Frictional Cooling

1. Frictional Cooling Studies at Columbia University/Nevis Labs Raphael Galea, Allen Caldwell + Stefan Schlenstedt (DESY/Zeuthen) Halina Abramowitz (Tel Aviv University) How to reduce beam Emmittance by 106? 6D,N = 1.7 10-10 (m)3 Summer Students: Emily Alden Christos Georgiou Daniel Greenwald Laura Newburgh Yujin Ning Will Serber Inna Shpiro

2. Frictional Cooling Nuclear scattering, excitation, charge exchange, ionization Ionization stops, muon too slow • Bring muons to a kinetic energy (T) where dE/dx increases with T • Constant E-field applied to muons resulting in equilibrium energy • Big issue – how to maintain efficiency • First studied by Kottmann et al., PSI 1/2 from ionization

3. Problems/comments: • large dE/dx @ low kinetic energy  low average density (gas) • Apply E  B to get below the dE/dx peak • m+has the problem of Muonium formation s(Mm) dominates over e-strippingin all gases except He • m-has the problem of Atomic capture s small below electron binding energy, but not known • Slow muons don’t go far before decaying d = 10 cm sqrt(T ) T in eV so extract sideways (E  B )

4. Frictional Cooling: particle trajectorySome obvious statements? • In 1tm dm=10cm*sqrt{T(eV)} • keep d small at low T • reaccelerate quickly ** Using continuous energy loss

5. Phase rotation sections Cooling cells • 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). • He gas is used for m+,H2 for m-. There is a nearly uniform 5T Bz field everywhere, and Ex =5 MeV/m in gas cell region • Electronic energy loss treated as continuous, individual nuclear scattering taken into account since these yield large angles. Not to scale !!

6. 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 62 022512-1) • 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

7. Yields & Emittance Look at muons coming out of 11m cooling cell region after initial reacceleration. Yield: approx 0.002  per 2GeV proton after cooling cell. Need to improve yield by factor 3 or more. Emittance: rms x = 0.015 m y = 0.036 m z = 30 m ( actually ct) Px = 0.18 MeV Py = 0.18 MeV Pz = 4.0 MeV 6D,N = 5.7 10-11 (m)3 6D,N = 1.7 10-10 (m )3

8. Problems/Things to investigate… • Extraction of ms through window in gas cell • Must be very thin to pass low energy ms • Must be reasonably gas tight • Can we apply high electric fields in gas cell without breakdown (large number of free electrons, ions) ? Plasma generation  screening of field. • Reacceleration & bunch compression for injection into storage ring • The m- capture cross section depends very sensitively on kinetic energy & falls off sharply for kinetic energies greater than e- binding energy. NO DATA – simulations use theoretical calculation • +…

9. 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?

10.  4 MeV p

12. Contains 20nm window Accelerating grid Si detector To MCP Proton beam Gas cell Vacuum chamber

13. Initial conclusions: no obvious cooling peak, but very low acceptance due to lack of magnetic field. Use data to tune simulations. Redo experiment with a solenoidal magnetic field.

14. Lab situated at MPI-WHI in Munich

15. Future Plans • Frictional cooling tests at MPI with 5T Solenoid, a source • Study gas breakdown in high E,B fields • R&D on thin windows • Beam tests with muons to measure  capture cross section • -+H  H+ e+’s • muon initially captured in high n orbit, • then cascades down to n=1. • Transition n=2n=1 releases 2.2 KeV x-ray. Si drift detector Developed my MPI HLL

16. 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 MPI lab for additional questions

18. 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

19. Motion in Transverse Plane • Assuming Ex=constant Lorentz angle

20. 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 62 022512-1)

21. Scattering Cross Sections • Scan impact parameter q(b) to get ds/dq from which one can get lmean free path • Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) • Simulate all scatters q>0.05 rad

22. 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

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

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

26. Target & Drift Optimize yield • Maximize drift length for m yield • Some p’s lost in Magnet aperture

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