Resonance Crossing Experimentin PoP FFAG (preliminary report)

M. Aiba (Tokyo Univ.) for KEK FFAG Group

FFAG W.S. ’04 @ KEK

Motivation of Experiment• Beam dynamics of resonance crossing is studied f

or non-scaling FFAG.• There are few study on resonance crossing. Especi

ally, experimental studies are only… (as far as I know)– Fifth integer (Particle Trapping)

@ CERN ISR (1975) by A. W. Chao et al.

– Half integer@ TRIUMF Cyclotron (‘80) by R. Baartman et al.

– Third integer, coupling resonance etc..@ HIMAC (under going) by S. Machida et al.

• PoP FFAG is good machine for beam study.

Basic Parameter of PoP FFAGnum. of sector 8

k value 2.5

kinetic energy 50keV～500keV

magnetic field 0.14～0.32T(F mag.)

0.04～0.13T(D mag.)

average radius 0.81～1.14m

betatron tune 2.22～2.16(Horizontal)

1.26～1.23(Vertical)

repetition 1kHz

frequency & voltage 0.61～1.40MHz/4kVpp

・ Crossing speed can be changed in wide range.・ It is necessary to introduce a variation of tune.

Remodel of Magnet4mm iron plates are inserted to all 8 magnets.

Iron plate

Relatively, a gap outside is more widen than inside.Therefore, k value decrease as increasing radius.

r

Schematic view of magnet cross section

Mainly, horizontal tune varies.

Variation of Tunes

1.5 2.0 2.5 3.01.0

1.5

2.0

2.5

F: 5000AT

D:2000AT

D:2500AT

D:2600AT

D:2900AT(D:2870AT@exp.)D:3000AT

tune variation with 4mm iron plate

verti

cal t

une

horizontal tune

Third order(normal)

Fourth order(normal)

Integer or Half integer

open circle: experimentcolored plot: calculation

3Nx=7 is focused here.

Longitudinal Beam Handling(1)

Crossing speed is one of important parameter! However, it is impossible to accelerate all particles with same energy gain because of synchrotron oscillation.

For clear observation of speed dependence, careful attentions are paid to longitudinal beam handling.

Beam chopper: 100nsec chopped beam (～ ±10deg. of RF phase)

Mountain-plot: Bunch monitor signal is transferred to mountain plot to check an amplitude of dipole oscillation.

Longitudinal Beam Handling(2)

-60 -45 -30 -15 0 15 30 45 600

2

4

6

8

10

bunc

h si

gnal

+ o

ffse

t(tu

rn*0

.1)

(V)

RF phase (deg.)

-60 -45 -30 -15 0 15 30 45 600

2

4

6

8

10

bunc

h si

gnal

+ o

ffse

t(tu

rn*0

.1)

(V)

RF phase (deg.)

Example of Mountain Plot (RF capture @ injection energy)

Dipole oscillation is perfectly suppressed.

Driving Term (1)

0 5 10 15 20

- 2500

- 2000

- 1500

- 1000

- 500

0

500

1000

1500

Δ 50GaussＢ～

field error with RF core (r=0.9m)

Δ BL=2*4.5E- 4 (T- m)Bz

(Gau

ss)

theta (deg.)

with core without core

Straight Section Defocus Focus0 45 90 135 180 225 270 315 360

- 6

- 4

- 2

0

2

4

6

r0=0.9mRF error:-17mrad.@130keV

CO

D (

mm

)

theta (deg.)

Magnetic field error with RF core COD due to RF core

RF cores disturb magnetic field of straight section. COD and octupole becomes sextupole driving term (feed down).

Core

Feed Down:)33()( 322333 DxDDxxODxOOx

(calculated with TOSCA) (calculated with TOSCA field & RK-tracking)

Driving Term (2)

COD with weak excited magnets

Error

Error

Septum

0 45 90 135 180 225 270 315 360

- 30

- 20

- 10

0

10

20

30

40

F:5000AT-4800AT / D:2870ATr0=0.88m

CO

D (

mm

)

theta (deg.)Septum

Error Error

Variable driving term can be introduced with changing coil current.

