A. Ball

A. Gaddi

A. Hervé

B. Curé

H. Gerwig

M. Mulders

N. Amapane

R. Loveless

V. Calvelli

V. I. Klyukhin

Amapane, Nicola Carlo

Institutional Research Information System University of Turin

J Supercond Nov Magn (2015) 28:701–704DOI 10.1007/s10948-014-2809-4ORIGINAL PAPERValidation of the CMS Magnetic Field MapV. I. Klyukhin · N. Amapane · A. Ball · B. Cure´ ·A. Gaddi · H. Gerwig · M. Mulders · V. Calvelli ·A. Herve´ · R. LovelessReceived: 11 June 2014 / Accepted: 22 September 2014 / Published online: 26 October 2014© The Author(s) 2014. This article is published with open access at Springerlink.comAbstract The Compact Muon Solenoid (CMS) is a generalpurpose detector, designed to run at the highest luminosityat the CERN Large Hadron Collider (LHC). Its distinc-tive features include a 4-T superconducting solenoid with6-m-diameter by 12.5-m-length free bore, enclosed insidea 10,000-ton return yoke made of construction steel. Thereturn yoke consists of five dodecagonal three-layered bar-rel wheels and four end-cap disks at each end comprised ofsteel blocks up to 620 mm thick, which serve as the absorberplates of the muon detection system. To measure the fieldin and around the steel, a system of 22 flux loops and 82three-dimensional (3-D) Hall sensors is installed on thereturn yoke blocks. A TOSCA 3-D model of the CMSmagnet is developed to describe the magnetic field every-where outside the tracking volume measured with thefield-mapping machine. The magnetic field description iscompared with the measurements and discussed.Keywords Flux loops · Hall probes · Magnetic fieldmeasurements · Superconducting solenoidV. I. Klyukhin ()Skobeltsyn Institute of Nuclear Physics, Lomonosov MoscowState University, RU-119992 Moscow, Russiae-mail: Vyacheslav.Klyukhin@cern.chN. AmapaneINFN Turin and the University of Turin,I-10125, Turin, ItalyA. Ball · B. Cure´ · A. Gaddi · H. Gerwig · M. MuldersCERN, CH-1211 Geneva 23, SwitzerlandV. CalvelliINFN Genoa and the University of Genoa, I-16146, Genoa, ItalyA. Herve´ · R. LovelessUniversity of Wisconsin, Madison, WI 53706, USA1 IntroductionThe muon system of the Compact Muon Solenoid (CMS)detector includes a 10,000-ton yoke comprised of theconstruction steel plates up to 620 mm thick, which returnthe flux of the 4 T superconducting solenoid and serve asthe absorber plates of the muon detection system [1–4].During the Large Hadron Collider (LHC) long shutdownoccurring in 2013/2014 the CMS magnet yoke is upgrad-ing with the additional 14-m-diameter end-cap disks at theextremes of the muon detection system [5]. The presenceof the 0.125-m-thick disks changes the magnetic flux den-sity distribution in the adjacent end-cap disks by 25 % inaverage. This requires developing the new magnetic fieldmap to be used in the detector simulation and the eventreconstruction software.The magnetic flux density in the central part of the CMSdetector, where the tracker and electromagnetic calorime-ter are located, was measured with precision of 7 × 10−4with the field-mapping machine at five central field val-ues of 2, 3, 3.5, 3.8, and 4 T [6]. To describe the magneticflux everywhere outside the measured volume, a three-dimensional (3-D) magnetic field model of the CMS magnethas been developed [7] and calculated with TOSCA [8]when the detector began operation. The model reproducesthe magnetic flux density distribution measured inside theCMS coil with the field-mapping machine within 0.1 %[9]. The modification of this model for the upgraded CMSmagnet yoke requires validating the model by comparingthe calculated magnetic flux density with the measuredone at least in selected