Normal and Superconducting magnet for FFAG · Normal and Superconducting magnet for FFAG Masahiro...

NuFact03 @ Columbia Univ., New YorkNuFact03 @ Columbia Univ., New YorkNuFact03 @ Columbia Univ., New YorkNuFact03 @ Columbia Univ., New YorkNuFact03 @ Columbia Univ., New York 10th June 200310th June 200310th June 200310th June 200310th June 2003

Normal and Superconducting

magnet for FFAG

Masahiro Yoshimot, Toru Ogitsu

Masamitsu Aiba, Takasi Obana

Shinji Machida, Yoshiharu Mori

KEK


Magnet design for FFAG accelerator

Required magnetic field for FFAG : B r Br

rF h

r

r

k

( , ) ( ln )q q=Ê

ËÁˆ

¯̃-0

0 0

B r Br

r

k

( ) =Ê

ËÁˆ

¯̃00

B r Br

r

k

( ) = -Ê

ËÁˆ

¯̃00

focuse

focuse

defocus

Radial sector type FFAG:

How to be realized this field ?

(1) iron pole shape

(2) current distribution


The magnetic field is realized by changing the gap space !

for example : PoP-FFAG, & 150MeV-FFAG

radius

mag

netic

fie

ld

radiushalf gap

G =G0r0r

�

�

� �

�

�

� �

k

B =B0rr0

�

�

� �

�

�

� �

k

medium plane

METHOD-1 : Iron pole shape type

This method may not be suitable for the neutrino

factory base on the FFAG accelerator.

merit & demerit

merit:

- easy to design

- easy to operate

demerit

- impossible to change the k-value

- difficult to make the long pole magnet

(<= fringing field on the pole edge)

- difficult to make the high field magnet

(<= saturation in the pole iron)


METHOD-2: current distribution type

radius

mag

netic

fie

ld

radius

B =B0rr0

�

�

� �

�

�

� �

k

medium plane

The magnetic fields are produced by the current distribution !

merit vs. demerit

merit:

- possible to change the k-value !

- possible to make the long pole magnet !

- possible to make the high filed magnet !

demerit

- not easy to design conpare to pole shaple method

(<= find the nice sets of coil configuration)

- not simple to operate

(<= different currents are supplied to

each coil)


4 0

4.0

3.8

3.6

3.4

3.2

3.0

Loc

al K

-val

ue

540520500480460

radius [cm]

-20

-10

0

10

20

fluc

tuat

ion

rate

[%]

[ 0 Deg ] Local K Fitting K rate

3000

2500

2000

Bz

[Gau

ss]

540520500480460

[ 0 Deg ] By calculated fit_By_1_1

[ y = 9.9855e-07 x r^3.4935+0 ]

Fitting k-value & local k-value

The indicator of the field quality => fitting k-value & local k-value !

The field quality is judged by the ratio of the local k-value to the

fitting k-value !

k_fitting fit : y=a(r)^b

(with Levenberg-Marqurdt algorizm)

B Brr

Br

kBr

rr

kBr

rr

rr

kBr

BB

kBr

k

k

k

=ÊËÁ

ˆ¯̃

=ÊËÁ

ˆ¯̃

=ÊËÁ

ˆ¯̃

=

=

-

00

0

0 0

1

0

0 0

0

0

0

DD

k localBr

rB

_ =DD

typical results of the field calculated by the current distribution type magnet


OPERA-3dPre-processor 7.03

9/Feb/2002 14:04:40 Page 9

X440.0 X460.0 X480.0 X520.0 X540.0 X560.0Y

Z-40.0

Z-20.0

Z20.0

Z40.0

Z60.0

Magnet design 3 (with current distribution type)


3000

2500

2000

Bz

[Gau

ss]

540520500480460

radius [cm]

[ 0 Deg ] By calculated fit_By_1_1

[ y = 9.9855e-07 x r^3.4935+0 ]

4.0

3.8

3.6

3.4

3.2

3.0

Loc

al K

-val

ue

540520500480460

radius [cm]

-20

-10

0

10

20

fluc

tuat

ion

rate

[%]

[ 0 Deg ] Local K Fitting K rate

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Bz

0.200.150.100.050.00

q [rad]

r=450 r=460 r=470 r=480 r=490 r=500 r=510 r=520 r=530 r=540 r=550



race track coils or wind frame coils ?

1.5

1.0

0.5

0.0

mag

netic

file

d [T

]

6.05.55.04.54.0

radius [m]

302010

0

1.5

1.0

0.5

0.0

mag

netic

file

d [T

]

6.05.55.04.54.0

radius [m]

3020100

if small gap size (half gap = 3cm) .........

long !short !

simple !complex !



