1. Inverse Cyclotrons for Intense Muon Beams – Phase I Kevin Paul Tech-X Corporation Don Summers University of Mississippi ABSTRACT: I will summarize the progress on the current SBIR Phase I to begin investigating the feasibility of using inverse cyclotrons for intense muon beams. This Phase I is intended to focus on the physics within the core of the cyclotron, where the muons are captured and trapped. The main limitation is believed to be space charge. As such, this Phase I is intended to explore what fields are needed to trap 2 × 10 12 muons in the core and what the beam looks like after ejection.

2. Tech-X Corporation - 2008 Muon Collider Design Workshop 2 Phase I Main Objectives Demonstrate ejection from the cyclotron in vacuum with VORPAL –What are the space charge limitations? Investigate effects of material (ionization, muon capture, recombination) on ejection with VORPAL –Is space charge force mitigated? –What are muon capture losses?

3. Tech-X Corporation - 2008 Muon Collider Design Workshop 3 Phase I Tasks Implement one-body decay in VORPAL –Constant-weight (Monte Carlo) –Variable-weight (deterministic) Vacuum simulations of ejection with VORPAL –Vary confining fields Penning trap –Vary muon cloud density (number of muons) Ejection simulations with low-density gas –Comparison with vacuum simulations Improve algorithms for muon cooling simulations over full energy range –Necessary for full end-to-end simulations (Phase II)

4. Tech-X Corporation - 2008 Muon Collider Design Workshop 4 Vacuum Simulations of the Core Trap Models –Pierce-Penning (presented here) Cylindrical hyperbolic surfaces –Cylindrical Penning Cylinder with end-caps –Open Cylindrical Penning Cylinder without end-caps Ejection Models –Simple “open door” models (presented here) Ramping one side of the trap voltage down –External kicker models

5. Tech-X Corporation - 2008 Muon Collider Design Workshop 5 The Penning-Pierce Trap Upper/Lower End-caps: Cylindrical Ring: +V -V z B0B0 For stability: Assuming positive muons… r

6. Need voltages necessary to hold 2 × 10 12 muons –Assumes a uniform magnetic field: –For stability: –To contain muons at a temperature of 10 keV: Tech-X Corporation - 2008 Muon Collider Design Workshop 6 Penning-Pierce Trap VORPAL Models

7. Tech-X Corporation - 2008 Muon Collider Design Workshop 7 VORPAL Results – 3D Simulations

8. Tech-X Corporation - 2008 Muon Collider Design Workshop 8 VORPAL Trap Simulation Results: Transverse ( x-y ) Dynamics y x

9. Tech-X Corporation - 2008 Muon Collider Design Workshop 9 VORPAL Trap Simulation Results: Longitudinal ( x-z ) Dynamics z x

10. Tech-X Corporation - 2008 Muon Collider Design Workshop 10 VORPAL Trap Simulation Results: Transverse ( x ) Spatial Distribution

11. Tech-X Corporation - 2008 Muon Collider Design Workshop 11 VORPAL Trap Simulation Results: Transverse ( x ) Momentum Distribution

12. Tech-X Corporation - 2008 Muon Collider Design Workshop 12 VORPAL Trap Simulation Results: Longitudinal ( z ) Spatial Distribution

13. Tech-X Corporation - 2008 Muon Collider Design Workshop 13 VORPAL Trap Simulation Results: Longitudinal ( z ) Momentum Distribution

14. Tech-X Corporation - 2008 Muon Collider Design Workshop 14 Ejection from the Trap  Flip the voltage of the upper end-cap to -V -Ramp the voltage of the ring electrode to 0 -Assume this takes a total time of 100 ns -This produces ~0.1 G magnetic fields, which are ignored in the simulation -Particles measured at z = ~16 cm -V +V 0 z B0B0 r E

15. Tech-X Corporation - 2008 Muon Collider Design Workshop 15 VORPAL Ejection Simulation Results: Transverse ( x ) Spatial Distribution

16. Tech-X Corporation - 2008 Muon Collider Design Workshop 16 VORPAL Ejection Simulation Results: Transverse ( x ) Momentum Distribution

17. Tech-X Corporation - 2008 Muon Collider Design Workshop 17 VORPAL Ejection Simulation Results: Temporal ( t ) Distribution

18. Tech-X Corporation - 2008 Muon Collider Design Workshop 18 VORPAL Ejection Simulation Results: Energy ( KE ) Distribution

19. Tech-X Corporation - 2008 Muon Collider Design Workshop 19 Conclusions: Normalized Emittance after Ejection: –1D Transverse Emittance:380 mm-mrad –Longitudinal Emittance: 1.2 mm-mrad Confining magnetic field keeps transverse distribution unchanged Longitudinal distribution determined by kicker speed (how fast you can swing the door open)

20. Tech-X Corporation - 2008 Muon Collider Design Workshop 20 Work yet to do… Consider effects of gas in the core –Ionization –Muon capture (for negative muons) –Muonium formation (for positive muons) –Space-charge mitigation (???) Other trap fields –Cylindrical Penning Traps Easier to construct / inject / eject Requires larger voltages (especially for open traps) –Paul Traps (AC Penning Traps)