Inverse Cyclotrons for Intense Muon Beams – Phase I

Kevin PaulTech-X Corporation

Don SummersUniversity 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 × 1012 muons in the core and what the beam looks like after ejection.

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?

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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)

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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

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The Penning-Pierce Trap

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2z2 − r2 = 2z02

z0 = 75 mm

Upper/Lower End-caps:

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2z2 − r2 = −r02

r0 = 2z0

Cylindrical Ring:

+V

+V

-V

zB0

For stability:

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B0 >4mμV

ez02

Assuming positive muons…

r

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Φ(r,z) =V2z2 − r2

2z02

⎛

⎝ ⎜

⎞

⎠ ⎟

• Need voltages necessary to hold 2 × 1012 muons

– Assumes a uniform magnetic field:

– For stability:

– To contain muons at a temperature of 10 keV:

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Penning-Pierce Trap VORPAL Models

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V ≈ 60 kV

€

B0 =1 T

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V < 1197 kV

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VORPAL Results – 3D Simulations

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VORPAL Trap Simulation Results: Transverse (x-y) Dynamics

y

x

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VORPAL Trap Simulation Results: Longitudinal (x-z) Dynamics

z

x

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VORPAL Trap Simulation Results: Transverse (x) Spatial Distribution

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VORPAL Trap Simulation Results: Transverse (x) Momentum Distribution

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VORPAL Trap Simulation Results: Longitudinal (z) Spatial Distribution

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VORPAL Trap Simulation Results: Longitudinal (z) Momentum Distribution

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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

zB0

rE

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VORPAL Ejection Simulation Results: Transverse (x) Spatial Distribution

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VORPAL Ejection Simulation Results: Transverse (x) Momentum Distribution

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VORPAL Ejection Simulation Results: Temporal (t) Distribution

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VORPAL Ejection Simulation Results: Energy (KE) Distribution

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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)

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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)