LHC Project Note xxx
2009-09-01
bernhard.auchmann @cern.ch
Magnetic Model of the Superconducting Separation Dipole MBRC (D2)
B. Auchmann, A. Jain, and J. Miles, for the FiDeL team
CERN, Technology Department
Keywords: Superconducting Magnets, Magnetic Field Model, Harmonics, LHC.
1. Introduction
Function in the machine: The separation dipole MBRC (D2) is used in the four experimental
regions to change the beam separation from the nominal 194 mm in the LHC arcs. The D1-D2
dipoles bring the beams on the same orbit and then separate the beam again beyond the
collision point [1]. The MBRC is a double-aperture magnet with RHIC dipole coils. The
magnets were designed, manufactured, and tested by BNL [2-4]. The magnet is shown Fig. 1.
Fig. 1: Cross-section of the MBRC (D2)
Numbers and variants: Eight magnets equip the 4 interaction regions. One spare has been
manufactured, see Table I.
Table I: Number of measured and installed MBRB
Name
Installed
Spares
Rejected
Total
MBRC (D2)
8
1
0
9
Measured at room
temperature
8
Measured
at 4.5 K
5
This is an internal CERN publication and does not necessarily reflect the views of the LHC project management.
Naming convention: Magnet IDs read as follows: MBRCA001-BL00000x (x = 1…9). The
electrical circuits are given in Table II.
Expected operational cycles, range of current: The magnets operate at 4.5 K. They ramp with
the energy of the machine, and they are kept constant during squeeze. In Table II we
summarize the current at four different energy levels. Please note that the force required in
IR2 and IR8 is about one third larger than the force required in IR5 and IR1.This is due to the
fact that the D1 has different integrated strengths in IR2-8 and in IR1-5.
Table II: Slot allocation and powering information for the MBRC
Magnet
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000005
HCMBRCA001-BL000002
HCMBRCA001-BL000009
HCMBRCA001-BL000008
HCMBRCA001-BL000004
HCMBRCA001-BL000001
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000005
HCMBRCA001-BL000002
HCMBRCA001-BL000009
HCMBRCA001-BL000008
HCMBRCA001-BL000004
HCMBRCA001-BL000001
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000005
HCMBRCA001-BL000002
HCMBRCA001-BL000009
HCMBRCA001-BL000008
HCMBRCA001-BL000004
HCMBRCA001-BL000001
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000005
HCMBRCA001-BL000002
HCMBRCA001-BL000009
HCMBRCA001-BL000008
HCMBRCA001-BL000004
HCMBRCA001-BL000001
State E (GeV/c)
injection
450
injection
450
injection
450
injection
450
injection
450
injection
450
injection
450
injection
450
collision
3500
collision
3500
collision
3500
collision
3500
collision
3500
collision
3500
collision
3500
collision
3500
collision
5000
collision
5000
collision
5000
collision
5000
collision
5000
collision
5000
collision
5000
collision
5000
collision
7000
collision
7000
collision
7000
collision
7000
collision
7000
collision
7000
collision
7000
collision
7000
Circuit
RD2.L1
RD2.L2
RD2.L5
RD2.L8
RD2.R1
RD2.R2
RD2.R5
RD2.R8
RD2.L1
RD2.L2
RD2.L5
RD2.L8
RD2.R1
RD2.R2
RD2.R5
RD2.R8
RD2.L1
RD2.L2
RD2.L5
RD2.L8
RD2.R1
RD2.R2
RD2.R5
RD2.R8
RD2.L1
RD2.L2
RD2.L5
RD2.L8
RD2.R1
RD2.R2
RD2.R5
RD2.R8
B (T)
0.179
0.243
0.179
0.243
0.179
0.243
0.179
0.243
1.395
1.894
1.395
1.894
1.395
1.894
1.395
1.894
1.993
2.705
1.993
2.705
1.993
2.705
1.993
2.705
2.790
3.787
2.790
3.787
2.790
3.787
2.790
3.787
I (A)
283.6
385.0
283.7
385.0
283.7
384.9
283.8
385.0
2203.7
2992.6
2204.4
2992.7
2204.7
2991.8
2205.6
2992.7
3148.2
4275.1
3149.1
4275.3
3149.6
4274.0
3150.8
4275.3
4408.8
6015.6
4410.1
6016.1
4410.9
6014.8
4412.3
6016.1
Summary of manufacturing parameters, manufacturers, and operational temperature: The
MBRC magnets were designed, manufactured, and tested at Brookhaven National Laboratory.
