The CMS magnetic system consists of a super-conducting solenoid coil, 12.5 m
long and 6 m free bore diameter, and of an iron flux-return yoke, which
includes the central barrel, two end-caps and the ferromagnetic parts of the
hadronic forward calorimeter. The magnetic flux density in the center of the
solenoid is 4 T. To carry out the magnetic analysis of the CMS magnetic system,
several 3D models were developed to perform magnetic field and force
calculations using the Vector Fields code TOSCA. The analysis includes a study
of the general field behavior, the calculation of the forces on the coil
generated by small axial, radial displacements and angular tilts, the
calculation of the forces on the ferromagnetic parts, the calculation of the
fringe field outside the magnetic system, and a study of the field level in the
chimneys for the current leads and the cryogenic lines. A procedure to
reconstruct the field inside a cylindrical volume starting from the values of
the magnetic flux density on the cylinder surface is considered. Special
TOSCA-GEANT interface tools have being developed to input the calculated
magnetic field into the detector simulation package.Comment: 4 pages, 6 figures, 1 equation, 14 reference

Campi, D.

Curé, B.

Desirelli, A.

Farinon, S.

Gerwig, H.

Green, D.

Grillet, J. P.

Hervé, A.

Kircher, F.

Klyukhin, V. I.

Levesy, B.

Loveless, R.

Smith, R. P.

English

arXiv

The CMS magnetic system consists of a super-conducting solenoid coil, 12.5 m long and 6 m free bore diameter, and of an iron flux-return yoke, which includes the central barrel, two end-caps and the ferromagnetic parts of the hadronic forward calorimeter. The magnetic flux density in the center of the solenoid is 4 T. To carry out the magnetic analysis of the CMS magnetic system, several 3D models were developed to perform magnetic field and force calculations using the Vector Fields code TOSCA. The analysis includes a study of the general field behavior, the calculation of the forces on the coil generated by small axial, radial displacements and angular tilts, the calculation of the forces on the ferromagnetic parts, the calculation of the fringe field outside the magnetic system, and a study of the field level in the chimneys for the current leads and the cryogenic lines. A procedure to reconstruct the field inside a cylindrical volume starting from the values of the magnetic flux density on the cylinder surface is considered. Special TOSCA-GEANT interface tools have being developed to input the calculated magnetic field into the detector simulation package.The CMS magnetic system consists of a super-conducting solenoid coil, 12.5 m long and 6 m free bore diameter, and of an iron flux-return yoke, which includes the central barrel, two end-caps and the ferromagnetic parts of the hadronic forward calorimeter. The magnetic flux density in the center of the solenoid is 4 T. To carry out the magnetic analysis of the CMS magnetic system, several 3D models were developed to perform magnetic field and force calculations using the Vector Fields code TOSCA. The analysis includes a study of the general field behavior, the calculation of the forces on the coil generated by small axial, radial displacements and angular tilts, the calculation of the forces on the ferromagnetic parts, the calculation of the fringe field outside the magnetic system, and a study of the field level in the chimneys for the current leads and the cryogenic lines. A procedure to reconstruct the field inside a cylindrical volume starting from the values of the magnetic flux density on the cylinder surface is considered. Special TOSCA-GEANT interface tools have being developed to input the calculated magnetic field into the detector simulation package

Klyukhin, V.I.

Cure, B.

Grillet, J.P.

Herve, Alain

Smith, R.P.

CERN Document Server

428 IEEB TRANSAC'l'IDNS ON APPLIED SUPEHCONDWCI'IVIlY. VOL. io, NO. 1, MhRCII ZOO0 Y O P C n A 3 d  7 3D Magnetic Analysis of the CMS Magnet V.Z. Klioukhine'. D. Campi', B. CurC', A. Desirelli', S. Farinon3, H. Gerwig', D. Green', J.P. Grillet2, A. Hervc2, F, Kirchet, B. Lvesy4,  R. Lovelesss, R.P. Smith' PNAL, Batavia, I t ,  USA, CERN, Geneva, Switzerland, INFN, Genova, Italy, CEAISaclay, Gif-sur-Yvette, Francc, Univcrsily of Wisconsin, Madison, WI, USA. Absiruct-The CMS magnctic system consists of a super- conducting solenoid coil, 12.5 m long and 6 m free bore diameter, and of an iron flux-return yoke, which includes thc central barrel, two  end-caps and the ferromagnetic parts of tlic hadronic forward calorimeter. The magnetic flux density in the ccntcr of the suIenoid is 4 T. To cnrry out the magnetic analysis of the CMS magnctic systcni, several 3D modcls were developed to perform magnetic field and force calculatianv using tlic Vector Fields code TOSCA, Thc analysis includes a study of the general ficld behavior, thc calculntion of the forces on the coil gcncrilted by small axial, radial displacements and tingular tilts, the calculation OF the forccs on thc ferromagnetic parts, the calculation of the fringe field outside the magnctic system, and a study of the field Ievcl in the chimneys for tlic current leads and thc cryogenic lines. A procedure to reconstruct thc field inside a cylindrical voluinc starting from the values of the magnetic flux density cm the cylinder surface is considered. Special TOSCA- GEANT interface tmls have being developcd to input thc ci1lculated magnetic field into the cletcctor siinulation package. Iirdex Term-solcnoid, magnetic rorccs, ficld calculntfon I, INTRODUCTION This paper describes the 3D calculations of the magnetic field and forces in the Compact Muon Solenoid (CMS) magnetic system [ 11, which consists of il supeconducting solonoid coil, 12.5 m long and 6 m free bore diameter, and of an iron flux-return yoke. The yoke, 14 m outer diamctcr, includes the central barrel surrounding the coil, two cncl-caps located at each end of the solenoid, and the ferromagnetic parts of the hadronic forward calorimeter arranged downstream of the end-caps. The barrel is subdivided into five rings e x t i  comprising three layers joined by connecting brackets. An additional fourth layer, the tail catcher, exists onty insidc the central barrel ring. Each end-cap consists of one small nose disk and four large disks mounted axially along the solenoid axis line. The design value of the magnetic tlux density in thc coil center is 4 T. The calculations were performed with the finite-element analysis code TOSCA (21. The goal of the 3D analysis was to study the influence of azimuttially usymmctric parts of thc system on the field behavior, to calculate the forces caused by the coil misalignments within the iron yoke, to prepare the 3D field map for detector simulations, and to investigate the reconstruction of the field insidc the coil voluine starting from measurements of the field values near the coil inner sur face. Mnnuscript rcccived September 27, 1999, 11. THE MoDeLDESCRIrrroN To perform the magnetic analysis of the CMS magnetic system with the TOSCR code, several 315 modcls were developed [31, [4], [SI. The present model shown in Pig. 1 with one eighth of the magnetic flux return yokc takes into account such azimuthally asymmetric ferromagnetic parts of the system as brackets betwecn the barrel ring layers, the tail catcher, and 'uses II coil madct consisting of five concentric but axially separated modules. The finite-element mesh is constructed from 107784 nodcs. To describe the model, a Cartesian coordinate system with the origin plnccd in the center of the solenoid was used. The direction of the Z-axis is along the solenoid axis. The direction of the Y-axis is upward. In the model, the superconducting coil modules have length 2443.87 mm and they are spaced axially from one another by 47.6 mm. Each module consists of four coaxial layers of current each of radial thickness 20.63 mm a t  radii 3174.755, 3239.525,3304.295 and 3369.065 mm, The overall axial length of the assembly i s  12402.39 mm. The locations of the current layers in the calculations correspond to the positions of the superconducting cable in the conductor when the coil is at cryogenic temperature. The total current in the coil is 42.51 MA-turns [6] which gives 4.08T in the center of solenoid. The maximum magnetic flux densities;B, near the superconducting cable in each layer of the coil are 4.6, 3.5, 2 S  and 1.5 T. The full geometry of the flux return yoke and the steel magnetic properties are described elsewhere [5 ] .  