The project High Luminosity Large Hadron Collider (HL-LHC) calls for a streaking beam intensity and brightness in the LHC machine. In such a scenario, beam-environment electromagnetic interactions are a crucial topic: they could lead to uneven power deposition in machine equipment. The resulting irregular temperature distribution would generate local thermal gradients, this would create mechanical stresses which could lead to cracks and premature failure of accelerator devices. This work presents a method to study this phenomenon by means of coupled electro-thermomechanical simulations. Further, an example of application on a real HL-LHC device is also discussed

Carbajo Perez, David

Giordano, Francesco

Lamas Garcia, Inigo

Mazzacano, Giacomo

Migliorati, Mauro

Teofili, Lorenzo

English

TEOFILI, LORENZO

David Carbajo Perez

Francesco Giordano

Inigo Lamas Garcia

Giacomo Mazzacano

Mauro Migliorati

Archivio della ricerca- Università di Roma La Sapienza

A MULTI-PHYSICS APPROACH TO SIMULATE THE RF-HEATING 3DPOWER MAP INDUCED BY THE PROTON BEAM IN A BEAMINTERCEPTING DEVICE∗L. Teofili†,1,2, M. Migliorati1,2, Sapienza University of Rome, Rome, ItalyD. Carbajo, F. Giordano, I. Lamas, G. Mazzacano, CERN, Geneva, Switzerland1also at CERN, Geneva, Switzerland; 2also at INFN, Rome, ItalyAbstractThe project High Luminosity Large Hadron Collider (HL-LHC) calls for a streaking beam intensity and brightness inthe LHC machine. In such a scenario, beam-environmentelectromagnetic interactions are a crucial topic: they couldlead to uneven power deposition in machine equipment. Theresulting irregular temperature distribution would gener-ate local thermal gradients, this would create mechanicalstresses which could lead to cracks and premature failureof accelerator devices. This work presents a method tostudy this phenomenon by means of coupled electro-thermo-mechanical simulations. Further, an example of applicationon a real HL-LHC device is also discussed.INTRODUCTIONBeam induced RF-Heating on machine systems, i.e. theheat load due to electromagnetic interactions between parti-cles beam and equipment, is a crucial issue for high inten-sity/brightness particle accelerators. Taking as example theLHC, RF-Heating imposed severe limitations on its first op-erational run (2009-2013); some devices were damaged andnumerous actions had to be taken to reduce the RF-Heatingdetrimental effects [1].Well established results [2], show that the beam-equipment interaction causes a total power deposition pro-portional to the square of the beam intensity and to the realpart of the device impedance according to:∆P =(f0eNbeam)2p=+∞∑p=−∞| Λ(pω0) |2 Re [Z ‖(pω0)] (1)Where Nbeam is the beam intensity, e is the elementarycharge, f0 is the revolution frequency of the beam and ω0 =2pi f0, Λ is the normalized beam spectrum and Re[Z ‖]is thereal part of the longitudinal coupling impedance.RF-Heating is split in two contributions:• Resistive wall impedance (RWI) heating. This phe-nomenon distributes the heat flux regularly on the de-vice walls according to the electric conductivity of thematerial and to the inverse of the beam-wall distance.• High Order Modes (HOM) heating. Due to the pres-ence of trapped electromagnetic resonant modes in adevice, the heat flux is distributed in a highly irregularway dependent on the mode.∗ Work supported by LHC Injection Upgrade (LIU)† lorenzo.teofili@uniroma1.itAs a result, while RWI generates smooth temperature maps,HOMs can lead to an uneven temperature distribution. Tem-perature gradients or power deposition in unexpected areasmay induce intense mechanical stresses that can cause fail-ures, or generate other undesired effects as material dam-age [3]. With the increase in beam intensity in the nextgeneration of particle accelerators, the phenomenon has be-come a crucial issue for equipment design, particularly, forthe Beam Intercepting Devices (BIDs) as collimators orscrapers which work in close proximity to the particle beam,and can suffer of severe HOM and RWI heating.Thus, a method that allows to simulate accurately thethermo-mechanical effects of the RF-heating would be ex-tremely helpful in BIDs design. However, at present, justfew studies deal with this problem [3, 4]. In this context,this paper presents a rigorous way to obtain a 3D map of theHOMs RF-heating and explains how to take into accountthe RWI effects, to simulate their thermal and mechanicaleffects on accelerator devices. Further, it presents a practicalapplication of the method on a BID.METHODOLOGYThe current investigation defines a procedure to interfacethe two commercial programs CST studio suite® [5] andANSYS mechanical® [6]. These tools are well known andtested at CERN: CST studio suite® is a standard for deviceimpedance computations [7, 8], while ANSYS mechanical®is widely used for structural and thermal analysis [9–12]. Theformer simulates the RF-Heating map that is subsequentlyimported in the latter to calculate thermal and mechanicaleffects.The entire procedure is depicted in Fig. 1. There are threemain macro-areas: Electromagnetic Simulations (A,B and Cblocks for HOMheating and F input for RWI heating), CST®,Beam Power Dissipation and Interface (D and E blocks),Thermomechanical Simulations (G block), ANSYS®. Ev-ery macro-areas is divided in sub-blocks. Each of them isexplained taking as example the analysis done on the TargetDump Injection Segmented (TDIS) [13]. The TDIS is aBID that will protect LHC downstream equipment duringthe injection phase, absorbing the injected beam in case of amisfiring injection kicker [14].A, Eigenmode SimulationsThe device CAD model for production is taken as geome-try model for the electromagnetic