Magnetic Field Design of
a Superconducting Magnet for
the FFAG Accelerator
T.Obana, T.OgitsuA ,T.NakamotoA ,K.SasakiA A.YamamotoA ,
M.YoshimotoA, Y.MoriA ,T.OrikasaB
The Graduate University for Advanced Studies
High Energy Accelerator Research OrganizationA
Toshiba CorporationB
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
Why’s SC magnet required?
In some cases, compactness of the accelerator is important.
Medical applications
Required magnetic field…
- High magnetic field
- Static magnetic field
Superconducting magnet is proposed for
the FFAG accelerator.
Purpose
The purpose of this study is to develop a
superconducting magnet for the FFAG accelerator.
150MeV FFAG accelerator at KEK
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
How to generate the FFAG Field!
B
 r k

 B0 


R
0


 R0  x
 B0 
 R
0

k




k

 B0 1  r 0
R0

x  k (k 1)  x
r
r
2!R  r
2
0
0
2
0
Dipole
Sextupole
Quadrupole
2


   


0
FFAG field can be realized with
a multipole combination!
Current distribution
B
I=I0cos(nθ)
–
n=2
+
Y
–
+
+
X
Up to n=8
x  k (k 1)  x
r
r
2!R  r
2
0
0
2
0
2


   


0
X
Y
+
–

k

 B0 1  r 0
R0

Y
n=1
 r k

 B0 


 R0 
n=3
–
+
+
Multi-layer coil
–
X
–
Magnetic forces on the coil are complex
and are difficult to support !
Current distribution
n=1 Y
n=2
–
+
Y
–
+
Simplify!
X
n=3
–
Y
+
+
–
Y
X
–
–
+
+
X
＋
X
With single layer
–
Up to n=8
Left-Right asymmetry
Y
–
Downsize!
＋
X
Left-Right asymmetry & Ellipse
Cross-Section
Injection beam
FFAG for Medical applications
FFAG
Extraction beam
Parameters of the FFAG Accelerator
Excursion
Extraction energy
~200 MeV
Beam current
Several 100 μA
Major axis of the beam pipe
0.8 m
Minor axis of the beam pipe
0.6 m
Geometrical field index, k
10
Ro
5m
Excursion
0.4 m
Turn number
120
Bo
1.0 T
Local k value & Field distribution @ 2D
Excursion
Excursion
Local k is used to evaluate the magnetic field closely.
k local 
B r
r B
Positions of the conductor can be optimized in 2D!
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
3D Design
The coil end greatly influences the field distribution,
because the ratio of the physical length of the coil end
to that of the straight section is large.
It is difficult to meet the design requirement locally.
The 3D coil is designed so that the design requirement
can be satisfied in terms of integral magnetic field.
“Single winding coil” is proposed !
Single winding coil @ 3D Design
0.3
Y
0
The even layer
-0.3-0.4
0
X
0.4-6
The odd layer
-3
3
0
6
0.3
Z
Y
0
-0.3-0.4
0
X
0.4-6
-3
0
3
Z
6
Single Winding coil @ 3D Design
2 layers with 2 coils
Y
0.3
0
-0.3-0.4
0
0.4-6
-3
0
3
6
Z
X
The characteristic of the single winding coil
- The difference of the straight length of the coil in each turn can
be minimized when the number of the coil layers is even.
Superconducting wire
Parameters
Superconducting wire
Diameter (mm)
Cu/NbTi ratio
0.9 mm
NbTi
0.9
4.0
Winding Technique
Direct Winding technique
Superconducting wire can be directly adhered to the base.
Reference
http://www.bnl.gov/magnets/BioMed/BioMed.asp
Local k value at each angle@3D
Beam trajectory
Accelerator center
12
Coil
11.5
o
10.5
10
9.5
9
8.5
0.0
-0.4
11
Localk value
5.8°
4°
2°
0°
Single w inding@ 0°
Single w inding@ 2°
Single w inding@ 4°
D esign requirem ent
0.4
X [m]
Calculated area on the top view
8
-0.2
-0.1
0
X [m ]
0.1
It is difficult to meet the design requirement
at each angle!
0.2
Local K+1 value by BL at each radius
@3D
“ BL=  B rd ”
B
 r k

