2002/7/02 NuFact02@Imperial College, London Muon Phase Rotation at PRISM FFAG Akira SATO Osaka...
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Transcript of 2002/7/02 NuFact02@Imperial College, London Muon Phase Rotation at PRISM FFAG Akira SATO Osaka...
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
2002/7/02 NuFact02@Imperial College, London
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
2002/7/02 NuFact02@Imperial College, London
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
2002/7/02 NuFact02@Imperial College, London
RF modelingTotal # of RF cavity : 12
4gaps/cavity
RF wave field type:SinusoidalSaw tooth
25cm
2 m
2002/7/02 NuFact02@Imperial College, London
100 cm
Information @θ =0
(r,θ,z)momentumToFParticle ID
θ
θ =0
2002/7/02 NuFact02@Imperial College, London
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
2002/7/02 NuFact02@Imperial College, London
Typical Muon Track
54.4MeV/c μBecause FFAG has momentum dispersion, radius of the muon orbit becomes lager gradually.
2002/7/02 NuFact02@Imperial College, London
01
23
45
Sinusoidal RFRF : 5MHz, 128kV/m
Energy spread after 5turnsΔp/p = 68MeV/c+8%-6%ΔE/E
= 20MeV+12%-10%
2002/7/02 NuFact02@Imperial College, London
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.
2002/7/02 NuFact02@Imperial College, London
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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2002/7/02 NuFact02@Imperial College, London
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
2002/7/02 NuFact02@Imperial College, London
Dose an acceptance depend on betatron tune?
Selection of Betatron Tune
2002/7/02 NuFact02@Imperial College, London
5 turns Acceptance- Number of lost particle
Region1 Region2
FFAG acceptance depends on betatron tune.
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.