The Super Proton Synchrotron SPS will be used as injector for the Large Hadron Collider LHC and needs adaptation to meet LHC requirements. The SPS injection kicker magnets MKP will undergo important modifications to comply with the requirements on magnetic field rise-time and ripple. The injection kicker presently installed has a return conductor of beryllium to minimise the risk of metal evaporation from its surface due to heating caused by beam impact. In the context of refurbishing the MKP to satisfy LHC requirements these conductors need replacement, preferably with a less delicate material. This article presents the transient thermal analysis of energy deposition caused by beam loss on the conductor plate. The expected time structure of the beam is taken into account. Simulations comparing different conductor materials have been performed, leading to the result that a significantly cheaper and fully inoffensive titanium alloy can satisfy the needs

Knaus, P

Uythoven, J

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN – SL DIVISIONCERN-SL-2000-034 BTTRANSIENT THERMAL ANALYSISOF INTENSE PROTON BEAM LOSS ON AKICKER MAGNET CONDUCTOR PLATEP. Knaus, J. UythovenAbstractThe Super Proton Synchrotron SPS will be used as injector for the Large Hadron Col-lider LHC and needs adaption to meet LHC requirements. The SPS injection kicker magnetsMKP will undergo important modifications to comply with the requirements on magneticfield rise-time and ripple. The injection kicker presently installed has a return conductor ofberyllium to minimise the risk of metal evaporation from its surface due to heating causedby beam impact. In the context of refurbishing the MKP to satisfy LHC requirements theseconductors need replacement, preferably with a less delicate material.This article presents the transient thermal analysis of energy deposition caused by beamloss on the conductor plate. The expected time structure of the beam is taken into account.Simulations comparing different conductor materials have been performed, leading to theresult that a significantly cheaper and fully inoffensive titanium alloy can satisfy the needs.Presented at EPAC2000, 26-30 June 2000Vienna, AustriaGeneva, SwitzerlandJuly 2000TRANSIENT THERMAL ANALYSIS OF INTENSE PROTON BEAM LOSSON A KICKER MAGNET CONDUCTOR PLATEP. Knaus, J. Uythoven, CERN, Geneva, SwitzerlandAbstractThe Super Proton Synchrotron SPS will be used as injectorfor the Large Hadron Collider LHC and needs adaption tomeet LHC requirements. The SPS injection kicker magnetsMKP will undergo important modifications to comply withthe requirements on magnetic field rise-time and ripple.The injection kicker presently installed has a return con-ductor of beryllium to minimise the risk of metal evapora-tion from its surface due to heating caused by beam impact.In the context of refurbishing the MKP to satisfy LHC re-quirements these conductors need replacement, preferablywith a less delicate material.This article presents the transient thermal analysis ofenergy deposition caused by beam loss on the conductorplate. The expected time structure of the beam is takeninto account. Simulations comparing different conductormaterials have been performed, leading to the result thata significantly cheaper and fully inoffensive titanium alloycan satisfy the needs.1 INTRODUCTIONA study is presented of the damage expected to be causedby beam loss in the MKP hadron kicker magnet during in-jection into the SPS. The energy deposition on the returncurrent conductor plate actually made of beryllium (Be) iscompared to a less delicate titanium alloy, Ti6Al4V. Rele-vant material properties are listed in Table 1. The possiblefailure modes, resulting in different beam impact angles,were determined and the most critical scenario analysed indetail. The Monte-Carlo code FLUKA [1] was used forthe simulation of the instantaneous energy deposition bythe beam and its secondary particles. The transient thermalanalysis is then performed by numerical integration of thediffusion equation.2 SPS INJECTION KICKER SYSTEMThe SPS injection kicker magnets MKP [2] are of the trav-elling wave type with the ferrite yoke, matching capaci-tive plates, HV and return conductor as a part of the vac-uum system (Figure 1). For the injection of the LHC typelead ion beam in the SPS a field rise-time of less than115 ns is required. To obtain this short rise-time the mag-nets presently installed will be increased in characteristicimpedance from 12.50 to 16.67   and the number of cellswill be decreased from 22 to 17. This reduction requires ashortening of the actual Be return conductor. As Be dust isTable 1: Material properties of Be and Ti6Al4V at 20  C.In the simulation the temperature dependence of these pa-rameters is taken into account.Parameter Be Ti6Al4VDensity  [g/cm ] 1.85 4.43Specific heat  [J/(kg K)] 1840 561Therm. conductivity  [W/(m K)] 147 6.6Diffusivity  [cm	 /s] 0.42 0.029highly toxic, an alternative conductor material has been in-vestigated. The modified injection kicker system will con-sist of 16 travelling wave magnets, located in four differentvacuum tanks (Figure 2). The return conductor limits thehorizontal physical aperture towards the inside of the SPS(negative horizontal position in Figure 2). Due to bad steer-ing in the transfer line it can not be excluded that injectedbeam hits the return conductor. Optics calculations weremade to determine the angles under which the beam canimpinge on the conductor. The possible angles range fromless than 1 mrad to a few mrad. As the path length of thebeam through the conductor determines the amount of en-ergy deposited, the worst case, a 0  angle between incidentbeam and conductor plate, is taken for the thermal analysiscalculations.Figure 1: MKP magnet gap limited by return current con-ductor (1), high voltage conductor (2) and ferrites (3).3 SPS BEAM TYPESDuring the LHC era three beam types will be injected inthe SPS: a 26 GeV p beam for LHC, a 14 GeV p beam forCNGS (CERN Neutrino beam to Gran Sasso) or fixed tar-get physics, as well as a 5.11 GeV/u Pb	 beam for LHCor fixed targed physics. From the point of view of expecteddamage in case of beam loss the p beam for LHC repre-sents the most critical case, because of its high intensityand brightness. The present study focuses on this beam.0.1-00.10 10longitudinal position [m]0.2Particle LHCp=(1)(2) (3)(4)20(5)Septum5040(6)30dumped beaminjected beamOptics: standard dist. =Size of injected beam is 5 sigmadp/pEmittance==0.00110.11 mmmradHV3HV2HV1===48.448.448.4kVkVkVmm35.8mrad0 / 5.5=ThetaMDSHQuad displ. = -4.8 mmmrad-1.62=angleSeptumhorizontal position [m]Figure 2: Layout of the SPS injection region with the MKP kicker magnets. The numbers in the drawing correspondto the following elements: (1) injection septum magnet, (2) high–energy beam dump, (3) quadrupole magnet, (4) kickermagnet vacuum tanks, (5) dump magnet for injected beam, (6) beam dump for the injected beam.3.1 SPS Proton Cycle For LHCThe LHC proton cycle in the SPS [3] will consist of ei-ther three or four PS injections at 3.6 s intervals: the in-jection plateau will last up to 10.8 s. To bring the beamfrom 26 GeV/c to 450 GeV/c a 8.3 s acceleration phase isrequired. A 1 s flat top is presently assumed to prepare theextraction equipment and about 1.5 s are reserved to resetthe RF system and prepare the next injection. This resultsin a total SPS proton cycle of 18.0 s or 21.6 s, for three orfour PS batches respectively.Each PS batch contains 72 bunches, spaced by 25 ns.For the ultimate LHC beam the single bunch intensity willbe 1.70 10  p. A three-batch SPS cycle will thus accel-erate 3.67 10 p while the four-batch intensity will rise to4.90 10 p. The described SPS cycle is repeated 12 timesfor each LHC ring. The three– and four–batch cycles willbe interleaved in the form 334 334 334 333 in order to filleach ring with a total of 2808 bunches.4 ENERGY DEPOSITIONCALCULATIONS4.1 Energy to Temperature ConversionA small amount of energy  deposited in a volume of a material with density  causes a temperature rise determined by    . The proportionalityconstant   is the specific heat of the considered material.The larger the value of   , the smaller the temperature risecaused by an energy deposit  . For important energy de-positions the specific heat can no longer be considered asconstant, but its temperature dependence must be taken intoaccount. The specific heat ﬀﬁﬃﬂ for the two materials ofinterest, beryllium and Ti6Al4V, is shown in Figure 3. Now must be extracted from "!$#  !ﬀﬁ%ﬂ&' (1)by solving numerically for the upper limit of the integral.The conductor temperature before the beam impact is )( .0 100 200 300 400 500 600 700Ti6Al4V6306506705705906102600280018002400Be2000Ti6Al4V2200temperature T [ C]°ccpp(T) [J/(kg K)](T) [J/(kg K)]BeFigure 3: Specific heat   ﬀ*ﬃﬂ of Be and Ti6Al4V [4].4.2 Instantaneous Energy DepositionBeam impact on the MKP kicker produces a hadronic andelectromagnetic cascade resulting in energy deposition allalong the conductor plate. For the longest possible particletrajectory in matter, i.e. for a zero angle beam impact onthe conductor, the longitudinal total energy deposition pro-file was simulated by FLUKA. The equivalent temperatureincrease  in a slab of 52 bins of size +-, .0/1+-, ./+2.3, . mmeach, all along a conductor that was hit centrally by a PSbatch is displayed in Figure 4. The curves shown corre-spond to a 1.0 and a 2.5 mm thick conductor plate of eitherBe or Ti6Al4V. As long as the beam size is larger than theconductor, any further increase in conductor thickness willresult in a higher temperature along the bins on the beamaxis. The reason is that secondary particles produced out-side the central bins are scattered such that they end up inthe central bin slab and contribute to the energy depositedthere. For this to happen the impact of the primary protonmust be less than a Molie`re radius away from the centralbin.Similar temperature profiles are obtained for both ma-terials. Due to the lower density of beryllium the Bethe-Bloch formula predicts a lower 54'6 and the high valuesof   ﬀﬁ%ﬂ cause the corresponding temperature increase tobe modest: the temperature profiles reach maxima of 5.6  Cfor a 1 mm and 6.4  C for a 2.5 mm Be conductor as com-pared to the 22 and 26  C for Ti6Al4V.temperature increase [ C]o2.5 mm1.0 mm234560 100 200 300 400 500conductor length [mm]Be2.5 mm2520151050 100 200 300 400 500Ti6Al4Vconductor length [mm]1.0 mmtemperature increase [ C]oFigure 4: Instantaneous longitudinal temperature increasecaused by a single PS proton batch impinging on a 1.0 and2.5 mm thick Be and Ti6Al4V conductor.4.3 Transient Thermal AnalysisIn case of repeated beam loss the temperature builds upwith time and leads to a hot spot on the conductor: mate-rial could sublimate from its surface and be deposited onsensible parts of the kicker which could provoque sparkingor even a short circuit.To determine the peak temperature that may occur thebeam time structure must be taken into account: everyinjected batch measures 1.80 7 s only (72 bunches, 25 nsspacing) and thus its energy deposition is considered in-stantaneous. Then 3.6 resp. 10.8 s are left to the inducedtemperature distribution to diffuse (Figure 5). The temper-ature distribution ﬃﬀﬁ698;:"ﬂ before injection of the subsequentbatch is determined by numerical solution of the diffusionequation <>=ﬃﬀﬁ698;:"ﬂ?@A/<	Bﬃﬀﬁ698;:"ﬂ (2)with the initial condition ﬃﬀﬁ698C.DﬂﬃE)(&ﬀﬁ6Fﬂ and boundaryconditions  B ﬀHGJIK8;:"ﬂ9@LJM/NﬃﬀCGJI'8;:"ﬂ quantifying the heatflux through the top and bottom boundary of the conductor(cf. (1) in Figure 1). Diffusivity  and Biot’s number M aretemperature dependent.Biot’s number is defined as the ratio of convection O andthermal conductivity Pﬀ*ﬃﬂ . It is also weighted with the ra-tio between the contact surfaces of the conductor and thestainless steel support which is 2.5:1. A particular prob-lem resides in finding a significant numerical value for Mbecause the convection coefficient O depends strongly oncharacteristics of the contact surfaces like surface rough-ness, contact pressure, presence of an oxide layer or even-tually presence of a contact liquid in the interspace betweenthe two materials. An approximate numerical value ofQ.1..SR42TU	>V for a stainless steel to stainless steel contact[5] was assumed. The influence of under– and overestimat-ing this value by a factor 100 was examined and is foundto cause only a minor change of G5+2. % in the equilibriumtemperature reached after about 100 injections (Figure 6).The temperature increase  with every new injectionadds to the remainings of the previous injection. Though, will decrease with increasing temperature because ofthe temperature dependence of the specific heat   ﬀﬁ%ﬂ . AtShot1454035302520- 4 - 2 0 2 4y [cm]t=3.6st=0sT[C]°T[C]°20406080100120140t=216.0st=226.8s42]cm[y0- 24-Shot39Figure 5: Instantaneous transverse temperature profile(continuous line) in a 2.5 mm thick Ti6Al4V conductor and3.6 resp. 10.8 s later (dashed line).some point an equilibrium between additional temperaturerise by new injections and diffusion is reached: this equilib-rium temperature is 30  C for Be and 190  C for the titaniumalloy (Figure 6). Cooling by thermal radiation is negligibleat these temperatures.2550751001251501750 100 200 300 400time [s]500 600Ti6Al4VBetemperature T [ C]oFigure 6: Temperature built-up of the hottest spot on theTi6Al4V conductor due to continued beam loss. A non-critical equilibrium temperature is found.5 CONCLUSIONSThe maximum temperature attained by repeated LHC typeproton beam impact in a Ti6Al4V conductor is 190  Cand is about six times higher than the maximum of 30  Creached in pure beryllium. Nevertheless this value is fullyacceptable: no material sublimation is expected.Due to the toxicity of beryllium dust special care mustbe taken when machining the material. By avoiding thismachining considerable financial savings were realized.6 REFERENCES[1] A. Fasso`, A. Ferrari, J. Ranft, P. Sala, “Fluka 99 User’s Man-ual”, 1999.[2] J. Bonthond, L. Ducimetie`re, G. Schro¨der, J. Uythoven,G. Vossenberg, “The Future of the SPS Injection Channel”,PAC’99, New York, 1999.[3] P. Collier, “SPS Cycles for LHC Injection”, LHC-PLC meet-ing 00-59, http://sl.web.cern.ch/SL/sli/Cycles.htm, Geneva,May 2000.[4] P. Knaus, J. Schinzl, N. Stapley, “MATPROP: TheOn-Line SL Materials DataBase”, WWW access athttp://oraweb01:9000/matprop/owa/accisweb.welcome,Geneva, April 2000.[5] G. Guglielmini, C. Pisoni, “Elementi di Trasmissione delCalore”, editoriale Veschi, Milano, 1990.

Transient Thermal Analysis of Intense Proton Beam Loss on a Kicker Magnet Conductor Plate

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