1
Conceptual Design of the New D1 Magnet
by using Nb-Ti LHC Dipole Cable and Nb3Sn Cable
Q. Xu, T. Nakamoto, E. Todesco

Abstract—The development of a large-aperture (130-150 mm)
dipole magnet is proposed in the framework of the CERN-KEK
cooperation program. The application target is the D1 magnet
(separation dipoles) replacement for the HL-LHC (High
Luminosity - Large Hadron Collider) upgrade. The Cos-theta
type coil cross section is adopted in the conceptual design of this
magnet. The nominal field is 6 ~ 7 T at 1.9 K with a 30-mm-width
coil arranged in two layers. The candidates of superconductor are
Nb-Ti and bronze route Nb3Sn. The Nb-Ti LHC dipole cable
(inner) is the baseline for the coil winding. We present the key
parameters and the magnetic simulation of this magnet including
the field quality in the aperture, the effect of iron saturation and
filament magnetization and the stray field with iron cryostat.
Index Terms— Superconducting accelerator magnets, Largeaperture, Cos-theta type coil, LHC dipole cable.
with the current LHC dipole magnets. This makes stray field a
critical aspect of the design.
II. ANALYTICAL ESTIMATION OF THE MAGNETIC FIELD
The critical current density (Jc) of the superconductors Nb-Ti
and bronze route Nb3Sn can be fitted by using simple functions
in Table I [3, 4]. The fitting error is within 5% on a wide
domain. Fig. 1 shows the fit lines of these superconductors.
The central magnetic field of a Nb-Ti dipole magnet at the
short sample limit Bss can be expressed as a function of the
aperture radius r, the equivalent coil width weq, the critical
current density of the superconductor and the geometry
parameters of the cable and of the coil without iron. This
function is based on a simple sector coil model [3]
4500
Q. Xu, T. Nakamoto are with the High Energy Accelerator Research
Organization (KEK), Tsukuba, Japan (e-mail: qingjin.xu@kek.jp).
E. Todesco is with the European Organization for Nuclear Research
(CERN), Geneva, Switzerland (e-mail: Ezio.Todesco @cern.ch).
Non-Cu Jc (A/mm2)
H
L-LHC (High Luminosity-Large Hadron Collider) is an
upgrade project of the current LHC. The main objective is
to implement a hardware configuration and a set of beam
parameters that will allow LHC to reach a peak luminosity of 5
× 1034 cm-2s-1 and an integrated luminosity of 250 fb-1 per year,
which is ten times more than the integrated luminosity of the
first 10 years of the LHC lifetime [1]. The conventional
room-temperature magnet modules D1 (separation dipoles) are
considered to be replaced by large-aperture radiation-hard
superconducting magnets. The nominal field of the current D1
magnet is 1.28 T [2]. The new superconducting D1 magnet will
increase the nominal field to above 6 T with an aperture
diameter of 130-150 mm. The integrated field is also increased
from 26 T m to 40 T m. The candidates of superconductor are
Nb-Ti and bronze route Nb3Sn. The Nb-Ti LHC dipole cable
(inner) is the baseline for the coil winding. If necessary, the
higher Critical temperature of bronze route Nb3Sn is expected
to provide more enthalpy margin than Nb-Ti to against the heat
deposition by irradiation.
In this report we present a preliminary analysis of the
magnetic design: First we address the margin issue and then we
estimate the expected nominal field for the two conductors for
apertures ranging from 130 to 150 mm. We analyzed the effect
of iron saturation and filament magnetization on the field
quality and the stray field including the influence of iron
cryostat. The outer diameter of the magnet is 570 mm, same
NbTi 1.9K
NbTi 4.2K
Bronze Nb3Sn 1.9K
Bronze Nb3Sn 4.2K
ITER TF strand
4000
I. INTRODUCTION
3500
3000
2500
2000
1500
1000
500
0
6
7
8
9
10
11
12
13
14
15
Magnetic field (T)
Fig 1: Jc fit of the superconductors by using the functions in Table 1.