regions of the CMS magneticsystem.A direct measurement of the magnetic flux density in theyoke-selected regions was provided during the CMS mag-net test of 2006 with 22 flux loops of 315 ÷ 450 turns wound702 J Supercond Nov Magn (2015) 28:701–704around the yoke blocks. The “fast” (190 s time-constant)discharges of the CMS coil made possible by the protectionsystem, which is provided to protect the magnet in the eventof major faults [10, 11], induced in the flux loops the vol-tages caused by the magnetic flux changes. An integrationtechnique [12, 13] was developed to reconstruct the averageinitial magnetic flux density in steel blocks at the full mag-net excitation, and the contribution of the eddy currents wascalculated with ELECTRA [14] and estimated on the levelof a few per cent [15].The results of the magnetic flux measurements donewith the flux loops and comparison the obtained valueswith the calculations performed with the previous TOSCACMS magnet model are described elsewhere [16].In present paper, we compare the calculations done withthe recent CMS magnet model with the measurementsperformed with the flux loops in the yoke steel and withthe 3-D Hall probes installed at the steel-air interfaces inthe gaps between the CMS yoke parts. These comparisonsallow validating the magnetic field maps to be used for theupgraded CMS detector.2 The CMS Magnet Model DescriptionThe CMS magnet model for the upgraded detector is pre-sented in Fig. 1. The central part of the model comprisesthe coil four layers of the superconductor and the full mag-net yoke that consists of five barrel wheels of the 13.99 minscribed outer diameter and 2.536 m width, two nose disksof 5.26 m diameter on each side of the coil, three largeend-cap disks of the 13.91 m inscribed outer diameter onFig. 1 3-D model of the CMS magnetic systemeach side of the magnet, two small end-cap disks of 5 mdiameter, and two additional 0.125-m-thick end-cap disks ofthe 13.91 m inscribed outer diameter mounted around thesesmall disks.The total length of the central part is 21.61 m. On bothsides of the central part the hadronic forward calorime-ter absorbers and shields, the steel collars and rotatingshields of the beam pipe are included into the model.The 40-mm-thick steel floor of the experimental under-ground cavern has the length of 36.4 m and the width of9.9 m.Each barrel wheel except of central one has three layersof steel connected with brackets. The central barrel wheelcomprises the fourth most inner layer, tail catcher, madeof steel and turned by 5◦ in the azimuth angle withrespect to dodecagonal shape of the barrel wheels. Thecoordinate system used in the model corresponds to theCMS reference system where the X-axis is directed inhorizontal plane toward the LHC center, the Y -axis isupward, and the Z-axis coincides with the supercon-ducting coil axis and has the same direction as the positiveaxial component of the magnetic flux density.The model comprises 21 conductors, the barrel feet, andthe end-cap disk carts and contains 7,111,713 nodes of thefinite element mesh shown in the XY-plane in Fig. 2.The dimensions of the yoke parts and the supercon-ducting coil modules are described elsewhere [16]. Theoperational current of the CMS superconducting coil is18.164 kA.Fig. 2 The XY-plane of the finite element mesh used to extrude the 3-D model. The black crosses near the azimuth angle of 255◦ display thelocation of the 3-D Hall sensors measured the magnetic flux density atthe steel-air interfacesJ Supercond Nov Magn (2015) 28:701–704 7032.1 Steel Magnetic Properties DescriptionThree different B-H curves of the construction