Beam Dynamics Studies of FFAG

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Beam Dynamics Studies of FFAG

• Akira SATO
• Osaka University

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Contents

• PRISM FFAG studies
• Large gap FFAG
• Experimental studies of PoP FFAG
• Summary

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PRISM FFAG Studies

• PRISM Overview
• Phase Rotation
• Acceptance

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PRISM Beam Characteristics
Phase Rotated Intense Slow Muon source

• intensity 1011-1012m/sec
• muon kinetic energy 20 MeV (68 MeV/c)
• range about 3 g
• kinetic energy spread 0.5-1.0 MeV
• a few 100 mg range width
• beam repetition about 100Hz

Search µN?eN with sensitivity of 10-18 Cf. MECO
_at_BNL-AGS 10-16
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PRISM layout

• Pion capture section
• Decay section
• Phase rotation section
• FFAG Based
• a ring instead of linear systems
• reduction of of rf cavities
• reduction of rf power consumption
• compact

not in scale
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FFAG for Phase Rotation
Fixed Field Alternating Gradient Synchrotron

• synchrotron oscillation for phase rotation
• not cyclotron (isochronous)
• large momentum acceptance
• larger than synchrotron
• several 10 is aimed
• large transverse acceptance
• strong focusing
• large horizontal emittance
• reasonable vertical emittance at low energy

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Phase Rotation

• Phase Rotation decelerate particles with high
  energy and accelerate particle with low energy by
  high-field RF
• A narrow pulse structure (lt1 nsec) of proton beam
  is needed to ensure that high-energy particles
  come early and low-energy one come late.

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PRISM FFAG Simulation

• Muon phase rotation was studied by the GEANT3.21
  3D simulation.
• except kicker parts.
• GEANT3 has single precision.
• Cf. Double precision
• DPGeant
• Geant4

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Magnet Model and Field

• Field gradient was made by gap size.
• Magnitude of the field
• D Bz -0.0717(r(m)/r0)5 (T)
• F Bz 0.435(r(m)/r0)5 (T)
• r0 5 m for 68MeV/c

• 3D magnetic field of FFAG magnet was calculated
  by TOSCA.

FFAG Lattice Triplet DFD
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Typical Muon Track

• 54.4MeV/c µ
• Because FFAG has momentum dispersion, radius of
  the muon orbit becomes lager gradually.

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Phase Rotation

• RF 5MHz, 128kV/m
• ?E/E 20MeV12-10

• RF 5MHz, 250kV/m
• ?E/E 20MeV4-5

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How to realize saw tooth

• It is difficult to realize saw tooth with a field
  gradient of 250kV/m.
• Fit the saw tooth wave to the function
• Each RF have just sinusoidal wave.

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Simulation Result
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Horizontal Phase Space
Horizontal Acceptance 10000pi mm mrad
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Vertical Phase Space
Vertical Acceptance 2000pi mm mrad
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Survival Rate vs. Momentum

• Why do large momentum particles have low survival
  rate?
• Gap ? (r0/r)5
• Physical aperture limits the dynamical
  acceptance.
• Lager Gap Magnet
• ? Lager Acceptance
• We Need Lager Gap Magnet !

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FFAG Magnet with Large Gap(1)
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Dose an acceptance depend on betatron tune?
Selection of Betatron Tune
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Long Term Acceptance (Region1)
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Long Term Acceptance (Region2)
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Studies of the beam dynamics in the PoP-FFAG

• Beam Acceleration
• Horizontal acceptance
• Dynamic aperture

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Beam position monitor
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Beam Acceleration
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Horizontal acceptance
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Beam motion at the resonance conditions
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150-MeV proton FFAG

• With return yoke free magnet
• Now under construction

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Summary

• The PoP FFAG worked as designed.
• Proton can be accelarated in 1msec.
• PRISM phase rotation was studied by GEANT3.21.
• Energy spread of ?E/E-5 was achieved.
• The present design PRISM FFAG has large
  acceptance H10000, V2000pmm mrad. These
  acceptance was limited by physical aperture.
• We have some idea to get lager acceptance FFAG.
  These will be studied soon.