LHC Project Note XXX
2009-08-31
Vittorio.remondino@cern.ch
Magnetic model of the dipole correctors in the triplet MCBX and MCBXA
V. Remondino for the FiDeL team
CERN, Technology Department
Keywords: Superconducting Magnets, Magnetic Field Model, Harmonics, LHC.
1. Summary of main parameters
Function in the machine: Each of the eight inner triplets of the LHC is equipped with three
combined horizontal and vertical correction dipoles for closed orbit correction, the MCBX.
These superconducting single-aperture magnets have a bore of 90 mm diameter to create space
for the MCSTX insert. The complete MCBX magnets are 730 mm long, have an outer
diameter of 350 mm and an approximate mass of 480 kg. In the cold mass configurations of
the inner triplets, the MCBX magnets are flanged to the end plate of the high gradient
quadrupoles (MQXA and MQXB). One out of three MCBX has the MCSTX insert: in this
case its name changes to MCBXA. The nominal strength is 3.26 T for the horizontal field and
3.35 T for the vertical one at the nominal current of 550 A, with a magnetic length of 480 mm
and 450 mm respectively. The measured strengths are 6-7% larger for both types of dipoles
(see Table I).
Fig. 1: MCBX cross-section (without MCSTX insert): cross-section (left) and photo (right)
This is an internal CERN publication and does not necessarily reflect the views of the LHC project management.
Table I: Summary of MCBX parameters
N° correctors
Aperture
Outer diameter support
Overall length
Weight
Nominal strength
Measured strenght
Nominal current
Magnetic length
Nominal current/short sample at 1.9 K
Max ramp rate
Resistance at room temperature
Inductance
Stored energy at nominal
[mm]
[mm]
[mm]
[Kg]
[T]
[T]
[A]
[m]
[A/s]
[Ω]
[mH]
[kJ]
MCBXV MCBXH
16 MCBX + 8 MCBXA
90
120.8
350
730
465
3.26
3.35
3.49
3.56
550
0.48
0.45
44%
47%
10
10
18.8
22.7
175
287
26.5
43.4
Numbers and variants: Three magnets are located in each inner triplet, therefore the total
number of the MCBX (2 MCBX and 1 MCBXA type) is 24. The MCBXA type contains an
MCTX insert. Three spares are available.
Naming convention: The MCBX correctors are identified with the prefix “HCMCBX_001SP00” followed by a 4-digit progressive number; MCBXA are identified with the signature
“HCMCSX_999-CR00”. Horizontal coils have the prefix “HCMCBXH022-SP00” and
vertical coils the prefix “HCMCBXV021-SP00” followed by the same 4-digit progressive
number that identifies the assembly.
Expected operational cycles, range of current and operational temperature: These correctors
operate at 1.9 K, They are used to create the separation of the orbits, i.e. not to have collisions
at injection and during the ramp. Moreover, they are used to generate the crossing angle. In
2010, the operational current has been within 20 A at injection and within 150 A at 3.5 TeV.
Summary of manufacturing parameters, and manufacturers: the MCBX have been built by
SIGMAPHI. They use type 4 superconductor.
2. Layout
Slots and positions: Three MCBX correctors are located in the inner triplets as shown in Fig. 2
and Table II.
Circuits: Each magnet is individually powered by a circuit name whose prefix is “RCBX”.
The maximum specified ramp rate is 10 A/s (Table I).
