The 15 m long LHC superconducting dipole magnets, which contain two beam channels in a common mechanical structure, produce a magnetic field of 8.3 T required to deflect protons with 7 TeV/c momentum along a circular trajectory in the already existing LEP tunnel. The dipoles are bent in their horizontal plane to provide the largest possible mechanical aperture to the circulating beam. This paper describes the theoretical geometry of the dipole cold mass and the alignment requirements, which are imposed to satisfy the demands of LHC machine operation. A short description of the measuring and alignment procedures and of the measuring instruments is given. Results of a small series of prototype cold masses are presented and discussed

Bajko, M

Savary, F

Scandale, Walter

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsGEOMETRY AND ALIGNMENT REQUIREMENTS FOR THE LHC MAIN DIPOLEW. Scandale, M. Bajko and F. SavaryThe 15 m long LHC superconducting dipole magnets, which contain two beam channels in a commonmechanical structure, produce a magnetic field of 8.3 T required to deflect protons with 7 TeV/cmomentum along a circular trajectory in the already existing LEP tunnel. The dipoles are bent in theirhorizontal plane to provide the largest possible mechanical aperture to the circulating beam. This paperdescribes the theoretical geometry of the dipole cold mass and the alignment requirements, which areimposed to satisfy the demands of LHC machine operation. A short description of the measuring andalignment procedures and of the measuring instruments is given. Results of a small series of prototypecold masses are presented and discussed.LHC DivisionPresented at the Seventh European Particle Accelerator Conference  (EPAC 2000)26-30 June 2000, Vienna, AustriaGeneva, Large Hadron Collider ProjectAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandLHC Project Report 426Abstract23 September 20001GEOMETRY AND ALIGNMENT REQUIREMENTS FOR THE LHC MAINDIPOLEW. Scandale, M. Bajko and F. Savary, CERN, Geneva, SwitzerlandAbstractThe 15 m long LHC superconducting dipole magnets,which contain two beam channels in a commonmechanical structure, produce a magnetic field of 8.3 Trequired to deflect protons with 7 TeV/c momentumalong a circular trajectory in the already existing LEPtunnel. The dipoles are bent in their horizontal plane toprovide the largest possible mechanical aperture to thecirculating beam. This paper describes the theoreticalgeometry of the dipole cold mass and the alignmentrequirements, which are imposed to satisfy the demandsof LHC machine operation. A short description of themeasuring and alignment procedures and of themeasuring instruments is given. Results of a small seriesof prototype cold masses are presented and discussed.1 INTRODUCTIONThe LHC uses superconducting magnets operating at atemperature of 1.9 K to guide the circulating particles. Aspecific feature of the magnets is the two-in-one conceptwith two magnetic channels in a common force-retainingstructure. As a consequence, the two accelerator ringsare mechanically linked and have to be alignedsimultaneously during their fabrication up to theirinstallation in the existing LEP tunnel. Thisunprecedented feature has important consequences ongeometric tolerances of the cold mass assembly (CMA)of the 15 m long, 30 tonnes dipole. Persistent currents, induced in the superconductingcables by the field variation during the acceleratoroperation, have detrimental effects on beam stability,especially during the injection plateau. Correctormagnets, placed at the ends of each CMA, mayeventually compensate in an almost local manner thenon-linear perturbation of the beam trajectories. The keyissue is the accuracy of the alignment between thecorrector itself and the magnetic axis of the dipole, bywhich detrimental second-order effect, i.e.uncompensated multipole feed-down, can be limited [1].In section 2, we describe the geometry and thealignment of the CMA. In Section 3, we present thegeometric tolerances required for the CMA. In section 4,we report about the geometric shape of CMA prototypes,assembled at CERN and measured by high precision 3-Dlaser tracker. In Section 5, we draw some conclusions.2 DIPOLE GEOMETRYThe specification of the LHC dipole geometry is basedon three main constraints:• The cold mass is to be bent around the beam orbit, tomaximize the mechanical aperture, whilst minimizingthe aperture of superconducting coils, i.e. their size.• The corrector magnets at the ends of the CMA must bealigned with respect to the dipole axis, to reduce themultipolar feed-down effect.