simulations once simpli-fied. Only the electromagnetic important elements should beThisisapreprint—thefinalversionispublishedwithIOP9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK093THPAK0933452ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.05 Beam Dynamics and EM FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsDeviceEigenmodeSimulationsThermal LossComputationDissipated 3DPower MapBeam PropertiesAB CDDissipated PowerSpectrumInterface E3D MapRescalingoutputGThermomechanicalSimulationsGeometryF,ResistiveWallHeatingtime [s]BeamProfile[a.u.]Bunch lenghtDistancebetweenBunch ShapebunchesFigure 1: Block diagram of the methodology with some of the beam properties.considered (screws, little grooves, small surfaces should beremoved, see Fig. 2 for example), in order to obtain the bal-ance between accuracy of the model and simulation speed.Subsequently, the presence of trapped HOM in the device isinvestigated through the CST eigenmode solver [15]. Thesolver provide for each of them the resonating frequency fm,the quality factor Q, the Shunt impedance Rs , the local valueof electric and magnetic fields and the surface currents inthe entire geometry [16]. Since the beam can excite only thefirst N modes in its spectrum bandwidth, henceforth, onlythey should be considered.B, Thermal Loss ComputationBy processing the data from eigenmode, the local dissi-pated power for each mode can be obtained. CST® considerspower losses per unit volume due to Joule effects in dielec-tric materials (D), Eq. (2), [17]. While using the flux ofthe real part of the Poyinting vector, Eq. (3), it computesthe power which flows and is dissipated within the walls ofgood conductors (C) [16].P(x, y, z, fm) = σE2rms(x, y, z, fm) (2)P(x, y, z, fm) =√pi fmµ04σ| Ht (x, y, z, fm) |2 . (3)Where σ is the electric conductivity of the material, Ermsis the root mean square value of the local electric field, Htis the local surface current vector and µ0 is the vacuumpermeability.C, Dissipated 3D Power MapThe results of the previous step can be mapped into thedevice model geometry using the CST thermal solver® [18].This generates a 3D map of the power dissipated on thedevice by each HOM. However, the map does not takeinto account the properties of the real beam that is pass-ing through the device: beam revolution frequency f0 andintensity Nbeam, bunch shape, bunch length, distance be-tween bunches and number of bunches, see Fig. 2 top rightdetail. Indeed, the eigenmode solver calculates the electro-magnetic field pattern solving an eigenmode problem withno excitation applied [19]. This implies that, while the 3Ddissipated power distribution on the device is correct, the lo-cal absolute value is not. There is a scale factor between thepower dissipated by the actual beam and the one computedby the eigenmode solver.D, Dissipated Power SpectrumTo obtain this scale factor the real beam characteristic areconsidered to compute the beam spectrum Λ( f ) and so thethe deposited power ∆P( f ) by Eq. (4), [2]:∆P( f ) = ( f0eNbeam)2 | Λ( f ) |2 Re [Z ‖( f )], (4)where f is a generic frequency. Furthermore, a sensitiv-ity analysis of the impedance induced power should be per-formed. The real part of the device impedance is obtained foreverymode considering its Q factor, its Shunt impedance andits resonating frequency from Eq. (5), [20], where i =√−1.Z ‖( f ) =Rs1 + iQ( fmf− ffm) (5)Then, the impedance profile of each mode is singly movedwithin an arbitrary frequency range to maximise the couplingbetween beam spectrum and impedance, i.e. the maximuminduced power loss. This is the value considered as totalpower dissipated by the beam at the mode frequency ∆P( fm).The frequency tolerance can be set considering the geomet-rical simplifications done to the CAD model, as example weFigure 2: CAD model and simplified TDIS model.Thisisapreprint—thefinalversionispublishedwithIOP9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK09305 Beam Dynamics and EM FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsTHPAK0933453ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.0 0.5 100.51f [GHz]BNS[a.u.]00.51·104Re(Z‖)[Ω]020406080DissipatedPower[W]Figure 3: Power spectrum, Beam normalized spectrum(BNS) and longitudinal impedance real part, in differentscales, refer to colors.used ±10MHz for the TDIS. Figure 3 shows the TDIS longi-tudinal impedance, the HL-LHC beam normalized spectrum(BNS) and the dissipated power spectrum.E, 3D Map RescalingFor every mode, the 3D power map distribution, P(x, y, z),is rescaled and added to the contributions of the other HOMs,according to the following relation:PHOM (x, y, z) =m=N∑m=1∆P( fm)KmP(x, y, z, fm) (6)where N is the number of HOMs considered andKm =1∭D P(x, y, z, fm)dV +∬C P(x, y, z, fm)dS(7)is the inverse of the total dissipated power computed by theCST eigenmode solver. Thus, in Eq. (6), KmP(x, y, z, fm) isthe unit 3D dissipated power map for the mode i.e. its inte-gral on the whole device is one. Subsequently, multiplyingby the expected dissipated power for that mode (∆P( fm)),the 3D power map with the local correct absolute values ofthe dissipated power is obtained. Finally, the heating con-tribution of every HOM is summed in order to have the 3Dmap of the total heating flux PHOM .F, The Resistive Wall Impedance HeatingIn accelerators, in general, one wants to have good con-ductors in close proximity to the beam to limit impedance.In such a case, the total RWI heating can be taken into ac-count using Eq. (1), considering only the broad band part ofthe longitudinal impedance obtained by the CST wakefiledsolver® [21]. The power is then distributed as a heat flux inthe geometry according to the beam-wall