The coils are straight, RHIC-type dipole coils. The field polarity in the two apertures is
identical. Main parameters are summarized in Table III.
-2-
Table III: Main parameters of the superconducting separation dipole MBRC
Magnetic length
(m)
Operational temperature
(K)
Coil inner diameter
(mm)
Beam separation
(mm)
Nominal field at nominal current
(T)
Measured field at nominal current (T)
Nominal current
(A)
Min operational current
(A)
Max operational current
(A)
9.45
4.5
80
188
3.8
3.83
6050
284
6016
2. Layout
Slots and positions: The slot numbers of individual magnets are given in Table II. In Figs. 2-4
we show the layout of IRs 1, 2, 5, and 8.
Fig. 2: Layout [1] of IR1 (IR5 lay-out is the same)
Fig. 3: Layout [1] of IR2
-3-
Fig. 4: Layout [1] of IR8
3. Measurements
Device: A 1-m-long rotating coil of 25 mm radius was used to measure all field harmonics in
ten different longitudinal positions. Integral harmonics were computed from the local
measurements. During room temperature measurements, the integrated dipole field was also
measured using a 10-m-long non-rotating coil with two orthogonal dipole windings [3]. All
magnets were measured horizontally in their cryostats at 4.5 K [6].
3.1 ROOM TEMPERATURE MAGNETIC MEASUREMENTS
Powering: Room temperature measurements were performed at approximately ±15 A.
Available and missing measurements: Room temperature measurements are available for all
magnets except HCMBRCA001-BL000005. Local measurements are available, as well as
integral values.
Rejected or faulty measurements: No rejected or faulty measurements.
Use of the measurements in FiDeL: The room temperature measurements were used to
extrapolate the geometric components of the field harmonics at cryogenic temperatures in
those magnets that were not measured at 4.5 K. The missing room temperature measurement
of HCMBRCA001-BL000005 has been replaced by the average of the other eight magnets.
3.2 MAGNETIC MEASUREMENTS AT 4.5 K
Powering: Data is available for the ramp up in the range of 50 – 6400 A, covering the entire
operational range. For going from one current to the next, a ramp rate of 10 A/s was used.
Measurements were taken 40 s after reaching the desired current level.
Available and missing measurements: 4.5 K measurements are available for the following
magnets:
HCMBRCA001-BL000004
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
Local measurements are available, as well as integral values.
Pre-cycle: The field measurements were done after a cycle from 25 A to 6400 A at a constant
ramp rate during up and down of 10 A/s. The cycle was followed by an 8 minutes waiting
period before the measurements were started.
Rejected or faulty measurements: No rejected or faulty measurements.
-4-
Use of the measurements in FiDeL: The harmonics were rescaled from 25 mm to 17 mm
reference radius. Only the integral measurements have been used. The missing data at 4.5 K
were extrapolated from the room temperature measurements according to the standard
procedure.
4. Transfer function
Geometric: Data are summarized in Table IV. The geometric values for transfer functions are
taken as a mean value between 2200 and 3000 A, where the TF has a plateau and both
saturation and DC magnetization should be negligible (see Fig. 5). The room temperature-4.5
K correlation (1) was used to compute the geometric values. The measured spread in the
transfer function is about 11 units. The offset from room temperature to 4.5 K is about 40
units.
Table IV: Transfer function of the MBRC measured at room temperature and at 4.5 K (values extrapolated from
room temperature in italic)
TF-geometric (units)
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
Average
Spread
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
Average
Spread
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(units)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(T m/A)
(units)
Aperture Room temperature
1
5.95E-03
1
5.96E-03
1
5.95E-03
1
5.96E-03
1
5.96E-03
1
5.96E-03
1
5.96E-03
1
5.96E-03
1
5.96E-03
1
5.96E-03
1
11.0
2
5.95E-03
2
5.96E-03
2
5.95E-03
2
5.95E-03
2
5.96E-03
2
5.96E-03
2
5.96E-03
2
5.96E-03
2
5.95E-03
2
5.96E-03
2
11.3
4.5 K
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
13.2
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
5.98E-03
11.1
10
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
0
1000
2000
3000 4000 5000
Current (A)
6000
7000
Fig. 5: Measured transfer function of the MBRC (blue markers), average of measurements (black line), and
FiDeL fit (red line)
-5-
Saturation and magnetization: As shown in Fig. 5, saturation starts to be significant at about
3600 A. At 6000 A (nominal current in IR2 and IR8) it has an impact on the transfer function
of 0.55%. Persistent-current effects amount to 8 units at 300 A. Measurements and the FiDeL
model are shown in Fig. . As not all the MBRC have been measured at 4.5 K, the saturation
and the DC magnetization of the average of the measured magnets are used to model the
entire family. In Table V we summarize the fit parameters and the fit errors (one unit). For the
DC-magnetization fits of the transfer functions the parameter DCMAG-q was fixed at 2.