• The radial displacement of bellows in the magnet tomagnet interconnection should not exceed 4 mm. Thisissue is critical for magnet installation and impliesaccurate monitoring of the ground motion during LHCoperation.2.1 Geometrical parametersThe LHC ring contains 1232 dipoles, the maingeometrical parameters of which are given in Table 1.Table 1: Geometrical parameters of the LHC dipole1.9 K 300 KMagnetic length [m] 14.300 14.343Bending angle [mrad] 5.099988 5.099988Sagitta [mm] 9.12 9.14Bending radius [m] 2803.928 2812.360Axes separation [mm] 194.00 194.52During LHC operation at 1.9 K, two counter-rotatingbeams follow flat straight trajectories which becomecircular along the 14.3 m long active part of each dipole.The two orbits are separated by 194 mm, i.e. thenominal distance between the twin-coil axes. The CMAaxes should be aligned along them. In assemblingconditions at 300 K, one has to take into account thethermal effects, which bring to 14.343 m the magneticlength and to 194.52 mm the distance between the coilaxes. The dipole is thus curved in the horizontal planewith an apical angle θ of about 5 mrad, identical to thebending angle of the circulating protons. The length ofthe curved section equals the magnetic length. The twochannels have the same curvature. Indeed, the dipolegeometry is determined from the functional specificationat 1.9 K, whilst, the temperature-induced variation of thegeometry after cool down is determined by both thelongitudinal and the transversal thermal contraction ofthe CMA. The vertical shape should be straight. In fact,the CMA is distorted by about 0.3 mm, between thethree supporting pads, by the effect of the self-weightand of the given flexural strength of the shrinkingcylinder. During production, the originally straightdipoles are curved as they are assembled with pre-bentshells in an appropriate jig and a welding press. Theresulting shape of the cold bore axes is measured with ahigh precision 3-D laser tracker. The data are used to fit2the position of the two ideal cold bore axes abovedefined, shown in Fig.1 and 2, and to identify thehorizontal and vertical CMA reference planes. Tooptimize this procedure a methodology for thedimensional inspection of the dipole cold mass has beendefined. Its particularity is the implementation of 3-Dmeasurements as part of the cold mass assemblingprocedures. To this scope, a 3-D portable measuringsystem, allowing all the necessary measurements duringthe different assembling steps of the cold mass has beenspecified and tested (also in industrial conditions) on thefirst three 15 meter long prototype CMA withsatisfactory results [2].Figure 1: Horizontal theoretical shape of the cold mass inassembling conditionsFigure 2: Vertical theoretical shape of the cold mass innominal supporting conditions (three support pads).2.2 Corrector magnetsThe LHC dipoles are affected by unavoidable field-shape imperfections mostly due to fabrication tolerances,persistent currents and iron saturation. The field errorsare minimized by optimization of the coil cross-section.However, the effect of persistent currents is too large tobe fully compensated by design.  The residual multipolesinduce beam instabilities, especially at injection field,which should be locally corrected in each dipole. To thisscope, at the connection end of the CMA there is asextupolar corrector about 150 mm long and at the lyra-side end, there are combined octupolar-decapolarcorrectors about 110 mm long. Since they are very closeto the source of error, they can be very efficient on thecondition that they are well aligned to the beamchannels. Indeed, a multipolar lens of order n traversedoff-axis by a charged particle can be described by anappropriate combination of multipolar terms of order k,with k ≤ n. This effect is referred to as the feed-down ofthe multipolar harmonics. In presence of misalignment,dipoles and associated correctors can have unequaldisplacements from the reference orbit. In this case thefeed-down harmonics of a given multipolar error oforder n and of the corresponding corrector are different,except at the order n itself. Consequently, thecompensation is still very good at the order n itself, butit is imperfect at the lower orders. In [1] there arequantitative estimates for the multipole feed-down dueto misalignments and an evaluation of allowedtolerances for the alignment of the correctors at thedipole ends. Random misalignments of the correctorswith respect to the dipole axis with standard deviationsup to 0.5 mm do not introduce additional detrimentalnon-linear effects. Systematic misalignments of thecorrectors may be more disturbing. In particular, thefeed-down effect overcomes the upper limit of field-shape errors, expected in the dipoles, for an offset largerthan 0.3 mm. In positioning the correctors, we assumethat the geometric and magnetic dipole axes coincidewithin 0.1 mm.3 GEOMETRY TOLERANCEIn the curved part of the CMA, two toroidal sectorsare generated by a circle of 1 mm radius and movedalong the circumference of the theoretical geometricaxes of each beam channel. In the straight ends, a 0.3mm radius cylinder represents the tolerance range. Thecombination of the toroidal sectors with the straightcylinders gives the shape tolerance for the axis of eachmagnet aperture.  