LHC Project Note XXX
2009-06-01
Ezio.Todesco@cern.ch
Magnetic model of the inner triplet quadrupole MQXB
Joe Di Marco, P. Schlabach, E. Todesco and G. V. Velev for the FiDeL team
CERN, Technology Department
Keywords: Superconducting Magnets, Magnetic Field Model, Harmonics, LHC.
1. Introduction
Function in the machine: The MQXB is a superconducting quadrupole with 70 mm aperture
and operational current of ~12000 A and nominal gradient of ~200 T/m [1] (see Table I).
Together with the MQXA, it is a part of the inner triplet present on each side of the four
experimental areas. Its optical function is to focus the beam in the interaction point.
Fig. 1: MQXB cross-section
Numbers and variants: we have 16 MQXB, two per side of each of the four experimental
areas. They are all the same. 18 cold masses have been manufactured; two of them have been
rebuilt.
Naming convention: Cold masses are labelled by HCMQXB_001-FL0000xx, with xx a
progressive number ranging from 1 to 20. Cold masses 4 and 14 are not present since they
had insufficient quench performance, they were rebuilt, and new numbers were assigned.
Two cold masses make a cryostat, labelled by HCLQXB_001-FL0000yy, with yy ranging
from 1 to 11, and skipping 2 and 7. Cryostat 1, including cold masses 02 and 01, is a spare.
The list of slots, cryostats and cold masses is given in Table II.
This is an internal CERN publication and does not necessarily reflect the views of the LHC project management.
Table I: Main parameters of MQXB (currents calculated based on measurements presented in Section 3)
Magnetic length (m)
Operational temperature (K)
Aperture (mm)
Current at injection in IP1 And IP5 (A)
Gradient at injection in IP1 and IP5 (T/m) *
Current at injection in IP2 And IP8 (A)
Gradient at injection in IP2 and IP8 (T/m) *
Current at collision (A)
Gradient at collision (T/m) *
Minimal operational current (A)
Maximal operational current (A)
* Assuming nominal magnetic lenght
2*5.5
1.9
70
716.7
13.2
776.1
14.3
11380
205
716.7
11380
Table II: Slot allocation, position in the machine, cryostat name and cold mass id for the MQXB
Slot
MQXB.A2R1
Position (m)
35
Cryostat
HCLQXB_001-FL000010
Cold mass
HCMQXB_001-FL000019
MQXB.B2R1
41
HCLQXB_001-FL000010
HCMQXB_001-FL000018
MQXB.B2L2
MQXB.A2L2
MQXB.A2R2
MQXB.B2R2
MQXB.B2L5
MQXB.A2L5
MQXB.A2R5
3291
3298
3367
3374
13288
13295
13364
HCLQXB_001-FL000011
HCLQXB_001-FL000011
HCLQXB_001-FL000009
HCLQXB_001-FL000009
HCLQXB_001-FL000005
HCLQXB_001-FL000005
HCLQXB_001-FL000003
HCMQXB_001-FL000015
HCMQXB_001-FL000020
HCMQXB_001-FL000017
HCMQXB_001-FL000016
HCMQXB_001-FL000008
HCMQXB_001-FL000011
HCMQXB_001-FL000006
MQXB.B2R5
MQXB.B2L8
MQXB.A2L8
MQXB.A2R8
13371
23274
23281
23350
HCLQXB_001-FL000003
HCLQXB_001-FL000004
HCLQXB_001-FL000004
HCLQXB_001-FL000008
HCMQXB_001-FL000005
HCMQXB_001-FL000012
HCMQXB_001-FL000010
HCMQXB_001-FL000003
MQXB.B2R8
MQXB.B2L1
MQXB.A2L1
23357
26618
26624
HCLQXB_001-FL000008
HCLQXB_001-FL000006
HCLQXB_001-FL000006
HCLQXB_001-FL000001
HCLQXB_001-FL000001
HCMQXB_001-FL000013
HCMQXB_001-FL000009
HCMQXB_001-FL000007
HCMQXB_001-FL000002
HCMQXB_001-FL000001
spare
spare
Expected operational cycles, range of current and operational temperature: The transfer
function is approximately 0.0343 T m/A. The injection current is 717-779 A, corresponding
to a gradient of 13.2-14.3 T/m. During the ramp, the current increases with the energy as for
the main magnets, i.e., reaching 11380 A and a operational gradient of 205 T/m. During the
squeeze the current remains stable within a few percent.
