Ionization stops, muon too slow Frictional Cooling Nuclear scattering, excitation, charge exchange, ionization • 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 1/2from ionization
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 )
Trajectories in detailed simulation Transverse motion Motion controlled by B field Fluctuations in energy results in emittance Lorentz angle drift, with nuclear scattering Final stages of muon trajectory in gas cell
Results of simulations to this point Phase rotation sections Cooling cells • Full MARS target simulation, optimized for low energy muon yield: 2 GeV protons on Cu/W 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 !!
Summary of Simulations • 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 Effectparameterized data from Agnello et. al. (Phys. Rev. Lett. 74 (1995) 371) • Only used for the electronic part of dE/dx • Energy loss in thin windows • For RARAF setup proton transmitted energy spectrum is input from SRIM, simulating protons through Si detector • (J.F. Ziegler http://www.srim.org) Cooling factors of 105-107!!!
Assumed initial conditions • 20nm C windows • 700KeV protons • 0.04atm He Punch through protons Cooled protons TOF=T0-(Tsi-TMCP) speed Kinetic energy
Add windows 300nm 721KeV p Add gas No gas/grid/windows Extract time offsets 0.06atm
Cool protons??? MC exp Flat constant Background Background exponential with m>0
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 • +… R&D with industry? 1 student + 1 Postdoc…group is growing…
Lab situated at MPI-WHI in Munich Sharper peak in Energy than peak from measuring time.
Future Plans • Frictional cooling tests at MPI with 5T Solenoid, alpha 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 n=15 orbit, then cascades down to n=1. Transition n=2n=1 releases 2.2 KeV x-ray. Si drift detector Developed my MPI HLL
Conclusions • No clear sign of cooling but this is expected from lack of Magnetic field & geometric MCP acceptance alone • The Monte Carlo simulation can provide a consistent picture under various experimental conditions • Can use the detailed simulations to evaluate Muon Collider based on frictional cooling performance with more confidence….still want to demonstrate the cooling • Work at MPI on further cooling demonstration experiment using an existing 5T Solenoid and develop the m- capture measurement A lot of interesting work and results to come.