distance and theelectric conductivity of the wall material. This contributionis added to the HOM heating PHOM . An example of theRWI heating map for the Proton Shynchrotron Booster Ab-sorber Scraper (PSBAS) can be found in the work of Teofiliet al. [22].G, Output and Thermo-mechanical SimulationsThe map PHOM is imported in the ANSYS workbench®and mapped as a surface heat load for good conductors orImported heat Flux W/m2Figure 4: Example of a mode RF-HOM Heating map im-ported in ANSYS®, for the TDIS core components.Temperature C◦Figure 5: Global Temperature distribution of the TDIS.Von Mises Stress MPaFigure 6: Maximum mechanical stresses in the TDIS.as volume heat load for dielectrics to perform the thermo-mechanical simulations. The same geometrical model ofthe electromagnetic simulations was used with slight modi-fications. An example of imported power map for the TDISis shown in Fig. 4. As validation a steady state thermalsimulations is done, the heating source is set as the PHOMmap along with a fictitious convection on all the bodies. Ifthe RF heat load is correctly imported the power evacuatedby the convection must be the one expected from Eq. (1).RESULTSSuch a method was applied to test the design quality oftwo different BIDs: the PSBAS [22], and the TDIS [23]. Asexample of the achievable results of the method, we reportthe temperature distribution and the mechanical stresses onthe TDIS, Fig. 5 and 6.CONCLUSIONIn this study, we illustrated an accurate multiphysics ap-proach to simulate the RF-Heating mechanical and thermaleffects on accelerator devices. We explained its work flowand we showed examples of its use. As expected, the methodrevealed possible critical points of the design providing tem-perature and stresses maps. Future work will benchmarksimulation results against measurements on physical devicesto fully validate the method. We believe that this could be akey approach to deal with RF-heating design problems offuture high intensity, low emittance hadron accelerators.Thisisapreprint—thefinalversionispublishedwithIOP9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK093THPAK0933454ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.05 Beam Dynamics and EM FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsREFERENCES[1] B. Salvant et al., “Beam Induced RF Heating in LHC in2005”, in Proc. 7th Int. Particle Accelerator Conf. (IPAC’16),Busan, Korea, May 2016, paper MOPOR008, pp. 602–605.[2] M. Furman, H. Lee and B. Zotter, “Energy loss of bunchedbeams in RF cavities”, Lawrence Berkeley Laboratory,Berkeley, California, Rep. SSC-086, 1986.[3] D. Lipka, “Heating of a DCCT and a FCT due to wake lossesin PETRAIII, simulations and solutions”, presented at theSimulation of Power Dissipation & Heating from WakeLosses Workshop, Diamond Light Source, Oxfordshire, UK,Jan. 2013, unpublished.[4] C. Zannini, “Multi-physics simulations of impedance effectsin accelerators”, presented at the ICFA Mini-Workshop onImpedances and Beam Instabilities in Particle Accelerators,Benevento, Italy, Sept. 2017, unpublished.[5] CST Studio Suite, https://www.cst.com/products/csts2[6] ANSYS, https://www.ansys.com/[7] C. Zannini, “Electromagnetic Simulation of CERN ac-celerator Components and Experimental Applications”,Ph.D. thesis, Phys. Dept., Ecole Polytechnique, Lausanne,Switzerland, 2010.[8] B. Salvant, “Impedance model of the CERN SPS and aspectsof LHC single-bunch stability”, Ph.D. thesis, Eng. Dept.,Ecole Polytechnique, Lausanne, Switzerland, 2013.[9] A. Dallocchio, “Study of Thermo-mechanical effects inducedin Solids by High Energy Particle Beams: Analytical andNumerical Methods”, Ph.D. thesis, Phys. Dept., Politecnicodi Torino, Torino, Italy, 2008.[10] C. Torregrosa, “Comprehensive Study for an OptimizedRedesign of the CERN’s Antiproton Decelerator Target”,Ph.D. thesis, Eng. Dept., Universidad Politecnica de Valencia,Valencia, Spain, 2017.[11] G. Romagnoli et al., “Design of the New PS InternalDumps, in the Framework of the LHC Injector Upgrade(LIU) Project”, in Proc. 8th Int. Particle AcceleratorConf. (IPAC’17), Copenhagen, Denmark, May 2017, paperWEPVA109, pp. 3521–3523.[12] I. Lamas et al., “LHC Injection Protection Devices,Thermo-mechanical Studies through the Design Phase”,in Proc. 7th Int. Particle Accelerator Conf. (IPAC’16),Busan, Korea, May 2016, paper THPMY019, pp. 3698–3701.[13] D. Carbajo Perez et al., “Operational Feedback and Analysisof Current and Future Designs of the Injection ProtectionAbsorbers in the Large Hadron Collider at CERN", in Proc.8th Int. Particle Accelerator Conf. (IPAC’17), Copenhagen,Denmark, May 2017, paper WEPVA108, pp. 3517–3520.[14] C. Bracco, A. lechner, D. Carbajo, A. Perillo, "TDIS -Functional Specification". CERN, 2017, EDMS 1865250.[15] CST Studio Suite: Eigenmode Solver, https://www.cst.com/products/cstmws/solvers/eigenmodesolver[16] E. Jensen, “RF Cavity Design”, in CAS - CERN AcceleratorSchool: Advanced Accelerator Physics Course, Trondheim,Norway, 18-29 Aug 2013, edited by W. Herr, CERN-2014-009, (CERN, Geneva, 2014), pp. 405–429.[17] J. Jackson, Classical electrodynamics, 3rd ed. edition, NewYork, NY, USA, Wiley, 1999.[18] CST Studio Suite: Thermal Solver, https://www.cst.com/products/cstmps/solvers/solverthermal[19] CST Studio Suite® online help, "Eigenmode SolverOverview".[20] H. 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(IPAC’18), Vancouver,Canada, May 2018, paper 2585, this conference..Thisisapreprint—thefinalversionispublishedwithIOP9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK09305 Beam Dynamics and EM FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsTHPAK0933455ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.