steel of theCMS magnet yoke are used in the model. The first curvedescribes the magnetic properties of the barrel wheel thickplates in the second and third layers. The second curvedescribes the magnetic properties of thin plates aroundthe thick plates of the second and third barrel wheel lay-ers, and also the properties of the plates of the first lay-ers and the tail catcher plates of the barrel wheels. Thiscurve is used as well for the extensions of the forth end-cap disks, the forward hadronic calorimeter absorbers andshields, and steel collars and rotating shields around thebeam pipe. Finally, the third curve describes the magneticproperties of the nose and end-cap disks, the cart plates,keels, and the steel floor.3 Comparison of the Measured and CalculatedMagnetic Flux DensityThe measurements used for the comparisons were obtainedin the CMS magnet test during two current cycles on August17 and 28, 2006, shown in Fig. 3.In the first cycle on August 17, the current reachesthe maximum value of 17.55 kA, and after 140 min, thefast discharge was manually triggered. In the second cycleon August 28, the current reaches the maximum value of19.14 kA, and after 71 min, the fast discharge was trig-gered accidently. These flat current time intervals wereused to measure the magnetic flux density with the 3-DFig. 3 The CMS magnet current cycles of August 2006 used in theflux loops and 3-D Hall sensors measurements at 17.55 kA (17 Aug)and 19.14 kA (28 Aug)Hall sensors installed in the XY-planes at Z-coordinates of1.273, −1.418, −3.964, −4.079, −6.625, and −7.251 m.In present analysis, only 18 sensors located in the planetilted at X < 0 m by the angle of 15◦ with respect to thevertical plane and shifted at the Y-coordinate of −4.805 mwith respect to the vertical plane by 0.56 m as shown inFig. 2 are used.The magnetic flux density in the CMS yoke steel ismeasured using the voltages induced in the fluxloops during the fast discharges of the coil fromthe maximum currents. The average magnetic fluxdensity in steel was reconstructed by the off-line integration of the voltages [16]. The currentvalues of 17.55 and 19.14 kA produce the magneticflux density in the CMS coil center of 3.68 and 4.01 T,accordingly. The operational central magnetic flux den-sity of 3.81 T used in the CMS magnet is between thesevalues.In Figs. 4–5, the measured values of the magneticflux density vs. Z- and Y-coordinates are displayed andcompared with the calculated field values obtained withnew CMS model at the currents of 17.55 and 19.14 kA.To perform the comparisons, the model geometry of thesame finite element mesh is adapted to the configurationof the CMS magnet used in the 2006 test. The exten-sions of the forth end-cap disks, one small forth end-cap disk, the steel floor, the forward hadronic calorimeterabsorbers and shields, steel collars, and rotating shieldsare removed from the model. The contribution of allFig. 4 Axial magnetic flux density measured (filled markers) and cal-culated (opened markers) in the first (rhombs), second (triangles), andthird (circles) barrel layers vs. Z-coordinate at the current of 17.55 kA.The lines represent the calculated values along the Hall sensors loca-tions at the Y -coordinates of −4.805 m (solid line), −5.66 m (dashedline), and −6.685 m (dotted line), corresponded to the first, second,and third barrel layers blocks, respectively704 J Supercond Nov Magn (2015) 28:701–704Fig. 5 Axial magnetic flux density measured (filled markers) and cal-culated (opened markers) in the first (rhombs), second (triangles), andthird (circles) barrel layers vs. Z-coordinate at the current of 19.14 