Study of Resonance Crossing in FFAG

Masamitsu Aiba (KEK)

Contents1. Introduction2. Crossing experiment at PoP FFAG3. Crossing experiment at HIMAC synchrotron4. Summary

Introduction• FFAG accelerator:

– For proton driver– For muon acceleration, phase rotation

• Resonance crossing– In scaling FFAG: tune variation due to

imperfection of scaling – In non-scaling FFAG: tune variation in wide range

• Dynamics of resonance crossing is important. 　　 Experimental study at PoP FFAG and HIMAC

Crossing experiment at PoP FFAG

sector number 8 (DFD triplet)k value 2.5

kinetic energy 50-500keVfmagnetic field 0.14-0.32T(F)

0.04-0.13T(D)average radius 0.81-1.14mbetatron tune 2.22-2.16(Hor.)

1.26-1.23(Ver.)revolution freq. 0.61-1.40MHz

RF voltage 5kVpp

Parameter list

PoP FFAG: radial sector type scaling FFAG

Experiment of resonance crossing withvarious driving term and crossing speed

Remodeling magnets

Crossing third order resonance during acceleration

0 50 100 150 200 250 300 350 400 450

2.20

2.25

2.30

2.35

2.40

3x=7 (

x=2.333)

hori

zont

al tu

ne

Beam Energy (keV)

After remodeling Before remodeling

4mm iron plates

Driving term

0 45 90 135 180 225 270 315 360

-20

-10

0

10

20

⑧⑦⑥⑤④③②①

current error

current error

septum

COD with current error

CO

D (

mm

)

azimuthal angle (deg.)

)33()( 32233 DxDDxxODxO Feed Down:Driving term with COD

Controlling COD

Driving term can be varied and controlled.

Beam measurementBeam scraping & intensity measurement

turn

intensity

Particle distribution in beam emittance was measuredbefore and after crossing.

Fast crossing

0 250 500 750 1000 1250 15000.0

5.0x10- 4

1.0x10- 3

1.5x10- 3

2.0x10- 3

2.5x10- 3

3.0x10- 3

3.5x10- 3

4.0x10- 3

dI/dW

(

mm

-m

rad.

-1 )

emittance ( mm- mrad.)

BeforeCrossingAfter

Fast crossing: no clear signal of a damage due to crossing

110 130 150 (keV)

40 60 80 100 120 140 160

0.0

0.2

0.4

0.6

0.8

1.0

current error -2%, speed1

Nor

. int

ensi

ty

r from 50keV (mm)

scrp. 868mm scrp. 888mm scrp. 908mm

Energy gain 1.6kV/turn = x 1.4×10-3

Current error –2%Scraping data

Particle distribution in beam emittance

Slow crossing

80 100 120 140 160 1800.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

inte

nsity

(-)

r from 50keV (mm)

scraper 888mm scraper 908mm scraper 928mm scraper 948mm

Slow crossing: a part of beam is transported to large amplitude

0 1000 2000 3000 40000.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

2.5x10-3

3.0x10-3

3.5x10-3

dI/d

a (

mm

-mra

d.)

emittance (mm-mrad.)

Crossing After 130 150 170 190 (keV)

Energy gain 0.13kV/turn = x 1.2×10-4

Current error –2%Scraping data

Particle distribution in beam emittance

“Particle trapping” modelReference: A.W.Chao and M.Month, NIM 121, P.129 (1974) “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER NONLINEAR RESONANCE”

Phase space topology during crossing third order resonance

p3

1Distance from resonance

This model explains the experimental result.

Assuming: nonlinear detuning (octupole) driving term (sextupole)

Trapping efficiency

,43 eNL

0012 aBNL

2

1

03 aApe

)(2

0160

OdB

)(8

2

0

2

1

Sipp edA

3

2

1 4

eNL

pL 3

1

eL 23

:2

4

32

12

sA

)exp( 1

s

TA

P

1,1

,1,

1

11

if

ifs

Nonlinear detuning:

Driving term:

Linear tune shift:

Nonlinear tune shift:

Excitation width:

s： the beam emittance of island center

the total area of islands

the adiabatic parameter

The adiabatic parameter means a speed of islands moving during crossing.

Crossing speed:

:

Trapping efficiency for third order resonance

*Assuming >>1 to derivethe trapping efficiency

Comparison of trapping efficiencies

500 600 700 800 900 1000 11000.0

0.2

0.4

0.6

0.8

1.0

error 2%, speed 0.13kV/turn, scraper 948mm

Nor

. int

egra

l (-)

num. of turn 0.0 0.1 0.2 0.30

5

10

15

20

25

30

35

trap

ping

eff

icie

ncy

(%)

energy gain (kV/turn)

current error theory: -2% theory: 0% theory: -3% exp.: -2% exp.: 0% exp.: -3% sim.: -2% sim.: 0% sim.: -3%

The experiment results are consistent to simulations.

Efficiency in experimentTrapping efficiencies

are about 3.