Table V: Fit parameters for TF in MBRC magnets
DCMAG-mu
DCMAG-p
DCMAG-q
DCMAG-h
DCMAG-Tc0
DCMAG-Tmeas
DCMAG-Ic
DCMAG-I_inj_ref
SAT1-s
SAT1-I0
SAT1-s
SAT1-I_nom_ref
Min error
Max error
RMS error
(T m/A)
(adim)
(adim)
(adim)
(K)
(K)
(A)
(A)
(T m/A)
(A)
(adim)
(A)
(units)
(units)
(units)
-5.640E-06
1.25
2
2
9.5
4.5
7000
300
2.358E-04
7390
3.392
6000
1.0
-1.0
0.6
5. Field errors
For b3 and b5 we compute a static FiDeL model using geometric, DC-magnetization,
saturation, and residual magnetization components. The same models are used for both
apertures. For b2, there is a systematic component at low field, changing sign from aperture 1
to aperture 2. It has been modeled using the residual magnetization component.
Geometric: Geometric values are taken at 3600 A. For magnets which have been not
measured at 4.5 K, they were extrapolated from room temperature measurements given in
Table VI. The systematic b3 is about -1.5 unit, and the systematic b5 is ~0.1 units. There is
also a systematic a3 of about -0.45 units that is attributed to the lead ends in [8].
Measurements at 4.5 K confirm the low value of systematic multipoles, with an average b3
within 1 unit, and a systematic b5 within 0.1 units (see Table VII). The systematic a3 is also
confirmed.
The quadrupole component in room-temperature- and 4.5-K-measurements has been analyzed
extensively by BNL. The effect is due to cross-talk at very low as well as very high excitation.
The reason for cross-talk at both, low and high, currents lies in the fact that the relative
magnetic permeability of the yoke steel is not monotonous. It takes values around 200 at low
excitation, then rises steeply to above 2000, and decreases again with saturation. The sign
difference between room temperature and 4.5 K measurements is explained by the fact that
the 4.5-K-data contains remnant magnetization, whereas it is subtracted from roomtemperature data.
-6-
Table VI: Room temperature data of the MBRC field harmonics
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
average
spread
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
average
spread
Ap.
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
b2
-3.18
-3.09
-3.66
-4.14
-3.75
-3.93
-3.90
-3.69
-4.37
-3.75
1.28
3.52
3.53
3.41
3.60
3.65
3.51
4.03
3.54
4.03
3.65
0.63
a2
1.36
-0.21
0.65
0.22
0.56
0.80
0.29
0.83
0.51
0.56
1.57
1.00
-1.69
2.94
-0.54
-0.45
-0.20
-1.29
-1.88
-1.90
-0.45
4.84
b3
-1.91
-2.26
-2.46
-1.86
-1.60
0.01
-1.57
-1.29
-1.44
-1.60
2.47
-2.27
-1.43
-2.68
-1.26
-1.59
-0.56
-1.58
-0.72
-2.25
-1.59
2.12
a3
-0.19
-0.64
-0.01
-0.50
-0.44
-0.45
-0.72
-0.51
-0.50
-0.44
0.71
-0.42
-0.74
0.02
-0.37
-0.45
-0.31
-0.66
-0.68
-0.42
-0.45
0.76
b4
0.03
-0.03
0.03
0.01
0.02
-0.02
0.06
0.04
0.01
0.02
0.08
0.00
0.07
-0.06
0.02
0.04
0.03
0.12
0.10
0.02
0.04
0.18
a4
-0.09
0.10
-0.18
0.02
0.02
0.23
-0.02
0.08
0.04
0.02
0.41
0.19
0.05
0.25
-0.09
0.07
0.61
-0.16
-0.30
0.01
0.07
0.91
b5
0.30
0.05
0.03
0.21
0.13
0.21
0.04
0.14
0.01
