27. Summary Frictional Cooling is being persued as a potential cooling method intended for Muon Colliders Simulations of mostly ideal circumstances show that the 6D emittance benchmark of 1.7x10 -10 (  m) 3 can be achieved & surpassed physics/0410017 Simulations have been supported by data from Nevis Experiment & will be tested further at the Frictional Cooling Demonstration to take place at MPI Munich Future investigations are also on the program: R&D into thin window or potential windowless systems Studies of gasbreakdown in high E,B fields Capture cross section measurements at  beams Frictional Cooling is an exciting potential alternative for the phase space reduction of muon beams intended for a Muon Collider