kA.The lines represent the calculated values along the Hall sensors loca-tions at the Y-coordinates of −4.805 m (solid line), −5.66 m (dashedline), and −6.685 m (dotted line), corresponded to the first, second,and third barrel layers blocks, respectivelythe removed ferromagnetic parts into the central mag-netic flux density is 0.03 %. The same contribution of theyoke central part is 7.97 %. Thus, the configuration of theyoke used in the 2006 test is acceptable for the modelvalidation.The comparison gives the differences between the cal-culated and measured values of the magnetic flux densityas follows: (0.59 ± 7.41) % in the barrel wheels and(−4.05 ± 1.97) % in the end-cap disks at the maximumcurrent of 17.55 kA; (1.41 ± 7.15) % in the barrelwheels and (−2.87 ± 2.00) % in the end-cap disks at themaximum current of 19.14 kA. The error bars of the mag-netic flux density measured with the flux loops are of±8.55 % and include the errors in the knowledge of the fluxloops geometries and the errors of the measured magneticfluxes. The error bars of the 3-D Hall sensor measurementsare ±(0.025 ± 0.015) mT at the current of 17.55 kAand ±(0.012 ± 0.001) mT at the current of 19.14 kA. Inaddition to these comparisons, the model perfectlydescribes the magnetic flux density distribution insidethe CMS coil within 0.1 %, in accordance with the pre-vious model consisted of two separate halves of theyoke [9, 16].4 ConclusionsThe new CMS magnet model is developed to prepare themagnetic field maps for the upgraded CMS detector. Themodel is validated by the comparison of the calculatedmagnetic flux density with the measurements done in theCMS magnet selected regions with the flux loops and 3-DHall sensors.Open Access This article is distributed under the terms of the Cre-ative Commons Attribution License which permits any use, distribu-tion, and reproduction in any medium, provided the original author(s)and the source are credited.References1. Herve´, A., Acquistapace, G., Campi, D., et al.: IEEE Trans. Appl.Supercond. 12(1), 385–390 (2002)2. Herve´, A., Blau, B., Campi, D., et al.: IEEE Trans. Appl.Supercond. 14(2), 542–547 (2004)3. Herve´, A.: Mod. Phys. Lett. A 25(20), 1647–1666 (2010)4. CMS Collaboration: JINST 3(S08004), 1–334 (2008)5. CMS Collaboration: CERN-LHCC-2011-06. CMS UG-TP-1,243–244 (2011)6. Klyukhin, V.I., Ball, A., Bergsma, F., et al.: IEEE Trans. Appl.Supercond. 18(2), 395–398 (2008)7. Klioukhine, V.I., Campi, D., Cure´, B., et al.: IEEE Trans. Appl.Supercond. 10(1), 428–431 (2000)8. TOSCA/OPERA-3d 16R1 Software, Cobham CTS Limited,Kidlington, Oxfordshire, U. K.9. Klyukhin, V.I., Amapane, N., Andreev, V., et al.: IEEE Trans.Appl. Supercond. 20(3), 152–155 (2010)10. Cure´, B., Lesmond, C.: CEA/Saclay, Saclay, France,DSM/DAPNIA/STCM Technical Report 5C 2100 T – 1000 03298 (1999)11. Klioukhine, V.I., Smith, R.P.: CERN, Geneva, Switzerland, CMSInternal Note 2000/071 (2000)12. Smith, R.P., Campi, D., Cure´, B., Gaddi, A., Gerwig, H.,Grillet, J.P., Herve´, A., Klyukhin, V., Loveless, R.: IEEE Trans.Appl. Supercond. 14(2), 1830–1833 (2004)13. Klyukhin, V.I., Campi, D., Cure´, B., Gaddi, A., Gerwig, H.,Grillet, J.P., Herve´, A., Loveless, R., Smith, R.P.: IEEE Trans.Nucl. Sci. 51(5), 2187–2192 (2004)14. ELEKTRA/OPERA-3d Software, Cobham CTS Limited,Kidlington, Oxfordshire, U.K.15. Klyukhin, V.I., Campi, D., Cure´, B., Gaddi, A., Gerwig, H.,Grillet, J.P., Herve´, A., Loveless, R., Smith, R.P.: IEEE Trans.Nucl. Sci. 52(3), 741–744 (2005)16. Klyukhin, V.I., Amapane, N., Ball, A., Cure´, B., Gaddi, A.,Gerwig, H., Mulders, M., Herve´, A., Loveless, R.: J. Supercond.Nov. Magn. 26(4), 1307–1311 (2013)

