LHC Project Note xxx
2009-09-02
bernhard.auchmann @cern.ch
Magnetic Model of the Superconducting Separation Dipole MBRB (D4)
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 dipoles are used in several insertions to change the
nominal beam separation (194 mm) of the LHC arcs. In the RF insertion (IR4), the D3
(MBRS) and D4 (MBRB) superconducting magnets are used to create a beam separation of
414 mm to make space for the RF system [1]. The MBRB is a double-aperture magnet. The
field polarity is the same in both apertures. The yoke width is evaluated in order to
accommodate the return flux. The magnets were designed, manufactured, and tested by BNL
[2-4]. The magnet cross section is shown in Fig. 1. It is very similar to the MBRC (D2),
except for the beam separation (194 mm in D4, 188 mm in D2).
Fig. 1: Cross-section of the MBRB (D4) cold mass, from Ref. [4]
Numbers and variants: Two magnets plus one spare have been manufactured (see Table I).
Table I: D4 number and measurements
Name
Installed
Spare
Rejected
T otal
MBRB (D4)
2
1
0
3
Measured at Measured at
room
1.9 K
temperature
3
3
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: HCMBRBA001-BL00000x (x = 1…3). The
electrical circuits are given in Table.
Expected operational cycles, range of current: Table II summarizes the excitation of
individual magnets at three different energy levels. The required field is 0.25 T at injection,
and 3.88 T at 7 TeV.
Table II: Slot allocation and powering of the MBRB
Magnet
State
E (GeV/c)
Circuit
B (T )
I (A) FiDeL
HCMBRBA001-BL000002
injection
450
RD4.L4
0.25
394.69
HCMBRBA001-BL000001
injection
450
RD4.R4
0.25
394.72
HCMBRBA001-BL000002
collision
3500
RD4.L4
1.942
3068.09
HCMBRBA001-BL000001
collision
3500
RD4.R4
1.942
3068.09
HCMBRBA001-BL000002
collision
5000
RD4.L4
2.774
4385.12
HCMBRBA001-BL000001
collision
5000
RD4.R4
2.774
4385.12
HCMBRBA001-BL000002
collision
7000
RD4.L4
3.883
6175.73
HCMBRBA001-BL000001
collision
7000
RD4.R4
3.883
6177.62
Summary of manufacturing parameters, manufacturers, and operational temperature: The
MBRB 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.
Table III: Main parameters of the superconducting separation dipole MBRB
Magnetic length (m)
9.45
Operation temp. (K)
4.5
Coil inner diameter (mm)
80
Beam separation
194
Nominal field (T ) at nominal current
3.80
Measured field (T ) at nominal current
3.83
Nominal current (A)
6050
Min operational current (A)
395
Max operational current (A)
6178
2. Layout
Slots and positions: The slot numbers of individual magnets are given in Table II. Fig. 2
shows the schematic layout drawing of IR 4.
Fig. 2: Layout [1] of the right-hand side of the matching section in IR 4 (RF)
-2-
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 [8].
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. Local measurements are available, as well as integral values.
Rejected or faulty measurements: No rejected or faulty measurements have been observed.
Use of the measurements in FiDeL: The room temperature measurements were not directly
used for the FiDeL model, as 4.5 K measurements are available for the entire magnet family,
but they can be used for cross-check.
3.2 MAGNETIC MEASUREMENTS AT 4.5 K
Powering: Field quality at 4.5 K is available for the ramp up in the range of 200 – 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: Measurements at 4.5 K are available for all MBRB
magnets. 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 min waiting period
before the measurements were started.
Rejected or faulty measurements: No rejected or faulty measurements have been observed.
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.
4. Transfer function
The geometric values for transfer functions are taken at 2500 A, see Fig. 3. In Table IV we
give the room temperature and the geometric values at 4.5 K. In both cases the spread is about
5 units. No systematic difference between the apertures is observed. The 4.5 K measurements
are about 40 units larger than room temperature measurements.