 B0 


 R0 
Accelerator center
p
 r  k 1

 p 
0

 R0 
Beam trajectory
k 1local
15°
o
0°
0.0
-0.4
0.4
X [m]
Calculated area on the top view
Localk+1 value
Coil
5.8°
BL
12.6
12.4
12.2
12
11.8
11.6
11.4
11.2
11
10.8
10.6
-0.2

 r  k 1

 B 0 L0 


 R0 
BL r
r BL
Single W inding
R edesigned Single W inding
D esign requirem ent
-0.1
0
0.1
X [m ]
It is possible to meet the design requirement for the
integrated magnetic field along the trajectory.
0.2
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
Tracking a particle in the FFAG accelerator with the magnetic field
which almost meets the design requirement by BL
Layout of the FFAG accelerator
6 with some closed orbits
4
B eam energy[M eV ]
[m]
Tracking
2
0
-2
-4
Beam energy at each radius
200
180
160
140
120
100
80
60
40
20
0
4.7
-6
-6
-4
-2
0
[m]
2
4
4.8
4.9
5
5.1
radius [m ]
5.2
5.3
5.4
6
Particles will circulate stably in the accelerator at each beam orbit
if the integral magnetic field comes close to satisfying the design
requirement.
Tune
Tune diagram
4
Tune at each energy
4.5
4
3.5
3
3
Tune
tune-h
3.5
2.5
2
H orizontal
V ertical
1.5
2.5
1
0.5
2
0
2
2.5
3
tune-v
3.5
4
0
50
100
Energy [M eV ]
150
Tune shifts and crosses some resonance lines
because of the beam acceleration.
200
Contents
1.
2.
3.
4.
5.
Background & Purpose
2D Coil Design
3D Coil Design
Tracking
Conclusion
Conclusion
• A superconducting magnet design is proposed
which is suitable for an FFAG.
• The cross section of the coil is optimized by a
computer program that we have developed.
• The 3D coil configuration is designed to satisfy the
design requirement in terms of the integral field.
• Particles are transported stably in the field for
which the local k+1 meets the design requirement.
Future plan
• Development of a multi-layer coil with “Single winding”
is in progress, and a full scale model coil is to be made
and tested.
Practical single winding coil
Y
Z
X
Type of the magnet
Radial sector
Major axis of the beam pipe
0.8 m
Major axis of the beam pipe
0.6 m
Coil Length
1.06m
Turn number
Layer number
120
30
Z
Y
X
X
Peak field
Y[m]
0.6
0.4
0.4
0.3
0.2
0.2
0
-0.2
-0.4
Z[m]
0.1
0
-0.1
-0.2
-0.4
-0.1
-0.2
-0.3
0.40
0.3
0.2
0.1
-0.6
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-0.3
-0.4
-0.3
X[m]
0
0.3
0.6
-0.6
-0.2
-0.4
0.4
0.2
0
X[m]
Current = 360A
B0 @x =0 m
Peak field
1.0 T
4.1 T
Parameters are adjusted to reduce the peak field.
- Turn number
- Distance between conductors at the coil end
- Ratio of the major axis of the aperture to the minor of the aperture
How to optimize the position of the conductor
Obtain the current distribution.
Divide the portion with the same area.
Arrange the conductor with same current.
Current
Current distribution
S
S
180°
S
S
S
S
angle
Conductor
Acceptance
Injection beam
Extraction beam
0.08
0.06
0.04
0.02
0
-0.02
-0.04
Excursion
-0.06
-0.08
4.6 4.65 4.7 4.75 4.8 4.85 4.9 4.95
radius [m]
5
4.8
0.08
0.06
0.06
0.04
0.04
0.02
0
-0.02
angle [radian]
0.08
5.0
radius [m]
5.2
0.02
0
-0.02
-0.04
-0.04
-0.06
-0.06
-0.08
4.8 4.85 4.9 4.95 5 5.05 5.1 5.15 5.2
radius [m]
-0.08
5
5.05 5.1 5.15 5.2 5.25 5.3 5.35 5.4
radius [m]
How to adjust the design requirement!
K+1 value
K+1 value
Adjust the design requirement!
Calculation
Difference
Calculation
Design requirement
Design requirement
X[m]
X[m]
Adjust the 2D design requirement
so that the local k+1 value can reach 3D design requirement.
Single winding @ 3D
In single winding, one coil makes one layer.
Y
Y
Z-Y plane
Superconducting wire
'1th.txt'
Y
0.3
0.2
0.1
0
Z
-0.1
-0.2
-0.3
-0.4 -0.3 -0.2
-0.1
X
Straight section
Z-Y plane
0.1
0.2
0.3
Superconducting wire
'2th.txt'
YY
0.3
0.2
0.1
0
Z
Y
0
X
1.5
0.5 1
-0.5 0
Z
-1
-1.5
0.4-2
Z
-0.1
-0.2
-0.3
-0.4 -0.3 -0.2
-0.1
X
X
Straight section
0
0.1
0.2
0.3
1.5
0.5 1
-0.5 0
Z
-1
-1.5
0.4-2
Z
Conventional winding @ 3D
In conventional winding, two coils make one layer.
'1th-up.txt'
Superconducting
wire
Y
Y
Y
Z-Y plane
0.3
0.2
Z
0.1
0
-0.1
-0.2
Straight section
Z-Y plane
Y
-0.3
-0.2
-0.1
X
0
0.1
X
0.3
0.2
0.3
0.4-2
-1.5
-1
-0.5
0
Z
Z
Superconducting wire
0.2
0.1
Z
Y
-0.3
-0.4
Y
1.5
1
'1th-down.txt'
0.5
0
-0.1
-0.2
-0.3
-0.4
Straight section
-0.3
-0.2
-0.1
X
X
0
0.1
0.2
0.3
0.4-2
-1.5
-1
-0.5
0
0.5
1
1.5
ZZ
Magnetic Field for FFAG
B
 r k

