Detailed Design Report
Chapter 3
MAX IV 1.5 GeV Storage Ring
3.5. MAX IV 1.5 GeV Storage Ring Magnets
MAX IV Facility
CHAPTER 3.5.
MAX IV 1.5 GEV STORAGE RING MAGNETS • 1(10)
3.5. MAX IV 1.5 GeV Storage Ring Magnets
3.5.
MAX IV 1.5 GeV Storage Ring Magnets.................2
3.5.1.
2D Design .................................................................................................... 5
3.5.2.
3D Design ...................................................................................................10
3.5.3.
Bibliography................................................................................................10
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MAX IV 1.5 GEV STORAGE RING MAGNETS • 2(10)
CHAPTER 3.5.
3.5. MAX IV 1.5 GeV Storage Ring Magnets
The 1.5 GeV storage ring lattice consists of twelve double bend achromats, with straight
sections in between. The starting point for the design of the 1.5 GeV storage ring magnets
is the “initial” lattice design “m5-20100325-501” (see chapter 3.2.1). In this lattice, the
magnets are defined as hard edge elements. The magnets are designed by performing 3D
field simulations and evaluating the integrated field in longitudinal slices. The lattice is
refined by replacing the hard edge elements with slices as obtained from the 3D field
simulations. A final refined lattice and magnet design is obtained by iterating towards a
design which yields the same results in optics calculations as the initial lattice.
The magnet types in the m5-20100325-501 lattice are listed Table 1 and shown
schematically in Figure 1. In Figure 1, the direction of the coordinate axes in beam optics
calculations are shown. The magnet polarities in the lattice files are to be understood in the
sense of this coordinate system.
Table 1: Magnet types in the 1.5 GeV storage ring.
Element
L [m]
Field strength
Comment
B’ = 28.71 T/m, B’’/2 = 183.6 T/m2
Combined quadrupole/sextupole
SQFo
0.2
SCo,
SCi
0.02
SDo,
SDi
0.1
B’’/2 = -460.1 T/m2, -366.5 T/m2
1
DIP
1
B0 = 1.310 T, B’ = -6.747 T/m
Gradient dipole
SQFi
0.4
B’ = 25.02 T/m, B’’/2 = 140.3 T/m2
Combined quadrupole/sextupole
Corrector
1 The lattice elements sdo and sdi differ only in strength, corresponding to one magnet type operated at two
field strengths.
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CHAPTER 3.5.
MAX IV 1.5 GEV STORAGE RING MAGNETS • 3(10)
Figure 1: Sketch of the 1.5 GeV storage ring lattice “m5-20100325-501”, one double bend achromat.
View from above – the beam direction is clockwise, as indicated by the s-axis direction.
NB – the y-axis direction is into the picture! That is, vertically downward!
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MAX IV 1.5 GEV STORAGE RING MAGNETS • 4(10)
CHAPTER 3.5.
In addition to the lattice design, further constraints and specifications for the magnet
design are introduced from other aspects of the accelerator design. Such additional
specifications are listed in Table 2 and Table 3.
Table 2: Additional specified parameters for magnet design.
Parameter
Value
Unit
Good field width:
2
Dip
±10
mm
Other elements
±20
mm
40 × 20
mm
Vacuum chamber inner dim.
(elliptical)
Comment
Coolant water:
See chapter 3.2.2
Saknar ref
Pressure drop (∆p)
2
bar
Inlet temperature (Tin)
25
°C
Temperature rise (∆T)
< 10
°C
Table 3: Additional specifications for magnet design.
2
Spec.
Description
1
All magnets in one double bend achromat are integrated into one solid iron block. See chapter
3.2.1
2
All magnets of the same type and strength are connected electrically in series.
See chapter
3.2.6
3
Individual magnets shall be shunted electrically, before installation, to within …
Saknar info
4
In the Kraków option, the magnets will be ramped from 400 MeV to 1.5 GeV. The
magnet design shall be optimized for 1.5 GeV operation, but also evaluated for
the corresponding field range.
(1)
(4), based on initial lattice βx, see chapter 3.2.2.
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Comment
MAX IV 1.5 GEV STORAGE RING MAGNETS • 5(10)
CHAPTER 3.5.
3.5.1.
2D Design
The first step of the 1.5 GeV storage ring magnet design was the transverse cross section
of each magnet type. In this subchapter, this design step as defined by the initial lattice is
presented. The design was performed with the help of 2D field simulations, using the
FEMM (2) code. The minimum required transverse cross section dimensions for each
magnet type, found by 2D simulations, defines the required dimensions of the magnet
block. A sketch of the magnet block is shown in Figure 2.
Figure 2: A sketch of the 1.5 GeV storage ring magnet block.
3.5.1.1.
Combined Quadrupole/Sextupole “SQFo”
The lattice element “SQFo” is a combined quadrupole/sextupole magnet. The specifications on which the design of this magnet type is based are listed in Table 4.
Table 4:
Basic specifications for the magnetic element “SQFo”. From lattice design “m5-20100325-501” unless otherwise noted.
Parameter
Value
Unit
Effective length (Leff)
0.2
Quadrupole strength (k)
5.736667
/m2
36.676825
/m3
Sextupole strength (m)
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m
Comment
MAX IV 1.5 GEV STORAGE RING MAGNETS • 6(10)
CHAPTER 3.5.
Based on the specified inner size of the vacuum chamber (see Table 2), we estimate that a
pole aperture of 44 mm will be sufficient. Another factor which controls the design of this
magnet is the close proximity of the adjacent bpm and sextupole corrector “SCo” (see
Figure 1.). Due to this, the coil length needs to be < 0.2 m, which in turn requires that the
pole root is shorter than the pole face (see Figure 2).
