Muon Phase Rotation at PRISM FFAG

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Muon Phase Rotation at PRISM FFAG

• Akira SATO
• Osaka University

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Contents

• PRISM Overview
• Tracking Simulation by Geant3.21
• Phase rotation
• Acceptance of FFAG
• Muon decay - survival rate
• Large Gap FFAG
• Betatron tune dependence
• Summary

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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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Simulation of the PRISM Phase Rotator

• By GEANT3.21 Full simulation
• Muon decay -gt intensity
• Interaction -gt background
• Acceptance study
• Phase rotation study
• Muon survival rate

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Simulation Setup

• 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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RF modeling

• Total of RF cavity 12
• 4gaps/cavity
• RF wave field type
• Sinusoidal
• Saw tooth

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?0

• Information
• _at_?0
• (r,?,z)
• momentum
• ToF
• Particle ID

?
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Muon injection

• Muon was injected from ?0
• momentum 68MeV/c-20
• 54.4, 61.2, 68.0, 74.8, 81.6MeV/c
• Phase space
• r r(p)-8 cm
• ur 0-0.2 rad.
• z 0-16 cm
• uz 0-0.08 rad.
• Timing
• Arrival time to solenoid exit is taken into
  account.

81.6
71.2
68.0
61.2
54.4MeV/c
t0,-5ns
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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 Study

• Sinusoidal
• Saw tooth

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Sinusoidal RF

• RF 5MHz, 128kV/m
• Energy spread after 5turns
• ?p/p
• 68MeV/c8-6
• ?E/E
• 20MeV12-10

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Saw tooth RF

• RF 5MHz, 250kV/m
• Energy spread after 5turns
• ?p/p
• 68MeV/c2-2
• ?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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Acceptance Study

• Horizontal acceptance
• Vertical acceptance
• Survival rate
• Large gap FFAG

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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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Muon surviving
of surviving muon after 5 turns

• Surviving rate after 5turns 60
• e- contamination lt 1/1600

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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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5 turns Acceptance- Number of lost particle
Region1
Region2
FFAG acceptance depends on betatron tune.
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Surviving Rate (Region2)
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Summary

• PRISM phase rotation was studied by GEANT3.21.
• We can achieve energy spread of ?E/E-5 after
  phase rotation.
• Even 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. These
  will be studied soon.