Criterion to avoid trapping

2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30tr

appi

ng e

ffic

ienc

y (%

)

adiabatic parameter

current error -2% current error 0% current error -3%

Adiabatic parameter more than 7 will be harmless.

Crossing experiment at HIMACFlat bottom operation parameter

circumference 129.6msuper period / cell ６／１２

particle carbon 6+inj. energy 6MeV/u

operation point (3.69, 2.13)

Crossing: Varying quadrupole strengthDriving term:　 SXFr*2 sextupole Nonlinear detuning: Second order effect of SXH sextupole

Crossing 3vx=11 in both directionObserving beam profile with Gas Sheet Monitor directly

SXFr

SXFr

SXH for all SPGas SheetMonitor

Crossing in a direction of tune decreasing

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)-40 -30 -20 -10 0 10 20 30 40

0

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

x=3.668 x=3.662 x=3.661 x=3.660

x=3.658 x=3.652 x=3.647Crossing speed:

4.6*10-6

Nonlinear detuning:2.52m-1

Driving term:0.019m-1/2

Beam profiles during crossing

Crossing in a direction of tune increasing

-40 -30 -20 -10 0 10 20 30 400.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

t

x (mm)-40 -30 -20 -10 0 10 20 30 40

0.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

tx (mm)

-40 -30 -20 -10 0 10 20 30 400.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

t

x (mm)

x=3.654 x=3.657

x=3.676 x=3.711

Crossing speed:4.6*10-6

Nonlinear detuning:2.52m-1

Driving term:0.019m-1/2

Beam profiles during crossing

Simulation – tune decreasing

-100 -50 0 50 100

-20-15-10-505

101520

x=3.647

x' (

mra

d.)

x (mm)

-60 -40 -20 0 20 40 600

100

200

300

400

500

x=3.660

Num

ber

of p

arti

cle

x (mm)

-50 -40 -30 -20 -10 0 10 20 30 40 50

-8-6-4-202468

x=3.668

x' (

mra

d.)

x (mm)-60 -40 -20 0 20 40 60

-15

-10

-5

0

5

10

15 x=3.660

x' (

mra

d.)

x (mm)

-60 -40 -20 0 20 40 600

100

200

300

400

500 x=3.668

Num

ber

of p

arti

cle

x (mm)-60 -40 -20 0 20 40 60

0

100

200

300

400

500 x=3.647

Num

ber

of p

arti

cle

x (mm)

Simulation – tune increasing

-40 -20 0 20 40-8

-6

-4

-2

0

2

4

6

8 x=3.654

x' (

mra

d.)

x (mm)

-100 -50 0 50 100

-20-15-10-505

101520

x=3.705

x' (

mra

d.)

x (mm)

-60 -40 -20 0 20 40 600

100

200

300

400

x=3.654

Num

ber

of p

artic

le

x(mm)-60 -40 -20 0 20 40 600

100

200

300

400

x=3.705

Num

ber

of p

artic

le

x (mm)

Difference due to crossing direction

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

-40 -30 -20 -10 0 10 20 30 400

1000

2000

3000

4000

5000

6000

7000

8000

coun

t

x (mm)

x=3.668 x=3.647

-40 -30 -20 -10 0 10 20 30 400.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

t

x (mm)

x=3.654

-40 -30 -20 -10 0 10 20 30 400.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

coun

t

x (mm)

x=3.711

Tune decreasing

Tune increasing

The effect due to crossing depends upon crossing direction.

In one direction: “particle trapping”In other direction: “emittance growth”

Crossing without sextupoles (1)

Crossing speed:8.5*10-6

Nonlinear detuning:0 m-1

Driving term:0 m-1/2

Beam profiles during crossing (tune decreasing)

“Particle trapping” occurred even when all magnets are linear elements.

Possible source for nonlinear components:allowed poles, fringing field …

-60 -40 -20 0 20 40 600

1000

2000

3000

4000

5000

6000

7000

8000

Cou

nt (

A.U

.)

x (mm)-60 -40 -20 0 20 40 60

0

1000

2000

3000

4000

5000

6000

7000

8000

Cou

nt (

A.U

.)

x (mm)

-60 -40 -20 0 20 40 600

1000

2000

3000

4000

5000

6000

7000

8000

Cou

nt (

A.U

.)

x (mm)

Crossing without sextupoles (2)

In tune decreasing In tune increasing

Beam intensity during crossing

Beam loss due to crossing 3Nx=11

Crossing speed:5.5*10-6

Nonlinear detuning:0 m-1

Driving term:0 m-1/2

*Data acquired by Machida and Uesugi

Summary

• Experiment at PoP FFAG (crossing 3x=7)– “Particle trapping” due to resonance crossing was obser

ved.– Trapping efficiency are understood qualitatively.– Adiabatic parameter more than 7 was harmless.

• Experiment at HIMAC (crossing 3x=11)– Difference due to crossing direction was clearly observ

ed.– Even sextupoles are not excited, the effect of crossing

was “particle trapping”.