105l-8223/00$l0.00 0 2003 IEEB 429 comparable to this. ln  the last two cnd-cap disks Ihe radial component is about half that in the first two disks, 111. GENERALPIBI,~) BEHAVIOR The magnetic flux density contuurs in the horizontal XOZ- plnne arc shown in Fig. 2. Contours are plottcd cvery 0.5 T. The maximum valuc of S ?' is reached inside the hadronic end-cap catorimeter support tube. The line near Z = 2 m corresponds to I3 = 4 T. ,xe 0 1 From this map obtainctl using a special map extraction proccrlure developcd for this purpose [7], one can scc that the field ncnr tlie coil cclges, bctwccn the barrel and thc cnd-cap, inside thc nase nnd inside and between the first two end-cap disks is strongly inhrimogeneous. The magnetic flux dcnsity has non-negligible radial component, B,, and large variation of axial component, B,, i n  thc rcgions of the first laycr of the end-cap miion chambers as was shown earlier in [8]. Between the bmcl ring layers near the brackets, thc field variations are large BS well. This complexity of the field behavior requires the use of a 3D ficld map in detector simulntiniis outside the coil voluine. In Fig. 3, B, and B, are displayed along the coil axis mid ncar the cui1 inner nnd antcr radii. This figure shows the influence of thc gaps bctwccn rtre cail modules on the field behavior near the coil. At the coil ends ttie absolute values of the axial and radial components arc approximately equal to one half tlie ceiitral field valuc. Along the line at the coil inner radius the €3, values in thc First two end-cap disks are The stray field outside the yoke was calculatcd out to n radius of 50 m from the coil axis. As shown i n  Fig. 4, at 0.5 m radially outside thc yoke the stray Rcld has tnaximn of 65-188 mT near the gaps between the barrel rings and betwccn the end-cap disks. -0 F ) v s  L (m) al R = 7.5 m, Irdogml- 1 14Tm --I3 F ) v 3  2 (m) at Ft -9 m Integral - 0 67Tm _ _ _ _ _ _  B (T)va Z (m) a\ R -10.6 rii, Inlegral -049T m -,_._ B v) vs 2 (m) ai R = 12 m, lnlogral - 0.37 T m Fig. 4. Stray fields a t  radii 7 . 5 , 9 ,  10.5. and 12 m fromZ-axis The stray field in  the barrel region dccrcases faster than in the cnd-cap regions. At. radius o F  50 m the value of the fringc field is npproxitnatcly 0.4 mT. Two chimneys penclrate the CMS barrel yoke: the vertical chimney contains the cryogenic lines, and the second onc. inclincd at 30" tu thc vertical, contains the electrical leads. A special 4n-gcoinetry modcl was developed to cstimate the field valuc inside these chimneys. In Fig. 5 the behavior of H, and B, inside the chimneys, starting from thc coil cryostat, are displayed. 0 1  II . n o  I I ~~ ~ RT'-3 R 4. B 5 8  6 . 0  7.8 8.8 t : + - i  638 t-r ma +.i.mo * - i .mn +.I 538 +.i 530 - 0.2 (r) vs R (m) In cryocpnlc llm chlmnoy, lntogral - -1 3 3  T m - - BR (T) vs R (m) In cryaaariic Ilms chlmney, Integral - 0.01 6 T m ...... BZ(T)vsR (m)Insleclrlcil lu& chlmnuy. lntegrirl- 1 . 4 7 T m  _._._ BR (T) vs n im) In eledrlcal Laad3 chimney, Integral - -0,014 Tm Fig. 5 .  Axial and radial fields inside the chiiiiiicys The radial componcnt is 50-80mT between the cryostat and barrel yoke. The axial compuncnt oscillates, incrcasing inside the barrel steel plirtes nnd dccrcasing between them The maximum B, nbsolutc value is 055 T. 430 1v. FORCES ON FEKKO-MAGNETIC PARTS The forces acting on various parts of the yoke were cnlcdated by integrnting ttie Maxwell Stress tensor over the volumes or the .surfaces of the yoke picccs [51. When the integration surfaces pass through. ferromagnetic material, an infinitely thin gap at the integration surface is assumed and the following formula is used': E' = j [H,(B n) - p o ( ~ ~ ,  I I , ) ~ / ~ I ~ s ,  (1) where H, = H + ( (B/k  - H) n)n. B is R vector of the milgnetic flux density, H is a vector of the magnetic field strength, n is a normal unit vector external to surface uf region, and S = 4n: I O 7  (V s)i{A m). The axial magnetic forces on the first end-cap disk, the nose, and the hadronic end-cap calorimeter support tube itre 58.GMN. Taking into account the inward deflection of the end-cap disks by 30 mm artcr reaching the nominal current in thc coil, this axial fwcc increases to 59.3 MN. These values are close to the values obtained carlict in [9]. The full table of forces on the yoke iron parts is grcscnted in [51. To get B feeling of the order of magnitude of the forces, an engineering estimation based on a simple version o f  the previous formula. which considers only the normal components of the ficlds, was done by S .  