Due to the field asymmetry of the LHC dipoles, the magnetic field integral calculated from the centre of the aperture to the outside of the cold mass does not vanish. During a magnet quench this asymmetry generates an electromotive force and thus a current with a resultant lateral force on the beam screen. This induced force was observed indirectly when measuring the deformation of the beam screen cross-section during a quench using a precision displacement transducer, which will be described. The transducer (based on optical gratings) was developed specially to study the beam screen deformation in cryogenic environments and high magnetic fields. The results of the measurements are compared to calculations and to direct measurements of the induced voltage along the current path. An estimation of the forces exerted on the cold bore by the beam screen and of the actual current induced in the beam screen will be given

Caspers, Friedhelm

Pugnat, P

Rathjen, C

Russenschuck, Stephan

Siemko, A

CERN Document Server

CURRENTS IN, FORCES ON AND DEFORMATIONS/DISPLACEMENTSOF THE LHC BEAM SCREEN EXPECTED DURING A MAGNET QUENCHC. Rathjen, F. Caspers, P. Pugnat, S. Russenschuck, A. Siemko, CERN, Geneva, SwitzerlandAbstractDue to the field asymmetry of the LHC dipoles, themagnetic field integral calculated from the centre of theaperture to the outside of the cold mass does not vanish.During a magnet quench this asymmetry generates anelectromotive force and thus a current with a resultantlateral force on the beam screen. This induced force wasobserved indirectly when measuring the deformation ofthe beam screen cross-section during a quench using aprecision displacement transducer, which will bedescribed. The transducer (based on optical gratings) wasdeveloped specially to study the beam screen deformationin cryogenic environments and high magnetic fields. Theresults of the measurements are compared to calculationsand to direct measurements of the induced voltage alongthe current path. An estimation of the forces exerted onthe cold bore by the beam screen and of the actual currentinduced in the beam screen will be given.1 INTRODUCTIONFig. 1 shows a section through one beam pipe (coldbore tube) of a LHC dipole magnet. The main purpose ofthe beam screen is to reduce the beam induced heat inputinto the cold mass of the super conducting magnet and toinsure vacuum stability. To reduce the impedance of theLHC machine, a thin copper layer is required on the insideof the stainless steel beam screen. One drawback of thedesired low impedance is that it facilitates the induction ofeddy currents (mainly in the copper layer because of itsvery low resistance at 20 K). As a consequence, thedecaying magnetic field generates Lorentz forces whichexpand the beam screen horizontally (see Fig. 2).According to measurements and calculations [1], theLorentz forces are approximately proportional to BdB/dt(flux density B, Fig.2). For a quench at nominal field of8.3 T maximal Lorentz forces in the order of 4 N/mm3 aregenerated 190 ms after the quench started. The maximumsum of all Lorentz forces in one half of the beam screen isapproximately 10 kN/m. At 210 ms the sum of all eddycurrents reaches its maximum of about 1.8 kA.As no transducers for high magnetic fields andcryogenic environments (also small enough for the beamscreen) were available, CERN’s vacuum group developeddisplacement transducers (Fig. 3) to measure quenchinduced deformations in a precise and reliable manner [2].Pumping slotsBeam screen (46x38x1 mm)Cold bore tube (53/50 mm)Copper layer (0.05 mm)Cooling tubeSupportFigure 1: Test beam screen inside cold bore tube.Lorentz forceson copper layerDeformedbeam screenEddycurrentsMagneticfieldBFigure 2: Induced eddy currents and resulting deformationof a beam screen during a LHC dipole quench. Figure 3: Optical displacement transducers with opticalfibres (left) and with attached electronics.2 MEASUREMENTSQuenches under different initial conditions wereperformed in a 15 m long LHC dipole magnet prototype[3] (beam screen temperatures: 6~30 K; magnetic field< 9 T). Fig. 3 shows the two transducers used for themeasurements. One transducer had its electronics (IR-LED and photodiodes) inside the magnetic field. Sincethe transducer electronics could not be pre-tested underquench conditions, a second transducer was equippedwith optical fibres to measure fully independent ofcryogenic temperatures and high magnetic fields; thevisible diode laser and 4 photodiodes were installed insidethe cryostats insulation vacuum close to room temperaturebut outside the magnetic field. Finally both transducersperformed well under quench conditions.2.1 InstrumentationThe optical transducer is based on the method ofcounting fringes on an optical grating (that is used as ameasurement scale). Fig. 4 shows the essential parts ofthe transducer version with optical fibres. Themeasurement grating (fixed on one side of the beamscreen) is subjected to the displacement to be measured.The grating consists of 10 µm broad fringes of chrome,having a pitch of 20 µm, on a glass substrate. A detector,fixed on the other side of the beam screen, counts thefringes passing