-2-
Q3
M
C
S
O
X
M
C
B
X
A
Q2
M
Q
S
X
MQXA
B
P
M
MQXB
M
C
B
X
MQXB
A1 / B1
B6 / B3
A2
MQXA
B
P
M
LMQXA
LMQXC
LMQXB
B4
A4
A3
M
C
B
X
Q1
A1 / B1
A1 / B1
To IP 
FNAL supplied
KEK supplied
CERN supplied
Fig. 2: Inner triplet: position of the MCBXA and MCBX
Table II. Position of the MCBX in the inner triplets
IR1
IR5
Assembly
Circuit
Module
Assembly
HCMCBX_001-SP000023
RCBXH3.L1
HCMCBXH022-SP000023
HCMCBX_001-SP000027
RCBXH3.L5 HCMCBXH022-SP000027
-53.814
HCMCBX_001-SP000023
RCBXV3.L1
HCMCBXV021-SP000023
HCMCBX_001-SP000027
RCBXV3.L5 HCMCBXV021-SP000027
-53.814
HCMCBX_001-SP000013
RCBXV2.L1
HCMCBXV021-SP000013
HCMCBX_001-SP000012
RCBXV2.L5 HCMCBXV021-SP000012
-38.019
HCMCBX_001-SP000013
RCBXH2.L1
HCMCBXH022-SP000013
HCMCBX_001-SP000012
RCBXH2.L5 HCMCBXH022-SP000012
-38.019
HCMCBX_001-SP000014
RCBXV1.L1
HCMCBXV021-SP000014
HCMCBX_001-SP000010
RCBXV1.L5 HCMCBXV021-SP000010
-29.842
HCMCBX_001-SP000014
RCBXH1.L1
HCMCBXH022-SP000014
HCMCBX_001-SP000010
RCBXH1.L5 HCMCBXH022-SP000010
-29.842
HCMCBX_001-SP000024
RCBXV1.R1
HCMCBXV021-SP000024
HCMCBX_001-SP000022
RCBXV1.R5 HCMCBXV021-SP000022
29.842
HCMCBX_001-SP000024
RCBXH1.R1 HCMCBXH022-SP000024
HCMCBX_001-SP000022 RCBXH1.R5 HCMCBXH022-SP000022
29.842
HCMCBX_001-SP000034
RCBXH2.R1 HCMCBXH022-SP000034
HCMCBX_001-SP000004 RCBXH2.R5 HCMCBXH022-SP000004
38.019
HCMCBX_001-SP000034
RCBXV2.R1
HCMCBXV021-SP000034
HCMCBX_001-SP000004
RCBXV2.R5 HCMCBXV021-SP000004
38.019
HCMCBX_001-SP000031
RCBXV3.R1
HCMCBXV021-SP000031
HCMCBX_001-SP000030 RCBXH3.R5 HCMCBXH022-SP000030
53.814
HCMCBX_001-SP000031
RCBXH3.R1 HCMCBXH022-SP000031
HCMCBX_001-SP000030
IR2
Circuit
Module
RCBXV3.R5 HCMCBXV021-SP000030
IR8
Position (m)
53.814
Position (m)
HCMCBX_001-SP000018
RCBXH3.L2
HCMCBXH022-SP000018
HCMCBX_001-SP000021
RCBXV3.L8 HCMCBXV021-SP000021
-53.814
HCMCBX_001-SP000018
RCBXV3.L2
HCMCBXV021-SP000018
HCMCBX_001-SP000021
RCBXH3.L8 HCMCBXH022-SP000021
-53.814
HCMCBX_001-SP000007
RCBXV2.L2
HCMCBXV021-SP000007
HCMCBX_001-SP000006
RCBXH2.L8 HCMCBXH022-SP000006
-38.019
HCMCBX_001-SP000007
RCBXH2.L2
HCMCBXH022-SP000007
HCMCBX_001-SP000006
RCBXV2.L8 HCMCBXV021-SP000006
-38.019
HCMCBX_001-SP000028
RCBXV1.L2
HCMCBXV021-SP000028
HCMCBX_001-SP000003
RCBXH1.L8 HCMCBXH022-SP000003
-29.842
HCMCBX_001-SP000028
RCBXH1.L2
HCMCBXH022-SP000028
HCMCBX_001-SP000003
RCBXV1.L8 HCMCBXV021-SP000003
-29.842
HCMCBX_001-SP000025
RCBXH1.R2 HCMCBXH022-SP000025
HCMCBX_001-SP000016
RCBXV1.R8 HCMCBXV021-SP000016
29.842
HCMCBX_001-SP000025
RCBXV1.R2
HCMCBXV021-SP000025
HCMCBX_001-SP000016 RCBXH1.R8 HCMCBXH022-SP000016
29.842
HCMCBX_001-SP000026
RCBXH2.R2 HCMCBXH022-SP000026
HCMCBX_001-SP000019 RCBXH2.R8 HCMCBXH022-SP000019
38.019
HCMCBX_001-SP000026
RCBXV2.R2
HCMCBX_001-SP000019
RCBXV2.R8 HCMCBXV021-SP000019
38.019
HCMCBX_001-SP000020
RCBXH3.R2 HCMCBXH022-SP000020
HCMCBX_001-SP000029 RCBXH3.R8 HCMCBXH022-SP000029
53.814
HCMCBX_001-SP000020
RCBXV3.R2
HCMCBX_001-SP000029
53.814
HCMCBXV021-SP000026
HCMCBXV021-SP000020
RCBXV3.R8 HCMCBXV021-SP000029
3. Measurements
In Table III we give a summary of the available measurements. No distinction is done between
MCBX and MCBXA magnets. Room temperature magnetic measurements are available only
for the vertical field (MCBXH).