TABLE I: FITTING FUNCTION OF THE SUPERCONDUCTORS
Superconductor
Bronze Nb3Sn
@ 4.2K
Bronze Nb3Sn
@ 1.9K
NbTi @ 4.2K
NbTi @ 1.9K
Fitting function
B
c
b

jc  c  1
B 
21
1.0E+09
23.1
10
13
1.1E+09
6.0E+08
6.0E+08
jc  c(b  B)
Bss 
Error
5% for 10-12 T *
* Comparing with data
from Hitachi cable
5% for 5-10 T [4]
5% for 6-13 T [4]
kcb 0 weq
1  kc 0 ( weq  ar )
(1)
where k is the filling factor of the coil pack: k =
kw-ckc-i/(1+vcu-sc); kw-c is the area ratio of strands to conductor
(cable), kc-i is the area ratio of bare conductor to insulated
conductor, and vcu-sc is the Cu/Non-Cu ratio of the strand; c and
b are parameters of Jc fit in Table 1, γ0 is the central field per
2
unit of current density and unit of coil width, a is a constant
number in the following function: λ=1+ar/weq; where λ is the
ratio of the peak field to the central field.
The above expression is valid for the short sample field: a
critical aspect is the margin on the load line (one minus the ratio
between operating current and short sample current), which
usually ranges between 20% and 30% in most accelerator
magnets. Due to the position of the magnet, which is right after
the interaction point and therefore heavily irradiated, we take a
conservative margin of 30%, i.e. it works at Bop=0.7 Bss.
The iron effect can be calculated roughly by using the
following equation, with the assumption that the iron is not
saturated, the permeability is uniform, and the thickness of iron
is infinite [5]



B1iron
  1 ( r  w) r

noniron
  1 R I2
B1
(2)
where RI is the inner radius of iron yoke. If we assume the
spacer thickness between coil and iron yoke is around 20 mm, a
filling factor of k=0.34, a=0.05, we get the dependence of
central magnetic field Bop on coil width for Nb-Ti
superconductor, as shown in Fig. 2. For Nb3Sn superconductor,
we have a similar equation with (1) [4]
Bss 

kc 0 weq 
4b

 1  1

2  kc 0 ( weq  ar )

III. DESIGN WITH NB-TI LHC DIPOLE CABLE (INNER)
A. Main electromagnetic parameters
We studied the two cases (150 mm aperture and 130 mm
aperture) for the Nb-Ti LHC dipole cable (inner) by using
ROXIE [6]. The coil layout is optimized at the nominal
operating current. The target is to reduce the multipole
coefficients from b3 to b13 to less than 1 unit (10-4 relative to the
main field) at 2/3 of the aperture radius. The proposed
cross-section of the magnet for the 150 mm (diameter) case is
shown in Fig. 3. Six coil blocks are distributed in two layers in
each quadrant of cross-section, and the same superconducting
cable is adopted for the inner and outer layers (no grading, since
it would increase stresses). The outer diameter of the iron yoke
is 550 mm, which is identical to the size of the current LHC
dipole magnets. A ~20 mm spacer is placed between the iron
yoke and coil packs. The diameter of the heat exchanger of the
current design is 50 mm. If necessary, it can be increased to
above 80 mm.
Assuming the load line margin is 30% at 1.9 K, the nominal
dipole field of the magnet is ~ 6.4 T and the operating current is
~ 9.3 kA. The average stress in coil caused by Lorenz force is
50-70 MPa. The parameters of the magnet, cable and strand are
listed in Table II; the coil layout parameters are listed in Table
III; Fig. 4 and 5 show the magnetic field distribution in the coil
and iron yoke with the aperture diameter of 150 mm.
(3)
the corresponding result is also included in Fig. 2.
The second choice we make is the coil thickness. We choose
a rather large coil thickness to decrease the current density and
therefore the stresses, which are large in the case of large
aperture dipoles. For this reason we propose 30 mm arranged in
two layers of 15 mm each, as in the LHC main dipoles. An
aperture variation from 120 to 180 mm gives little impact on the
operational field. In Fig. 2 the 4.2 K case is also shown.
9
Central magnetic field B (T)
With iron and load line ratio 70%
8
7
Fig. 3: The cross-section of the magnet with aperture diameter of 150 mm.
6
5
4
NbTi r=65mm @ 4.2K
NbTi r=75mm @ 4.2K
ITER Nb3Sn r=65mm @ 4.2K
ITER Nb3Sn r=65mm @ 1.9K
3
10
20
30
NbTi r=65mm @ 1.9K
NbTi r=75mm @ 1.9K
ITER Nb3Sn r=75mm @ 4.2K
ITER Nb3Sn r=75mm @ 1.9K
40
50
60
Equivalent width of the coil defined in [1] (mm)
Fig. 2: The dependence of Bss on weq for aperture diameter of 130 mm and 150
mm, with load line margin 30%.