Saturation starts to be significant at about 3600 A (see Fig. 3). At nominal current it has an
impact on the transfer function of about 0.85% (85 units). Persistent-current effects are small
and amount to 6 units at 400 A. For the DC-magnetization fits of the transfer functions the
parameter DCMAG-q was fixed at 2 (this approach is called the “constrained fit” in the
documents of J. Miles). Measurements and the FiDeL model [9] are shown in Fig. 2. Table V
summarizes the fit parameters used for the static model of the MBRB transfer function, as
well as fit errors, which are below one unit.
-3-
TF (Tm/A)
10
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
0
1000
2000
3000 4000 5000
Current (A)
6000
7000
Fig. 2: Measured transfer function of both apertures of the MBRB family (blue markers), average of
measurements (black line), and the FiDeL fit (red line)
Table I: MBRB transfer function at room temperature and geometric at 4.5 K
Ap.
Room temperature Geometric at 4.5 K
HCMBRBA001-BL000001
(T m/A)
1
5.96E-03
5.98E-03
HCMBRBA001-BL000002
(T m/A)
1
5.96E-03
5.98E-03
HCMBRBA001-BL000003
(T m/A)
1
5.96E-03
5.98E-03
Average
(T m/A)
1
5.96E-03
5.98E-03
(units)
1
4.8
4.6
HCMBRBA001-BL000001
(T m/A)
2
5.96E-03
5.98E-03
HCMBRBA001-BL000002
(T m/A)
2
5.96E-03
5.98E-03
HCMBRBA001-BL000003
(T m/A)
2
5.96E-03
5.98E-03
Average
(T m/A)
2
5.96E-03
5.98E-03
(units)
2
3.3
4.6
Spread
Spread
Table V: Fit parameters for the transfer function of the MBRB magnets
DCMAG-m
DCMAG-p
DCMAG-q
DCMAG-h
DCMAG-Tc0
DCMAG-Tmeas
DCMAG-Ic
DCMAG-Iinjref
SAT1-s
SAT1-I0
SAT1-s
SAT1-Inomref
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)
-4.11E-06
1.27
2
2
9.5
4.5
7000
400
3.36E-04
7850
3.12
6200
-0.9
1.1
0.6
5. Field errors
In a dipole coil, allowed harmonics are b2n+1. For b3 and b5 multipoles we create a static
FiDeL model using geometric, DC-magnetization, saturation, and residual magnetization
components. The same models are used for both apertures. Moreover, DC-magnetization
models of the quadrupole component were created for each aperture.
-4-
Room temperature measurements are summarized in Table VI. Average b3 is about -1 units,
and b5 is about 0.2 units. There is a large systematic b2 of 3.5 units, with opposite signs in
each aperture. As in all others MBR, there is a systematic a3 of -0.3 units due to the
connection cables. The systematic b2, disappears in the geometric at 4.5 K, as in MBRC. In
4.5 K measurements at low currents, the b2 has the opposite sign than in room-temperature
measurements. The rest of the data confirm the room temperature measurements.
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.
Geometric: Geometric values were taken at 3000 A. The values are summarized in Table VII
Table VI: Room temperature data of the MBRB field harmonics (in units 10-4 at 17 mm reference radius)
ap
b2
a2
b3
a3
b4
a4
b5
a5
b6
a6
HCMBRBA001-BL000001
1
-3.92
0.78
-1.16
-0.25
0.00
-0.09
0.09
0.06
-0.01
-0.02
HCMBRBA001-BL000002
1
-2.94
0.35
-1.48
-0.16
0.04
0.23
0.16
0.08
0.01
0.03
HCMBRBA001-BL000003
1
-3.50
-0.86
-2.01
-0.31
-0.05
0.20
0.17
0.06
0.02
0.03
average
1
-3.45
0.09
-1.55
-0.24
0.00
0.11
0.14
0.07
0.01
0.01
spread
1
0.98
1.65
0.85
0.16
0.09
0.32
0.08
0.02
0.03
0.05
HCMBRBA001-BL000001
2
3.43
2.58
-0.74
-0.39
0.14
-0.03
0.18
0.02
-0.01
-0.03
HCMBRBA001-BL000002
2
3.37
-1.48
-1.30
-0.27
0.06
-0.13
0.20
0.04
0.00
-0.02
HCMBRBA001-BL000003
2
2.60
0.54
-0.77
-0.26
0.06
0.27
0.18
0.08
0.01
0.02
average
2
3.13
0.55
-0.94
-0.31
0.08
0.04
0.19
0.05
0.00
-0.01
spread
2
0.83
4.07
0.56
0.13
0.08
0.40
0.02
0.06
0.01
0.04
Table VII: Geometric values of the MBRB field harmonics (in units 10-4 at 17 mm reference radius)
ap
b2
a2
b3
a3
b4
a4
b5
a5
b6
a6
HCMBRBA001-BL000001
1
-0.29
0.73
-0.80
-0.24
0.05
-0.08
0.08
0.07
0.00
-0.01
HCMBRBA001-BL000002
1
0.11
0.27
-1.22
-0.18
0.04
0.17
0.12
0.07
0.00
0.03
HCMBRBA001-BL000003
1
-0.46
-0.82
-1.66
-0.35
-0.04
0.20
0.12
0.05
0.02
0.04
average
1
-0.21
0.06
-1.23
-0.25
0.02
0.10
0.11
0.07
0.00
0.02
spread
1
0.56
1.56
0.86
0.17
0.09
0.27
0.04
0.02
0.02
0.05
HCMBRBA001-BL000001
2
0.06
2.51
-0.45
-0.32
