Magnetic design of Magnetic design of a superconducting magnet for a superconducting magnet for

the FFAG acceleratorthe FFAG accelerator

T.Obana, T.OgitsuA ,T.NakamotoA ,K.SasakiA A.YamamotoA , M.YoshimotoA, Y.MoriA ,T.OrigasaB

The Graduate University for Advanced StudiesHigh Energy Accelerator Research OrganizationA

Toshiba CorporationB

ContentsContents

1. Background & Purpose2. How to generate FFAG field3. 2D &3D Calculation Results4. Conclusion

BackgroundBackground

Downsizing the FFAG accelerator is essential so that the FFAG can be widely used.

High energy physicsHigh energy physics Electric powerElectric power

High magnetic field is required.FFAG　field is constant.

Superconducting magnet is proposed 　　　　　　　　　　 for FFAG accelerator.

Cancer therapyCancer therapy

PurposePurpose

The purpose of this study is to develop the superconducting magnet of the FFAG accelerator.

150MeV 　 FFAG150MeV 　 FFAG

Conventional magnet of 150MeV FFAG

accelerator at KEK

Magnetic Field for FFAGMagnetic Field for FFAGk

rRr

BB

00

)(

R0

r

〕〔TB

0B

0

Beam tube

Beam area

Center of the magnetCenter of the acceleratorCenter of the accelerator

r : Distance from the accelerator center [m]

R0 : Distance between the accelerator center

and the magnet center [m]

Bo : Magnetic field at the magnet center [T]

K : K value ( Geometrical field index)

How to generate the FFAG How to generate the FFAG Field!Field!

2

02

0

2

000

00

0

0

0

00

!2

)1(1 r

xR

kkrr

xRk

rB

RxR

B

Rr

BB

k

k

Di-poleQuadru-pole

Sextu-pole

Realize FFAG magnetic field

with mutipole combination ！

Current Current distributiondistribution

2

02

0

2

000

00

00

!2

)1(1 r

xR

kkrr

xRk

rB

Rr

BBk

++

–

–

X

Y

+

+

+

–

–

–

X

+–

Y

X

Y

It’s too difficult to make a multi layer coil !

n=3n=2

n=1

Up to n=8Up to n=8I=I0cos(nθ)

Multi layer coil

Current Current distributiondistribution

– ＋ X

Y

Simplify!

– ＋X

Y

Left-Right asymmetry & EllipseLeft-Right asymmetry & Ellipse

++

–

–

X

Y

+

+

+

–

–

–

X

+–

Y

X

Y

Downsize!

With single layer

Left-Right asymmetryLeft-Right asymmetryUp to n=8Up to n=8

n=1

n=2 n=3

Major axis 0.8 m

Minor axis 0.6 m

K value 10

Ro 5.0 m

Excursion 0.4 m

Turn numberBo

1201.2 T - 0.5

0

0.5

- 0.5 0 0.5

X m〔 〕

Ym〔

〕

＋

－

Excursion

Coil

Coil parameters of FFAG for cancer therapy

– ＋ X

YCurrent distribution

FFAGFFAG

FFAG forFFAG for cancer therapy cancer therapy

Energy ～ 200Mev

Current ～ Several 100μA

FFAG for cancer therapyHigh　 Energy　 Beam

Low　 Energy Beam

Cross-SectionCross-Section

+-

K value & Field distributionK value & Field distribution on mid-planeon mid-plane@ 2D@ 2D

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

10.3

10.4

10.5

-0.2 -0.1 0 0.1 0.2X m〔 〕

Kva

lue

TargetCalculation

0

0.5

1

1.5

2

2.5

-0.2 -0.1 0 0.1 0.2X[m]

By/

By@

X=0

m

TargetCalculation

K valueK value Field distributionField distribution

Excursion Excursion

Br

rB

KLocal_

Local K is used to evaluate K value.

K v

alu

e

By/B

y@x=

0m

Positions of the conductor can be optimized in 2D!

Single winding@3D coil

'2th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2 -1.5 -1 -0.5 0 0.5 1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

In single winding, one coil makes one layer.

'1th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2 -1.5 -1 -0.5 0 0.5 1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

YY

XZ

XZ

Y

Z

Y Z-Y plane

Z

Y Z-Y plane

Straight section

Straight section

Superconducting wire

Superconducting wire

Single winding@3D coil

'1th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2 -1.5 -1 -0.5 0 0.5 1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

'2th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2 -1.5 -1 -0.5 0 0.5 1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Coil end is large.

