Study of Resonance Crossing in FFAG

1
Study of Resonance Crossing in FFAG

• Contents
• Introduction
• Crossing experiment at PoP FFAG
• Crossing experiment at HIMAC synchrotron
• Summary

• Masamitsu Aiba (KEK)

2
Introduction

• FFAG accelerator
• For proton driver
• For muon acceleration, phase rotation
• Resonance crossing
• In scaling FFAG tune variation due to
  imperfection of scaling
• In non-scaling FFAG tune variation in wide range

• Dynamics of resonance crossing is important.
• Experimental study at PoP FFAG and HIMAC

3
Crossing experiment at PoP FFAG
PoP FFAG radial sector type scaling FFAG
Parameter list
Experiment of resonance crossing with various
driving term and crossing speed
4
Remodeling magnets
Crossing third order resonance during
acceleration
4mm iron plates
5
Driving term
Driving term with COD
Feed Down
Controlling COD
Driving term can be varied and controlled.
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Beam measurement
Beam scraping intensity measurement
intensity
turn
Particle distribution in beam emittance was
measured before and after crossing.
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Fast crossing
Energy gain 1.6kV/turn Dnx 1.410-3 Current
error 2
Scraping data
110 130 150 (keV)
Particle distribution in beam emittance
BeforeCrossingAfter
Fast crossing no clear signal of a damage due to
crossing
8
Slow crossing
Energy gain 0.13kV/turn Dnx 1.210-4 Current
error 2
Scraping data
Particle distribution in beam emittance
130 150 170 190 (keV)
Crossing After
Slow crossing a part of beam is transported to
large amplitude
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Particle trapping model
Reference A.W.Chao and M.Month, NIM 121, P.129
(1974) PARTICLE TRAPPING
DURING PASSAGE THROUGH
A HIGH-ORDER NONLINEAR RESONANCE
Phase space topology during crossing third order
resonance
Assuming nonlinear detuning (octupole)
driving term (sextupole)
Distance from resonance
This model explains the experimental result.
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Trapping efficiency
Trapping efficiency for third order resonance
Crossing speed
Nonlinear detuning
asthe beam emittance of island center
Driving term
the total area of islands
Linear tune shift
Nonlinear tune shift

the adiabatic parameter
Excitation width
The adiabatic parameter means a speed of islands
moving during crossing.
Assuming kgtgt1 to derive the trapping efficiency
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Comparison of trapping efficiencies
Trapping efficiencies
Efficiency in experiment
k are about 3.
The experiment results are consistent to
simulations.
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Criterion to avoid trapping
Adiabatic parameter more than 7 will be harmless.
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Crossing experiment at HIMAC
Gas Sheet Monitor
SXH for all SP
SXFr
Crossing Varying quadrupole
strength Driving term SXFr2 sextupole
Nonlinear detuning Second order effect of
SXH sextupole
SXFr
Crossing 3vx11 in both direction Observing beam
profile with Gas Sheet Monitor directly
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Crossing in a direction of tune decreasing
Beam profiles during crossing
nx3.668
nx3.662
nx3.661
nx3.660
nx3.658
nx3.652
nx3.647
Crossing speed 4.610-6 Nonlinear
detuning 2.52m-1 Driving term 0.019m-1/2
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Crossing in a direction of tune increasing
Beam profiles during crossing
nx3.654
nx3.657
Crossing speed 4.610-6 Nonlinear
detuning 2.52m-1 Driving term 0.019m-1/2
nx3.676
nx3.711
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Simulation tune decreasing
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Simulation tune increasing
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Difference due to crossing direction
nx3.668
nx3.647
Tune decreasing
nx3.654
nx3.711
Tune increasing
The effect due to crossing depends upon crossing
direction.
In one direction particle trapping In other
direction emittance growth
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Crossing without sextupoles (1)
Beam profiles during crossing (tune decreasing)
Crossing speed 8.510-6 Nonlinear detuning 0
m-1 Driving term 0 m-1/2
Particle trapping occurred even when all
magnets are linear elements.
Possible source for nonlinear components allowed
poles, fringing field
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Crossing without sextupoles (2)
Beam intensity during crossing
Data acquired by Machida and Uesugi
In tune decreasing
In tune increasing
Beam loss due to crossing 3Nx11
Crossing speed 5.510-6 Nonlinear detuning 0
m-1 Driving term 0 m-1/2
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Summary

• Experiment at PoP FFAG (crossing 3nx7)
• Particle trapping due to resonance crossing was
  observed.
• Trapping efficiency are understood qualitatively.
• Adiabatic parameter more than 7 was harmless.
• Experiment at HIMAC (crossing 3nx11)
• Difference due to crossing direction was clearly
  observed.
• Even sextupoles are not excited, the effect of
  crossing was particle trapping.