1. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 1 Simulations of Muon Cooling With an Inverse Cyclotron Introduction G4beamline Work ICOOL Work Plans and Goals

2. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 2 Introduction Started new appointment with U. of Mississippi –Don Summers is my boss –I’ll 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. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 3 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 Introduction

4. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 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. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 5 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 Introduction

6. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 6 G4beamline Work Don sent me program generating B z of spiral sector cyclotron –Number of sectors –Spiral angle –B z,high, B z,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. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 7 θ1θ1 θ2θ2 r2r2 r1r1 B z = 2 TB z = -0.5 T θ 1 + θ 2 = 60 º sin(θ 1 /2) = (r 2 /r 1 ) × sin(θ 2 /2) = 4 × sin(θ 2 /2) r 1 = (50 MeV)/(e × c × 2 T) = 83.33 mm r 2 = (50 MeV)/(e × c × 0.5 T) = 333.33 mm Numerical evaluation of angles, lots of algebra yield r min = 191.85 mm r ave = 202.91 mm r max = 214.62 mm ave r ave min r min max r max

8. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 8 Plugging Calculated Orbit into G4beamline Simulation pretty close to calculation –~40 orbits before escape –Red dashed line: calculated r ave Why not exact closed orbit? –Probably due to G4beamline linear field interpolation between grid points “fields not symplectic”?

9. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 9 Try Energy Loss With Hydrogen Gas Add 0.001 g/cm 3 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. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 10 What’s Needed to Go On Focusing in cyclotron plane needs azimuthal (B x, B y ) fields –Much harder than B z, but programs available Use soft-edged fields instead of hard-edged fields Energy loss –Hydrogen gas of varying densities –Lithium hydride wedges

11. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 11 ICOOL Work Bob Palmer sent me zip file with input, output files of inverse cyclotron simulation I’ve been studying ICOOL files, ICOOL User’s 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. December 10, 2008Terry Hart, U. of Mississippi., Muon Collider Design Workshop 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 what’s already known and developed so that I don’t do too much redundant studies Keep working with Don, Kevin, Kevin, Bob, Rick, and others on developing inverse cyclotron simulations for muon cooling