by. Principal components of the detectorare a collimated light source, a reference grating of thesame pitch and a receiver with photodiodes. The referencegrating consist of four 90° phase shifted gratings which0-7803-7191-7/01/$10.00 ©2001 IEEE. 192Proceedings of the 2001 Particle Accelerator Conference, Chicagoenable a more sophisticated fringe counting withinterpolation that can also distinguish between forwardand backward movement. The measurement grating has tobe guided parallel to the reference grating with highprecision. The guidance is realised by a parallelogram offour folded leaf springs, which make the transducerhysteresis free and avoid jamming at cold.The advantage of the transducer is the use of periodicsignals. Even if the signals are distorted the possible errorstays within the signal period of 20 µm as long as fringecounting is possible. Since the deformation to bemeasured is coded in the phase of the signals rather thanin the amplitude, a synchronous amplitude or offsetchange does not affect the phase measurement if 4 phaseshifted signals are processed. However, this type oftransducer is very sensitive to misalignment. If themeasurement and the reference grating are not properlyaligned parallel, the signal modulation drops practically tozero. As a consequence the risk of a total system failure ishigh, but, if signals are received, a high precision of themeasurement is guaranteed.These advantages allow for transducers that do not haveto be calibrated at cold if the thermal contraction of thegrating material is sufficiently well known. Having a welladjusted set-up a precision better than 1 micron can beachieved due to the high quality of the gratings in use.regleFixationscrewSupportholeMirror (45°)Elastic gratingguidanceCold boretubeBeamscreenReferencegratingAdapterpieceEmitter fibreMeasurementgrating4 Receiver fibresLight source(collimating lensand mirrornot shown)Fig. 4: Optical transducer mounted inside beam screen.2.2 Beam screen deformation during quenchFig. 5 shows a sine-cosine signal pair generated (bysubtracting the 180° phase shifted signals) of thetransducer with electronics inside the magnetic fieldduring a quench at nominal field. This signal pair wasdemodulated and unwrapped using common phasemeasuring techniques. Offset removal and amplitudeequalisation were done by software keeping errors lessthan one eighth of the grating pitch without cumbersomefine-tuning of the transducer. Fig. 6 shows the resultingdeformations of the beam screen for the same quench.The maximal error of these measurements wasdetermined including all possible sources to be less than3 µm for the electronic version and less than 6 µm  for theversion with optical fibres (due to smaller sensingapertures of the read out fibres and not corrected errorsmentioned in Fig. 7). The high quality of the signals inFig. 5 insured that no fringe counting errors occurred.Even one signal was sufficient to determine the highestdeformation (period counts, comp. Fig. 5).-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29Time in sVoltageinVCos-signal : channel 1 - channel 3Sin-signal : channel 2 - channel 4Figure 5 : Signal pair from transducer with electronicsinside the magnetic field during a quench.-100-500501001502002503003500 0.1 0.2 0.3 0.4 0.5 0.6Time in sDeformationinmTransducer with optical fibers* Ripple of double grating frequency.(Reason: constant phase-shiftand amplitude errors)Transducer with electronicsinside the magnetic field*Beam screentemperature: 6 KFigure 6: Horizontal deformation of beam screen during aquench measured at two different locations.-100-50050100150200250300350-250 -200 -150 -100 -50 0BdB/dt in T2/sDeformationinmHeat-up increases resistanceTransducer with electronicsContact of beam screento cold bore tube on one sideSense of rotation due tomagneto resistance0 s8.3 T0.15 s6.2 T0.19 s4 T0.21 s3.5 T160  mcompressionFigure 7: Beam screen deformation versus BdB/dt.2.3 Discussion of the measurementsFor the first time reliable deformation measurementswith a known precision could be performed on a beamscreen at working conditions. Measurements with straingauges [4] and resistors performed in the past were inagreement (rising slopes and maximum deformationswere consistent). A new observation was a compressionof the beam screen at the end of the quench (see Fig. 6).Since the model of Fig. 2 could not describe compression,an explanation had to be found.To investigate the phenomena, Fig. 7 shows thedeformation plotted versus BdB/dt which isapproximately proportional to the Lorentz forces. At thebeginning of the quench the beam screen deforms asexpected from past measurements. Comparison withsimulations could identify slight effects thanks to the highprecision of the transducer (Fig. 7: change of slope due toheat up of the beam screen, sense of rotation due to193Proceedings of the 2001 Particle Accelerator Conference, Chicagodecreasing magneto resistance). About 190 ms afterquench begin, the beam screen leaves the expected(straight) path and is compressed. This compressionpersists until the magnetic forces have vanished.After the quench test, the beam screen was dismountedto generate a