Normal and Superconducting magnet for FFAG · Normal and Superconducting magnet for FFAG Masahiro...
Transcript of Normal and Superconducting magnet for FFAG · Normal and Superconducting magnet for FFAG Masahiro...
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Normal and Superconducting
magnet for FFAG
Masahiro Yoshimot, Toru Ogitsu
Masamitsu Aiba, Takasi Obana
Shinji Machida, Yoshiharu Mori
KEK
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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
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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)
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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)
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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
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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)
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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
Magnet design 3 (with current distribution type)
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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 !
Magnet design 4 (with current distribution type)
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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
Magnet design 4 (with current distribution type)
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
+–
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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 + ...
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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...
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Let’s make it SIMPLE!
Required current distributionfl
Sum of all cosine theta currentfl
Asymmetric CoilNeed R&D!
+– ++–+
–
–
–
–
+
+
+–
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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!
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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
+–
+–
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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
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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
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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
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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)
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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