0.13
0.29
0.26
0.09
-0.03
0.23
0.11
0.18
0.07
0.11
-0.02
0.11
0.28
a5
0.07
0.04
-0.05
0.04
0.03
0.04
0.00
0.03
0.04
0.03
0.12
0.03
0.00
0.02
0.05
0.03
0.04
0.01
0.02
0.05
0.03
0.05
b6
0.01
0.00
0.00
-0.01
0.00
0.00
0.00
0.00
-0.01
0.00
0.02
0.00
-0.01
-0.02
0.00
0.00
0.00
-0.01
-0.01
0.01
0.00
0.03
a6
-0.01
0.02
-0.03
-0.03
0.00
0.01
-0.01
0.02
0.01
0.00
0.06
0.03
0.01
0.00
0.00
0.01
0.08
0.01
-0.03
0.01
0.01
0.10
Table VII: Geometric values of the MBRC field harmonics (in italic: data extrapolated from room temperature
measurements)
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
average
spread
HCMBRCA001-BL000001
HCMBRCA001-BL000002
HCMBRCA001-BL000003
HCMBRCA001-BL000004
HCMBRCA001-BL000005
HCMBRCA001-BL000006
HCMBRCA001-BL000007
HCMBRCA001-BL000008
HCMBRCA001-BL000009
average
spread
Ap.
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
b2
0.55
0.64
0.08
-0.42
-0.27
-0.45
-0.07
-0.04
-0.38
-0.04
1.09
-0.28
-0.27
-0.39
-0.30
-0.06
-0.22
0.31
-0.10
0.03
-0.14
0.70
a2
1.25
-0.32
0.53
0.27
0.42
0.67
-0.01
0.75
0.42
0.44
1.57
1.03
-1.65
2.97
-0.24
-1.13
-0.74
-1.12
-1.73
-1.82
-0.49
4.79
b3
-1.40
-1.75
-1.96
-1.30
-0.72
0.45
-1.05
-0.84
-0.86
-1.05
2.41
-1.79
-0.96
-2.21
-0.85
-0.80
-0.21
-0.99
-0.31
-1.66
-1.09
2.00
a3
-0.21
-0.65
-0.02
-0.53
-0.55
-0.53
-0.66
-0.49
-0.52
-0.46
0.64
-0.39
-0.71
0.05
-0.39
-0.46
-0.31
-0.60
-0.63
-0.35
-0.42
0.76
b4
0.04
-0.02
0.03
0.00
0.02
-0.02
0.09
0.03
0.02
0.02
0.11
-0.03
0.03
-0.10
-0.02
0.02
0.01
0.09
0.03
-0.01
0.00
0.19
a4
-0.14
0.06
-0.23
0.00
0.02
0.17
-0.11
0.03
0.02
-0.02
0.40
0.18
0.04
0.24
-0.14
0.00
0.55
-0.15
-0.29
0.05
0.05
0.84
b5
0.26
0.02
0.00
0.16
0.09
0.16
0.02
0.12
-0.01
0.09
0.28
0.23
0.06
-0.06
0.19
0.08
0.12
0.06
0.09
-0.03
0.08
0.28
a5
0.08
0.05
-0.05
0.03
0.03
0.02
0.02
0.04
0.05
0.03
0.12
0.04
0.01
0.03
0.04
0.04
0.03
0.03
0.02
0.07
0.04
0.07
b6
0.02
0.01
0.01
0.00
0.00
0.00
0.01
0.01
0.00
0.01
0.02
0.00
-0.01
-0.02
-0.01
0.00
-0.01
0.00
0.00
0.01
0.00
0.03
a6
-0.01
0.03
-0.03
-0.03
0.00
0.01
-0.01
0.01
0.02
0.00
0.06
0.04
0.01
0.00
0.01
0.02
0.09
0.01
-0.03
0.02
0.02
0.11
Magnetization and saturation: The average of all 4.5 K measurements, minus the geometric, is
used to model the DC-magnetization, the saturation, and the residual magnetization. Note that,
in order to obtain high-quality fits in the low-field range, the constraint on the DCMAG-q
parameter in the DC-magnetization fit, which was used in the transfer function model, was
dropped. Using Gnuplot for optimal fitting yields DCMAG-q values of about 12. A proper fit
of the b5 data at injection current requires taking into account the penetration phase of the DCmagnetization. For this purpose, the residual magnetization component in the FiDeL model is
used. A summary of the fit parameters is given in Table VIII. The errors of the fit are within
0.3 units for b2 and b3, and less than 0.1 units for b5. Measurements and FiDeL fits of the b3,
b5, and b2 harmonics are shown in Fig. 6-8.