Summary of manufacturing parameters, and manufacturers: the MQXB have been built at
Fermilab as a special contribution by US [1].
2. Layout
Slots and positions: 16 MQXB cold masses are allocated to 8 Q2 positions (see Fig. 2),
according to the Table II, which refers to as installed in 1-9-2008.
- -
Circuits: the two MQXB cold masses are powered in series, through two power converters:
the first one powers in series also the Q1 and Q3, the second powers only the Q2 to make
them reach the nominal current of ~12 kA.
Fig. 2: Schematic lay-out [1] of the triplet (interaction point is 23 m on the right of Q1)
3. Measurements
3.1 “INTEGRAL” STRETCHED WIRE MEASUREMENTS FOR TRANSFER
FUNCTION AT 1.9 K
Device: Single Stretched Wire (SSW) measurement system. Measurements are performed at
1.9 K for both magnets together in the cryostat, with wire motion in the horizontal plane.
Available and missing measurements: we have four sets of measurements for each magnet,
corresponding to different currents, namely injection (669 A), 5460 A, collision at 7 TeV
(11345 A), and ultimate (11923 A). Measurements generally start within a few minutes of
reaching target current, and take between 15 and 30 minutes to complete since several
tensions are used. Longer starting delays sometimes have occurred (e.g. when measurements
have had to be repeated). Measurements of 9 cryostats are present; cryostat 2 (LQXB03) has
an anomalous set which is missing the ultimate current measurement. Data taken at multiple
tensions are extrapolated to infinite tension to remove the effects of wire susceptibility.
Pre-cycle: Measurements were preceded by a ramp to high current (11345A).
Rejected or faulty measurements: All measurements sent to CERN are validated data.
Use of the measurements in FiDeL: These are the reference measurements for the integrals in
a machine cycle. In order to have a detailed model as a function of the current, the “DCloop”
set is also used. This second set has a much denser scan of the current, but is not covering the
whole magnet (see next section).
3.2 “DCLOOP” MEASUREMENTS FOR TRANSFER FUNCTION AT 1.9 K
Device: An 810-mm-long rotating coil probe is utilized. The probe is positioned
approximately in the geometrical centre of the magnet. All the measurements are done in the
Magnet Test Facility at Technical Division, Fermilab.
Available and missing measurements: For each loop we have about 70 currents in the ramp
up, from 50 A to 11300 A, 25 at 11300 A, and 70 currents with ramp down (see Fig. 3). This
corresponds to 40 A/s ramp up and down. During the measurement, the loop was repeated 3
times and the averaged values for the harmonics were reported. Measurements are available
only for half of the cold masses, i.e., 1,2,5,6,9,10,11,13,17.
- -
12000
Current (A)
10000
8000
6000
4000
2000
0
0
50
100
150
Measurement
200
250
Fig. 3: Current cycle used in “DCloop” measurements
Pre-cycle: There was no pre-cycle, the magnet was not quenched and these measurements
started after the integral ones. Ramp rate is 40 A/s.
Rejected or faulty measurements: Measurement of cold mass 17 is rejected.
Use of the measurements in FiDeL: These measurements give a fine track of transfer function
and multipoles along the loadline. They are used to have a detailed scan of TF versus current.
The DC magnetization is computed on the DCloop data.
3.2 FIELD HARMONICS “INTEGRAL” MEASUREMENTS AT 1.9 K
Device: An 810-mm-long rotating coil probe is utilized. The probe was positioned in 9 nonoverlaying positions, covering the full length of the magnet (~5.5 m). After this, the integral
harmonics were calculated, reweighting the ends accordingly. All the measurements are done
in the Magnet Test Facility at Technical Division, in Fermilab.