Fig. 4: The magnetic field distribution in the coil for 150 mm aperture.
3
B. Effect of iron saturation and filament magnetization on
field quality
The type of iron used for this magnet is the same as that of
the MQXA magnet [7]. The peak field in the iron yoke is ~3.8 T
at the nominal operating current, as shown in Fig. 5; most parts
of the iron are saturated. Iron saturation causes the variation of
sextuple and decapole coefficients along with the increasing of
the operating current. Another source of severe field distortions
at low excitation is persistent magnetization currents. It is
proportional to the filament diameter and the critical current
density of the superconductor [8]. The persistent magnetization
currents generate all multipoles which are allowed by coil
symmetry, and the multipole fields have opposite signs for
increasing and decreasing main field.
Fig. 5: The magnetic field distribution in the iron yoke for 150 mm aperture.
TABLE II: KEY PARAMETERS OF THE MAGNET WITH LHC
DIPOLE CABLE (INNER)
Value
150 mm
130 mm
6.35 T
6.48 T
9.3 kA
9.2 kA
<0.01% (Rref=50/43 mm)
7.06 T
7.08 T
70% / 63.7%
70% / 64.8%
@1.9 K
@1.9 K
2.9 K
2.9 K
16.1 / 13.6
12.8 / 10.6
mH/m
mH/m
588.1 kJ/m
448.6 kJ/m
2/6
1.11
1.09
2.1/0.97 MN/m
1.96/0.86 MN/m
71 MPa
57 MPa
550 mm
254 mm
234 mm
1.065
1.65
15.1* 1.9mm2 /
0.16 mm (radial) 0.135 (azimuthal)
28
1.24 °
1000 A/mm2
989 A/mm2
Ratio
1.15
0.98
1.01
/
0.997
1
COIL
BLOCKS
RADIUS
(MM)
150
1
2
3
4
5
6
1
2
3
4
5
6
75
75
75
75
91
91
65
65
65
65
81
81
PHI
(DEG)
1.0032
25.9868
49.0401
68.0
0.6440
30.0936
130
1.0678
27.3967
50.5653
69.0
0.9015
26.9318
* Phi – positioning angle; Alpha – Inclination angle.
150 mm aperture
130 mm aperture
25
1.31
/
1.02
/
1.25
/
1.09
/
/
/
/
/
1.01
TABLE III: COIL LAYOUT PARAMETERS FOR 2 CASES
APERTURE
DIAMETER (MM)
30
1
1.28
Multipole coefficients b3
Item
Bore diameter
Nominal field (dipole)
Operating current
Field homogeneity
Peak field in the coil
Load line ratio
(Inner / Outer layer)
Temperature margin
Inductance
(low field / nominal field )
Stored energy
No. of layers/blocks
Peak field/central field
Lorenz force X/Y
Estimated coil stress
Outer dia. of iron yoke
Inner dia. of iron yoke
Strand diameter
Cu/Non-Cu ratio
Cable dimension /
Insulation
No. of strands
Keystone angle
Supercon. current density
Fig. 6 shows the dependence of sextuple coefficient on the
operating current for the current design caused by the effect of
iron saturation and filament magnetization. The filament
diameter of the Nb-Ti strand is ~ 7 μm. In both cases, the
variation of b3 from injection (~500 A) to the nominal current is
about 30 units. The influence on the other multiple coefficients
(b5, b7 …) is less than 1 unit. Table IV shows the field quality at
different operating currents in the ramp-up and ramp-down
processes. Simulations are needed to check if these large
multipoles are tolerable at injection or if a corrective strategy
should be envisaged. Fig. 7 shows the transfer function of the
magnet caused by iron saturation. It decreases by ~ 13% from
low current to the nominal current.
20
15
10
5
0
-5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
Operating current (kA)
Fig. 6: The effect of iron saturation and filament magnetization on b3. The
influence of iron cryostat is not included.
