1. FNAL-27-10-2009 Frictional Cooling Caldwell MPI f. Physik, Munich

2. compared to protons: • colliding point particles rather than complex objects antiquark gluon quark Motivation: Muon Collider • compared to electrons: • no synchrotron radiation problem P  (E/m)4 • very high energy circular accelerator can be built Allen Caldwell

3. Drift region for  decay  30 m ’s ’s Proton beam Solenoidal Magnets: few T … 20 T Target after drift estimate beam description using 6D emittance (6D phase space of the beam) rms:x,y,z 0.05, 0.05, 10 m px,py,pz 50, 50, 100 MeV 6D,N  1.710-4 (m)3 required COOLING 6D,N  1.710-10 (m)3  beam production Allen Caldwell

4. Proton accelerator – 2-16 GeV, few MW (1022 p/year)  production target  decay channel  cooling channel  accelerators Muon collider Typical muon collider scheme • standard techniques too slow • new techniques are being developed • energy loses in interactions with matter • reaccelerating • magnetic focusing Allen Caldwell

5. big issue – how to maintain efficiency • similar idea first studied by Kottmann et al. at PSI Frictional cooling Idea • bring muons to kinetic energy T where dE/dx increases with energy • apply constant accelerating E field to muons resulting in equilibrium energy Equilibrium energy Allen Caldwell

6. apply EB to get below the dE/dx peak Frictional cooling Problems/Comments • large dT/dx at low T • low average density of stopping medium  gas E vB • slow ’s don’t go far before decaying • with T in eV • sideward extraction (EB) • + problem – muonium formation dominates over e-stripping except for He • – problem – muon capture at low energies;  not known • keep T as high as possible Allen Caldwell

7. Neutralization Stripping For , energy lower by M/MP From Y. Nakai, T. Shirai, T. Tabata and R. Ito, At. Data Nucl. Data Tables37, 69 (1987) Allen Caldwell

8. Frictional Cooling: particle trajectory ** Using continuous energy loss Allen Caldwell

9. cooling cell target phase rotation capture & drift reacceleration Simulations performed to this point collider ring Full MARS simulation of the proton interactions in target (Cu) showed • He gas used for + • H gas for – • transverse E field 5 MV/m • continuous electronic energy loss • individual nuclear scatters simulated • they result in large angles • larger low energy  yield in transverse directions • nearly equal + and – yields with T < 100 MeV Muon collider scheme based on frictional cooling Not to scale !! Allen Caldwell

10. Target System • cool m+ & m- at the same time • calculated new symmetric magnet with gap for target GeV Allen Caldwell

11. 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). Allen Caldwell

12. Target & Drift Optimize yield • Optimize drift length for m yield • Some p’s lost in Magnet aperture Allen Caldwell

13. Phase Rotation • First attempt simple form • Vary t1,t2 & Emax for maximum low energy yield Allen Caldwell

14. Cooling cell simulation He gas is used for +, H2 for -. • Individual nuclear scatters are simulated – crucial in determining final phase space, survival probability. • Incorporate scattering cross sections into the cooling program • Include m- capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1) • Electronic energy loss treated as continuous Allen Caldwell

15. Scattering Cross Sections • Scan impact parameter and calculate q(b), ds/dq from which one can getlmean free path • Use screened Coulomb Potential(Everhart et. al. Phys. Rev. 99 (1955) 1287) • Simulate all scatters q>0.05 rad • Simulation accurately reproduces ICRU tables for protons Allen Caldwell

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

17.  rms. Oscillations around equilibrium define the emittance Simulation of the cooling cell Allen Caldwell

18. Resulting emittance and yield Muon beam coming out of 11 m long cooling cell and after initial reacceleration: rms:x,y,z 0.015, 0.036, 30 m px,py,pz 0.18, 0.18, 4.0 MeV Results for +, still working on - 6D,N  5.710-11 (m)3 • better than required 1.710-10 (m)3 • Yield  0.002  per 2 GeV proton after cooling cell • need improvement byfactor of5 or more Allen Caldwell

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23. Future plans • run the experiment – demonstrate the frictional cooling Develop scheme for producing slow muon beam using surface muon source (paper in preparation) Allen Caldwell