Demerit

'1th.txt'

'2th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2 -1.5 -1 -0.5 0 0.5 1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

MeritStraight length is same in each turn with 2 layers.

2 layers with 2 coilsZ

Y

Z

Y

Z-Y plane

Z-Y plane

Y

X Z

XZ

Y

Twin winding@3D coil

'1th-down.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2-1.5

-1-0.5

0 0.5

1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

In twin winding, two coils make one layer.

X

XZ

Z

Y

Y'1th-up.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2-1.5

-1-0.5

0 0.5

1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

ZX

X

Z

Y

Z

Y

Z-Y plane

Z-Y plane

Straight section

Straight section

Superconducting wire

Superconducting wire

Twin winding@2D coil

'1th-down.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2-1.5

-1-0.5

0 0.5

1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

'1th-up.txt'

'1th-down.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2-1.5

-1-0.5

0 0.5

1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Straight length is different in each turn.

　 Coil end is small.

Merit Demerit

1 layer with 2 coils

'1th-up.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -2-1.5

-1-0.5

0 0.5

1 1.5

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Z

Y

Z

Y

Z-Y plane

Z-Y plane

X

XZ

Z

Y

Y

Field distribution Field distribution on mid-plane@on mid-plane@ ３３DD 　　　　

'120turn-C-1th-1mm-k10.txt'

-0.4-0.3

-0.2-0.1

0 0.1

0.2 0.3

0.4

X

0 0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.2-0.1 0 0.1 0.2 0.3

'60turn-C-1th-1mm-k10.txt'

-0.4-0.3

-0.2-0.1

0 0.1

0.2 0.3

0.4

X

0 0.1

0.2

0.3

0.4

0.5

0.6

Z

0 0.05 0.1 0.15 0.2 0.25 0.3

Single Winding Twin Winding

Coil end

Coil end

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5 6 7 8 9 10Azimuthal angle[degree]

By/

By@

X=0

Single winding @X=0.0m

Twin winding @X=0.0m

X

Z Z

X

Z-X plane

By/B

y@x=

0m

Trajectory

X=0 m

5.8°

10.0°

0° Coil

Center of FFAG

Top view

θ

K value K value @ @ ３３ D-ResultD-Result

'120turn-C-1th-1mm-k10.txt''0.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.2-0.1 0 0.1 0.2 0.3

θ= 0°

'60turn-C-1th-1mm-k10-sita.txt''0.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.25-0.2-0.15-0.1-0.05 0

Single Winding

9

9.2

9.4

9.6

9.8

1010.2

10.4

10.6

10.8

11

-0.2 -0.1 0 0.1 0.2X[m]

Kva

lue

Single windingTwin windingTarget

Coil endCoil end

0°

θX=0 m

5.8° Coil

Center of FFAG

Top view

X X

Z Z

Z-X plane

Twin Winding

K v

alu

e

X[m]

K value K value @ @ ３３ D-ResultD-Result

99.2

9.49.69.8

1010.210.410.6

10.811

-0.2 -0.1 0 0.1 0.2X[m]

Kva

lue

Single windingTwin windingTarget

'60turn-C-1th-1mm-k10-sita.txt''2.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.25-0.2-0.15-0.1-0.05 0

θ= 2°

0°

θX=0 m

5.8° Coil

Center of FFAG

Top view

2°

'120turn-C-1th-1mm-k10.txt''2.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.2-0.1 0 0.1 0.2 0.3

Z Z

XX

Z-X planeSingle winding Twin winding

Coil end Coil end

K v

alu

e

K value K value @ @ ３３ D-ResultD-Result

'60turn-C-1th-1mm-k10-sita.txt''4.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.25-0.2-0.15-0.1-0.05 0

θ= 4°

'120turn-C-1th-1mm-k10.txt''4.txt'

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

X

0

0.1

0.2

0.3

0.4

0.5

0.6

Z

-0.3-0.2-0.1 0 0.1 0.2 0.3

Single winding Twin winding

9

9.2

9.4

9.6

9.8

10

10.2

10.4

10.6

10.8

11

-0.2 -0.1 0 0.1 0.2X[m]