…
3.5.1.2.
Sextupole Corrector
…
3.5.1.3.
Sextupole
…
3.5.1.4.
Gradient Dipole
The lattice element “DIP” is a gradient dipole magnet. The specifications on which the
design of this magnet type is based are listed in Table 5.
Table 5:
Basic specifications for the magnetic element “DIP”. From lattice design “m5-20100325-501” unless otherwise noted.
Parameter
Value
Unit
Bend angle
15
°
Entrance/exit angle
0
°
Effective length (Leff)
1
m
-1.347963
/m2
Pole face strip ∆k
min. ±2
%
Return yoke geometry
C-dipole
Quadrupole strength (k)
Comment
Sector magnet
= ± 0.026959 /m2, see chapter 3.2.4
(3)
The required pole gap depends on the height of the vacuum chamber and height required
for the pole face strips, with some headroom for assembly and manufacturing tolerances.
Based on the specified inner height of the vacuum chamber, 20 mm (see Table 2), we
estimate that a pole gap of 28 mm (at x=0) will be sufficient. The gradient dipole is the
magnetic element in this lattice which requires the largest cross section. So, to minimize the
height of the iron block3 we have designed this magnet to be as small as possible in the
vertical direction. This means that that the coil was made as wide and low as possible,
taking into account the limited space between the gradient dipole and the adjacent
sextupole SDo (see Figure 2).
3 We assume here that the height is the most difficult factor in obtaining low carbon steel plate of the
required size.
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CHAPTER 3.5.
MAX IV 1.5 GEV STORAGE RING MAGNETS • 7(10)
The resulting magnet design is defined by the FEMM 2D-model “MJ100721-67, DIP.fem”
together with the design parameters listed in Table 5. This 2D-model is shown in Figure 3.
Simulation results are shown in Figure 4, Table 5 and Figure 5.
Figure 3: 2D field simulation result for the model “MJ100721-67, DIP.fem”, field distribution in the xy-plane.
The colour scale goes from 0 to 2 T. The field in the pole root and middle of the return yoke is 1.7-1.8 T.
The coil cross section is marked green. The model geometry corresponds to the cross section view D-D in Figure 2.
The directions of the coordinate axes in the model are indicated in the lower right corner.
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MAX IV 1.5 GEV STORAGE RING MAGNETS • 8(10)
CHAPTER 3.5.
Table 6: Technical data for the gradient dipole magnet “DIP”.
Parameter
Magnet type
Pole gap
Value
Unit
Comment
Gradient dipole
28
mm
At x=0
Nominal field (B0)
1.31035
T
At x=0
Gradient (B’)*
-6.74840
T/m
< ±1
G
See Figure 5.
32116
A
See Table 5
Within gfw, residual field*
Corresponds to k = -1.34829 /m2, see
Table 5
Coils:
Total current /magnet (NI)*
No of coils /magnet
Conductor
Mean length /turn
2
OFHC copper, 12×12 mm, Ø7.5 mm internal cooling channel
2.41
m
No of turns /coil
20
No of turns /magnet (N)
40
Nominal current (I)
803
A
Resistance/coil at 20°C
8.4
mΩ
Coil cooling
5 turns in width × 4 turns in height
direction
Water cooled
No of cooling circuits /coil
2
Pressure drop (∆p)
2
bar
Flow /cooling circuit
5.5
l/min
Temperature rise (∆T)
7.5
°C
Voltage /magnet
14.2
V
22
l/min
Flow /magnet
Coil consists of two double pancakes in
parallel
= 342 V for all 24 magnets in series,
excl cabling
Yoke:
Yoke geometry
C-dipole
Material
Armco low carbon steel
Height
•
340
mm
= 170 mm per magnet half
Field simulation results for FEMM 2D-model “MJ100721-67, DIP.fem”.
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MAX IV 1.5 GEV STORAGE RING MAGNETS • 9(10)
CHAPTER 3.5.
Figure 4: 2D field simulation data for the model “MJ100721-67, DIP.fem, By(x) at y=0. The
simulation was repeated at three different current levels, corresponding to T = ca 400 MeV
to 1.5 GeV. The simulated field values are negative, corresponding to the field direction being
vertically down, which is the correct polarity for this magnet (cf Figure 1, Figure 3).
Table 5: Results calculated from the simulation data shown in Figure 4.
B0 [T]
B’ [T/m]
k [/m2]
4
5
NI=32116A
NI=15600A
NI=7800A
Comment
-1.31588
0.68519
0.34435
at x=0
6.77687
3.54736
1.78390
4
-1.34829
-1.35538
-1.35624
5
Calculated as linear fit over x=±10 mm.
k = B’/(-B0ρ), where it is minus B0 because the y-axis in the FEMM model is opposite to y-axis in the
optics calculations. (cf
Figure 1, Figure 3)
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MAX IV 1.5 GEV STORAGE RING MAGNETS • 10(10)
CHAPTER 3.5.
Figure 5: dB/B calculated from the data shown in Figure 4. dB/B(x) = (simulated By(x) – linear fit
By(x))/linear fit By(x), where the linear fit is over x=±10 mm. For the simulation at NI = 32116 A,
max-min dB/B is 0.00011 over x=±10 mm – this corresponds to 1.4 G max-min residual.
3.5.1.5.
Combined Quadrupole/Sextupole “SQFi”
…
3.5.2.
3D Design
…
3.5.3.
Bibliography
1. M. Eriksson (private communication, 100315).
2. D.C. Meeker, Finite Element Method Magnetics, version 4.2 02Nov2009
(Mathematica Build), http://www.femm.info.
3. L.-J. Lindgren (private communication, 100303) .
4. S. Leemann (private communication, 100713).
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