( r )  B0 


 R0 
r : Distance from the accelerator center [m]
R0 : Distance between the accelerator center and the magnet center [m]
B〔 T 〕
Bo : Magnetic field at the magnet center [T]
k : k value ( Geometrical field index)
Beam tube
B0
r
0
R
Accelerator center
0
Beam area
Magnet center
Various Accelerators
Field
Fix
Ramp
Fix
Large Move
Fix
Small Move
Focusing
Weak
Strong
Strong
Duty
Factor
Large
Small
Large
Closed
Orbit
Local k value at each angle
14
0°
13
1°
Localk value
12
2°
11
3°
10
4°
5°
9
6°
8
D esign
requirem ent
7
0.6
6
-0.2
0.5
-0.1
0
X[m ]
0.1
0.2
0.4
0.3
Z[m]
0.2
0.1
-0.4
-0.1
-0.2
-0.3
0.4
0.3
0.2
0.1
0
-0.6
-0.4
-0.2
0
0.2
0.4
0
0.6
X[m]
Local k values don’t meet the design requirement, even the angle is 0°
Expansion plane @ Single winding
-180°
-90°
・・・ the odd layer
・・・ the even layer
0°
90°
180°
・・・ Overlapped part
Accelerator Driven System (ADS)
neutron
Proton
FFAG
Reactor Core
Target
(Uranium )
How to evaluate K value
Roughly evaluation
Locally evaluation
Straight length with 2 layers
Y
Conventional winding
'3ban&4ban.txt'
Y
0.3
Odd layer
0.2
0.1
Z
Z-Y plane
0
Straight length
with 2layers
-0.1
Even layer
-0.2
Y
-0.3
-0.4
-0.3
-0.2
-0.1
X
0
0.1
0.2
0.3
0.4 -6
'3ban&4ban.txt'
4 6
0 2
Z
-4 -2
0.3
Y
0.2
0.1
0
Z-Y plane
-0.1
-0.2
-0.3
-0.4
-0.3
-0.2
-0.1
X
0
0.1
0.2
0.3
Single winding
'3ban.txt'
Y
Z
4 6
0 2
Z
-4 -2
0.4 -6
Odd layer
Y
Straight length
with 2layers
0.3
0.2
0.1
Z
Z-Y plane
0
-0.1
-0.2
-0.3
-0.4 -0.3 -0.2 -0.1
XY 0
0.1
0.2
0.3
0.4 -6
4 6
0 2
Z
-4 -2
Even layer
'4ban.txt'
Y
0.3
0.2
0.1
Z-Y plane
0
-0.1
-0.2
-0.3
-0.4 -0.3 -0.2
-0.1
X
0
0.1
0.2
0.3
6
2 4
Z
-2 0
-6 -4
Z
Single winding & Conventional winding
Conventional winding
(90°) -180° -90°
0°
90° 180° (-90°)
θ
Single winding
How to obtain K+1 value
Local _ K 1 
BL r
r BL

BL= 0
Br d

θ
r
Center of accelerator
Coil
X=0.0m
θ =0°
X
K value & K+1 value
X-Z plane
Beam traveling direction
Z
K value
Local evaluation of the field
B
K+1 value by BL
Total evaluation of the field
Z