-7-
Table IVIII: Fit parameters for MBRC magnets
Aperture
DCMAG-mu
DCMAG-p
DCMAG-q
DCMAG-h
DCMAG-Tc0
DCMAG-Tmeas
DCMAG-Ic
DCMAG-I_inj_ref
SAT1-s
SAT1-I0
SAT1-s
SAT1-I_nom_ref
RESMAG-r
RESMAG-I_ inj_ref
Min error
Max error
RMS error
(units)
(adim)
(adim)
(adim)
(K)
(K)
(A)
(A)
(units)
(A)
(adim)
(A)
(adim)
(A)
(units)
(units)
(units)
b3
1&2
-6.062
1.72
11.70
2
9.5
4.5
7000
300
-0.887
5290
4.515
6000
-0.201
0.241
0.099
b5
1&2
-0.272
2.32
11.98
2
9.5
4.5
7000
300
0.178
6355
3.884
6000
0.38
2.06
-0.007
0.016
0.005
b2
1
4.149
1.09
13.18
2
9.5
4.5
7000
300
-0.184
0.031
0.056
b2
2
-4.311
1.10
11.96
2
9.5
4.5
7000
300
-0.052
0.205
0.074
Fig. 6: Measured sextupole of the MBRC family (markers), average of the measured magnets and apertures
(black line), and the FiDeL fit (red line)
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b5-geometric (units)
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
0
1000 2000 3000 4000 5000 6000 7000
Current (A)
b2 -geometric (units)
Fig. 7: Measured decapole of the MBRC family (markers), average of the measured magnets and apertures
(black line), and the FiDeL fit (red line)
5
4
3
2
1
0
-1
-2
-3
-4
-5
Aperture 1
Aperture 2
0
1000 2000 3000 4000 5000 6000 7000
Current (A)
Fig. 8: Measured quadrupole of the MBRC family (markers), average of the measured magnets per aperture
(black lines), and the FiDeL fits per aperture (red lines)
6. Summary and critical points

Magnets in IR1 and IR5 are powered with about 70% of the current of IR2 and IR8.

All magnets but one have been measured at room temperature, five out of nine have
been measured at 4.5 K.

The transfer function spread among the nine magnets (18 apertures) is 11-13 units.

The transfer function has a saturation of 50 units at 7 TeV operational current in IR2
and IR8.

Field harmonics are optimized in the range 3.5-7 TeV operational current, where
normal sextupole is around -1 units. There is a skew sextupole systematic component
of about 0.5 units due to connections.

The sextupole component of the field at injection current is around -8 units. At low
currents, a quadrupole component is present in the field, which is of opposite sign in
the two apertures, and reaches 5 units at injection.
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Ackowledgements
We wish to thank L. Bottura for providing additional data, and L. Deniau for his advice in
generating the FiDeL models.
References
[1] O. Bruning, et al., CERN Report 2004-003 (2004).
[2] E. Willen. Functional specification: Superconducting beam separation dipoles. LHC Pro
ject Document LHC-MBR-ES-0001 rev. 2.0, CERN, June 2000.
[3] J. Muratore and et al. Test results for LHC insertion region dipole magnets. Proceedings of
the 2005 Particle Accelerator Conference, Knoxville, Tennessee, pages 3106–3108, 2005.
[4] E. Willen and et al. Superconducting dipole magnets for the LHC insertion regions.
Proceedings of EPAC 2000, Vienna, Austria, pages 2187–2189, 2000.
[5] P. Hagen, private communication, 2009.
[6] J. Muratore and et al. Test results for initial production of LHC insertion region dipole
magnets. Proceedings of EPAC 2002, La Villette, Paris, pages 2415–2417, 2002.
[7] Model specifications (EDMS 908232)
[8] R. Gupta and et al. Coldmass for LHC dipole insertion magnets. submitted to MT-15,
Fifteenth International Conference on Magnet Technology, Beijing, China, October 1997.
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