FCC-ee is a high luminosity lepton collider with a centre-of-mass energy from 91 to 365 GeV. Due to the machine parameters and pipe dimensions, collective effects due to electromagnetic fields produced by the interaction of the beam with the vacuum chamber can be one of the main limitations to the machine performance. In this frame, an impedance model is required to analyze these instabilities and to find possible solutions for their mitigation. This paper will present the contributions of specific machine components to the total impedance budget and their effects on the beam stability. Single bunch instability thresholds will be estimated in both transverse and longitudinal planes

Belli, Eleonora

Castorina, Giovanni

Migliorati, Mauro

Rumolo, Giovanni

Spataro, Bruno

Zobov, Mikhail

English

Eleonora Belli

Giovanni Rumolo

Giovanni Castorina

Mauro Migliorati

Bruno Spataro

Mikhail Zobov

Archivio della ricerca- Università di Roma La Sapienza

SINGLE BUNCH INSTABILITIES IN FCC-eeE. Belli∗, G. Rumolo, CERN, Geneva, SwitzerlandG. Castorina, M. Migliorati, University of Rome La Sapienza and INFN Sez.Roma1, Rome, ItalyB. Spataro, M. Zobov, INFN/LNF, Frascati (Rome)AbstractFCC-ee is a high luminosity lepton collider with a centre-of-mass energy from 91 to 365 GeV. Due to the machineparameters and pipe dimensions, collective effects due toelectromagnetic fields produced by the interaction of thebeam with the vacuum chamber can be one of the mainlimitations to the machine performance. In this frame, animpedance model is required to analyze these instabilitiesand to find possible solutions for their mitigation. Thispaper will present the contributions of specific machinecomponents to the total impedance budget and their effectson the beam stability. Single bunch instability thresholdswill be estimated in both transverse and longitudinal planes.INTRODUCTIONWithin the Future Circular Collider studies at CERN [1]which aim to design post-LHC particle accelerators, the highluminosity e+e− circular collider FCC-ee is considered as apossible first step towards FCC-hh, a 100 TeV hadron col-lider in the same tunnel of 97.75 km. The lepton colliderhas been designed to cover the beam energy range from45.6 GeV to 182.5 GeV to study the properties of the Z reso-nance, the W and top pair thresholds and the Higgs bosonwith unprecedent precision. Table 1 summarizes the mainbeam parameters at Z running, which represents the mostchallenging scenario from the instability point of view. Thispaper focuses on the impedance model and collective beaminstabilities induced by wakefields in the lowest energy case.It describes the effects of the main machine componentson the single bunch beam dynamics in both transverse andlongitudinal planes, giving special attention to the resistivewall (RW) impedance which represents the main source ofwakefields in the machine.RESISTIVE WALL IMPEDANCEThis section focuses on the impact of the RW impedanceon the single bunch dynamics. For these studies, the vacuumchamber is assumed to be circular with 35mm radius andthree layers: a first inner layer of copper with 2mm thick-ness, then 6mm of dielectric and finally iron with resistivityρ = 10−7Ω-m. A coating of the copper surface is foreseento reduce the Secondary Electron Yield (SEY) of the surface(for the mitigation of the electron cloud build up in the ma-chine) and to improve the pumping system for an optimumvacuum environment during operation. On the basis of thepositive experience of the LHC warm sections [2], it wasdecided to use Ti-Zr-V Non Evaporable Getter (NEG) filmsin order to ensure the required pressure and low background.