0.06
-0.02
0.16
0.04
0.00
-0.02
HCMBRBA001-BL000002
2
0.19
-1.31
-1.01
-0.21
0.02
-0.14
0.17
0.07
0.00
-0.02
HCMBRBA001-BL000003
2
-0.08
0.48
-0.47
-0.30
0.06
0.29
0.16
0.07
0.00
0.01
average
2
0.06
0.56
-0.64
-0.28
0.05
0.04
0.16
0.06
0.00
-0.01
spread
2
0.27
3.81
0.56
0.11
0.04
0.43
0.01
0.03
0.01
0.03
DC Magnetization and Saturation: The average of all 4.5 K measurements, corrected by the
geometric values, is used to model DC-magnetization and saturation for b3, b5 and b2. Note
that, in order to obtain high-quality fits in the low-field range, the constraint on the DCMAGq 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 for b3 and b5,
and 6 for b2. A proper fit of the b5 data at injection current requires taking into account the
penetration phase of the DC-magnetization. For this purpose, the residual magnetization
component in the FiDeL model is used. The b2 has a large deviation at low fields, which is
modeled through DC-magnetization. It has opposite sign in the two apertures. Two DCmagnetization models were therefore created, one per aperture. The fit agrees with
-5-
measurements within 0.2 units for b2 and b3, and within 0.01 units for b5. Fit parameters as
well as fit errors are summarized in Table VIII. The comparison of fit and measurements is
shown in Figs. 4 – Fig. 6.
Table VIII: Fit parameters for the MBRB magnets
b3 -geometric (units)
Aperture
DCMAG-m
DCMAG-p
DCMAG-q
DCMAG-h
DCMAG-Tc0
DCMAG-Tmeas
DCMAG-Ic
DCMAG-Iinjref
SAT1-s
SAT1-I0
SAT1-s
SAT1-Inomref
SAT2-s
SAT2-I0
SAT2-s
SAT2-Inomref
RESMAG-r
RESMAG-I_inj_ref
Min error
Max error
RMS error
(units)
(adim)
(adim)
(adim)
(K)
(K)
(A)
(A)
(units)
(A)
(adim)
(A)
(units)
(A)
(adim)
(A)
(adim)
(A)
(units)
(units)
(units)
b3
1&2
-4.43
1.77
13.26
2
9.5
4.5
7000
400
-0.66
4966
4.43
6200
-0.146
0.180
0.066
b5
1&2
-0.25
2.28
12.09
2
9.5
4.5
7000
400
0.17
6177
4.62
6200
0.19
2.04
-0.006
0.006
0.003
b2
1
2.71
0.96
6.22
2
9.5
4.5
7000
400
-0.143
0.018
0.042
b2
2
-2.81
0.98
6.31
2
9.5
4.5
7000
400
-0.041
0.156
0.046
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
0
1000
2000
3000
4000
Current (A)
5000
6000
7000
Fig. 3: Measured sextupole of both apertures of the MBRB family (markers), average of the measured magnets
and apertures (black line), and the FiDeL fit (red line)
-6-
0.6
0.5
b5 - geometric (units)
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
0
1000
2000
3000
4000
Current (A)
5000
6000
7000
Fig. 4: Measured decapole of the MBRB family (markers), average of the measured magnets and apertures
(black line), and the FiDeL fit (red line)
8
6
b2- geometric (units)
Aperture 1
4
2
0
-2
-4
Aperture 2
-6
-8
0
1000
2000
3000 4000 5000
Current (A)
6000
7000
Fig. 5: Measured quadrupole of the MBRB family (markers), average of the measured magnets per aperture
(black lines), and the FiDeL fits per aperture (red lines)
6. Summary and critical points

All magnets have been measured at 4.5 K and at room temperature.

The transfer function spread among the three magnets (six apertures) is about 5 units.

The transfer function has a saturation of 70 units at 7 TeV operational current.

Field harmonics are optimized in the range 3.5-7 TeV operational current, where
normal sextupole is around -1 units, and normal quadrupole is less than 0.3 units.

The sextupole component of the field at injection current is around -4 units. At low
currents, a quadrupole component is present in the field, which is of opposite sign in
the two apertures, and reaches 3-4 units at injection.
-7-
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] R. Ostojic. Engineering change order - Class I: LHC layout version 6.4: Layout of IR4,
Alice compensator, D2 and D4 cold masses. LHC Project Document LHC-LS64-EC-0001,
CERN, September 2001.
[6] R. Ostojic. Engineering change order - Class I: Modification of the cold bore separation in
D3 and D4 dipoles. LHC Project Document LHC-LBR-EC-0002, CERN, February 2003.
[7] P. Hagen, private communication, 2009.
[8] 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.
[9] Model specifications (EDMS 908232)
-8-