English

Validation of the CMS Magnetic Field Map

Springer - Publisher Connector

J Supercond Nov Magn (2015) 28:701–704
DOI 10.1007/s10948-014-2809-4
ORIGINAL PAPER
Validation of the CMS Magnetic Field Map
V. I. Klyukhin · N. Amapane · A. Ball · B. Cure´ ·
A. Gaddi · H. Gerwig · M. Mulders · V. Calvelli ·
A. Herve´ · R. Loveless
Received: 11 June 2014 / Accepted: 22 September 2014 / Published online: 26 October 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract The Compact Muon Solenoid (CMS) is a general
purpose detector, designed to run at the highest luminosity
at the CERN Large Hadron Collider (LHC). Its distinc-
tive features include a 4-T superconducting solenoid with
6-m-diameter by 12.5-m-length free bore, enclosed inside
a 10,000-ton return yoke made of construction steel. The
return yoke consists of five dodecagonal three-layered bar-
rel wheels and four end-cap disks at each end comprised of
steel blocks up to 620 mm thick, which serve as the absorber
plates of the muon detection system. To measure the field
in and around the steel, a system of 22 flux loops and 82
three-dimensional (3-D) Hall sensors is installed on the
return yoke blocks. A TOSCA 3-D model of the CMS
magnet is developed to describe the magnetic field every-
where outside the tracking volume measured with the
field-mapping machine. The magnetic field description is
compared with the measurements and discussed.
Keywords Flux loops · Hall probes · Magnetic field
measurements · Superconducting solenoid
V. I. Klyukhin ()
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow
State University, RU-119992 Moscow, Russia
e-mail: Vyacheslav.Klyukhin@cern.ch
N. Amapane
INFN Turin and the University of Turin,
I-10125, Turin, Italy
A. Ball · B. Cure´ · A. Gaddi · H. Gerwig · M. Mulders
CERN, CH-1211 Geneva 23, Switzerland
V. Calvelli
INFN Genoa and the University of Genoa, I-16146, Genoa, Italy
A. Herve´ · R. Loveless
University of Wisconsin, Madison, WI 53706, USA
1 Introduction
The muon system of the Compact Muon Solenoid (CMS)
detector includes a 10,000-ton yoke comprised of the
construction steel plates up to 620 mm thick, which return
the flux of the 4 T superconducting solenoid and serve as
the absorber plates of the muon detection system [1–4].
During the Large Hadron Collider (LHC) long shutdown
occurring in 2013/2014 the CMS magnet yoke is upgrad-
ing with the additional 14-m-diameter end-cap disks at the
extremes of the muon detection system [5]. The presence
of the 0.125-m-thick disks changes the magnetic flux den-
sity distribution in the adjacent end-cap disks by 25 % in
average. This requires developing the new magnetic field
map to be used in the detector simulation and the event
reconstruction software.
The magnetic flux density in the central part of the CMS
detector, where the tracker and electromagnetic calorime-
ter are located, was measured with precision of 7 × 10−4
with the field-mapping machine at five central field val-
ues of 2, 3, 3.5, 3.8, and 4 T [6]. To describe the magnetic
flux everywhere outside the measured volume, a three-
dimensional (3-D) magnetic field model of the CMS magnet
has been developed [7] and calculated with TOSCA [8]
when the detector began operation. The model reproduces
the magnetic flux density distribution measured inside the
CMS coil with the field-mapping machine within 0.1 %
[9]. The modification of this model for the upgraded CMS
magnet yoke requires validating the model by comparing
the calculated magnetic flux density with the measured
one at least in selected regions of the CMS magnetic
system.
A direct measurement of the magnetic flux density in the
yoke-selected regions was provided during the CMS mag-
net test of 2006 with 22 flux loops of 315 ÷ 450 turns wound
702 J Supercond Nov Magn (2015) 28:701–704
around the yoke blocks. The “fast” (190 s time-constant)
discharges of the CMS coil made possible by the protection
system, which is provided to protect the magnet in the event
of major faults [10, 11], induced in the flux loops the vol-
tages caused by the magnetic flux changes. An integration
technique [12, 13] was developed to reconstruct the average
initial magnetic flux density in steel blocks at the full mag-
net excitation, and the contribution of the eddy currents was
calculated with ELECTRA [14] and estimated on the level
of a few per cent [15].
The results of the magnetic flux measurements done
with the flux loops and comparison the obtained values
with the calculations performed with the previous TOSCA
CMS magnet model are described elsewhere [16].