-3-
Table III. Summary of MCBX / MCBXA measurements.
MCBXA
Measured at r.t
H type
1
yes
2
yes
3
yes
Measured at 1.9 K
H type
Installed
V type
yes
4
yes
6
yes
7
yes
8
yes
yes
yes
yes
9
10
11
yes
yes
yes
yes
12
yes
yes
yes
13
yes
yes
yes
14
yes
16
yes
yes
yes
18
yes
19
yes
20
21
yes
24
25
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
22
23
yes
yes
yes
26
27
yes
yes
28
yes
29
yes
31
yes
32
yes
33
yes
34
yes
35
yes
yes
yes
yes
yes
yes
3.1 ROOM TEMPERATURE MAGNETIC MEASUREMENTS
Device: Modules were measured at CERN using the second generation of CIMM. Modules
under test were placed vertically in the CIMM and carefully positioned with respect to some
geometrical references in such a way to determine the position of the geometrical centre with
precision. Field strength, orientation and harmonics were measured using two measuring coils
of 258 mm each in series in order to cover entirely the module length. As the tolerances given
on the harmonics are larger than for the other LHC magnets, the CIMM is equipped with a
single tangential coil; no compensation signal is therefore present for the determination of
higher harmonics (see Fig. 3) [2]. CIMM delivers the integral harmonics, which are expressed
w.r.t. the geometrical centre normalised to the current of 1 A. Harmonics are not normalized
-4-
w.r.t. the main harmonic. Some important values were omitted in the final result file, such as
the phase of the main harmonics and the position of the magnetic centre defined as the point
where C12 = 0. Measurements have required therefore some transformations to conform to the
field error naming conventions for LHC magnets [4] and to the LHC magnet polarities
convention [5], in particular, the harmonic normalisation with respect to the magnetic centre
and to the main harmonic (taking into account angular offset and transformation of the
harmonics in units).
Fig. 3: The CIMM: Geometrical vs magnetic centre (left), position of the measuring coil w.r.t the MO module
(middle), the measuring tangential coil (right)
Available and missing measurements: Thirteen correctors were measured at room temperature
at CERN several times (Table III). In total, 46 MCBXH measurements are available.
Use of the measurements in FiDeL: Room temperature measurements of the TF are
extrapolated at 1.9 K and are compared to the 1.9 K measurements to cross-check. The field
harmonics values are used to verify that they can be neglected in FiDeL.
3.2 MAGNETIC MEASUREMENTS AT 1.9 K
Devices: The MCBX correctors have been tested before their assembly in the triplets with the
measurement and power test equipment used for the tests of the main LHC dipole short
models. The cryostat is designed to test magnets with a maximum length of 2.1 m [3]. The
measuring coils assemblies are made of 5 identical coils adjacent to each other, the central one
being centred on the rotating axis. The measuring shaft used for the cold measurements
includes four coil assemblies, each with effective length of 0.2 m; the coils measure the
magnets individually. The samples were not all measured in the same conditions and, in
particular, the exciting currents values were different: some samples were measured up to
nominal current, some up to 594 A, and the intermediate levels were different.
