During LHC operation, magnet failures may affect the beam optics leading to proton losses in the collimators. These losses, with about 360MJ of stored energy per beam at nominal collision operation, are potentially dangerous for the accelerator equipment. The LHC Machine Protection Systems ensure that the beam is extracted safely before these losses can produce any damage. As a magnet failure develops, so does the distribution of the lost particles, longitudinally along the ring as well as transversally at each collimator. The transversal impact distributions of lost particles at the most affected collimators and their evolution with time have been studied for representative magnet failures in the LHC. It has been found that the impact distribution at a given collimator can be approximated by an exponential function with time-dependent parameters. The average impact parameter ranges from about 7 to $620 \mu$m for the cases studied

Gómez Alonso, A

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LHC-PROJECT-REPORT-116205Sep2008A. Gomez AlonsoEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsTRANSVERSE IMPACT DISTRIBUTION OF THE BEAM LOSSES AT THELHC COLLIMATORS IN CASE OF MAGNET FAILURESDuring LHC operation, magnet failures may affect the beam optics leading to proton losses in thecollimators. These losses, with about 360MJ of stored energy per beam at nominal collision operation, arepotentially dangerous for the accelerator equipment. The LHC Machine Protection Systems ensure that thebeam is extracted safely before these losses can produce any damage. As a magnet failure develops, so doesthe distribution of the lost particles, longitudinally along the ring as well as transversally at each collimator.The transversal impact distributions of lost particles at the most affected collimators and their evolution withtime have been studied for representative magnet failures in the LHC. It has been found that the impactdistribution at a given collimator can be approximated by an exponential function with time-dependentparameters. The average impact parameter ranges from about 7 to 620 μm for the cases studied.Large Hadron Collider ProjectAbstractLHC Project Report 1162CERN,CH-1211 Geneva 23SwitzerlandCERN, Geneva, SwitzerlandPresented atEPAC'08, 11th European Particle Accelerator Conference, Genoa, Italy - June 23-27, 2008TRANSVERSE      IMPACT          DISTRIBUTION        OF     THE      BEAM     LOSSES AT     THE     LHC COLLIMATORS      IN      CASE     OF     MAGNET        FAILURESA. Go´mez Alonso, CERN, Geneva, SwitzerlandAbstractDuring LHC operation, magnet failures may affect thebeam optics leading to proton losses in the collimators.These losses, with about 360MJ of stored energy per beamat nominal collision operation, are potentially dangerousfor the accelerator equipment. The LHC Machine Protec-tion Systems ensure that the beam is extracted safely beforethese losses can produce any damage. As a magnet failuredevelops, so does the distribution of the lost particles, lon-gitudinally along the ring as well as transversally at eachcollimator. The transversal impact distributions of lost par-ticles at the most affected collimators and their evolutionwith time have been studied for representative magnet fail-ures in the LHC. It has been found that the impact distri-bution at a given collimator can be approximated by an ex-ponential function with time-dependent parameters. Theaverage impact parameter ranges from about 7 to 620 μmfor the cases studied.INTRODUCTIONThe Large Hadron Collider (LHC) at CERN will be thehighest energy particle accelerator ever built. At its nom-inal mode of operation it will accelerate protons up to anenergy of 7 TeV, a factor of seven higher than the mostpowerful existing accelerators, while the stored energy perbeam will be a factor of 100 higher.The total energy stored in each proton beam at the LHCis about 360 MJ and the main electrical circuits store morethan 10 GJ. Estimations calculated so far indicate that lo-calized losses of about 1% of the beam at 450 GeV and0.01% at 7 TeV could damage the LHC components.At LHC, primary losses happen always at the collima-tors, being the most restrictive aperture limitations. TheLHC Collimation System has been designed to provide agood cleaning efficiency with normal operating conditions.In this case only particles far from the beam axis hit thecollimator and the average impact parameter is small (from0.3 to 5.07 μm [1]). Also, particles are intercepted first bya primary collimator. However, in case of magnet failure,these conditions do not apply:- All particles can reach the aperture limit if the beamis not extracted in time.- The average impact parameter can reach up to620 μm.