A multi-physics approach to simulate the RF heating 3D power map induced by the proton beam in a beam intercepting device

The project High Luminosity Large Hadron Collider (HL- LHC) calls for a streaking beam intensity and brightness in the LHC machine. In such a scenario, beam-environment electromagnetic interactions are a crucial topic: they could lead to uneven power deposition in machine equipment. The resulting irregular temperature distribution would gener- ates local thermal gradients, this would create mechanical stresses which could lead to cracks and premature failure of accelerator devices. This work presents a method to study this phenomenon by means of coupled electro-thermo- mechanical simulations. Further, examples of applications on real HL-LHC devices is also discussed.The project High Luminosity Large Hadron Collider (HL-LHC) calls for a streaking beam intensity and brightness in the LHC machine. In such a scenario, beam-environment electromagnetic interactions are a crucial topic: they could lead to uneven power deposition in machine equipment. The resulting irregular temperature distribution would generate local thermal gradients, this would create mechanical stresses which could lead to cracks and premature failure of accelerator devices. This work presents a method to study this phenomenon by means of coupled electro-thermo-mechanical simulations. Further, an example of application on a real HL-LHC device is also discussed

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A Multi-Physics Approach to Simulate the RF Heating 3D Power Map Induced by the Proton Beam in a Beam Intercepting Device

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A multi-physics approach to simulate the RF heating 3D power map induced by the proton beam in a beam intercepting device

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