A very important issue for the Future Circular Collider (FCC) is represented by collective effects due to the selfinduced electromagnetic fields, which, acting back on the beam, could produce dangerous instabilities. In this paper we will focus our work on the FCC electron-positron machine: in particular we will study some important sources of wake fields, their coupling impedances and the impact on the beam dynamics. We will also discuss longitudinal and transverse instability thresholds, both for single bunch and multibunch, and indicate some ways to mitigate such instabilities

Alexander, Novokhatski

Belli, Eleonora

Castorina, Giovanni

Migliorati, Mauro

Mikhail, Zobov

Persichelli, Serena

Spataro, Bruno

English

A very important issue for the Future Circular Collider (FCC) is represented by collective effects due to the self-induced electromagnetic fields, which, acting back on the beam, could produce dangerous instabilities. In this paper we will focus our work on the FCC electron-positron machine: in particular we will study some important sources of wake fields, their coupling impedances and the impact on the beam dynamics. We will also discuss longitudinal and transverse instability thresholds, both for single bunch and multibunch, and indicate some ways to mitigate such instabilities

Novokhatski, Alexander

Zobov, Mikhail

CERN Document Server

Coupling Impedances and Collective Effects for FCC-ee

Eleonora Belli

Mauro Migliorati

CASTORINA, GIOVANNI

Bruno Spataro

Mikhail Zobov

Alexander Novokhatski

Serena Persichelli

Archivio della ricerca- Università di Roma La Sapienza

COUPLING IMPEDANCES AND COLLECTIVE EFFECTS FOR FCC-eeE. Belli∗, M. Migliorati, University of Rome La Sapienza, RomeG. Castorina, B. Spataro, M. Zobov, INFN/LNF, Frascati (Rome)A. Novokhatski, SLAC, Menlo Park, CaliforniaS. Persichelli, LBNL, Berkeley, CaliforniaAbstractA very important issue for the Future Circular Collider(FCC) is represented by collective effects due to the self-induced electromagnetic fields, which, acting back on thebeam, could produce dangerous instabilities. In this paper wewill focus our work on the FCC electron-positron machine:in particular we will study some important sources of wakefields, their coupling impedances and the impact on the beamdynamics. We will also discuss longitudinal and transverseinstability thresholds, both for single bunch and multibunch,and indicate some ways to mitigate such instabilities.INTRODUCTIONThe FCC-ee is an e+e− circular collider designed to coverthe beam energy range from the Z pole (45.6 GeV) to the toppair threshold (175 GeV). It would be the first step towardsthe FCC-hh [1], a 100 TeV hadron collider in the same tunnelof 97.75 km. Collective effects represent a serious issue forsuch a kind of machine, since they can produce instabilitiesand limit its operation and performance. In this paper wewill focus on single bunch and multi bunch instabilities forthe Z pole caused by the resistive wall (RW) and describeother important impedance sources, i.e. Beam PositionsMonitors (BPMs), tapers and bellows with RF fingers. Forreference, Table 1 shows the FCC-ee beam parameter listused for these studies [2].Table 1: FCC-ee Beam Parameter ListBeam energy [GeV] 45.6Circumference C [km] 97.75Bunches/beam 73770Bunch population [1011] 0.4Beam current I [A] 1.45Rf frequency fRF [MHz] 400RF voltage VRF [MV] 88.8Momentum compaction αc[10−5] 1.465Bunch length σz [mm] 3.6Energy spread σe [%] 0.037Betatron tunes Qx\Qy 265.14\267.22Synchrotron tune Qs 0.0234RESISTIVE WALLWAKE FIELDSWhen the beam passes through the vacuum chamber, itinduces currents on the pipe walls. If the beam pipe walls∗ eleonora.belli@roma1.infn.ithave a finite resistivity, these currents extend behind theposition of the charges, creating electromagnetic fields whichcan act on the following particles and perturb their motion byincreasing the amplitude of their oscillations. This instabilitycan occur in both longitudinal and transverse directions [3,4].In the following, we will focus on the main single buncheffects due to the RW on the beam dynamics, by consideringa 35 mm radius vacuum chamber with three layers (a firstlayer of copper with 2 mm thickness [5], then 6 mm ofdielectric and finally iron with resistivity ρ = 10−7Ωm) anddifferent coatings of the pipe walls:• Amorphous Carbon (AC)thk = 200 nm, ρ = 10−4 Ωm [5]• Non-Evaporable Getter (NEG)thk = 1µm , ρ = 10−6 Ωm [6]• Titanium Nitride (TiN)thk = 200 nm, ρ = 0.5 · 10−6 Ωm [7, 8]All these materials are characterized by a low SecondaryElectron Yield (SEY) and a low desorption yield that couldreduce significantly the electron cloud build up in the ma-chine [9, 10]. Figure 1 shows the real and imaginary part ofthe transverse and longitudinal impedances