∗ eleonora.belli@cern.chTable 1: FCC-ee baseline beam parameters, where SR andBS stand for synchrotron radiation and beamstrahlung.Beam energy [GeV] 45.6Circumference C [km] 97.75Number of bunches/beam 16640Bunch population Np [1011] 1.7Beam current I [A] 1.39RF frequency fRF [MHz] 400RF voltage VRF [MV] 100Energy loss per turn [GeV] 0.036Momentum compaction αc[10−5] 1.48Bunch length σz,SR/σz,BS [mm] 3.5/12.1Energy spread σdp,SR/σdp,BS [%] 0.038/0.132Horizontal tune Qx 269.138Vertical tune Qy 269.22Synchrotron tune Qs 0.025Horizontal emittance  x [nm] 0.27Vertical emittance y [pm] 1.0Previous studies [3] pointed out that in the case of FCC-ee the typical NEG film thickness of 1µm makes the RWimpedance responsible of quite low single bunch instabilitythresholds, in both transverse and longitudinal planes. Ithas been demonstrated [4] that under certain assumptionsthe longitudinal and transverse impedances of a two-layerbeam pipe are given by the sum of two terms, one represent-ing the impedance of a single layer pipe and a second termrepresenting an inductive perturbation proportional to thethickness ∆ of the coating:Z ‖ (ω)C' Z0ω4picb{[sgn(ω) − i] δ2 − 2i∆ (1 − σ1σ2)}Z⊥(ω)C' Z02pib3{[1 − isgn(ω)] δ2 − 2i∆sgn(ω) (1 − σ1σ2)}where Z0 is the vacuum impedance, c the speed of light, bthe pipe radius and δ1, σ1 and δ2,σ2 the skin depths andconductivities of the coating and the substrate, respectively.If σ1σ2 << 1 (condition always verified in the FCC-ee case,also taking into account the variation of the NEG resitivitywith frequency [5]), then the second term becomes indepen-dent on the conductivities of the materials and the effects ofthe impedances on the single bunch dynamics are affectedmainly by the thickness of the coating.NEG Thin Films: Experimental ResultsIn this context, NEG thin films with thicknesses below250 nm have been investigated to find the minimum effectivethickness ensuring at the same time a good activation per-formance for vacuum pumping, a low SEY to minimize the9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK052THPAK0523336ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.05 Beam Dynamics and EM FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code Developmentselectron cloud build up in the machine and a reduction of theRW impedance contribution to ensure beam stability duringoperation. Copper samples have been coated with NEG thinfilms at thicknesses of 1000nm, 200nm, 100nm and 50nmvia DC magnetron sputtering [6], obtaining actual thick-nesses of 1100nm, 203nm, 87nm and 30nm, respectively.The surface composition was measured by X-ray Photoelec-tron Spectroscopy (XPS) and the activation performancewas evaluated by the reduction of the area of the oxygenpeak O1s during a cycle of 4 hours up to a temperature of250◦C. Figure 1 shows the O1s peak area as a function ofthe activation temperature: from the activation performancepoint of view, a good candidate for coating is the 100nmthickness that also ensures a margin of safety for the stability,as we will see in the next section. This experimental activityalso includes SEY measurements presented in [7].Figure 1: Activation performance: reduction of the area ofthe oxygen peak from the XPS spectrum after the fourthactivation cycle.The Impact of Thickness on Beam DynamicsThe most important effects of the RW impedance on thesingle bunch dynamics are the Microwave Instability (MI)in the longitudinal plane and the Transverse Mode Cou-pling Instability (TMCI) in the transverse plane. Numericalsimulations with the macroparticle tracking code PyHEAD-TAIL [8] were performed to study the impact of the coatingthickness on the instability thresholds. For these studies,NEG thin films with thicknesses of 1100nm, 200nm, 100nmand 50nm have been considered. The beam parameters usedfor simulations are listed in Table 1.MI Figures 2 and 3 show the bunch lengthening and theenergy spread increase due to the longitudinal RWwakefieldas a function of the bunch population for all the thicknessesunder study. As mentioned before, a coating of 1µm thick-ness makes the bunch unstable, while the thinner film of100nm allows to increase the MI threshold by a factor 7.TMCI The TMCI threshold has been evaluated with theanalytical Vlasov solver DELPHI [9] by taking into accountthe bunch lengthening due to the longitudinal wake (Fig 2).Figure 2: RMS bunch length as a function of the bunch pop-ulation given by numerical simulations by considering onlythe RW impedance produced by NEG films with differentthicknesses.Figure 3: RMS energy spread as a function of the bunch pop-ulation given by numerical simulations by considering onlythe RW impedance produced by NEG films with differentthicknesses. The black dashed line represents the nominalbunch population.In the transverse case, the instability threshold is affected to alesser extent by the coating thickness, because it is increasedby the higher bunch length at the same intensity. As shown inFig. 