Kva

lue

Single windingTwin windingTarget

Coil end Coil end

Z-X plane

X X

Z Z

0°

θX=0 m

5.8° Coil

Center of FFAG

Top view

4°

K v

alu

e

K+1 value K+1 value byby BL BL @@ ３３ D-ResultD-Result 　　　　

10

10.2

10.4

10.6

10.8

11

11.2

11.4

11.6

11.8

12

-0.2 -0.1 0 0.1 0.2X m〔 〕

Kva

lue

Single WindingTwin WindingTarget

1

000

k

Rr

LBLB

X=0.0m

5.8°

10.0°

0°

CoilCenter of FFAG

drBBL=

k

Rr

BB

00

1

00

k

Rr

PP

K+

1 v

alu

e

BLr

rBL

KLocal

1_

ConclusionConclusion• 2D & 3D FFAG magnetic fields are calculated.• The optimizing program of the conductor

position in 2D is developed.• Two types of 3D coil configuration are

compared in terms of K value & BL.

Future planFuture plan•Tracking will be done with 3D magnetic filed.

•Prototype of single winding coil will be made

from this October .

What’s FFAG accelerator ?What’s FFAG accelerator ?

Can be High repetition & High Intensity !

• Strong focusing in horizontal and vertical Synchrotron

• Constant magnetic field strength in time Cyclotron

FFAG 〔 Fixed Field Alternating Gradient 〕 accelerator

Properties ...

Various AcceleratorsVarious Accelerators

Field Fix Ramp Fix

Closed Orbit

Large Move Fix Small Move

Focusing Weak Strong Strong

Duty Factor

Large Small Large

Why’s SC magnet required?Why’s SC magnet required?

• Normal Conducting Magnets– Low Current Density < 10 A/mm2

• Field by Iron Pole– Iron Saturation 2 Tesla

• Superconducting Magnets– High Current Density< 500 A/mm2

• Field by Current– Tevatron 4.5 Tesla– LHC 8.4 Tesla

High magnetic field can be generated by SC magnet.

Accelerator size can be downsized !

Accelerator Driven System Accelerator Driven System (ADS)(ADS)

FFAG

Proton

Reactor Core

neutron

Target (Uranium )

Winding TechniqueWinding Technique

Direct Winding Direct Winding

Superconducting wire can adhere directly to the base.

Reference 　 http://www.bnl.gov/magnets/BioMed/BioMed.asp

Superconducting wireSuperconducting wire

Nb-Ti

Cu

1.0 mm

How to evaluate K valueHow to evaluate K value

Total field

Local field

'3ban&4ban.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -6 -4 -2 0 2 4 6

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Straight length with 2 layersStraight length with 2 layers

'4ban.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -6 -4 -2 0 2 4 6

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

'3ban.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -6 -4 -2 0 2 4 6Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Single winding

Z

Y

Z

Y

First

Second

First

Second

Z-Y plane

Z-Y plane

Z-Y plane

Z-Y plane Z

Y

Y

ZStraight length

with 2layers

Straight length with 2layers

'3ban&4ban.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -6 -4 -2 0 2 4 6

Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

YTwin winding

0° 90° 180°-90°-180° (-90°)(90°) θ

Expansion planeExpansion plane

θ

X

Y 0°

90°-90°

'120turn-1th.txt'

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4X -6-4-2 0 2 4 6 Z-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Y

Twin winding

Single winding

How to evaluate K+1 valueHow to evaluate K+1 value

0drBBL=

BLr

rBL

KLocal

1_

X=0.0m

θ =0°

CoilCenter of accelerator

θ

r

K value & K+1 value by BLK value & K+1 value by BL

Z

BZ

XX-Z plane

Local evaluation of the field

Beam traveling direction

K valueK value

K+1 value by BLK+1 value by BL

Total evaluation of the field

How to optimize the How to optimize the positions of the conductorpositions of the conductor

Current

angle180°S S S

S S S

1.Evaluate the current distribution

2.Divide the area so as to be same

HowHow 　　 to adjust the target!to adjust the target!

X[m]

K+

1 v

alu

e

X[m]

K+

1 v

alu

eAdjust the 2D targetAdjust the 2D target

so that K+1 can reach 3D targetso that K+1 can reach 3D target

Difference

Target

Target

Adjust target!Calculation Calculation