Muon Phase Rotation at PRISM FFAG

2002/7/02 NuFact02@Imperial College, London

Muon Phase Rotation at PRISM FFAG

Akira SATOOsaka University


ContentsPRISM OverviewTracking Simulation by Geant3.21

Phase rotationAcceptance of FFAGMuon decay - survival rate

Large Gap FFAGBetatron tune dependence

Summary


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


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


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


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


Simulation of the PRISM Phase Rotator

By GEANT3.21 Full simulationMuon decay -> intensityInteraction -> background

Acceptance studyPhase rotation studyMuon survival rate


Muon phase rotation was studied by the GEANT3.21 3D simulation.

except kicker parts.

GEANT3 has single precision.

Cf. Double precisionDPGeantGeant4

Simulation Setup


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


RF modelingTotal # of RF cavity : 12

4gaps/cavity

RF wave field type:SinusoidalSaw tooth

25cm

２ m


100 cm

Information @θ ＝０

(r,θ,z)momentumToFParticle ID

θ

θ ＝０


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


Typical Muon Track

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


Phase Rotation Study

SinusoidalSaw tooth


01

23

45

Sinusoidal RFRF : 5MHz, 128kV/m

Energy spread after 5turnsΔp/p = 68MeV/c+8%-6%ΔE/E

= 20MeV+12%-10%


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%


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.


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


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


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


Muon surviving -

e-

decay

Surviving rate after 5turns : 60%e- contamination : < 1/1600

Decay OFF

Decay ON

# of surviving muon after 5 turns


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


FFAG Magnet with Large Gap(1)


Dose an acceptance depend on betatron tune?

Selection of Betatron Tune


Long Term Acceptance (Region1)


Long Term Acceptance (Region2)


5 turns Acceptance- Number of lost particle

Region1 Region2

FFAG acceptance depends on betatron tune.


Surviving Rate (Region2)




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.

Documents

Muon Phase Rotation at PRISM FFAG