Driving Term (3)

dsesSeG lsix

i xx

)3()(3237,0,3 )(

24

2

0 1 2 30.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

G3,

0,7 (

10-8m

^3/2

)excitation error (%)

:Fourier amplitude of 3Nx=77,0,3G

x :horizontal beta-function:coefficient of sextupole)(sS

x :horizontal tune

x

x

dss

)( :phase advance

:phase factor

Due to the relation of phase between fixed and variable driving term, Fourier amplitude is not proportional to variable driving term.

Beam Size Measurement During acceleration, an orbit shifts to outer radius. Using a scraper and an intensity monitor, beam size, before and after crossing, can be measured.

turn

Results (1) –data of driving term 0.18*10-8(m^3/2)

40 50 60 70 80 900.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 1, scraper 300mm

Nor

. int

egra

l (-)

num. of turn

50 60 70 80 90 1000.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 1, scraper 320mm

Nor

. int

egra

l (-)

num. of turn

70 80 90 100 110 1200.0

0.2

0.4

0.6

0.8

1.0 error 2%, speed 1, scraper 340mm

Nor

. int

egra

l (-)

num. of turn

80 90 100 110 120 1300.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 1, scraper 360mm

Nor

. int

egra

l (-)

num. of turn

130 140 150 160 170 180 190 200 210 220 2300.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 3, scraper 300mm

Nor

. int

egra

l (-)

num. of turn

180 190 200 210 220 230 240 250 260 270 2800.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 3, scraper 320mm

Nor

. int

egra

l (-)

num. of turn

230 240 250 260 270 280 290 300 310 320 3300.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 3, scraper 320mm

Nor

. int

egra

l (-)

num. of turn

290 300 310 320 330 340 350 360 370 380 3900.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 3, scraper 320mm

Nor

. int

egra

l (-)

num. of turn

300 400 500 600 7000.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 5, scraper 300mm

Nor

. int

egra

l (-)

num. of turn

300 400 500 600 700 800 9000.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 5, scraper 320mm

Nor

. int

egra

l (-)

num. of turn

500 600 700 800 900 1000 11000.0

0.2

0.4

0.6

0.8

1.0error 2%, speed 5, scraper 340mm

Nor

. int

egra

l (-)

num. of turn

Speed0.13kV/turn

Speed0.49kV/turn

Speed1.6kV/turn

Scraper pos.r=908mm

Scraper pos.r=908mm

Scraper pos.r=908mm

Scraper pos.r=928mm

Scraper pos.r=948mm

Scraper pos.r=928mm

Scraper pos.r=948mm

Scraper pos.r=968mm

Scraper pos.r=928mm

Scraper pos.r=948mm

Scraper pos.r=968mm

Results(2)-trapping efficiency

speed (kV/ turn)driving term(10̂ - 8*m̂ 3/ 2) 0.13 0.21 0.49 1.04 1.56

0.18 12% 9% 0% 0% 0%1.1 17% 12% 0% 0% 0%1.6 23% 16% 0% 0% 0%

The result can be understood qualitatively.

Large driving term Large trapping efficiency

Slow Crossing Large trapping efficiency

Particle Trapping

Particle Trapping: When a non-linear detuning is very larger than a driving term, some particles are trapped by islands during crossing resonance.

Reference: “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER RESONANCE”, A.W. Chao and Melvin Month, NIM 121(1974) pp129-138

Phase space topology for third integer resonance

?Opposite Crossing?

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

0

1000

2000

3000

4000

5000

6000

7000

8000 135msec

count

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

0

1000

2000

3000

4000

5000

6000

7000

8000 142msec

count

x (mm)

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

0

1000

2000

3000

4000

5000

6000

7000

8000 150msec

coun

t

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

0

1000

2000

3000

4000

5000

6000

7000

8000 155msec

count

x (mm)

- 60 - 40 - 20 0 20 40 60

0

50000

100000

150000

200000

250000

300000

350000

count

x (mm)

60msec 100msec 120msec 150msec 205msec 210msec

Crossing 3Nx=11

HIMAC experiment

Num. of Cell =12

Particle trapping (tune decreases)

Growth? (tune decreases)

SummaryBeam study in PoP FFAG was carried out to study a dynamics of resonance crossing.

Tune crosses 3Nx=7, then…

There seems no effect, when crossing speed is fast enough.Particle trapping is observed. The dependence of trapping efficiency on crossing speed and driving term can be understood qualitatively.

Opposite crossing does not become trapping.