Available and missing measurements: 1.9 K measurements were performed on 13 correctors,
with both vertical and horizontal fields (see Table III).
Use of the measurements in FiDeL: These measurements were used to estimate the geometric
terms (linear transfer function) both for MCBXH and MCBXV and to estimate hysteresis and
saturation.
-5-
4. Transfer function
4.1 MCBXH
Geometric term: The comparison between transfer functions measured at room temperature
(see Fig. 4) and at 1.9 K (See Fig. 5) gives a difference of 2.5 % (see Table IV). This is the
precision of our absolute knowledge of the TF. The spread at 1.9 K is 80 units, value well in
the range of the precision of the 1.9 K measuring system. The room temperature spread of 30
units is a more precise estimate of the spread of the transfer function. The 1.9 K value of the
geometric term is used in the model.
Table IV: Integrated transfer function measured at room temperature and at 1.9 K
Measured at r.t.
Number of measurements
46
Average (T m /A)
3.1786E-03
Stdev (units)
31
Measured at 1.9 K
15
3.100E-03
80
Transfer function (T m /A)
0.00320
0.00319
0.00318
0.00317
0.00316
0.00315
0
10
20
30
Module
40
50
0.0035
1300
0.0033
650
0.0031
0
0.0029
-650
0.0027
-1300
0.0025
-1950
Units
TF [T m /A]
Fig. 4: Integrated transfer function measured at room temperature for MCBXH
0
100
200
300
400
Current (A)
500
600
Fig. 5: Integrated transfer function versus current for MCBXH, average over 14 modules
-6-
Saturation: There is a saturation effect in the order of 2%: the transfer function decreases from
0.0031 T m /A measured at 20 A to 0.00305 T m/A at 550 A (see Fig. 6). Table V shows the
resulting fit parameters and Fig. 7 the measured TF with respect to the calculated one. The
error of the fit is in the order of 7 units (see Fig. 7).
Residual Magnetization is 2-3% at 20 A, 3-7% at 10 A, and 13% at 5 A. It has not been
modelled.
Table V: FiDeL TF fit parameters for saturation (MCBXH).
325
3.10E-03
0
3.09E-03
-325
3.08E-03
-650
3.07E-03
-975
Measurements
3.06E-03
-1300
FiDeL fit
3.05E-03
-1625
3.04E-03
-1950
0
100
200
300
400
Current (A)
500
600
Fig. 6: Measurements versus FiDeL fit for MCBXH.
10
5
0
-5
-10
-15
-20
0
100
200
300
400
Current (A)
Fig. 7: Errors of the FiDeL fit for MCBXH.
-7-
500
600
TF (units)
Value
0.003100
0.0002073
645.2
2.501
550
3.11E-03
Error (units)
TF (T m/A)
Parameter
g
(T m /A)
s
(T m /A)
I0
(A)
S
(adim)
Inom
(A)
4.2 MCBXV
0.0033
1330
0.0032
980
0.0031
630
0.0030
280
0.0029
-70
0.0028
-420
0.0027
-770
0.0026
-1120
0
100
200
300
400
Current (A)
500
TF (units)
TF [T m /A]
Geometric term: The geometric coefficient is 0.002925 T m/A, based on measurements of 10
modules at 1.9 K (see Fig. 8).
600
Fig. 8: Integrated transfer function versus current for MCBXV, average over 10 measured modules.
Saturation: The measurements at 1.9 K show that the saturation effect at nominal is less than
1% (see Fig. 8). The residual magnetization is 1.5% of the TF at 50 A (half width), and 4-5%
at 10 A (see Fig. 8). It has not been modelled.
Residual Magnetization is 4% at 10 A, and 13% at 5 A. It has not been modelled.
5. Field errors
In Table VI we show the harmonic measured on the 46 samples measured at room temperature
for the MCBXH. As for all correctors, these values are not modelled in FiDeL.