ALPHA
NO. OF
(DEG) CONDUCTORS
0
23.0157
54.0
75.0
0
28.5926
0
23.0
45.0480
75.0
0
26.2173
15
10
7
5
17
20
13
8
6
4
15
21
TABLE IV: FIELD QUALITY IN THE RAMP-UP AND RAMP-DOWN
PROCESSES (INFLUENCE OF IRON CRYOSTAT IS NOT INCLUDED)
APERTURE
DIAMETER (MM)
OPERATING
CURRENT (KA)
B3
B5
B7
B9
B11
B13
150
0.5
4.5
9.3
4.5
0.5
0.5
4.5
9.2
4.5
0.5
10.9
14.0
0.2
14.6
28.5
-4.9
4.8
0.1
5.4
12.8
0.3
-0.2
-0.4
-0.2
-0.1
-0.2
-0.5
-0.4
-0.5
-0.7
0.4
0.8
0.5
0.8
1.1
0.4
0.7
0.5
0.7
1.0
-0.4
-0.5
-0.6
-0.5
-0.5
-0.5
-0.5
-0.6
-0.5
-0.5
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.1
0.0
0.0
0.0
0.0
0.1
0.0
0.1
0.0
0.0
130
4
0.82
150 mm aperture
Transfer function (T/kA)
0.8
130 mm aperture
0.78
0.76
0.74
0.72
0.7
0.68
0.66
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
Operating current (kA)
C. Stray field and field quality in the aperture including the
influence of iron cryostat
Although the new D1 magnet has a large aperture, the current
design assumes a limited diameter of the iron yoke to be 550
mm. The stray field of the magnet is relatively high. Assuming
the size of the cryostat is the same with the current LHC
cryostat: the outer diameter is 914 mm and the thickness is 12
mm; the magnet is 80 mm offset from the center of the cryostat,
the maximum stray field at the outer surface of the iron cryostat
is ~ 0.14 T for aperture diameter of 150 mm and ~ 0.1 T for
aperture diameter of 130 mm, as shown in Fig. 8 and Fig. 9. A
simple method to reduce the stray field is to increase the
thickness of the iron yoke. Fig. 10 shows the variation of the
stray field with different sizes of iron yoke. If we need to reduce
the stray field to less than 0.05 T at the outer surface of the
cryostat, the required diameter of the iron yoke is over 0.7 m for
an aperture diameter of 150 mm.
Fig. 9: Stray field at the outer surface of the iron cryostat for 150 mm aperture
and at nominal current (from 0 to 360 degrees, anti-clock direction).
0.18
0.16
Stray field (T)
Fig. 7: Transfer function of the magnet caused by iron saturation.
0.14
0.12
0.1
0.08
0.06
0.04
0.5
0.55
0.6
0.65
0.7
Yoke outer diameter (m)
Fig. 10: Maximum stray field at the outer surface of the cryostat with different
sizes of iron yoke for 150 mm aperture magnet.
Fig. 11 and Table V show the influence of iron cryostat on
the field quality in the aperture. The iron cryostat is not
included in the model during the optimization of the current
coil layout. Without iron cryostat, all the normal multipole
coefficients are less than one unit within the reference radius
(2/3 of the aperture radius); if we include the iron cryostat, but
the magnet is located at the center of the cryostat, b3 will be
increased from less than 1 unit to larger than 5 units; if we
further move the magnet from the center of the cryostat to the
upper side by 80 mm, the skew multipoles will be generated,
i.e. a2 is ~ 2.5 units in this situation.
TABLE V: FIELD QUALITY IN THE 150 MM APERTURE
INCLUDING IRON CRYOSTAT AND AT THE NOMINAL CURRENT
Fig. 8: Magnetic field in the iron yoke and iron cryostat for 150 mm aperture
and at nominal current.
CONDITIONS
B3
B5
IN FIG. 11
(A)
0.2
-0.4
(B)
5.8
-0.3
(C)
5.9
-0.3
* Reference radius:& 50 mm. All
below 0.1 unit.
B7
B9
B11
B13
A2
A4
0.5 -0.6 0.4 0.0
0
0
0.5 -0.5 0.4 0.0
0
0
0.5 -0.5 0.4 0.0
-2.5
-0.3
the other normal and skew multipoles are
5
Fig. 12: The cross-section of the magnet with aperture diameter of 150 mm.
Fig. 11: Field quality in the 150 mm aperture: (a) magnet without iron cryostat;
(b) magnet centered in the iron cryostat, b3 > 5 units; (c) magnet 80 mm offset
from the center of the iron cryostat, b3 > 6 units,a2 > 2 units.