The horizontal and vertical ranges oftolerance are also traced in Fig. 1 and 2. The correctormagnets are enclosed in the end covers of the dipolecold mass. Their magnetic centers have to be localisedon the straight ends of the CMA axes within ± 0.3 mm.Due to the laminated structure, a twist distribution alongthe dipole magnet may occur, which means that thegeometric axes of the two cold bore tubes do not lie in aperfect plane. The twist distribution in the curved part aswell as in the straight ends, i.e. the local twist along thecold mass assembly shall be within ± 1 mrad relative tothe CMA ideal axes. These tolerances ensure sufficientaperture for the circulating particles, tolerable harmonicfeed-down and limited offset of the bellow at theinterconnection.4 MEASUREMENTSThe 3-D optical system by which the dipole axes aremeasured is based on the interferometric laser techniqueand incorporates high-precision absolute distance meterand angular encoders. The measurement of the cold boreaxes necessitates a mechanical mole centered on theinner wall of the cold bore and holding a reflector. The54 00 54 00 2L IN E  V 1  an d  L IN E  V 2 N A TU RA L  S H A P E  O F  TH E  C O LD  M A S SS U P P O R T P A D S0.3W WV2V1V2V197.26R 2812360LINE V1R 2812360LINE  W97.26R 2812360LINE V2V22V1214343 LINE V114343 LINE V29.1433-D co-ordinates of the reflector center describe the axisof each tube. Thanks to the portable measuringinstrument and the adopted measuring technique, the twocold bore tubes and the different elements (correctors,support pads, end covers) are measured and aligned in acommon co-ordinates system.Figure 3 a: The curvature of the MBP2N2 prototypeFigure 3 b: The straightness of the MBP2N2 prototypeFigure 3 c: The twist of the MBP2N2 prototypeBy using typical co-ordinates transformation methods,the measured points are best fitted to the ideal geometryand the corrector magnets, the support pads and the endcovers are aligned with respect to the ideal geometry.Fig. 3 show results obtained on MBP2N2 prototype.Fig. 3a and 3b give the horizontal and vertical real axis,ideal axis and range of tolerance in one aperture. Fig. 3cshows local twist and its range of tolerance. This magnetsatisfies the geometrical specifications, with theexception of the twist, which exceeds the tolerance insome points. The two other dipole prototypes MBP2N1and MBP2O1 have similar features shown in Table 2.Table 2. Errors on the geometry of the prototypeCMAMBP2- N1min/maxN2min/maxO1min/maxHorizontalcurvature [mm]-0.8/+0.8 -0.4/+0.7 -0.8/+1.7Verticalstraightness[mm]-0.4/+1.0 -0.4/+0.8 -0.4/+0.4Twist [mrad] -1.1/+3.0 -3.0/+2.5 -2.5/+3.0Radial offset ofcorrectors [mm]V2/V10.67/1.03V2/V11.23/1.10V2/V10.19/0.185 CONCLUSIONSWe described the main features of the LHC twindipole geometry, horizontally curved around the beamorbit. We also presented the changes expected during thecool-down from assembling conditions at 300 K tooperational conditions at 1.9 K and the effect of thedipole self-weight. The tolerance on alignment is verytight since the dipole is very long and containsmultipolar correctors to improve beam stability. Thisimposes an assembling strategy assisted by highprecision geometrical measurements. Laser trackertechnology is well suited for this scope.Three 15 m long dipole prototypes, assembled atCERN with the measuring assisted procedure are wellwithin geometrical specifications both for the horizontaland the vertical plane. The twist distribution instead is insome points still out of tolerance and should beimproved for the forthcoming pre-series production.The authors gratefully acknowledge the contributionof M. Mayoud, J.P.Quesnel, D. Missiaen andW. Coosemans to the establishment of the dipolemeasuring procedures. They also suggested using thelaser tracker technology for this purpose. Thanks to J.Billan, D. Cochet, M. Duret, J. Garcia Perez, P.Gillieron for their help during geometricalmeasurements.REFERENCES[1] R. Bartolini and W. Scandale, “Multipole Feed-downdue to Dipole Misalignments”, LHC-MMS, InternalNote 97-12, (1997).[2] M. Bajko, F. Savary, W, Scandale “LHC DipoleMagnets Assembling Driven by DimensionalInspection”, LHC-MMS, Internal Note to bepublished.250 2000 4250 6500 8750 1.1 104 1.33 104 1.55 10499.0194.9290.8386.74measured valuetheoretical valueupper tolerancelower toleranceLength (mm)Horizontal curvature (mm)25 0 29 00 60 50 92 00 1.24 10 4 1.55 10 477.68.28.89.410co m p uted  va luem eas ured  va luetheore tica l va lueto le ra nceto le ra nceL eng th (m m )Vertical     straigthness (mm)222 3583.5 7389 1.12 104 1.5 10431.501.53measured valuesupper tolerancelower tolerancetheoreticalLength (mm)Twist  (  mrad)

Geometry and Alignment Requirements for the LHC Main Dipole

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