Available and missing measurements: we have four sets of measurements, corresponding to
different currents, namely injection (669 A), 5460 A, collision at 7 TeV (11345 A), ultimate
(11923 A). Measurements start after 1-3 min when the target current was reached.
Measurements of 18 cold masses are present, cold mass 06 has an anomalous set missing the
injection current. Cold mass 07 is measured twice, the second time after a thermal cycle.
Pre-cycle: no special pre-cycle was applied. After the training, the magnets were not
quenched specially for the magnetic measurements. Some of the magnets, which reached
(230 T/m, ~ 13kA) without quench, were ramped down and magnetic measurements were
started after ramping up from zero.
Rejected or faulty measurements: No rejected measurements.
Use of the measurements in FiDeL: The measurements are used to set the model for the field
harmonics, except the DC magnetization.
- -
4. Transfer function
4.1 GEOMETRIC
The geometric is taken at 1500 A (see Fig. 4), average of current ramping up and down.
Saturation starts to be significant at 2500 A, and at maximum current is about 2% (200 units).
The rather peculiar shape of saturation, which starts very early, is confirmed by the model
evaluation (see Fig. 4).
MQXB02
100
MQXB - integral (all)
50
TF (Units)
MQXB02 - DCloop
0
Roxie model
-50
-100
-150
-200
0
5000
Current (A)
10000
Fig. 4: Integrated transfer function versus current during “DCloop” measurements for cold mass 19, comparison
with “Integral” measurements of all cryostats, and Roxie model
Two sets of measurements are available: “Integral” and “DCloop”. The “Integral”
measurement is taken as the reference. The geometric is set by using the integral value at
5460 A and subtracting an average offset of 50 units that can be estimated as the difference
between average up-down at 1500 A and ramp up at 5500 on the “DCloop” measurements, as
shown in Table III. The list of the geometric components for each cryostat is given in Table
IV. The spread of the geometric is about 6 units, and is mainly driven by cryostats 5 and 10
(see Table IV).
The spread at injection and at high field is slightly larger than at 5460 A, see Table V. The
random component of DC magnetization seems not to contribute to the spread of the TF.
- -
Table III: Difference between local TF measurements at 5500 A, ramp up, and geometric (average 1500 A up
and down), using “DCloop” measurements
Local TF measurements "Dcloop"
Cold mass
Geometric 1500 A
5500 A up
Difference
-1
-1
-1
-1
(T m A )
(T m A )
(units)
2
0.018155
0.018071
46
6
0.018188
0.018102
47
10
0.018173
0.018080
51
11
0.018171
0.018078
51
1
0.018159
0.018076
46
5
0.018190
0.018104
47
9
0.018179
0.018082
53
13
0.018160
0.018058
56
Average
0.018172
0.018081
50
Table IV: Geometric component, based on “Integral” measurements and offset given in Table III
TF (T m /A) DTF (units)
Cryostat
HCLQXB_001-FL000001
0.0034317
-0.7
HCLQXB_001-FL000003
0.0034334
4.3
HCLQXB_001-FL000004
0.0034312
-2.1
HCLQXB_001-FL000005
0.0034348
8.4
HCLQXB_001-FL000006
0.0034333
4.0
HCLQXB_001-FL000008
0.0034304
-4.5
HCLQXB_001-FL000009
0.0034314
-1.6
HCLQXB_001-FL000010
0.0034283
-10.6
HCLQXB_001-FL000011
0.0034329
2.8
Average
0.0034319
Stdev (units)
5.6
Table V: Average and spread of “Integral” measurements.
Current (A)
TF (T m /A)
Stdev (units)
668
5460
11345
11923
0.0034389
0.0034148
0.0033687
0.0033633
6.0
5.6
7.0
7.9
4.2 STATIC COMPONENTS
The static part is modelled through three components, i.e., geometric, saturation and DC
magnetization.