In present paper, we compare the calculations done with
the recent CMS magnet model with the measurements
performed with the flux loops in the yoke steel and with
the 3-D Hall probes installed at the steel-air interfaces in
the gaps between the CMS yoke parts. These comparisons
allow validating the magnetic field maps to be used for the
upgraded CMS detector.
2 The CMS Magnet Model Description
The CMS magnet model for the upgraded detector is pre-
sented in Fig. 1. The central part of the model comprises
the coil four layers of the superconductor and the full mag-
net yoke that consists of five barrel wheels of the 13.99 m
inscribed outer diameter and 2.536 m width, two nose disks
of 5.26 m diameter on each side of the coil, three large
end-cap disks of the 13.91 m inscribed outer diameter on
Fig. 1 3-D model of the CMS magnetic system
each side of the magnet, two small end-cap disks of 5 m
diameter, and two additional 0.125-m-thick end-cap disks of
the 13.91 m inscribed outer diameter mounted around these
small disks.
The total length of the central part is 21.61 m. On both
sides of the central part the hadronic forward calorime-
ter absorbers and shields, the steel collars and rotating
shields of the beam pipe are included into the model.
The 40-mm-thick steel floor of the experimental under-
ground cavern has the length of 36.4 m and the width of
9.9 m.
Each barrel wheel except of central one has three layers
of steel connected with brackets. The central barrel wheel
comprises the fourth most inner layer, tail catcher, made
of steel and turned by 5◦ in the azimuth angle with
respect to dodecagonal shape of the barrel wheels. The
coordinate system used in the model corresponds to the
CMS reference system where the X-axis is directed in
horizontal plane toward the LHC center, the Y -axis is
upward, and the Z-axis coincides with the supercon-
ducting coil axis and has the same direction as the positive
axial component of the magnetic flux density.
The model comprises 21 conductors, the barrel feet, and
the end-cap disk carts and contains 7,111,713 nodes of the
finite element mesh shown in the XY-plane in Fig. 2.
The dimensions of the yoke parts and the supercon-
ducting coil modules are described elsewhere [16]. The
operational current of the CMS superconducting coil is
18.164 kA.
Fig. 2 The XY-plane of the finite element mesh used to extrude the 3-
D model. The black crosses near the azimuth angle of 255◦ display the
location of the 3-D Hall sensors measured the magnetic flux density at
the steel-air interfaces
J Supercond Nov Magn (2015) 28:701–704 703
2.1 Steel Magnetic Properties Description
Three different B-H curves of the construction steel of the
CMS magnet yoke are used in the model. The first curve
describes the magnetic properties of the barrel wheel thick
plates in the second and third layers. The second curve
describes the magnetic properties of thin plates around
the thick plates of the second and third barrel wheel lay-
ers, and also the properties of the plates of the first lay-
ers and the tail catcher plates of the barrel wheels. This
curve is used as well for the extensions of the forth end-
cap disks, the forward hadronic calorimeter absorbers and
shields, and steel collars and rotating shields around the
beam pipe. Finally, the third curve describes the magnetic
properties of the nose and end-cap disks, the cart plates,
keels, and the steel floor.
3 Comparison of the Measured and Calculated
Magnetic Flux Density
The measurements used for the comparisons were obtained
in the CMS magnet test during two current cycles on August
17 and 28, 2006, shown in Fig. 3.
In the first cycle on August 17, the current reaches
the maximum value of 17.55 kA, and after 140 min, the
fast discharge was manually triggered. In the second cycle
on August 28, the current reaches the maximum value of
19.14 kA, and after 71 min, the fast discharge was trig-
gered accidently. These flat current time intervals were
used to measure the magnetic flux density with the 3-D
Fig. 3 The CMS magnet current cycles of August 2006 used in the
flux loops and 3-D Hall sensors measurements at 17.55 kA (17 Aug)
and 19.14 kA (28 Aug)
Hall sensors installed in the XY-planes at Z-coordinates of
1.273, −1.418, −3.964, −4.079, −6.625, and −7.251 m.
In present analysis, only 18 sensors located in the plane
tilted at X < 0 m by the angle of 15◦ with respect to the
vertical plane and shifted at the Y-coordinate of −4.805 m
with respect to the vertical plane by 0.56 m as shown in
Fig. 2 are used.
