Simulations of Muon Cooling With an Inverse Cyclotron

1
Simulations of Muon Cooling With an Inverse
Cyclotron

• Introduction
• G4beamline Work
• ICOOL Work
• Plans and Goals

2
Introduction

• Started new appointment with U. of Mississippi
• Don Summers is my boss
• Ill be working on
• MICE
• MuCool
• Inverse cyclotron simulation working with
• Kevin Paul from Tech-X
• Kevin Beard from JLab. Muons, Inc.
• Bob Palmer from BNL

3
Introduction

• Inverse cyclotron intriguing scheme for 6D muon
  cooling
• Inverse Cyclotron Scheme
• Muon beam injected into cyclotron
• Lose energy through material interactions
• material wedges surrounded by gas
• Mid-plane foil relying on betatron oscillations
• Focus beam with sectored (straight or spiral)
  magnetic field
• Cooled muon beam coalesces at cyclotron center
  into one bunch
• Muon bunch extracted perpendicular to cyclotron

4
Introduction

• Inverse cyclotron illustration of energy loss
  injection
• ICOOL simulation from Bob Palmer
• Lithium hydride wedges
• 4 sectors, 1.8 T, soft edged magnetic field
• Three 172 MeV/c muons

5
Introduction

• References
• 6D Muon Ionization Cooling with an Inverse
  Cyclotron from COOL 05
• Summers, Bracker, Cremaldi, Godang, Palmer
  (2005)
• Focusing Properties of Superconducting Cyclotron
  Magnets,
• NIM 121, Blosser and Johnson (1974)
• Handbook of Accelerator Physics and Engineering,
• edited by Chao, Tigner
• Introductory Nuclear Physics,
  
• Krane

6
G4beamline Work

• Don sent me program generating Bz of spiral
  sector cyclotron
• Number of sectors
• Spiral angle
• Bz,high, Bz,low
• Transition regions
• Between sectors
• Z bottle
• G4beamline can import field from text file
• I wanted to generate stable orbits from
  trial/error and calculation
• No beam energy, angular spreads
• No energy loss

7
?1 ?2 60º sin(?1/2) (r2/r1) sin(?2 /2)
4 sin(?2 /2) r1 (50 MeV)/(e c 2 T)
83.33 mm r2 (50 MeV)/(e c 0.5 T) 333.33
mm Numerical evaluation of angles, lots of
algebra yield rmin 191.85 mm rave
202.91 mm rmax 214.62 mm
?2
r2
?1
r1
rmax
rave
rmin
Bz 2 T
Bz -0.5 T
8
Plugging Calculated Orbit into G4beamline

• Simulation pretty close to calculation
• 40 orbits before escape
• Red dashed line calculated rave
• Why not exact closed orbit?
• Probably due to G4beamline linear field
  interpolation between grid points
• fields not symplectic?

9
Try Energy Loss With Hydrogen Gas

• Add 0.001 g/cm3 hydrogen gas
• Two particles
• Spiral in (good)
• Escape (bad)
• Refine by
• varying gas pressure vs. radius in accordance to
  dE/dx vs. momentum
• And/or add lithium hydride wedges

10
Whats Needed to Go On

• Focusing in cyclotron plane needs azimuthal (Bx,
  By) fields
• Much harder than Bz, but programs available
• Use soft-edged fields instead of hard-edged
  fields
• Energy loss
• Hydrogen gas of varying densities
• Lithium hydride wedges

11
ICOOL Work

• Bob Palmer sent me zip file with input, output
  files of inverse cyclotron simulation
• Ive been studying ICOOL files, ICOOL Users
  Guide, and ICOOL Reference Manual
• Really close to reproducing output.
• Would like to further develop ICOOL inverse
  cyclotron simulations

• Inverse Cyclotron Illustration
• ICOOL simulation
• Lithium hydride wedges
• 4 sectors, 1.8 T, soft edged magnetic field
• Three 172 MeV/c muons

12
Plans and Goals

• Continue learning more accelerator physics,
  G4beamline, ICOOL,
• Learn more about sector cyclotron magnetic field
  programs
• Existing field in ICOOL simulations
• TOSCA, TRIUMF CYCLOPS,
• Develop inverse cyclotron simulations with
  G4beamline and ICOOL
• Find out whats already known and developed so
  that I dont do too much redundant studies
• Keep working with Don, Kevin, Kevin, Bob, Rick,
  and others on developing inverse cyclotron
  simulations for muon cooling