An Anticyclotron For Cooling Muons Terry Hart, Don Summers University of Mississippi Kevin Paul Tech-X Corporation Muon Accelerator Program – Winter Meeting Thomas Jefferson National Accelerator Facility Newport News, VA February 28, 2011 – March 4, 2011 March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Existing Anticyclotron to Slow Down Muons LEAR anticyclotron moved from CERN to Paul Scherrer Institute (PSI) to decelerate muons Initial pmuon = 30 MeV/c, p/m = γβ = 0.28 Another end-to-end idea at similar scale: Particle Refrigerator Tom Roberts, Dan Kaplan Compared to LEAR/PSI, our anticyclotron - has similar magnet size and field strength - cools higher momentum muons (180 MeV/c, γβ = 1.70) - uses sectored fields for increased focusing March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

An Anticyclotron to Cool Muons Cool p = 180 MeV/c muons in 3 steps Stop muons in hydrogen, outer sectored magnetic field which transitions to inner magnetic bottle Extract muons from hydrogen with 0.1 MV/m electric field Accelerate muons back to 180 MeV/c with 1 MV/m electric field G4Beamline simulation Decays turned off Schematic design not finalized, optimized March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

MAP Winter Meeting, Jefferson Laboratory G4Beamline View 1 of 2 guiding solenoids Ez = 1 MV/m for acceleration after muons stopped, extracted 2 coils for magnetic bottle Ez = 0.1 MV/m for extraction after muons stopped Hydrogen to stop muons 400 mm March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Hydrogen Density Vs. Radius 300-fold variation of density vs. radius driven by large variation of hydrogen stopping power vs. muon momentum March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Hydrogen Density Vs. Radius Need high density as long as possible for stopping times comparable to muon lifetime. Need muons to stop here to extract with reasonable Ez. Need to satisfy competing demands of short stopping time and low final hydrogen density MAP Winter Meeting, Jefferson Laboratory March 2, 2011 6

6-Sector Magnetic Field Magnetic field from specified Bz(r, θ, z = 0) 2 coils (r ~ < 0.2 m) providing inner magnetic bottle guiding solenoids above z = 0 midplane and coils B out of z = 0 midplane determined through 2nd order expansion March 2, 2011 MAP Winter Meeting, Jefferson Laboratory 7

Expansion of Bz(z = 0) Out of z = 0 Midplane Evaluation of high order terms with Mathematica Suggested in ZGOUBI manual Details in paper at www.mice.iit.edu/~hart/magnetic_field_midplane_expansion.pdf with proof by Kevin Paul, Tech-X March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Initial Muon Beam and Magnetic Field Bottle + 2 coils with r = 200 mm at z = ±200 mm + Bz = 2.4 T at center Outer focus field + Expanded to 2nd order in z - 2 guiding solenoids 200 muon input H container thickness = 200 mm ri = (533 ± 14) mm pri = (1.3 ± 1.5) MeV/c zi = (5.0 ± 12.1) mm pzi = (2.8 ± 2.1) MeV/c K.E.i = (103.1 ± 9.6) MeV ti = (1.4 ± 289) ns March 2, 2011 MAP Winter Meeting, Jefferson Laboratory 9

Orbit of Stopped Muon In Innermost Hydrogen stochastic processes on 26/200 initial muons stopped in rf < 65 mm, |zf| < 100 mm: 100 mbar hydrogen March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Start and Stop Times of 26 Stopped Muons Red: start times of 26/200 stopped muons tstart = (-16 ± 264) ns set by initial beam Black: stop times of 26/200 stopped muons tstop = (3979 ± 1094) ns March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Extraction and Reacceleration 26 stopped muons start in 100 mbar H at z = (3 ± 50) mm Ez,extract = 0.1 MV/m Leave H with p = 0.042 MeV/c K.E. = 8.4 eV Accelerated to 100 MeV over 100 m by Ez,accel = 1 MV/m in 585 ns stochastic processes off March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Initial and Final ‘x’ Normalized Emittance εr,Ni = 0.066 mm rad εx,Nf = 0.085 mm rad σr = 4.9 mm, σpr = 1.4 MeV/c σx = 17.4 mm, σpx = 0.61 MeV/c March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Initial and Final ‘y’ Normalized Emittance εz,Ni = 0.100 mm rad εy,Nf = 0.080 mm rad σr = 10.8 mm, σpr = 1.0 MeV/c σy = 13.7 mm, σpy = 0.61 MeV/c March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Initial and Final Longitudinal Normalized Emittance εL,Ni = 3567 mm rad εL,Nf = 0.197 mm rad σK.E. = 4.7 MeV, σt = 269 ns σK.E. = 0.00022 MeV, σt = 319 ns March 2, 2011 MAP Winter Meeting, Jefferson Laboratory 15

Plans and Optimizations Getting large longitudinal cooling in an end-to-end system, but need to make more realistic Close magnetic bottle to increase fraction of cooled muons (now ~ 13%) Penning traps RF Paul trap and electron/positron beam ion traps Reduce total spiral time (now ~ 3 muon lifetimes) Reduce inner bottle B field → lower energy muons can pass through higher density gas Brillouin space charge limit estimate: Skew quad triplet can turn a spinning beam into a flat, non-spinning beam March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Plans and Optimizations Getting large longitudinal cooling in an end-to-end system, but need to make more realistic Exploring muon capture, gas ionization, and knock-on electrons Many thanks to Kevin Paul, Tech-X 10-16 10-17 10-18 10-19 10-20 10-21 10-22 10-23 10-24 10-25 10-26 10-27 10-28 10-29 10-30 10-31 10-2 10-1 100 101 102 103 104 March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

Plans and Optimizations Getting large longitudinal cooling in an end-to-end system, but need to make more realistic Increase admittance to match beam to cyclotron lattice Al Garren’s simulations of tabletop rings with hydrogen, RF yielded 150 mm – 250 mm apertures Transition from 6 sectors to 3 sectors may enable smaller bottle, shorter spiral times Ionization may make foils necessary instead of hydrogen March 2, 2011 MAP Winter Meeting, Jefferson Laboratory

MAP Winter Meeting, Jefferson Laboratory Summary and Plans Have schematic, preliminary simulation of anticyclotron cooling 180 MeV/c muons longitudinally Initial exploration of real world processes Continued optimization, making more realistic March 2, 2011 MAP Winter Meeting, Jefferson Laboratory