muon phase rotation at prism ffag
DESCRIPTION
Muon Phase Rotation at PRISM FFAG. Akira SATO Osaka University. Contents. PRISM Overview Tracking Simulation by Geant3.21 Phase rotation Acceptance of FFAG Muon decay - survival rate Large Gap FFAG Betatron tune dependence Summary. PRISM Beam Characteristics. - PowerPoint PPT PresentationTRANSCRIPT
2002/7/02 NuFact02@Imperial College, London
Muon Phase Rotation at PRISM FFAG
Akira SATOOsaka University
2002/7/02 NuFact02@Imperial College, London
ContentsPRISM OverviewTracking Simulation by Geant3.21
Phase rotationAcceptance of FFAGMuon decay - survival rate
Large Gap FFAGBetatron tune dependence
Summary
2002/7/02 NuFact02@Imperial College, London
PRISM Beam Characteristics
intensity : 1011-1012±/secmuon 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 @BNL-AGS 10-16
Phase Rotated Intense Slow Muon source
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PRISM layoutPion capture sectionDecay sectionPhase rotation section
FFAG Baseda ring instead of linear
systemsreduction of # of rf cavitiesreduction of rf power consumptioncompact not in scale
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FFAG for Phase Rotation
synchrotron oscillation for phase rotation
not cyclotron (isochronous)
large momentum acceptancelarger than synchrotron± several 10 % is aimed
large transverse acceptancestrong focusinglarge horizontal emittancereasonable vertical emittance at low energy
Fixed Field Alternating Gradient Synchrotron
2002/7/02 NuFact02@Imperial College, London
Phase RotationPhase Rotation = decelerate particles with high energy and accelerate particle with low energy by high-field RF
A narrow pulse structure (<1 nsec) of proton beam is needed to ensure that high-energy particles come early and low-energy one come late.
energyenergy
time time
2002/7/02 NuFact02@Imperial College, London
Simulation of the PRISM Phase Rotator
By GEANT3.21 Full simulationMuon decay -> intensityInteraction -> background
Acceptance studyPhase rotation studyMuon survival rate
2002/7/02 NuFact02@Imperial College, London
Muon phase rotation was studied by the GEANT3.21 3D simulation.
except kicker parts.
GEANT3 has single precision.
Cf. Double precisionDPGeantGeant4
Simulation Setup
2002/7/02 NuFact02@Imperial College, London
Magnet Model and Field 3D magnetic field of FFAG magnet was calculated by TOSCA.
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
1 Cell = 45.0 deg.Straight sect. = 16.49 D = 2.46 FD 間 = 0.10 F/2 = 3.00
rrin=460
rout=550cm
Half gap = 10 x (500/r)5 cm
FFAG LatticeTriplet : DFD
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RF modelingTotal # of RF cavity : 12
4gaps/cavity
RF wave field type:SinusoidalSaw tooth
25cm
2 m
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100 cm
Information @θ =0
(r,θ,z)momentumToFParticle ID
θ
θ =0
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Muon injectionMuon was injected from θ=0momentum: 68MeV/c+-20%54.4, 61.2, 68.0, 74.8, 81.6MeV/c
Phase space:r : r(p)+-8 cmur : 0+-0.2 rad.z : 0+-16 cmuz : 0+-0.08 rad.
Timing :Arrival time to solenoid exit is taken into account.
10ns 10ns
81.6
71.2
68.0
61.2
54.4MeV/c
t=0,+-5ns
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Typical Muon Track
54.4MeV/c μBecause FFAG has momentum dispersion, radius of the muon orbit becomes lager gradually.
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Phase Rotation Study
SinusoidalSaw tooth
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01
23
45
Sinusoidal RFRF : 5MHz, 128kV/m
Energy spread after 5turnsΔp/p = 68MeV/c+8%-6%ΔE/E
= 20MeV+12%-10%
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012
3
4
5
Saw tooth RF RF : 5MHz, 250kV/m
Energy spread after
5turnsΔp/p
= 68MeV/c+2%-2%ΔE/E
= 20MeV+4%-5%
2002/7/02 NuFact02@Imperial College, London
How to realize saw toothIt 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.
V (t) Ansin(nt /L Bn )n1
3
phase(nsec)-100 -50 05 0 100
-2000
-1500
-1000
-500
0
500
1000
1500
2000
wave136.dat
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.6647)E = -275.00 sin( 2
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.6647)E = -275.00 sin( 2
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.9085)E = 250.00 sin( 3
Wav e Comp.
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Simulation Result1 0
3
2
4
phase(nsec)-100 -50 05 0 100
-2000
-1500
-1000
-500
0
500
1000
1500
2000
wave136.dat
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.6647)E = -275.00 sin( 2
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.6647)E = -275.00 sin( 2
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.1569)E = 350.00 sin( 1
Wav e Comp.
phase(nsec)-100 -500 50 100
-300
-200
-100
0
100
200
300
x / L + -0.9085)E = 250.00 sin( 3
Wav e Comp.
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Acceptance Study
Horizontal acceptanceVertical acceptance
Survival rateLarge gap FFAG
2002/7/02 NuFact02@Imperial College, London
Horizontal Phase SpaceInitial Phase
After 1 turn
After 2turns
After 3turns
After 4 turns
After 5turns
54.4 61.2 68.0 74.8 81.6MeV/c
Horizontal Acceptance 10000pi mm mrad
2002/7/02 NuFact02@Imperial College, London
54.4 61.2 68.0 74.8 81.6MeV/c
Initial Phase
After 1 turn
After 2 turns
After 3 turns
After 4 turns
After 5 turns
Vertical Phase Space
Vertical Acceptance 2000pi mm mrad
2002/7/02 NuFact02@Imperial College, London
Muon surviving -
e-
decay
Surviving rate after 5turns : 60%e- contamination : < 1/1600
Decay OFF
Decay ON
# of surviving muon after 5 turns
2002/7/02 NuFact02@Imperial College, London
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 !
rrin
rout
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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.
2002/7/02 NuFact02@Imperial College, London
Surviving Rate (Region2)
2002/7/02 NuFact02@Imperial College, London
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2002/7/02 NuFact02@Imperial College, London
SummaryPRISM phase rotation was studied by GEANT3.21.We can achieve energy spread of ΔE/E=+-5% after phase rotation.Even present design PRISM FFAG has large acceptance : H=10000, V=2000mm mrad. These acceptance was limited by physical aperture.We have some idea to get lager acceptance. These will be studied soon.