comparable compression in the lab. Neithervibration nor bending tests gave compressions in the orderof -100 µm. Only a compression of the beam screenagainst a cold bore tube could generate this signal. Thehigh reliability of the transducer left as only possibleexplanation for the undershoot a contact of the beamscreen with the cold bore tube at the end of the quench.3 MODEL OF BEAM SCREEN CONTACTA slightly unbalanced magnetic field in the magnetyoke was found as an explanation. Fig. 8 shows a sectionof a LHC dipole cold mass. Indicated  in the figure is theloop formed by the beam screen and the external cylinderof the magnets cold mass. The integral of the magneticflux density across the loop is not equal to zero. Thus achange of the magnetic field induces a current I in theloop (superimposed to the eddy currents in Fig. 2). Thiscurrent in combination with the magnetic field in theaperture generates an inward directed force on the beamscreen that is responsible for the lateral contact and thesubsequent compression of the beam screen during aquench.BBFII= 0.08 Tmat B = 8.3 TFigure 8: Model to describe the contact of the beamscreen to the cold bore tube.4 CURRENTS AND FORCESAccording to calculations, the integral of the fluxdensity over a 14.3 m long loop, as indicated in Fig. 8, isequal to 1.145 Tm2 at the nominal field of 8.3 T.Furthermore, calculations demonstrate a proportionalityof the integral to the magnetic field in the aperture. Usingthis linearity the induced voltage can be expressed asUind = dB/dt 0.138 m2. Taking the maximal field decay inthe aperture of 34 T/s the induced voltage is about 4.7 V.Assuming a loop resistance of 15 mΩ results in amaximal current along the beam screen of about 313 A.This value corresponds quite well to measurementsperformed with a real loop when ramping a magnet (up to5 A/s and 1 kA). About 330 A were estimated for thecurrent [5]. Both currents result in a contact force of about1650 N/m at the maximal dB/dt at 5T.Considering that the beam screen is an elastic structure,the width of the loop in Fig. 7 can be taken to determinethe contact force. 210 ms after quench begin, at themoment of the highest field decay, 160 µm compressioncan be seen in Fig. 7. Referring to the compression testsperformed after the quench tests, this corresponds to acontact force of 1300 N/m. Considering the actingmagnetic field of 3.5 T results in a current of about365 A. This calculation assumes a contact forceproportional to BdB/dt. Therefore this contact force has tobe scaled up to the maximal BdB/dt, which results in2000 N/m. However, this high value is not likely to bepresent during a quench since the contact happens afterBdB/dt has reached its maximum (see Fig. 7). At themoment there is no explanation for this time delay.A second approach is to take the load due to eddycurrents at maximum deformation (7500 N/m in eachcurved side of the beam screen at 300 µm) to deduce thecontact force. At the moment when the current Icompensates the eddy currents on one side of the beamscreen the deformation should be zero. In Fig. 7 this is thecase 210 ms after quench begin. At this time Lorentzforces have halved to 3750 N/m. This values representsrather an upper limit for the contact force since thetransducer's fixation screws were elevated above the beamscreen contour by 0.6 mm, thus causing signalamplification due to force concentration. Tests areforeseen to quantify this signal amplification.5 CONCLUSIONSDuring a nominal quench the LHC dipole beam screenexpands horizontally by 300 µm. Shortly after maximalexpansion, eddy currents induced in the beam screenreach their maximum of about 1.8 kA. Superimposed tothese eddy currents, an additional current along the beamscreen, estimated to be 350 A, is induced in an externalloop. At the end of the quench, Lorentz forces generatedby this current in the order of 1500 N/m move andcompress the beam screen against the cold bore tube.Since the dynamics of this effect are not fully understoodyet, investigations are going on. Direct currentmeasurements in the interconnects of the LHC test cell("String 2") will also investigate the propagation of thisadditional current to neighbouring components andmagnets.5 REFERENCES[1] C. Rathjen, "A model to calculate LHC beam screendeformation in a dipole field during quench", Vac.Tech. Note 00-21, CERN LHC/VAC, Dec. 2000.[2] C. Rathjen, "Optical displacement transducer forapplications at cryogenic temperatures and highmagnetic fields", Vac. Tech. Note 00-22, CERNLHC/VAC, Dec. 2000.[3] J. Martinez-Darve et al., "Measurement of themechanical behaviour of the LHC beam screen duringa quench", PAC, Session WPAH035, June 2001.[4] C. Rathjen, “First quench tests of a prototype LHCracetrack type beam screen in a short dipole magnetmodel”, Tech. Note CERN EST-ESI/99-13.[5] P. Pugnat et al., "Induced voltages measured acrosswire loops in a full scale LHC-dipole", LHC-MTA-IN-2000-142, CERN, Dec. 2000.194Proceedings of the 2001 Particle Accelerator Conference, Chicago

Currents in, Forces on and Deformations/Displacements of the LHC Beam Screen Expected during a Magnet Quench

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