The high luminosity foreseen in the future electron-positron circular collider (FCC-ee) necessitates very intense multi-bunch colliding beams with very small transverse beam sizes at the collision points. This requires transverse beam emittances comparable to those of modern synchrotron light sources. At the same time, the stored beam currents should be close to the best values achieved in the last generation of particle factories. This combination of demanding factors poses a major challenge, namely preserving a high beam quality, while, at the same time, avoiding machine performance degradation. In consequence, a careful study of the collective effects and identification of stabilizing mechanisms are required to mitigate the foreseen instabilities. In this contribution, we discuss the current status of these studies

Carideo E.

Migliorati M.

Zimmermann F.

Zobov M.

English

Archivio della ricerca- Università di Roma La Sapienza

PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation∗Emanuela Carideo,𝑎,𝑐,∗ Frank Zimmermann,𝑎 Mikhail Zobov𝑏 and MauroMigliorati𝑐𝑎CERN, Geneva, Switzerland𝑏INFN-LNF, Frascati, 00054 Roma, Italia𝑐University of Rome “La Sapienza” and INFN - Sezione Roma 1, 00185, Roma, ItalyE-mail: emanuela.carideo@cern.chThe high luminosity foreseen in the future electron-positron circular collider (FCC-ee) necessitatesvery intense multi-bunch colliding beams with very small transverse beam sizes at the collisionpoints. This requires transverse beam emittances comparable to those of modern synchrotronlight sources. At the same time, the stored beam currents should be close to the best valuesachieved in the last generation of particle factories. This combination of demanding factors posesa major challenge, namely preserving a high beam quality, while, at the same time, avoidingmachine performance degradation. In consequence, a careful study of the collective effects andidentification of stabilizing mechanisms are required to mitigate the foreseen instabilities. In thiscontribution, we discuss the current status of these studies.41st International Conference on High Energy physics - ICHEP20226-13 July, 2022Bologna, Italy∗Speaker© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation1 Emanuela Carideo1. IntroductionFollowing the 2020 European Strategy Update, a feasibility study for a future circular collider(FCC) has been launched. The first stage of the FCC is an electron-positron collider (FCC-ee [1])with centre-of-mass collision energies ranging from 91.2 to 365 GeV. According to the last updatedparameter list, presented in Table 1, the FCC has a circumference of about 91 km.Table 1: Baseline beam parameters for the FCC-ee in different modes of operation. The acronyms “SR” and“BS” signify synchrotron radiation and beamstrahlung, respectively.For a particle accelerator like FCC-ee, the impact of collective effects needs to be evaluated.Such effects are generated by self-induced electromagnetic fields (wakefields), which perturb thebeam dynamics, and are likely to represent one of the main limitations to machine operation andperformance. Wakefields are responsible for instabilities in both the longitudinal and transverseplanes.In this paper, we focus on the effects generated by the interaction of the beam with someimportant sources of wakefields for the FCC-ee main ring, at the Z pole energy. This lowestmachine energy is supposed to be the most critical with regard to collective effects.Our study focuses on single beam instabilities, in particular on the microwave instability (MI)and on the transverse mode coupling instability (TMCI), which occur in the longitudinal andtransverse planes, respectively [2]. The longitudinal MI manifests itself through a sudden increaseof the energy spread and bunch length above a given intensity threshold. In this regime, even if thebunch is not lost, its longitudinal shape could oscillate, thereby reducing the machine performance.On the contrary, with TMCI, the transverse oscillations increase exponentially making the bunch tohit the pipe walls.Additionally, we will discuss possible mitigation for these instabilities.2. Wakefield and impedanceThe beam pipe model used for the evaluation of the resistive wall (RW) coupling impedance andthe associated wakefield, which results to be the most important impedance source of the machineso far, is taken to be a circular tube with a radius of 35 mm made up of four different layers. For our2PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation2 Emanuela Carideo70 60 50 40 30 20z (mm)0.20.10.00.10.2relative energy deviation (%)0.20.40.60.81.0normalized densityFigure 1: Left-hand side: longitudinal phase space at nominal intensity. Right-hand side: bunch length(bottom) and RMS energy spread (top) as a function of bunch population under the influence of the longi-tudinal RW impedance, for the case with (BS) and without (SR) beamstrahlung. Here, the effect of BS isconsidered to be constant, independent of the longitudinal impedance.simulations of collective effects, we assume a NEG film thickness of 150 nm, that constitutes a goodcompromise between minimum thickness for a small impedance and the requirements coming fromthe vacuum and electron cloud effects. The NEG film is deposited on a 2 mm thick copper beampipe. On the outer side, first a layer of air and, finally, thick iron follow, to model the influence of themachine magnets [3, 4]. Using the code IW2D [5], we calculate the RW coupling impedance and itsassociated beam wakefield, taking into account this multilayer system [6]. We also approximate theeffect of small perturbations introduced by the lateral winglets for synchrotron radiation absorption,by multiplying the RW impedance and wakefield obtained for the circular pipe by a factor of 1.1, avalue obtained from CST Microwave Studio [7] simulations.The same CST code was also used to evaluate a number of other impedance sources, namelythe bellows, the beam position monitors (BPMs), the RF cavity system and tapers connecting eachcryomodule (housing 4 RF single cell cavities) to a circular beam pipe. In Ref. [8] the method tocalculate the wake potential for our analysis and the relevant results are presented in detail. Themachine impedance modelling is still in progress.3. Microwave instabilityAbove a certain intensity threshold, the energy spread starts to increase, in what is known asthe MI regime, which is characterized by a turbulent behavior of the longitudinal phase space. Withthe longitudinal wakefield as input, PyHEADTAIL [9, 10] simulations yield the bunch length andenergy spread as a function of the intensity, as are shown in Fig.1, right-hand side. Indeed, in thesame figure, on the left-hand side, we can see the longitudinal phase space distribution at nominalbunch intensity strongly distorted due to the turbulent behavious of the bunch.Since the nominal bunch population is 25×1010, we are in the MI regime if we do not take intoaccount the effect of the collision (single beam red curves). If we also include the beamstrahlungeffect for colliding beams (green curves), the energy spread is much larger and it remains constant,and the bunch length is only slightly modified by the impedance, due to potential wall distortion.Hence, in this latter case, no MI is observed.From these results we can conclude that the beamstrahlung helps to mitigate the MI, but thesesimulations are not fully self-consistent, since the beamstrahlung also depends on the bunch length,3PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation3 Emanuela Carideowhile in this study we considered the beamstrahlung and the collective effects due to the wakefieldsindependently of each other. This self-consistency aspect has been investigated more closely in astudy of beam-beam interactions [11, 12].4. TMCIThe TMCI can affect high intensity bunches in circular accelerators. This single bunch effectoccurs if two transverse coherent oscillation modes couple with each other [13]. The effect can bereproduced and visualized with the code PyHEADTAIL [14]. When increasing the bunch intensity,due to the wakefield, the coherent betatron frequencies of the intrabunch modes are shifting. TheTMCI occurs above a given bunch intensity when the frequencies of two neighbouring coherentoscillation modes merge together and the particles’ motion grows exponentially.Figure 2, left-hand side, shows the results of simulations with only the transverse wakefield.Above a certain threshold, at an intensity of about 21×1010 particles per bunch, a coupling betweenthe modes 0 and −1 is clearly seen. The inclusion of the longitudinal wakefield effect furtherreduces the TMCI instability threshold, as is shown in the right-hand side of the figure. TheFigure 2: Real part of the frequency shift of the low-order coherent oscillation modes as a function ofthe bunch population without beamstrahlung, considering only the transverse impedance (left) or both thetransverse and longitudinal impedance (right).threshold reduction is due to a spread of the synchrotron frequencies introduced by the longitudinalwakefield.5. