1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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 with proof by Kevin Paul, Tech-X
March 2, 2011
MAP Winter Meeting, Jefferson Laboratory

9. 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

10. 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

11. 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

12. 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 = MeV/c
K.E. = 8.4 eV
Accelerated to 100 MeV over 100 m by Ez,accel = 1 MV/m in ns
stochastic processes off
March 2, 2011
MAP Winter Meeting, Jefferson Laboratory

13. Initial and Final ‘x’ Normalized Emittance
εr,Ni = mm rad εx,Nf = 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

14. Initial and Final ‘y’ Normalized Emittance
εz,Ni = mm rad εy,Nf = 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

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

16. 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

17. 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
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March 2, 2011
MAP Winter Meeting, Jefferson Laboratory

18. 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

19. 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