due to RW as afunction of the frequency for all the cases mentioned above.These impedances have been obtained from the Impedance-Wake2D code [11] and will be used in the following to ana-lyze the effects of the RW on the beam dynamics.Single Bunch EffectsThis section is focused on the most important effects of theRWon the single bunch dynamics: theMicrowave Instability(MI) and the Transverse Mode Coupling Instability (TMCI)in the longitudinal and transverse planes, respectively. Thesetwo kinds of instability can limit the bunch intensity in theaccelerator: it is well known from the theory [12] that thefrequencies of the intra-bunch modes depend on the bunchintensity and as it increases the mode frequencies shift andmerge, giving rise to the instability. The instability thresholdis localized in the point where there is the mode coupling.Above this threshold, the bunch is lost in the transverse casewhile in the longitudinal case there is an increase of thebunch length and the energy spread and sometimes bunch in-ternal oscillations can be observed which could be particularharmful in beam-beam collisions.MI In order to evaluate the MI threshold, several simu-lations were performed by using the macroparticle trackingcodes PyHEADTAIL [13] and SBSC [14, 15]. Figs. 2, 3THPAB020 Proceedings of IPAC2017, Copenhagen, DenmarkISBN 978-3-95450-182-33734Copyright©2017CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsFigure 1: Real and imaginary part of the transverse (top)and longitudinal (bottom) RW impedances as a function ofthe frequency in the case of no coating, NEG coating, TiNcoating and Carbon coating.show the bunch lengthening and the energy spread increasedue to the RW wakes for all the coatings under study. TheNEG coating gives a MI threshold around the nominal bunchpopulation, while the threshold for TiN and AC coatings isabout 1.6− 1.8 · 1011, i.e. four times larger than the nominalintensity.Figure 2: RMS bunch length as a function of the bunchintensity given by PyHEADTAIL by considering only theRW impedance in the case of no coating and NEG, TiN andAC coatings.TMCI As in the longitudinal case, the TMCI thresholdhas been evaluated with PyHEADTAIL, by including alsothe bunch lengthening due to the longitudinal wake of Fig. 2.All the coatings show a good margin of safety. As an ex-Figure 3: RMS energy spread as a function of the bunchintensity given by PyHEADTAIL by considering only theRW impedance in the case of no coating and NEG, TiN andAC coatings.ample, Fig. 4 shows the real part of the frequency shift ofthe first two radial modes for the first five azimuthal modesgoing from -2 to 2 as a function of the bunch population, inthe case of Carbon coating.Figure 4: TMCI threshold evaluated with PyHEADTAILby taking into account the bunch lengthening due to thelongitudinal wake in the case of Carbon coating.Multi Bunch EffectsIn case of long range transverse and longitudinal wakefields, coupled bunch modes have to be taken into account.In the transverse plane, the instability growth rate depends onthe real part of the coupling impedance [3,4] which dependsin turn on the sign of the frequency. This means that modeswill be unstable for negative frequencies. With the parameterlist given in Table 1, themost dangerous coupled bunchmodeis µ = 73504 with the lowest negative frequency shown inFig. 5. The corresponding growth rate is about 494.8 s−1,which means a rise time of about 6 turns. Therefore, a robustfeedback is necessary to cope with the fast instability. Forthe longitudinal case, refer to [3, 4].OTHER IMPEDANCE SOURCESBesides the RW, there are other important sources ofimpedance in the machine to be studied with particular care.Proceedings of IPAC2017, Copenhagen, Denmark THPAB02005 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsISBN 978-3-95450-182-33735 Copyright©2017CC-BY-3.0andbytherespectiveauthorsFigure 5: Coupled bunch spectrum and real part of the RWimpedance in the case of no coating as a function of thefrequency for the fractional tune νβ = 0.14.In [3, 4, 9], the beam coupling impedance for the interac-tion region vacuum chamber, synchrotron light absorbersand RF cavities with tapers has been evaluated. In additionto these impedance sources, diagnostic elements like four-button BPMs [16] (Fig. 6.a) are planned to be installed inthe machine, for a total number of about 4000. Because ofthe particular shape of the vacuum chamber in the arcs [17],a special type of winglet-to-circular tapers (Fig. 6.b) hasbeen designed for this purpose, for a total number of 4000double tapers. 8000 bellows with RF fingers (Fig. 6.c) willbe installed before and after each BPM. In order to evalu-ate the contribution of these other devices to the machineimpedance budget, CST [18] wakefield simulations in timedomain were performed by using a Gaussian bunch of 4mmRMS bunch length. As example, the longitudinal wake po-tentials are shown in Fig. 7 and compared with the RW one,computed analytically as the convolution between the wake-field obtained from ImpedanceWake2D in the case of nocoating and a 4mmGaussian bunch. It is clear that the contri-butions of tapers and bellows cannot be neglected and theirimpact on the beam dynamics would result in a decrease ofthe MI threshold. In principle, it would be possible to avoidtapers and use different designs for flanges and bellows, forexample the comb-type RF shield proposed for KEK [19].Figure 7: Longitudinal wake potentials for a 4mm Gaussianbunch given by RW, BPMs, tapers and bellows with RFfingers.CONCLUSIONSIn this paper we have presented the most important collec-tive effects issues for FCC-ee. In particular, the MI thresholdis around the nominal bunch intensity for the NEG coatingwhile it is about a factor of 4 higher in the case of TiN andAC. The single bunch TMCI does not seem to be danger-ous: its threshold is far beyond the nominal bunch intensity.The rise time of the transverse multibunch instability is asfast as 6 revolution turns: this means that a robust feedbacksystem is required for the instability suppression. The ge-ometric impedance has been evaluated for many vacuumchamber components showing that these elements can givecontributions comparable with the RW one. Our studieshave indicated that the considered Sirius BPM design is agood candidate from the impedance point of view whilethe impedance due to the other devices can be improvedby reducing the number of tapers (by placing BPMs andquadrupoles on the vacuum chamber with winglets) andconsidering the use of the comb-type bellows and flangessimilar to those of SuperKEKB.Figure 6: CST models of BPMs, tapers and bellows with RF fingers.THPAB020 Proceedings of IPAC2017, Copenhagen, DenmarkISBN 978-3-95450-182-33736Copyright©2017CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsREFERENCES[1] https://tlep.web.cern.ch/content/fcc-hh[2] K. Oide, “A preliminary 60 degree optics for Z”, presentedat the 49th FCC-ee Optics Design meeting, 17 March 2017,CERN, https://indico.cern.ch/event/623722/[3] M. Migliorati et al., “Collective effects issues for FCC-ee”,presented at 58th ICFAAdvanced BeamDynamicsWorkshopon High Luminosity Circular e+e-Colliders, Daresbury, UK,24-27 October 2016, paper TUT3AH1, unpublished.[4] E. Belli, M. Migliorati, S. Persichelli and M. Zobov (2016),“Single beam collective effects in FCC-ee due to beam cou-pling impedance”, arXiv preprint arXiv:1609.03495.[5] R. Kersevan, private communication, Feb. 2017.[6] http://kt.cern/sites/knowledgetransfer.web.cern.ch/files/technology_brief/NonEvaporableGetterThinFilmCoatings.pdf[7] K. Shibata et al., “Development of TiN coating system forKEKB vacuum chambers”, in Proc. of the4th Annual Meetingof Particle Accelerator Society of Japan and the 32nd LinearAccelerator Meeting in Japan, August 1-3 2007, Wako, Japan,pp. 209–211.[8] https://www.memsnet.org/material/titaniumnitridetinbulk/[9] E. Belli et al., “Electron cloud and collective effects in theinteraction region of FCC-ee”, presented at 58th ICFA Ad-vanced Beam Dynamics Workshop on High Luminosity Cir-cular e+e-Colliders, Daresbury, UK, 24-27 October 2016,paper TUT3AH7, unpublished.[10] E. Belli, “HOMs and e-cloud in FCC-ee”, presented atthe 97th HSC section meeting, 12 December 2016, CERN,https://indico.cern.ch/event/592610/[11] N. Mounet, 2011. ImpedanceWake2D, https://twiki.cern.ch/twiki/bin/view/ABPComputing/ImpedanceWake2D[12] A.W. Chao, Physics of Collective Beam Instabilities in HighEnergy Accelerators, Wiley, 1993.[13] https://github.com/PyCOMPLETE/PyHEADTAIL[14] M. Migliorati et al., Phys. Rev. ST Accel. Beams, vol. 16, p.031001, 2013.[15] M. Migliorati and L. Palumbo, Phys. Rev. ST Accel. Beams,vol. 18, p. 031001, 2015.[16] Rodrigues, A. R. D. et al. “Sirius status report”, Proc. ofIPAC’16, paper WEPOW001, p. 2811.[17] R. Kersevan, “FCC-ee vacuum effects and simulations”,presented at the FCC Week 2016, Rome, Italy, 11-15April 2016, https://indico.cern.ch/event/438866/contributions/1085121/[18] https://www.cst.com[19] Y. Suetsugu, M. Shirai, and K. Shibata. “Possibility of comb-type rf shield structure for high-current accelerators”, Phys.Rev. ST:AB, vol. 6.10, p. 103201, 2003. APAProceedings of IPAC2017, Copenhagen, Denmark THPAB02005 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsISBN 978-3-95450-182-33737 Copyright©2017CC-BY-3.0andbytherespectiveauthors

Coupling impedances and collective effects for FCC-ee

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Coupling impedances and collective effects for FCC-ee

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