Bottura, L

Faus-Golfe, A

Walckiers, L

Wolf, R

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23Switzerland12 July 1996LHC Project Report 17Large Hadron Collider ProjectField Quality of the Main Dipole Magnets for the LHC AcceleratorL. Bottura*, A. Faus-Golfe**, L. Walckiers* and R. Wolf*AbstractShort and long dipole model magnets for the LHC are measured in detail to optimize thefield quality to the different operation phases of the accelerator. We will report on recentprogress to understand and quantify effects related to the magnetization of thesuperconductor, to time dependent effects at fields corresponding to beam injection andto behaviour during acceleration. A parametrization for the measurements is proposed.The contributions from any misalignment of the dipoles and correctors magnets iscompared to expected field quality of the dipoles.*LHC Division, ** SL DivisionPaper presented at the 5th European Particle Accelerator Conference,  Sitges, 10-14  June 1996.FIELD QUALITY OF THE MAIN DIPOLE MAGNETSFOR THE LHC ACCELERATORL. Bottura, A. Faus-Golfe, L. Walckiers, R. Wolf, CERN, Geneva, SwitzerlandABSTRACTShort and long dipole model magnets for the LHC aremeasured in detail to optimize the field quality to thedifferent operation phases of the accelerator. We willreport on recent progress to understand and quantifyeffects related to the magnetization of the superconductor,to time dependent effects at fields corresponding to beaminjection and to behaviour during acceleration. Aparametrization for the measurements is proposed. Thecontributions from any misalignment of the dipoles andcorrectors magnets is compared to expected field qualityof the dipoles.1  INTRODUCTIONThe LHC accelerator will produce head on collisionsbetween beams of 7 TEV protons [1]. Beam opticscalculations indicate that the performance of the LHCwill be limited by the field quality mainly at low energythrough a limitation of the dynamic aperture. Experiencefrom the Tevatron [2] and Hera [3] machines have shownthat time dependent effects on the field errors can lead tounstable beams during the injection and at the beginningof the acceleration where an abrupt “snap-back” to thefield errors at start of injection takes place. Field rampsnecessary for the beam acceleration create couplingcurrents between the strands of the superconducting cablesof the winding, resulting in degradation of the fieldquality.The field expansion used is relative to the mainfield, B1,of the magnet at x = Rref = 10 mm. Here n=1 isa dipole field, n=2 is a quadrupole field etc. The bn and anrepresent the normal and skew relative field errors.B By x nrefnnn nrefnni C zRB b ia zR+ =æŁççöł÷÷=+ æŁççöł÷÷=¥-=¥-å å111 41110( )This paper will concentrate on field errors that coulddominate the behaviour of the LHC at low energy.2  ALIGNMENT OF THE DIPOLESAND THE END CORRECTORSThe harmonics allowed by the symmetry of thedipole are large at injection field due to the cablemagnetization. A misalignment of the dipole containinga multipole of order n+1 produces an additional one oforder n. Table 1 compares the errors generated by amisalignment of 0.5 mm to the expected random errorss (bn) and s (an) of the dipole field. Moreover, the decapoleand sextupole correctors mounted at each end of the maindipoles will produce similar quadrupole and octupoleterms if misaligned with respect to the dipoles. Somecare will therefore be needed to avoid systematicmisalignment of the end correctors with respect to themain dipoles.Table 1. Comparison for even harmonics (in units of 10-4 of injectionfield at 10 mm radius), between the errors resulting from amisalignment of 0.5 mm of the dipole and the standard deviation (s)  ofthe field errors expected in the dipoles.n bn+1  expectedin the dipoleb an n2 2+   for0.5mm mis.s  (bn) s  (an)2 -3.9 0.4 0.4 14 0.25 0.05 0.1 0.16 -0.026 0.008 0.06 0.013  INTERSTRAND EDDY CURRENTSCurrent ramps induce field distortions for allharmonics. These effects are dominated by couplingcurrents inversely proportional to the interstrandsresistance of the superconducting cables [4]. Table 2shows, for three different 10 m long models, that thedeviations are important for all harmonics. Systematicfield errors due to this effect could happen for instance dueto the bending of the dipoles to the radius of curvature ofthe LHC.A tight control of the LHC dynamic aperture isrequired. A systematic study based on these measuredvalues was performed on the resulting loss of dynamicaperture at the beginning of the acceleration [5]. It makesthe assumption that an exponential increase of theacceleration