theoretical and experimental studies of a straight scaling ffag … · 2011-09-14 · 16 straight...

Theoretical and Experimental Studies of a Straight Scaling FFAG Line at KURRI

JB. Lagrange, Y. Mori

FFAG’11 Workshop - 11-16 September 2011

Scaling FFAG law

Study of Straight Scaling FFAG: experiment at KURRI

Example of Application: PRISM

2

Outline

Theoretical and Experimental Studies of a Straight Scaling FFAG Line at KURRI - JB. Lagrange

Scaling FFAG law



3

Outline


D(p0) = p0

!!r

!p

"

p0

=r

k + 1

Bz = B0

!r

r0

"k

k =r

B

!!Bz

!r

"& Magnetic field:

with

NB: In the linear approximation, k =r

!n

! =1

k + 1

Dispersion function:

4

Scaling law: classical case- Similarity of the closed orbits- Invariance of the betatron oscillations

Momentum compaction factor:

! ! r


D(p0) = p0

!!r

!p

"

p0

=r

k + 1

Bz = B0

!r

r0

"k

k =r

B

!!Bz

!r

"& Magnetic field:

with

NB: In the linear approximation, k =r

!n

! =1

k + 1

Dispersion function:

5

Scaling law: classical case- Similarity of the closed orbits- Invariance of the betatron oscillations


! ! r


!!

!

O(machine center)

! = 0

Dispersion function: D(p0) = p0

!!x

!p

"

p0

=1m

m =1B

!!Bz

!x

"with

& Magnetic field:

NB: In the linear approximation, m =n

!

Bz = B0em(x!x0)

limr0!"

!r

r0

"k

= limr0!"

#!1 +

x

r0

" r0x

$ xr0

k

=

#lim

r0!"

!1 +

x

r0

" r0x

$n! x

= en! x = emxLinear approx.:

6

Scaling law: straight case- Similarity of the closed orbits- Invariance of the betatron oscillations


! = const.


! = 0

Dispersion function: D(p0) = p0

!!x

!p

"

p0

=1m

m =1B

!!Bz

!x

"with

& Magnetic field:

NB: In the linear approximation, m =n

!

Bz = B0em(x!x0)

limr0!"

!r

r0

"k

= limr0!"

#!1 +

x

r0

" r0x

$ xr0

k

=

#lim

r0!"

!1 +

x

r0

" r0x

$n! x

= en! x = emxLinear approx.:

7

Scaling law: straight case- Similarity of the closed orbits- Invariance of the betatron oscillations


! = const.


!!

!

X

Y

1 2 3

Scaling FFAG law



8

Outline


In Kyoto University, an experiment is under construction to verify the straight field law.

9

Study of Straight Scaling FFAG

0 0.1 0.2

0 0.5 1 1.5 2x [m]

y [m]


10

Layout of the experiment

Use of 2 energies: 7 MeV and 11 MeV.

H- linac injection beam line

Experiment


11

Layout of the experiment2 Collimators 3 magnets End of line


12

Layout of the experiment2 Collimators 3 magnets End of line


Set the Twiss Parameters at the entrance

13

Layout of the experiment3 magnets End of line

150 150300

100 100 100 100 100 100

400400

350 350500

60 60 60 60 60 60

165

65

80

11 MeV

100

F FD

2 Collimators


14


beam

movableslit

Fluorescent

camera

screen

Faradaycup

2 Collimators


15


beam

movableslit

Fluorescent

camera

screen

Faradaycup

2 Collimators


Emittance & Twiss Parameters measurement

16

Straight Scaling FFAG cell design


Type FDFm-value 11 m!1

Length of F magnet 15 cmLength of D magnet 30 cmDrift length 60 cmMax. B Field 0.3 THorizontal phase advance 60 deg.Vertical phase advance 81 deg.

• C-shape Magnets to have easy access to the pole.• Cell able to move horizontally to match the different reference trajectories.• Rectangular magnets.

• Coils:• Max 3500 A.T/coil.• 18 turns x 4 layers = 72 turns of 5 mm x 2 mm cross section wire.