- -
Saturation: the fit is made on the “Integral” measurements, for each cryostat. Indeed, these
measurements have the disadvantage of having very few current points. Therefore, we
integrate them with the Roxie model, i.e. we shift the Roxie saturation curve to have a perfect
match with the “Integral” measurement at 11345 A (see Fig. 5). The fit is made with Inom=1
A; parameters are evaluated for each cryostat (see Table VI). The error between the fit and
the “Integral” - Roxie data is within 5 units in the range 5400 A - 11300 A (see Table VII).
These 5 units are the intrinsic precision of the FiDeL model in the range 4-7 TeV.
MQXB-FL10
100
50
TF (Units)
0
-50
LQXB01 - integral
-100
Satur FiDeL
-150
Magn FiDeL
-200
Magn+Sat FiDeL
Roxie model
-250
0
5000
Current (A)
10000
Fig. 5: Integrated transfer function for cryostat 10: “Integral” measurements, Roxie model fitted at 11300 A on
“Integral” measurements, saturation and DCmagnetization components
Table VI: Parameters of the saturation component
Cryostat s/ggeo (units)
1
2
4
5
6
8
9
10
11
231
237
204
216
210
228
204
204
204
s
I0
0.000185
0.000185
0.000220
0.000205
0.000210
0.000190
0.000220
0.000220
0.000220
8000
7950
8000
7850
8000
8050
7950
7950
7950
Table VII: Error between the “Integral”+Roxie model data and saturation fit
- -
Cryostat
Current
1
2
4
5
6
8
9
10
11
Average
4780
5378
5975
6573
7170
7768
8365
8963
9560
10158
10755
11353
-7
-3
0
2
2
1
-1
-3
-4
-3
-1
3
-4
0
3
3
3
2
0
-3
-4
-4
-2
2
-7
-1
3
4
4
2
0
-3
-4
-3
-2
3
-5
0
3
4
4
3
-1
-3
-3
-2
0
4
-7
-2
2
4
3
2
-1
-2
-4
-3
-1
4
-7
-2
1
3
4
2
0
-2
-4
-3
-1
3
-5
0
3
5
5
3
1
-2
-3
-3
0
5
-6
-1
2
4
4
2
0
-3
-4
-4
-1
4
-5
0
3
5
5
3
1
-2
-3
-3
0
5
-6
-1
2
4
4
2
0
-2
-3
-3
-1
4
DC magnetization: A generic component has been evaluated for all cryostats. The fit is done
on the available DCloop measurements (8 cold masses), and gives errors up to 10 units (see
Table VIII). Since the other cold masses are not measured, a generic term with q=1, p=2.8
and = 8010-4 ggeo has been taken. This corresponds to having at 670 A about 55 units. The
“Integral” data give less than one half of magnetization, i.e. about 20 units: this is due to the
waiting time at each current step, and therefore data are believed to be less representative. An
example of the fit for cold mass 02 is given in Fig. 6.
Table VIII: DC magnetization components evaluated for 8 cold masses (not directly used in FiDeL)
Cold mass /ggeo (units)
2
6
10
11
1
5
9
13
84
66
80
83
140
91
78
57
- -
p
q
err (units)
2.90
2.60
2.60
2.80
2.85
2.90
2.80
2.80
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
3
4
11
7
3
7
6
2
MQXB02
100
MQXB - integral (all)
MQXB - DCloop
saturation
DC magnetization
Satur+magn FiDeL
Roxie model
TF (Units)
50
0
-50
-100
-150
-200
0
5000
Current (A)
10000
Fig. 6: DCloop measurements of cold mass 02, Roxie model fitted at 11300 A, saturation, and DC
magnetization components
5. Field errors
5.1 ALLOWED: GEOMETRIC AND STATIC COMPONENTS
Geometric: the allowed harmonics have been carefully optimized at high field: average b6
is within 0.1 units, with a spread of 0.35 units, and b10 is zero within 0.05 units (see Table IX).