rate gives a constant perturbation all over theacceleration.Table 2. Field errors due to cable coupling currents (in units of 10-4 ofthe injection dipole field at 10 mm) at 8T/20min ramp-rate, in four 10m long dipole models. Also reported the average interstrand resistanceas deduced from loss measurements.n MTP1A1 MTP1A2 MTP1A3 MTP1N2b1 88 10.8 9.8b2 -0.96 -1.11 -0.052 1.32a2 10.8 0.89 1.052 1.06b3 4.6 0.95 0.3 0.55a3 -0.16 -0.19 -0.035 0.14b4 0.45 -0.13 0.019 -0.047a4 0.82 0.08 0.13 0.24b5 2.08 0.05 0.002 -0.09a5 -0.34 -0.02 - 0.026Rcable( m W)1.6 6.8 14 6.7This study shows that a spread comparable to theimperfections of MTP1A1 would significantly reduce theLHC dynamic aperture during the ramp. What matters isreally the spread of all harmonic terms for the wholepopulation of dipoles, the average b3 and b5 can indeed becorrected with the end correctors. A spread comparable tothe imperfections of MTP1A2 or even better of MTP1A3would not degrade significantly the dynamic aperture.MTP1A2 might be seen as an acceptance limit at theexpense of a significant increase of the already long ramptime. These conclusions should be confirmed by furthertracking studies.4  MAGNETIZATION DECAY AND“SNAP-BACK”LHC superconducting dipoles are characterized by asignificant drift of the magnetic field when the current isconstant, with typical time scales in the order of severalminutes to several hours [4]. At the restart of the ramp(beam acceleration phase) the field quickly bounces back,“snaps back”, reaching within 25 to 40 A (approximately20 to 30 mT of field change) the original value at thestart of the injection plateau. This can be of concern forthe start of beam acceleration. All harmonics are subjectto the field drift. On allowed harmonics the drift issystematic in the direction decreasing the contributionfrom the filaments magnetization, while it is random onnon-allowed harmonics.In accordance with previous measurements onTevatron[2], HERA[3] and SSC[6] magnets, we havefound that the amount of decay on all harmonics (andthus the snap-back) depends on the time spent at highcurrent, and on the number of operating cycles.Typically, for the LHC dipoles, the decay requires verylong flat-tops at high current to saturate (times longerthan _ hour). A few cycles (of the order of 5) to nominaloperating current produce an asymptotically stablesituation. Quenching resets previous history effects. Formachine operation this implies that magnets who havefollowed different histories will have a different behaviourat injection field.We speculate that the long term drift and thesnapback are associated with the interaction between thechanging cable internal field associated with the strandcurrent distribution and the magnetization of the singlestrands. We have started measurements of typical fielddecays and snap-back amplitudes, investigating on theinfluence of several parameters such as pre-cycles andtemperature drifts in order to establish suitable proceduresto minimize this effect. The main findings of thesestudies are listed below.• Snap-back is associated with field change rather thanwith field change rate. This is shown in Fig. 1 wheremeasurements in a 10 m long prototype are shown inthe case of different ramp-rates after the injectionplateau. The magnitude of the snap-back isapproximately the same in all cases, but the timespan for the snap-back scales inversely with thecurrent ramp-rates.• A pre-injection plateau at a lower current reduces theamount of field decay and snap-back at injection. A» 25 % smaller snap-back was measured on b3 after a15 minutes pre-injection plateau. The reduction is nota critical function of the pre-injection current.• The magnitude of the snap-back on the allowedharmonics at different temperatures scales as the ratioof the contributions of DC magnetization to theharmonic at the same temperatures. This demonstratesthe relation between field decay, snap-back and DCmagnetization.