The magnetic flux density in the CMS yoke steel is
measured using the voltages induced in the flux
loops during the fast discharges of the coil from
the maximum currents. The average magnetic flux
density in steel was reconstructed by the off-
line integration of the voltages [16]. The current
values of 17.55 and 19.14 kA produce the magnetic
flux density in the CMS coil center of 3.68 and 4.01 T,
accordingly. The operational central magnetic flux den-
sity of 3.81 T used in the CMS magnet is between these
values.
In Figs. 4–5, the measured values of the magnetic
flux density vs. Z- and Y-coordinates are displayed and
compared with the calculated field values obtained with
new CMS model at the currents of 17.55 and 19.14 kA.
To perform the comparisons, the model geometry of the
same finite element mesh is adapted to the configuration
of the CMS magnet used in the 2006 test. The exten-
sions of the forth end-cap disks, one small forth end-
cap disk, the steel floor, the forward hadronic calorimeter
absorbers and shields, steel collars, and rotating shields
are removed from the model. The contribution of all
Fig. 4 Axial magnetic flux density measured (filled markers) and cal-
culated (opened markers) in the first (rhombs), second (triangles), and
third (circles) barrel layers vs. Z-coordinate at the current of 17.55 kA.
The lines represent the calculated values along the Hall sensors loca-
tions at the Y -coordinates of −4.805 m (solid line), −5.66 m (dashed
line), and −6.685 m (dotted line), corresponded to the first, second,
and third barrel layers blocks, respectively
704 J Supercond Nov Magn (2015) 28:701–704
Fig. 5 Axial magnetic flux density measured (filled markers) and cal-
culated (opened markers) in the first (rhombs), second (triangles), and
third (circles) barrel layers vs. Z-coordinate at the current of 19.14 kA.
The lines represent the calculated values along the Hall sensors loca-
tions at the Y-coordinates of −4.805 m (solid line), −5.66 m (dashed
line), and −6.685 m (dotted line), corresponded to the first, second,
and third barrel layers blocks, respectively
the removed ferromagnetic parts into the central mag-
netic flux density is 0.03 %. The same contribution of the
yoke central part is 7.97 %. Thus, the configuration of the
yoke used in the 2006 test is acceptable for the model
validation.
The comparison gives the differences between the cal-
culated and measured values of the magnetic flux density
as follows: (0.59 ± 7.41) % in the barrel wheels and
(−4.05 ± 1.97) % in the end-cap disks at the maximum
current of 17.55 kA; (1.41 ± 7.15) % in the barrel
wheels and (−2.87 ± 2.00) % in the end-cap disks at the
maximum current of 19.14 kA. The error bars of the mag-
netic flux density measured with the flux loops are of
±8.55 % and include the errors in the knowledge of the flux
loops geometries and the errors of the measured magnetic
fluxes. The error bars of the 3-D Hall sensor measurements
are ±(0.025 ± 0.015) mT at the current of 17.55 kA
and ±(0.012 ± 0.001) mT at the current of 19.14 kA. In
addition to these comparisons, the model perfectly
describes the magnetic flux density distribution inside
the CMS coil within 0.1 %, in accordance with the pre-
vious model consisted of two separate halves of the
yoke [9, 16].
4 Conclusions
The new CMS magnet model is developed to prepare the
magnetic field maps for the upgraded CMS detector. The
model is validated by the comparison of the calculated
magnetic flux density with the measurements done in the
CMS magnet selected regions with the flux loops and 3-D
Hall sensors.
Open Access This article is distributed under the terms of the Cre-
ative Commons Attribution License which permits any use, distribu-
tion, and reproduction in any medium, provided the original author(s)
and the source are credited.
References
1. Herve´, A., Acquistapace, G., Campi, D., et al.: IEEE Trans. Appl.
Supercond. 12(1), 385–390 (2002)
2. Herve´, A., Blau, B., Campi, D., et al.: IEEE Trans. Appl.
Supercond. 14(2), 542–547 (2004)
3. Herve´, A.: Mod. Phys. Lett. A 25(20), 1647–1666 (2010)
4. CMS Collaboration: JINST 3(S08004), 1–334 (2008)
5. CMS Collaboration: CERN-LHCC-2011-06. CMS UG-TP-1,
243–244 (2011)
6. Klyukhin, V.I., Ball, A., Bergsma, F., et al.: IEEE Trans. Appl.
Supercond. 18(2), 395–398 (2008)
7. Klioukhine, V.I., Campi, D., Cure´, B., et al.: IEEE Trans. Appl.
Supercond. 10(1), 428–431 (2000)
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Validation of the CMS Magnetic Field Map

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