For each magnet we set the geometric b6 and b10 as the values, ramp up, at 11350 A,
evaluated in the “Integral” measurements, and the saturation is set to zero (see Table X). This
is can be done since the saturation is negligible, (for instance, it is less than 0.1 units for b6).
This ensures the best fit at high field, where the beam dynamics is more sensitive to these
magnets.
DC Magnetization: In average, the persistent current component of b6 is about -1.7 units,
with a spread of about 0.36 units. This is taken into account by a generic term, the same for
every magnet:
The fit is done on the average of the “Integral” measurements (see Fig. 7), with 6=-1.24,
p6=0.3 and q6=2, and with Iinj=750 A and Ic=14000 A. Modelling this contribution as a
generic term, and not magnet by magnet, one has to add for each magnet at injection an
uncertainty of 0.19 units (1 sigma, see Table IX). The b10 component of the persistent current
is less than 0.1 units and is therefore neglected.
- -
Table IX: Average and standard deviation of allowed harmonics at ~injection, intermediate and high field, and
average and standard deviation between injection and high field
b6
Ave -1.52
669 A
Stdev 0.61
Ave 0.06
5460 A
Stdev 0.36
Ave 0.07
11347 A
Stdev 0.36
Ave 0.07
11925 A
Stdev 0.36
Ave -1.67
669 A - 11347 A
Stdev 0.19
b10
0.05
0.02
0.01
0.01
0.02
0.01
0.02
0.01
0.04
0.01
Table X: Geometric allowed components in each MQXB cold mass, “Integral” measurements
Cold mass
1
2
3
5
6
7
8
9
10
11
12
13
15
16
17
18
19
20
Average
Stdev
b6
-0.401
-0.309
-0.403
0.163
0.353
0.224
-0.012
0.218
0.372
0.398
0.181
0.309
0.427
0.220
0.157
-0.231
0.415
-0.859
b10
0.016
0.019
0.020
0.028
0.026
0.016
0.044
0.020
0.029
0.031
0.023
0.019
0.018
-0.001
0.015
-0.009
0.003
0.030
0.07
0.36
0.02
0.01
- -
b6 (units)
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
-1.8
Measurement
Fit
0
5000
Current (A)
10000
Fig. 7: Fit of the DC magnetization component of b6
5.2 NOT ALLOWED: GEOMETRIC
Since the MQXB dominate the dynamics after the squeeze, also for the non allowed
harmonics we propose to set the geometric on the value measured at high energy, i.e. at the
squeeze, ramp up, and to have no persistent or saturation component. In this way the highest
precision is reached at high field, which is the most relevant current.
7 TeV correspond to 11380 A. Here we use the measurement “Integral” taken at the
closest value of the current, i.e. 11345 A in seven cases, and 11066 A in two cases. An
overview of average and standard deviations are given in Table XI. All harmonics have an
average close to zero (within a fraction of unit) with the exception of b4, which has a small
systematic component of about 0.10-0.12 units with a low spread (0.14 units).
The set of measurements at 5460 A, corresponding to 3.3 TeV, and at 11350 A (7 TeV)
show a negligible dependence of the multipoles on the energy in this range (see Table XI).
Therefore one should not expect variations from 3.5 to 7 TeV runs. Our model assumes to
have at injection the same values as at high field. The validity of this assumption is checked
in the last two rows of Table XI. The average of each multipole change between injection and
high field, taken over the set of magnets is zero within a fraction of unit. The last line of the
Table gives that spread to be added to MAD simulations to correctly model the injection
values. The model is given individually for each magnet (see Table XII).
Measurements given in [2] are slightly different, giving a non negligible a4 component of
about 0.2 units (see Fig. 2).
