2002/7/04 NuFact02@Imperial College, London Beam Dynamics Studies of FFAG Akira SATO Osaka University

2002/7/04 NuFact02@Imperial College, London

Beam Dynamics Studies of FFAG

Akira SATOOsaka University


Contents

PRISM FFAG studiesLarge gap FFAGExperimental studies of PoP FFAGSummary


PRISM FFAG Studies

PRISM OverviewPhase Rotation

Acceptance


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


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

except kicker parts.

GEANT3 has single precision.

Cf. Double precisionDPGeantGeant4

PRISM FFAG Simulation


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


Typical Muon Track

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


01

23

45

Phase Rotation

RF : 5MHz, 128kV/mΔE/E = 20MeV+12%-10%

012

3

4

5

RF : 5MHz, 250kV/mΔE/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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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


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)




Studies of the beam dynamics in the PoP-FFAG

Beam AccelerationHorizontal acceptanceDynamic aperture

PoP FFAG



Beam position monitor


Beam Acceleration


Horizontal acceptance


Beam motion at the resonance conditions


150-MeV proton FFAG

With “return yoke free” magnetNow under construction


150 MeV FFAG Roadmap

23

fiscal 2002 45 Construction6789

1011 Commissioning12123 Experiment

fiscal 2003 456

Inspection by Government

making the proposalof the radioactive instrument

Permission of the commissioning


SummaryThe PoP FFAG worked as designed.

Proton can be accelarated in 1msec.

PRISM phase rotation was studied by GEANT3.21.

Energy spread of ΔE/E=+-5% was achieved.The present design PRISM FFAG has large acceptance : H=10000, V=2000pmm mrad. These acceptance was limited by physical aperture.

We have some idea to get lager acceptance FFAG. These will be studied soon.

Documents

2002/7/04 NuFact02@Imperial College, London Beam Dynamics Studies of FFAG Akira SATO Osaka University