4, for a coating of 100nm thickness the TMCI thresholdis about a factor 2.5 higher than the nominal bunch intensity.Figure 4: Real part of the frequency shift of the first coherentoscillation modes as a function of the bunch populationfor 100nm coating. The green dashed line represents thenominal bunch intensity.9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK05205 Beam Dynamics and EM FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsTHPAK0523337ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.OTHER IMPEDANCE SOURCESIn addition to the RW impedance, there are other sourcesof wakefields in the machine. At Z running, the RF systemconsists of 52 cavities at 400 MHz with a single cell [10]that will be arranged in groups of four cavities connected by26 0.5m long tapers. In order to cut off the beam halo and tosuppress the background, collimators based on PEP-II andSuperKEKB design [11, 12] are planned to be installed inthe machine, for a total number of 20 (10 for each plane).The impedance contribution of the 10000 absorbers to copewith the synchrotron radiation (SR) has been minimized byusing a circular chamber with 35mm radius and two rectan-gular antechambers on both sides, where the SR absorberswill be installed. This model also includes 4000 Beam Po-sition Monitors [13] and 8000 comb-type bellows with RFshielding [14] to be installed before and after each BPM.Longitudinal Impedance ModelFigure 5: Longitudinal wake potentials for a Gaussian bunchwith nominal bunch length σz = 3.5 mm due to the mainFCC-ee components compared with the RW contribution(blue line).The contribution of all the current machine componentsto the longitudinal impedance budget has been evaluatedby means of ABCI [15] and CST [16] simulations in timedomain for a Gaussian bunch with nominal bunch lengthof σz = 3.5mm. Figure 5 shows the longitudinal wakepotentials of each component. Table 2 summarizes the cor-responding loss factors. The major contribution to the ma-chine impedance is given by the RW with a total loss factorat nominal intensity and bunch length of 210 V/pC. The to-tal dissipated power at nominal intensity is 13.6 MW, abouta factor 3.7 smaller than the total SR power dissipated bythe beam of 50 MW. However, this value of power loss isexpected to be lower due to the bunch lenghtening effect. Byusing as Green function for the PyHEADTAIL code the wakepotential of a bunch with σz ' 110σz,nom, the MI thresholdhas been evaluated by considering all the current machinecomponents and 100nm NEG coating and is about 2.5 ·1011,a factor of 1.5 larger than the nominal bunch intensity, asshown in Fig. 6.Table 2: Power loss contribution of the main FCC-ee com-ponents at nominal intensity and bunch length, in the lowestenergy case of 45.6 GeV.Component Number kloss[V/pC] Ploss[MW]Resistive wall 97.75km 210 7.95Collimators 20 18.69 0.7RF cavities 52 17.14 0.65RF double tapers 13 24.71 0.93BPMs 4000 40.11 1.5Bellows 8000 49.01 1.85Total 359.6 13.6Figure 6: RMS energy spread as a function of the bunchpopulation given by numerical simulations by consideringthe impedance contribution of all the machine components.The black dashed line represents the nominal bunch intensity.CONCLUSIONSIn this paper we have presented the main sources ofimpedance in FCC-ee and their effects on the single bunchdynamics. The RW impedance represents the main sourceof wakefields in the machine and its contribution to theimpedance budget can be reduced by decreasing the thick-ness of the coating needed for pumping and electron cloudmitigation. Numerical simulations and experimental resultshave indicated that the 100nm thickness is a good candidatefor coating, satisfying at the same time impedance, vacuumand electron cloud requirements. The geometric