- -
Table XI: Not allowed multipoles, average and spread over the 18 magnets, at four different currents (“Integral”
data)
669 A
5460 A
11347 A
11925 A
669 A - 11347 A
Ave
Stdev
Ave
Stdev
Ave
Stdev
Ave
Stdev
Ave
Stdev
b3
-0.06
0.66
0.05
0.61
0.06
0.61
0.09
0.64
-0.13
0.25
b4
0.10
0.14
0.10
0.14
0.12
0.14
0.12
0.14
-0.02
0.05
b5
0.06
0.12
0.07
0.11
0.09
0.13
0.09
0.13
-0.03
0.09
b7
0.03
0.04
0.01
0.03
0.01
0.04
0.01
0.03
0.02
0.02
b8
-0.02
0.01
0.00
0.01
-0.01
0.01
-0.01
0.01
-0.01
0.01
b9
0.00
0.01
0.00
0.01
-0.01
0.01
-0.01
0.01
0.01
0.01
a3
-0.07
1.12
0.09
1.00
0.08
0.99
0.08
1.00
-0.15
0.37
a4
-0.16
0.58
-0.10
0.51
-0.08
0.52
-0.08
0.52
-0.08
0.16
a5
-0.01
0.19
0.02
0.17
0.02
0.18
0.02
0.18
-0.03
0.07
a6
-0.01
0.08
-0.04
0.10
-0.08
0.19
-0.07
0.20
0.06
0.18
a7
-0.01
0.04
-0.01
0.04
0.00
0.04
-0.01
0.04
-0.01
0.01
a8
-0.03
0.03
-0.01
0.03
-0.01
0.03
-0.02
0.03
-0.02
0.03
a9
0.00
0.01
0.00
0.01
0.01
0.01
0.00
0.01
0.00
0.01
Table XII: Geometric used in FiDeL for MQXB magnets (values at 11350 A, ramp up, “Integral” data)
Cold mass
1
2
3
5
6
7
8
9
10
11
12
13
15
16
17
18
19
20
b3
0.930
0.375
0.483
-0.511
1.281
0.335
-0.814
-0.182
-0.845
0.109
0.388
0.160
-0.945
0.090
-0.511
0.445
-0.075
0.446
b4
0.143
-0.183
0.178
0.126
0.286
0.350
-0.005
0.230
0.254
0.168
-0.020
0.149
0.054
0.034
0.109
0.042
0.267
-0.059
b5
-0.054
-0.012
0.036
-0.075
0.164
-0.019
0.379
0.155
0.264
0.251
0.161
0.229
0.113
0.095
0.024
-0.120
0.062
-0.022
b7
0.030
0.007
-0.004
-0.026
0.054
-0.007
-0.069
0.008
-0.038
0.016
-0.032
0.053
0.030
0.053
-0.023
0.009
0.045
-0.011
b8
-0.005
0.002
-0.007
-0.010
0.000
-0.004
0.018
-0.004
-0.004
-0.007
-0.014
-0.008
-0.014
-0.014
-0.008
-0.008
-0.008
-0.002
b9
-0.011
-0.002
-0.006
-0.010
-0.001
-0.009
0.017
-0.001
-0.014
-0.019
0.001
-0.012
-0.012
-0.017
-0.003
-0.014
-0.029
-0.008
a3
0.831
0.395
0.694
0.801
-0.253
0.941
0.281
0.103
1.122
-0.742
-0.169
-1.719
1.292
0.036
-0.203
0.628
-2.622
0.060
a4
-0.464
0.759
0.252
-0.074
0.189
-0.134
0.173
-0.348
-0.028
0.933
-0.152
-0.580
0.597
-0.007
-0.077
-0.800
-0.600
-1.040
a5
0.044
-0.095
0.199
0.143
0.205
0.093
0.015
0.017
0.209
-0.153
-0.099
-0.204
0.199
-0.030
-0.019
0.218
-0.447
0.070
a6
-0.106
0.065
0.110
-0.073
-0.007
-0.032
-0.768
-0.165
-0.014
-0.046
-0.103
-0.125
-0.063
-0.081
0.085
-0.035
0.032
-0.036
Fig. 8: Average and stdev of field harmonics according to [2].