Vorojtsov [51. To cross-chcck thc TOSCA results, the simplified POISCR [ 101 2D computer model was used. Both of  those alternative approaches yielded results comparable with the TOSCA cdculations. v. FORCES ON THE COlL In the described model with centercd coil, the axial force on the coil module next to the central onc is 26 MN and that on the externat module is 118 MN. In the models with decentered coil (145339 nodes) a calculation of the axial force gcnerntcd by a small coil axial displacement yielded a value of 843 kN/cm, which agrees welt with the previous results obtained with the ANSYS 2D [ 111, CASTBM 2000 [121, and TOSCA [3,4] codes. From nine inodcls (117611-148311 nodes) used for the calculation of the radial forcc causcd by a small coil radial displacement the average value of the force was 59 k 1 9 W k m .  This value is lowcr than the value of the radial force obbincd in [12] and [3,41. The force acts in the direction of increasing the coil radial displacement. From six models (117611-149581 nodes} used for the calculation of torquc cuused by a small coi l  angular titt the average value of the torque was 914 f 98 kN dmrad .  This value is lower thnn the valuc of torquc obtained earlier in [ 121 and higher than the value obtained in [3,4]. The torque direction tends to increase (tie tilt of the coil. As shown jn [3,12] tlie force and torque depcndencc From the coil displacements and tilt is linear for thc misalignments considered. VI. FIELD RECONSTRUCTION A possibility to dctcrminc the ficld inside ~1 cylindrical volume using the valucs of n, on the cylinder surface is investigated. The fieId boundary values extracted from TOSCA are used for B, and B, reconstruction in the volume with help of the CERN codes MAGFIT2 [13] and MAGFIT [ 141. Both these programs give approximately the same results but need modification to obtain the desired accuracy. In tlie fitting, 10 radial points (spaced 0.3 m, starting from the coil axis), 16 azimuthal points (spaced 22.5"), 113 uxinl points (spaced 0.1 m), for A totnl of 18080 points, were used on the surface of a cylinder with a rarliiis of 2.95 m and with a length of 11.2 m. In Fig. G the valucs of 13, on this surface are plotted in contours with an interval 102.5 m?' between them, The B, minimum and maximum values are 2.98 and 4.21 T, respectively. Fig. 6. Axial component of B iiem the cryoslnt inncr siihcc In the MAGFIT2 codc thc Flux densities are expanded in Fourier series along thc cylinder surface, around rings at the ends of the cylinder surface, and on discs at the ends of the cylinder. The total number of coefficicnts used in thc cxpansion'is 924. With this parameterization the axial and radial compflncnts of thc magnetic flux density along the line at radius 2.95 m and at zero azimuth were reconstructed and then the comparisons with the input f idd values were done. The accuracy of the B, reconstruction is 0.75 mT at the edges and 0.25 mT in the middtc of the given line, thc accuracy of thc B, is 19.5 mT at the cdgcs and around 5 mT in the middle. The number of radial, azimuthal, and axial points chosen in the fitting were nearly equal to the maxima allowed in the prescnt version of MAGFIT2. It is believed that increasing those limits in the code will enable the program to predict the field more accurately. VII. CONCLUSION l*hc substantial inhomogeneity of thc CMS magnetic field outside the coil volume requires the use of 3D modeling to prcpare ~1 field map for detector simulations. The special TOSCA-GEANT interface tools were dcveloped to perform this task. The simulations of thc CMS miignetic system with sevcral TOSCA 3D models give thc forces acting on vnriuus parts uf fbc yoke in agrccmcnt with carlier cakulations. In the TOSCA 3D models the forces acting on thc coil due to the coil radial misalignmcnts and tilts are sinallcr than prcdicteil in previous models. Thc nxinl forces clue to the coil axial misalignments are in agreement with earlier force calculations. A possibility to dctermine the field inside R cylindrical volume by making mcasurements of axial component of  the magnetic flux density un the surFace i s  investigated. The cxjsting softwarc will. need modificntion to predict thc tkld more accuratety. REI:l!RF,NCES [ I ]  A. HcrvC, 7%e CMS Dtlrcmr Magriel, stilmitted to 16”’ International Confercncc on Mngncl Tcchiiology, h ” c  Vcdra IJeitcIi, FL, USA, Septcmber 26 -October 2, 1799. 

3D magnetic analysis of the CMS magnet

3D Magnetic Analysis of the CMS Magnet

3D Magnetic Analysis of the CMS Magnet

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