IV. DESIGN WITH BRONZE NB3SN CABLE
A. Main electromagnetic parameters
The higher Critical temperature of bronze route Nb 3Sn is
expected to provide more enthalpy margin than Nb-Ti to
against the heat deposition by irradiation. We studied the two
cases (150 mm aperture and 130 mm aperture) by using 11 mm
wide bronze Nb3Sn cable. The coil layout is optimized at the
nominal operating current. The target is to reduce the multipole
coefficients from b3 to b13 to less than 1 unit at 2/3 of the
aperture radius. The proposed cross-section of the magnet for
the 150 mm (diameter) case is shown in Fig. 12. Six coil blocks
are distributed in two layers in each quadrant of cross-section,
and the same superconducting cable is adopted for the inner and
outer layers. The outer diameter of the iron yoke is 550 mm. A
~ 20 mm spacer is placed between the iron yoke and coil packs.
The diameter of the heat exchanger is 50 mm. If necessary, it
can be increased to above 80 mm.
Assuming the load line margin is 30% at 1.9 K, the nominal
dipole field of the magnet is ~ 6.2 T, and the operating current is
~ 7 kA. The average stress in coil caused by Lorenz force is
around 100 MPa. The parameters of the magnet, cable and
strand are listed in Table VI; the coil layout parameters are
listed in Table VII; Fig. 13 and 14 show the magnetic field in
the coil and iron yoke with aperture diameter of 150 mm.
Fig. 13: The magnetic field in the coil with aperture diameter of 150 mm.
Fig. 14: The magnetic field in the iron yoke with aperture diameter of 150 mm.
6
130
1
2
3
4
5
6
65
0.8645
65
28.3592
65
51.9829
65
69.0
77
0.5
77
33.4382
* Phi – positioning angle; Alpha – Inclination angle.
0
32.6823
45.4294
75.0
0
29.5739
35
18
11
8
5
20
17
150 mm aperture
130 mm aperture
25
Multipole coefficients b3
B. Effect of iron saturation and filament magnetization on
field quality
The type of iron used for this magnet is the same as that of
the MQXA magnet [7]. The peak field in the iron yoke is ~3.6 T
at the nominal operating current, as shown in Fig. 14; most
parts of the iron are saturated. Fig. 15 shows the dependence of
sextuple coefficient on the operating current caused by the
effect of iron saturation and filament magnetization. The
filament diameter of the Nb3Sn strand is ~ 10 μm. In both cases,
the variation of b3 from injection (~350 A) to the nominal
current is about 40 units. The influence on the other multiple
coefficients (b5, b7 …) is less than 1 unit. Table VIII shows the
field quality at different operating currents in the ramp-up and
ramp-down processes. Simulations are needed to check if these
large multipoles are tolerable at injection or if a corrective
strategy should be envisaged. Fig. 16 shows the transfer
function of the magnet caused by iron saturation. It decreases
by ~ 13% from low current to the nominal current.
15
5
-5
-15
TABLE VI: KEY PARAMETERS OF THE MAGNET WITH LHC
DIPOLE CABLE (INNER)
Item
Bore diameter
Value
150 mm (MBXE)
130 mm (MBXD)
Ratio
1.15
Nominal field (dipole)
6.19 T
6.31 T
0.98
Operating current
7.1 kA
7.0 kA
1.01
Field homogeneity
<0.01% (Rref=50/43 mm)
-25
0
1
2
3
4
5
6
7
Operating current (kA)
Fig. 15: The effect of iron saturation and filament magnetization on b3. The
influence of iron cryostat is not included.