OPERA-3Pre-processor 7.03

11/Mar/2003 18:10:45

X440.0X460.0X480.0X500.0X520.0X540.0X560.0X580.0X600.0X620.0X640.0X660.0

Y-100.0

Y-80.0

Y-60.0

Y-40.0

Y-20.0

Y20.0

Y40.0

Y60.0

Y80.0

Z-20.0Z0.0

Z20.0Z40.0

Z60.0Z80.0

Z120.0Z140.0

Z160.0Z180.0

Z200.0Z220.0


Conventional SC magnets forAccelerator

• Cosine theta design– For example: Dipole– Cos(nq) > 2n-pole magnet

• Well established for– Dipole, Quadrupole

• ~ 8T ~5cm aperture• ~5T ~20cm aperture

– Higher order coils• Smaller coils but some are

combined with larger main coil

+–


What to do with FFAG field?

What about combination of multipole fields

†

B(r) = B0rr0

Ê

Ë Á

ˆ

¯ ˜

k

= B0 +kr0

B0r +k(k -1)

2!r02 B0r

2 +k(k -1)(k - 2)

3!r03 B0r

3 + ...


Combined Multipole Coil?

• Can change B0 and k inwide range within theconductor limit.

• Can even change thefield profile.

• Isn’t it too complicated?– Magnetic force?– Can be expensive...


Let’s make it SIMPLE!

Required current distributionfl

Sum of all cosine theta currentfl

Asymmetric CoilNeed R&D!

+– ++–+

–

–

–

–

+

+

+–


Example of Asymmetric CoilJ-PARC Neutrino CF-SC Magnet

Stainless ShellCorrector /Cold Tube

Holes for He Coolant

Phenol Plastic Spacer

Superconducting Coil

Holes for Stack Tube

Iron Yoke

Yoke Key

Press Shoulder

• Dipole Field– ~2.6 T

• Quad. Field– ~18.5 T/m

• Op. Current– ~7kA

• Op. Margin– ~70%

• Inductance– ~15mH

• Field Quality– <10-3 @ 5 cm

• Cable– LHC Dipole

outer cable

Prototype Development in FY2003!


Elliptic Structure• Round Asymmetric Coil

– May be Feasible!• But, large beam excursion

– Requires large aperture– Large Stored Energy

• Difficult to protect– More superconductor

• More moneyfl

Elliptic StructureNeed R&D as well

+–

+–


Reference Design 1a• B0=6.0T, r0=120m, k=450, beam excursion 0.18m

1. Main Coil• Asymmetric & Elliptic• Rutherford Cable~ 2X15mm• Operation Current ~6.8kA• Stored Energy: ~1MJ/m

2. Corrector Coil• Wind & glue (BNL)• ~10A/delta-K

3. Collar• Pre-stress ~90MPa• Horizontal EMF ~ 3.9 MN• Aluminum collar to gain

pre-stress during cool down

4. Iron Yoke• Off centered yoke

for EMF balance• Warm Iron

80mm

R500mm

Aluminum Coller

Off Centered Warm Iron Yoke

Asymmetric Elliptic Coil

0.15

0.10

0.05

0.00

0.20.10.0-0.1-0.2


K corrector• K correction?

– Does it need to be widerange?

– If not, first order correction

†

B(r,k + Dk) = B0rr0

Ê

Ë Á

ˆ

¯ ˜

k +Dk

~ B(r,k) +dB(r, k)

dkDk

~ B0rr0

Ê

Ë Á

ˆ

¯ ˜

k

+ B0rr0

Ê

Ë Á

ˆ

¯ ˜

k

ln rr0

Ê

Ë Á

ˆ

¯ ˜ Dk

Current distribution can be derived using the same method as that of main coil

B0 = 4.5, r0 = 200, k = 620, dk = 10, 20, 40Red lines represent definite equation, whileBlue lines represent first order approximation.

Reference Design 1aField Map & Beam Aperture

0.25

0.20

0.15

0.10

0.05

0.00

0.30.20.10.0-0.1-0.2

8

7.5

7 7

6.5

6.5

6

6

5.5 5.5

5.5

5

5

5

5

5

4.5

4.5

4.5

4

4

3.5

3.5

3.5

3.5

3.5

3

3

3 3

3

3

2.5

2.5

2.5

2.5

2.5 2

2

2

2

2

2

1.5

1.5

1.5

1.5

1.5

1

1

0.5


Reference Design 1aField quality of main coil

6

5

4

3

Field (T)

-0.10 -0.05 0.00 0.05 0.10

x (m)

450

449

448

447

446

445

444

Local-k


Reference Design 1ak corrector

Works fine up to dk ~ ±20

490

480

470

460

450

Local-k

-0.10 -0.05 0.00 0.05 0.10x (m)



SUMMARY

Normalconducting magnet:

-pole shape type

-distribution current type

Superconducting magnet:

-Asymmetric Elliptical Coil

-First Order Delta-K Correction Coil

Issues to be studied

-3d end design

-Detailed mechanical analysis

Normal and Superconducting magnet for FFAG · Normal and Superconducting magnet for FFAG Masahiro...

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