impedancehas been evaluated for important machine components show-ing that the contribution of these elements is up to 5 timessmaller than the RW one. The MI instability threshold isaround 2.5 · 1011, about a factor of 1.5 higher than the nomi-nal bunch intensity. However, it is important to mention thatoperation with beamstrahlung allows to further increase theinstability thresholds in both planes, due to the higher bunchlength and energy spread.ACKNOWLEDGEMENTSThe authors would like to thank P. Costa Pinto, D. Letant-Delrieux, H. Neupert, K. Oide, V. Petit, A. Sapountzis, T.Sinkovits, M. Taborelli, F. Zimmermann for their contribu-tions. This work was supported in part by the EuropeanCommission under the HORIZON 2020 Integrating Activityproject ARIES, grant agreement 730871.9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK052THPAK0523338ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.05 Beam Dynamics and EM FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsREFERENCES[1] Future Circular Collider Study, https://fcc.web.cern.ch[2] P.C. Pinto, "History and potential of Non Evaporable Getter(NEG) technology", presented at Workshop on AdvancedMaterials and Surfaces, 19-20 November 2013, CERN,Geneva, Switzerland, https://indico.cern.ch/event/229108/contributions/1539894/[3] E. Belli, "Impedance model and collective effects forFCC-ee", presented at FCC Week 2017, Berlin, Ger-many, https://indico.cern.ch/event/556692/contributions/2590409/[4] M. Migliorati, E. Belli and M. Zobov, "Impact of the resistivewall impedance on beam dynamics in the Future Circular e+e-Collider", Phys. Rev. Accel. Beams, vol. 21, p. 041001, 2018.[5] E. Koukovini Platia, "High Frequency Effects of Impedancesand Coatings in the CLIC Damping Rings", CERN, Geneva,Switzerland, Rep. CERN-THESIS-2015-152.[6] P. Chiggiato, P. Costa Pinto, "Ti-Zr-V nonevaporable getterfilms: From development to large scale production for theLarge Hadron Collider", Thin Solid Films, vol. 515, 2006.[7] E. Belli et al., "Electron cloud studies in FCC-ee", paperMOPMK012, this conference.[8] PyHEADTAIL, https://github.com/PyCOMPLETE/PyHEADTAIL[9] DELPHI, https://twiki.cern.ch/twiki/bin/view/ABPComputing/DELPHI[10] A. Butterworth, "Cavity design and beam-cavity in-teraction", presented at FCC Week 2017, Berlin, Ger-many, https://indico.cern.ch/event/556692/contributions/2484361/[11] S. DeBarger et al., "The PEP-II movable collimators", No.SLAC-PUB-11752, 2001.[12] T. Ishibashi et al., “Low impedance movable collimatorsfor SuperKEKB”, in Proc. IPAC’17, Copenhagen, Denmark,May 14-19, 2017.[13] H.O.C. Duarte, L. Sanfelici, and S.R. Marques, "Design andimpedance optimization of the SIRIUS BPM button", in Proc.IBIC2013, Oxford, UK, Sep. 16-19, 2013.[14] Y. Suetsugu, M. Shirai, and K. Shibata, "Possibility of comb-type rf shield structure for high-current accelerators", Phys.Rev. ST Accel. Beams, vol. 6, p. 103201, 2003.[15] ABCI, http://abci.kek.jp/abci.htm[16] CST, https://www.cst.com9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW PublishingISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-THPAK05205 Beam Dynamics and EM FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsTHPAK0523339ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.

Single Bunch Instabilities in FCC-ee

FCC-ee is a high luminosity lepton collider with a centre-of-mass energy from 91 to 365 GeV. Due to the machine parameters and pipe dimensions, collective effects due to electromagnetic fields produced by the interaction of the beam with the vacuum chamber can be one of the main limitations to the machine performance. In this frame, an impedance model is required to analyze these instabilities and to find possible solutions for their mitigation. This paper will present the contributions of specific machine components to the total impedance budget and their effects on the beam stability. Single bunch instability thresholds will be estimated in both transverse and longitudinal planes

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Single Bunch Instabilities in FCC-ee

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