~5 A/mm2 Indirect water cooling system.• Power supply per magnet (D): 50 A, 15 V.•Whole system power consumption: ~1 kW.

17

Magnet designPole shape configured with POISSON, then TOSCA.

Magnetic field inF magnet (15 cm long).

TOSCA model.

Magnetic field inD magnet (30 cm long).

TOSCA model.


18

Tracking in TOSCA Field map

Local m value vs horizontal abscissa

Horizontal (plain) and vertical (dot) phase advances

vs kinetic energyTheoretical and Experimental Studies of a Straight

Scaling FFAG Line at KURRI - JB. Lagrange

0

20

40

60

80

100

120

6 8 10 12 14 16 18

!x, !z [deg.]

Ekin [MeV]

9

9.5

10

10.5

11

11.5

12

0 2 4 6 8 10 12 14 16

mloc [m-1]

x [cm]

19




vs kinetic energyTheoretical and Experimental Studies of a Straight


0

20

40

60

80

100

120

6 8 10 12 14 16 18

!x, !z [deg.]

Ekin [MeV]

9

9.5

10

10.5

11

11.5

12

0 2 4 6 8 10 12 14 16

mloc [m-1]

x [cm]

20

Horizontal (plain red) and vertical (dotted purple) betafunctions in the straight FFAG line

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5

! [m]

s [m]



21

FIELD MEASUREMENT

• Magnets delivered early August 2011

• Measurement of the field in the good field region done last week

Picture of the Straight Cell prototype.

Measurement field map created and

tracking in this map


22Theoretical and Experimental Studies of a Straight


23

Comparison TOSCA - Measurement


4

5

6

7

8

9

10

11

0 0.5 1 1.5 2

x [cm]

y [m]

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.5 1 1.5 2 2.5

Bz [T]

s [m]

4

5

6

7

8

9

10

11

0 0.5 1 1.5 2

x [cm]

y [m]

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.5 1 1.5 2 2.5

Bz [T]

s [m]

11 MeV11 MeV

7 MeV7 MeV

TOSCA

Mea

surem

ent

24

Comparison TOSCA - Measurement



vs kinetic energy

0

20

40

60

80

100

120

6 8 10 12 14 16 18

!x, !z [deg.]

Ekin [MeV]

TOSCAMeasure

TOSCAMeasure

9

9.5

10

10.5

11

11.5

12

2 4 6 8 10 12 14

mloc [m-1]

x [cm]


Scaling FFAG law



25

Outline


PRISM project

Muon phase rotator (at Osaka University)

•Momentum acceptance: 68MeV/c ± 20%

• Transverse acceptance:

•hor.: 30 000π mm.mrad

•vert.: 3 000π mm.mrad

26

Applications


Race-track scaling FFAG PRISM

27

Applications

Bending cell FDF tripletk-value 2.55Average radius 2.7mPhase advances:Horizontal µx 60 deg.Vertical µz 90 deg.Dispersion 0.8m

Straight cellm-value 1.3 m!1

Length 1.8mPhase advances:Horizontal µx 27 deg.Vertical µz 94 deg.Dispersion 0.8m


Acceptances of race-track PRISM

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3

X' [rad]

X [m]

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

-0.1 -0.05 0 0.05 0.1Z' [rad]

Z [m]

Horizontal (left) and vertical (right) acceptance of the ring over 30 turnsFar collimators identify lost particles

28

Applications


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20

! [m]

s [m]

βx

βz

29

ApplicationsHorizontal (plain red) and vertical (dotted purple) betafunctions of half the ring in race-track PRISM


Recently a new field law has been found to guide particles with no overall bend in scaling FFAGs.

An experiment is under construction to study this new law. Magnets have been manufactured, delivered and field measurement has been done. Next step: Actual experiment with beam.

It is very promising in various applications, to solve problems and improve accelerator performances.

30

Summary


31

Thank you for your attention

Scaling FFAG Straight Line - JB. Lagrange

theoretical and experimental studies of a straight scaling ffag … · 2011-09-14 · 16 straight...

Documents