- -
a7
-0.005
0.059
-0.012
-0.022
-0.064
0.028
0.055
0.004
0.023
0.003
0.030
-0.091
-0.013
0.034
-0.033
-0.001
-0.022
-0.044
a8
-0.047
0.008
0.010
-0.025
-0.019
-0.036
0.046
-0.020
0.013
0.005
0.005
-0.022
0.033
-0.008
-0.020
-0.044
-0.053
-0.060
a9
-0.001
0.018
0.005
0.010
0.010
0.009
0.022
0.003
0.011
0.003
0.005
-0.008
0.003
0.013
-0.001
0.012
-0.010
-0.008
5.3 DECAY
Measurements have been reported in [2,3,4]. Data relative to b6 are recorded for an
injection plateau of 900 s. A logarithmic fit has been done in [5] over this time domain,
according to the equation
Parameters are listed in Table XIII. Using this fit, precise within 0.05 units [2], we
regenerated the data and we applied the FiDeL exponential fit:
The fit agrees with the reconstructed data within 0.02 units. The three costants are listed in
Table XIII. One observes a rather small spread of the constants  and d, suggesting that the
exponential fit is more physical than the logarithmic one. The average decay at 1200 s is 1.7
units, with a spread of 0.4 units. We decided to neglect this decay, at least in the first phase of
beam commissioning.
Table XIII: Geometric used in FiDeL for MQXB magnets (values at 11350 A, ramp up, “Integral” data)
Cold mass
1
2
3
5
6
8
9
10
11
12
13
17
19
Ave
Stdev
b6,1
0.50
0.35
0.50
0.30
0.50
0.26
0.34
0.35
0.33
0.55
0.35
0.54
0.23
0.39
0.11
ts
13.3
8.9
12.9
9.8
13.9
8.1
9.5
9.8
8.7
15.3
9.3
15.6
7.6
11.0
2.8
c
1.41
1.75
2.40
1.48
2.32
1.33
1.69
1.72
1.66
2.55
1.75
2.49
1.20
1.83
0.46
- -
d
0.40
0.44
0.42
0.42
0.40
0.44
0.42
0.42
0.44
0.40
0.42
0.40
0.44
0.42
0.02

55
50
60
50
55
50
50
50
50
60
50
60
50
53
4
Db6 at 1200 s
1.34
1.68
2.25
1.42
2.20
1.28
1.62
1.65
1.59
2.38
1.68
2.32
1.15
1.7
0.4
2.5
b6 (units)
2.0
1.5
1.0
Measurement (log fit)
FiDeL fit
0.5
0.0
0
200
400
600
800
1000
1200
Fig. 9: Measurements of the b6 decay reconstructed using the logarithmic fit and data in [5], and FiDeL
exponential fit of cold mass 19.
6. Summary and open issues






The transfer function spread among the magnets is 5 to 8 units. The model in the
range 3.5-7 TeV has an error of less than 5 units. On the other hand, at injection the
two set of measurements differ by 20-30 units, depending on the measurement
conditions: this is the precision of the model.
The first allowed multipole b6 is very well optimized in the range 3.5-7 TeV, i.e.
within 0.1 units. There is a small systematic b4 component of about 0.1 units.
Data presented in [2] give a small systematic a4 component of about 0.2 units at high
field, which is not seen in the data in our possession.
In general field harmonics show the same spread at injection and at high field: this is
an anomalous behaviour. This could be due either to the magnet or to the
measurement system.
We have no information relative to the decay of the transfer function at injection.
Field quality in the heads is not available
Ackowledgements
We wish to thank R. Ostoijc for remarks and comments.
References
[1] M. Lamm, et al., EPAC (2006) 2637.
[2] G. Velev, et al., IEEE Trans. Appl. Supercond. 17 (2007) 1109.
[3] G. Velev, et al., IEEE Trans. Appl. Supercond. 15 (2005) 1102.
[4] G. Velev, et al., EPAC (2004) 1777.
[5] G. Velev, et al., EPAC (2004) 1780.
- -