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