-8-
Table VI: Measured field errors, MCBXH
Measured
MCBXH
Mechanical
T argets
systematic
sigma
Inf. limit
Sup. limit
Inf. limit
Sup. limit
mod (T m /A)
3.179
0.010
3.140
3.078
3.140
3.078
phase (mrad)
-3.856
4.531
3.5
-3.5
3.5
-3.5
systematic
sigma
systematic
sigma
systematic
sigma
b1
10000
-
-
-
-
-
b2
-1.596
4.135
-
0.710
4.08
-
b3
-9.301
1.185
-0.88
0.24
86.70
0.46
b4
-0.076
0.415
-
0.07
0.29
0.54
b5
-0.795
0.061
-0.54
0.02
6.68
0.48
b6
-0.002
0.013
-
0.01
1.29
0.37
b7
0.000
0.006
-
-
0.68
0.12
b8
0.001
0.003
-
-
0.25
0.05
b9
0.002
0.002
-
-
0.35
0.02
b10
0.000
0.001
-
-
0.05
0.47
b11
0.000
0.002
-
-
0.08
0.20
b12
0.000
0.000
-
-
0.00
0.00
b13
0.000
0.001
-
-
0.00
0.00
b14
0.000
0.002
-
-
0.00
0.00
b15
0.000
0.000
-
-
0.00
0.00
a1
-
-
-
-
-
-
a2
1.422
5.796
-
2.03
2.04
-
a3
-2.618
0.536
-2.19
0.65
7.72
0.46
a4
0.172
1.178
-
0.21
0.11
0.54
a5
0.109
0.018
0.07
0.07
1.53
0.48
a6
0.002
0.013
-
0.02
0.65
0.37
a7
-0.006
0.006
-
0.01
0.24
0.12
a8
-0.002
0.006
-
-
0.13
0.05
a9
0.000
0.002
-
-
0.07
0.92
a10
-0.001
0.003
-
-
0.02
0.47
a11
0.000
0.001
-
-
0.18
0.20
a12
0.000
0.000
-
-
0.00
0.00
a13
0.000
0.001
-
-
0.00
0.00
a14
0.000
0.001
-
-
0.00
0.00
a15
0.000
0.000
-
-
0.00
0.00
Xc
0.00
0.03
0.00
0.03
Yc
0.00
0.03
0.00
0.03
-9-
5. Summary and critical issues




The TF of the MCBXH and MCBXV is known within 2-3%.
Saturation is relevant for the MCBXH, and it has been modelled. It is neglibile for the
MCBXV.
The residual magnetization has not been modelled but it is not negligible, neither for
the MCBXV nor for the MCBXH: 3-7% at 10 A. This can have an impact at injection,
were most of the correctors are powered with less than 20 A.
During operation the cross-talk between the two magnets can affect the TF. Dedicated
measurements are ongoing.
Acknowledgements
We wish to acknowledge R. Wolf for evaluating the FiDeL fit parameters used for the 2008
start-up, and W. Venturini Delsolaro, in charge of Block4 test station during the magnet
production.
References
LHC Design report, CERN-2004-003, 2004-4-6, Editorial Board, Bruning, Collier, Lebrun, Myers,
Ostojic, Poole, Proudlock
Qualification of the LHC corrector magnet production with the CERN-built measurement benches,
LHC Project Report 1088, Giloux, Karppinen, Mugnai, Remondino, Venturini-Delsolaro,Viret,
Walckiers, Wolf
Measurements of the LHC corrector magnets at room and cryogenic temperatures,LHC-Project report
201, Ang, Arn, Bottura, Giloux, Sievers,
Smirnov, Vincent, Walckiers
LHC magnet polarites, EDMS 90041, 2004-12-03, rev. 3, Engineering specification, prepared by P.
Proudlock, S. Russenschuck, M. Zerlauth.
Field error naming conventions for LHC magnets, EDMS 90250, 2001-10-24, rev 3.0, Engineering
specification, prepared by R. Wolf
- 10 -
This is an internal CERN publication and does not necessarily reflect the views of the LHC project management.