-1.2-1-0.8-0.6-0.4-0.200 500 1000 1500 2000time (s)b3 (0.05 A/s0.5 A/s 0.25 A/s0.1 A/sFigure 1. Snap-back in a 10 m long dipole prototype (MTP1N2) atdifferent ramp-rates after the injection plateau.In summary, a pre-injection plateau before theinjection phase decreases the snap-back. The residualmagnitude can be accommodated by slow ramps givingtime for the corrector scheme to react. Typicalmagnitudes for the snap-back of the first harmonics in theLHC 10 m long prototypes, measured after several daysof operation, are reported in Tab. 3. Systematic effects areexpected only on the allowed harmonics.Table 3. Change of multipoles due to snap-back for the LHC dipoles,estimated from the measured snap-back in 10 m long prototypes. Allquantities in units of 10-4 of the main field, at 10 mm reference radius.The standard deviations expected from geometrical errors in themagnets series are quoted as a reference.component D  (Snap-Back) s (geometric)b2 – 0.1 0.4a2 – 0.5 1b3 +0.8 0.5a3 – 0.2 0.15b4 – 0.5 0.1a4  0.0 0.1b5 -0.1 0.05a5  0.0 0.045 PARAMETRIZATION OF THEMEASUREMENTSIn a most general way, we can write that the field Bproduced by a magnet in arbitrary operating conditions isapproximated by:B B B B B B B= + + + + +geom s x y AC M MD D Dwhere we have evidenced the various contribution ofwinding geometry B geom (including the linear ironcontribution), iron saturation Bs, winding movementsBD x D y, coupling current BAC, filaments magnetization BMand long term magnetization drift and snap-back BD M. Foreach of them we are testing suitable parametricdependencies based on existing models or empirical fits.The present scaling for the coefficients Cn is givenin Tab. 4, where Cm indicates the main field component.Table 4. Scaling of the field contributions proposed for a parametricrepresentation.Main field Field errors (n ‡ m+1)Bgeom C Imgeomm= g C Cngeom n m= gBs+ BD xD y C I I Im m m mms s s= + +, , ,223334 C C C Cn n m n m n mms s s= + +, , ,223344BAC C dIdtmACm= t CdCdtnACnm= tBMCImMmm= +mm,,01CCnMnnm= +mm,,01BD M ( )[ ]C emM m t tD D= - - -1 0 / t († )( )( )[ ]C I t I ImM m oD D D= - -1 3/ (‡)( )C enMnt tDD= -ØºŒøßœ- -1 0/t(† )( )( )[ ]C I t I In M n oD D D= - -1 3/ (‡)(†) During a I= I0 current plateau starting at t=t0(‡) At ramp restart, between starting current I0 and current I0+ D I6  IMPLICATION FOR THE SERIESMEASUREMENTSA coils assembly able to measure the integral of thefield is under construction [7]. It is composed of 14measuring lengths separated for mechanical reasons bygaps equal to the twist pitch of the cable. It will allowmuch faster measurements for the series. The errorsavoided by an integrated measurement are listed below.• The residual error from a measuring coils having inaverage the length of the twist pitch that variesslightly between cable manufacturers is larger thanthestandard deviation from magnet to magnet.• Time dependent effects have a larger amplitude whenapproaching the ends of the magnets.• Point like variations of eddy currents have beenmeasured.• The randomness of the snap back effects is not yetunderstood. We believe that the standard deviationmeasured along the 15 m of the magnets can be ashigh as the deviation between magnets.The request to be able to measure the dipole axis andverify the centering of the spool piece correctors is notpossible with a integral shaft. These measurements willbe performed during warm tests of the final assemblieswith the help of a short coil. Differences between the axispositions in warm and cold conditions will be verified ona reduced number of magnets.7  CONCLUSIONExploratory measurements of both short and longmodels of the LHC superconducting dipole magnetsindicate the importance of methodically separatingdifferent effects. The reproduciblity of the time dependenteffects and dynamic effects may dominate the low fieldquality with respect to superconductor magnetization andharmonics due to the conductors locations. We havedefined a model for the magnetic measurements in orderto quantify and eventually correct these effects that couldlimit the dynamic aperture of the LHC machine at lowenergy.REFERENCES[1] "The Large Hadron Collider, Accelerator Project'',LHC Study Group, CERN/AC/95-05(LHC), Aug.1995.[2] R.W. Hanft, et al., “Studies of Time DependentFields in Tevatron Superconducting Dipole Magnets”,IEEE Trans. Magn., 25, (2), 1647-1651, 1989.[3] H. Brueck, et al., “Time Dependent Field Distortionsfrom Magnetization Currents in the SuperconductingHera Magnets”, Cryogenics, 30, 605-609, 1990.[4] J. Buckley, D. Richter, L. Walckiers, R. Wolf,“Dynamic magnetic measurements of superconductingmagnets for the LHC”, IEEE Trans. Of Appl. Sup., 5,(2), p 1024, 1995[5] A. Faus-Golfe "Minimization of the ramp-inducednon-linear field imperfections in LHC'', LHC ProjectNote 9, May 1995.[6] A. Devred, et al., “Time Decay Measurements of theSextupole Component of the Magnetic Field in a 4-cmAperture”, 17-m-Long SSC Dipole Magnet Prototype,Proc. of 14th Particle Accelerator Conference, SanFrancisco CA, May 6-9, 1991.[7] P. Sievers, “Towards series measurements of LHCmagnets”,CERN AT/94-11(MA), June 1994.

Field quality of the main dipole magnets for the LHC accelerator

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