/
TABLE VIII: FIELD QUALITY IN THE RAMP-UP AND RAMP-DOWN
PROCESSES (INFLUENCE OF IRON CRYOSTAT IS NOT INCLUDED)
Peak field in the coil
7.02 T
7.04 T
0.997
Load line ratio
(Inner / Outer layer)
Temperature margin
70.4% / 64.5%
@1.9 K
/
70.1% / 64.8%
@1.9 K
/
1
APERTURE
DIAMETER (MM)
OPERATING
CURRENT (KA)
B3
B5
B7
B9
B11
B13
/
Inductance
(low field / nominal field )
Stored energy
23.1 / 20.1
mH/m
507 kJ/m
18.0 / 16.3
mH/m
399 kJ/m
1.23
150
0.35
3.5
7
3.5
0.35
0.35
3.5
7
3.5
0.35
-0.2
16.2
0.9
17.3
33.3
-24.4
-4.8
0.1
-3.7
10.1
0.7
0.0
-1.0
0.0
0.0
0.1
-0.3
-0.9
-0.3
-0.5
0.5
1.1
0.9
1.2
1.8
0.3
1.0
0.8
1.1
1.8
-0.5
-0.6
-0.7
-0.6
-0.7
-0.7
-0.9
-1.0
-0.9
-1.0
0.7
0.7
0.8
0.7
0.8
0.7
0.8
0.9
0.8
0.8
-0.5
-0.5
-0.6
-0.5
-0.5
-0.9
-0.8
-0.9
-0.8
-0.8
No. of layers/blocks
1.27
2 layers; 6 blocks
/
Peak field/central field
1.13
1.12
1.01
Lorenz force X/Y
1.92/0.87 MN/m
1.78/0.77 MN/m
/
Estimated coil stress
103 MPa
86 MPa
1.2
220 mm
1.09
Outer dia. of iron yoke
Inner dia. of iron yoke
550 mm
240 mm
130
/
Strand diameter
0.82
/
1.02
Cu/Non-Cu ratio
0.97
/
1
Cable dimension /
insulation
No. of strands
11.0* 1.48mm2 /
0.15 mm (radial) 0.15 mm (azimuthal)
26
/
1.2 °
/
Supercon. current density
1033 A/mm
2
1018 A/mm
0.98
/
2
1.01
TABLE VII: COIL LAYOUT PARAMETERS FOR 2 CASES
APERTURE
COIL RADIUS
DIAMETER (MM) BLOCKS
(MM)
150
1
2
3
4
5
6
75
75
75
75
91
91
PHI
(DEG)
0.5841
26.3382
49.9177
68.7
1.2
32.4817
ALPHA
NO. OF
(DEG) CONDUCTORS
0
31.681
53.9957
74.9993
0
33.4981
19
13
10
6
22
18
Transfer function (T/kA)
Keystone angle
150 mm aperture
130 mm aperture
0.96
0.94
0.92
0.9
0.88
0.86
0
1
2
3
4
5
6
Operating current (kA)
Fig. 16: Transfer function of the magnet caused by iron saturation.
7
7
V. SUMMARY
The conceptual design work of the new D1 magnet for
HL-LHC upgrade is ongoing. The aperture diameter of this
magnet is 130-150 mm. Assuming a 30 mm wide coil by using
Nb-Ti LHC dipole cable (inner), or a 22 mm wide coil by using
bronze Nb3Sn cable; and a 30% margin on the load line, the
central magnetic field is 6.2 – 6.5 T at 1.9 K. The magnet
length is ~ 7 m to reach the integrated field of 40 T m. Nb3Sn
design with low-Jc ITER strand provides similar field as in
Nb-Ti, but 2-3 times larger temperature margin.
The average stress in coil caused by Lorenz force is 50-70
MPa for Nb-Ti option, around 100 MPa for Nb3Sn option. The
stray field is around 0.14 T for 150 mm aperture and 0.1 T for
130 mm aperture at the outer surface of the iron cryostat. If we
need to reduce the stray field to less than 0.05 T, the required
diameter of the iron yoke is over 0.7 m for 150 mm aperture.
Good field quality will be only required at the beam collision.
Further study on the strong saturation effects of the iron yoke
will be carried out and accordingly the shape of the iron yoke
will be modified.
The 3D coil end design, mechanical design, thermal analysis
will be done afterwards.
ACKNOWLEDGEMENT
This work is carried out both at the Cryogenics Science
Center of KEK and TE-MSC group of CERN. The authors
would like to thank all the colleagues in these two groups, for
their kind support of this R&D work.
Special thanks go to Thomas Taylor (CERN) for his
helpful comments on this work and Bernhard Auchmann
(CERN) for his kind technical support on the ROXIE
software.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
L.Rossi, “HL-LHC: scope, structure and management”, HL-LHC
internal kick-off day, 15 April 2011
LHC design report, volume I, chapter 8. Available:
http://lhc.web.cern.ch/lhc/LHC-DesignReport.html
L. Rossi, E. Todesco, "Electromagnetic Design of Superconducting
Dipoles Based on Sector Coils", Phys. Rev. STAB 10 (2007)
112401
L. Rossi, E. Todesco, `Electromagnetic design of superconducting
quadrupoles', Phys. Rev. STAB 9 (2006) 102401
"Superconducting accelerator magnets", USPAS, June 2007
ROXIE homepage. Available: https://espace.cern.ch/roxie
A. Terashima et.al., "Research and development of superconducting
quadrupole magnets for Large Hadron Collider at CERN", KEK
Report 2001-23, Feb. 2002
Superconducting accelerator magnets, K. -H. Mess, P. Schmuser, S.
Wolff, World scientific publishing Co., Ltd., 1996