- Particles may also hit a secondary collimator first, thusreducing dramatically the cleaning efficiency of thecollimation system.Therefore, the efficiency of the passive protection pro-vided by the collimation system in case of failure dependson two factors that do not need to be taken into accountwhen considering beam losses in normal operating condi-tions: the impact parameter of a collimated particle as wellas the type of collimator that it hits first.CRITICAL MAGNET FAILURESAn estimation of the criticality of magnet failures hasbeen presented in [2]. The transversal distribution of thelosses in a collimator is related to the time constant of thelosses produced by a magnet failure as well as to the typeand position of the failing magnet. Particle tracking hasbeen done with several failure cases in the LHC. These fail-ure scenarios are listed in table 1, together with the mostaffected collimator in each case, for which the impact dis-tribution has been studied.Circuit/Magnet Failure Mode CollimatorRD1.LR1 0 V Collision TCP.C6L7.B1RD1.LR1 Vmax Injection TCSG.6R7.B1RQ5.LR7 0V Injection TCP.B6L7.B1RQ5.LR7 Vmax Injection TCSG.A5L7.B1RQX.R1 Quench Collision TCSG.A4R7.B1MB.A25R3 Quench Collision TCSG.6R7.B1Table 1: Simulated circuits, failures and most affected collimatorin each case. 0 V and Vmax represent the voltage set by the failingpower converter.SIMULATION PROCEDUREThe tracking has been performed with MADX introduc-ing a turn-by-turn variable magnetic field. The particles aretracked for a single turn and the lattice values are changedbefore traking the next one. The time resolution is thereforelimited to 1 turn (89 μs), which is enough for the failuresconsidered where the fastest time constants are at least 70turns (typically, they exceed several hundred turns) [2].The change in the magnetic field is governed by thechange in the current in the magnet. For the simulations, ithas been approximated by analytical formulas as describedin [2].The number of turns while the failure develops can behigh, therefore the number of particles that can be simu-lated in a reasonable time is limited to values between 104and 105. In order to obtain a good resolution for the veryfirst losses, two particle distributions have been tracked foreach failure case: a full Gaussian beam distribution and aGaussian tail distribution with only the outer 0.1% of the 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 0  0.05  0.1  0.15  0.2  0.25  0.3N/NbeamImpact parameter (mm)a: TCP.C6L7.B1. Failure at RD1.LR1 (0V, Collision), σbeam=0.278mm20 turns30 turns40 turns50 turnsAll beam lost 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6N/NbeamImpact parameter (mm)b: TCSG.6R7.B1. Failure at RD1.LR1 (Vmax, Injection), σbeam=1.577mm30 turns35 turns40 turns50 turns60 turnsAll beam lost 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 0  0.01  0.02  0.03  0.04  0.05  0.06  0.07N/NbeamImpact parameter (mm)c: TCSG.6R7.B1. Energy extraction at MB.A25R3 (Collision), σbeam=0.414mm800 turns900 turns1000 turns1100 turns1400 turns1600 turnsAll beam lostFigure 1: Impact distributions after different numbers of turnsfor each dipole failure. The size of the beam in the axis of thecollimator is given for comparison with the width of the impactdistribution.beam. Thus, the obtained resolution for the first lost par-ticles reaches 10−7 for 10000 simulated particles, whichyields acceptable statistics for the first beam losses pro-duced by the failure. The full distribution is useful to obtaina better understanding of the evolution of the losses in caseof failure.The coordinates of the lost particles and the turn arerecorded at the location where each particle is lost. Onlyprimary losses are recorded. When a particle hits a colli-mator it can be scattered back into the beam. This fact isnot taken into account and the particles hitting a collima-tor are considered lost. Studies of further tracking of thescattered particles are presented in [3].IMPACT DISTRIBUTIONS FOR THESIMULATED FAILURESThe impact parameter (α) represents the transversal off-set of a lost particle in a collimator referred to the edge ofthe collimator [1]. The distribution of the impact parameterof all lost particles in a collimator is named hereafter as theimpact distribution for a given failure and collimator.Figure 1 shows the impact distribution for the dipole fail-ure cases that were simulated, recorded at the most affectedcollimators in each case. The width of the impact distribu-tion is strongly dependent on the failure case. Faster fail-ures (Figure 1a and 1b) produce losses with a larger impactdistribution than slower ones (Figure 1c). For comparison,the width of the impact distribution has to be referred to thesize of the beam in the axis the location of the collimatorwhere the losses are recorded.Figure 2 shows the impact distribution for thequadrupole failure cases that were simulated, recorded atthe most affected collimators in each case. A comparisonwith figure 1 suggests that the shape of the impact distri-bution in the case of a quadrupole failure is similar thanfor losses produced by a dipole failure. The amount oflosses recorded on the most affected collimator, however,is smaller in the case of quadrupole failures. This is mainlydue to two reasons:- Quadrupole failures produce losses distributed over alarger number of collimators than dipole failures.- The main disturbance on the beam produced by aquadrupole failure is transverse defocusing, which inthe absence of other effects leads to symmetric lossesin the collimators. Therefore the impact in a jaw ishalf than in the case of a dipole failure, where all thelosses are concentrated in one of the two collimatorjaws.A GENERAL FIT FOR IMPACTDISTRIBUTIONSThe data presented in the above figures show linear andparabolic trends (in logarithmic scale). The functions e(x),g(x) and f(x) (equation 1) have been evaluated as approx-imations of the probability density functions (pdf) of theimpact distributions, in three cases showing distributionswith different shapes.e(x) = Aee−xτeg(x) = Age− x22σg2 (1)f(x) = Afe−x22σ2− xτThe parameters Ag , σg , Ae and τe from e(x) and g(x)have been obtained directly from the impact parameter ofeach lost particle using the method of moments. For f(x) avariation of this method has been applied. Indeed, a betterfit is obtained by settingAf =Ae + Ag2and then applying the method of moments to obtain σ andτ . Table 2 summarizes the accuracy of the fits for eachfunction in three failure cases studied with loss distribu-tions of different shapes.Failure case 1Function e(x) g(x) f(x)RMS of Δyf(0)3.26×10−2 5.49×10−2 1.40×10−2Failure case 2Function e(x) g(x) f(x)RMS of Δyf(0)6.04×10−2 3.90×10−2 3.72×10−2Failure case 3Function e(x) g(x) f(x)RMS of Δyf(0)2.37×10−2 6.92×10−2 3.47×10−2Table 2: Accuracy of the fit for each case of failure studied.Figure 3 shows the evolution of the parameters Af , σ and 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 0  0.5  1  1.5  2  2.5  3N/NbeamImpact parameter (mm)a: TCSG.A5L7.B1. Failure at RQ5.LR7 (Vmax, Injection), σbeam=1.101mm70 turns100 turns120 turns180 turns185 turnsAll beam lost 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0  0.1  0.2  0.3  0.4  0.5N/NbeamImpact parameter (mm)b: TCP.B6L7.B1. Failure at RQ5.LR7 (0V, Injection), σbeam=0.885mm500 turns1000 turns1500 turns3500 turns4500 turnsAll beam lost 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 0  0.05  0.1  0.15  0.2  0.25N/NbeamImpact parameter (mm)c: TCSG.A4R7.B1. Quench at RQX.R1 (Collision), σbeam=0.262mm220 turns240 turns300 turns320 turns340 turnsAll beam lostFigure 2: Impact distributions after different numbers of turnsfor each considered quadrupole failure.τ with time in the case of a powering failure at RD1.LR1(Vmax, injection) recorded at TCP.C6L7.B1. Similar dataare obtained for each failure case and collimator, allowingan approximate reconstruction of the impact distribution atany time from only these three parameters. 0 2 4 6 8 10 0  10  20  30  40  50  60  70 0 0.2 0.4 0.6 0.8 1Afσ, τNumber of turns Impact at TCP.C6L7.B1. Failure at RD1.LR1 (Vmax, injection)Af(t)σ(t)τ(t)Figure 3: Evolution of the parameters of the fit functionwith time for a powering failure of RD1.LR1 (Vmax, injection)recorded at TCP.C6L7.B1.CONCLUSIONSIn case of failure during the LHC operation, particles arelost in the collimators as the failure develops. The evolutionwith time of the transverse distribution of these losses in thecollimators has been studied through tracking simulationswith variable magnetic field using MADX.The simulations show that in most cases the shape of theimpact distribution does not vary significantly with time,and the main change is its amplitude increase (number oflost particles). The impact distribution is smooth in allcases and can be approximated accurately with an expo-nential function. It has been found that slow failures pro-duces losses that are more concentrated in the edge of thecollimator, while faster failures produce larger impact dis-tributions in the collimators.A general fitting function whose parameters can be ob-tained directly from the impact parameter of the lost parti-cles has been found. The evolution of the parameters of thisfunction can be stored at each turn and the shape of the im-pact distribution reconstructed at any given time only fromthese three parameters.REFERENCES[1] G. Robert-Demolaize, “Design and Performance Optimiza-tion of the LHC Collimation System”, LHC Project Report981, CERN, 2006.[2] A. Go´mez Alonso, “Most probable failures in LHC magnetsand time constants of their effects on the beam”, LHC ProjectNote 389, CERN, November 2006.[3] A. Go´mez Alonso, “Tracking tools to estimate the quenchtime constants for magnet failures in LHC”, LHC ProjectNote 389, CERN, November 2006.

Impact Distribution of the Beam Losses at the LHC Collimators in Case of Magnet Failures

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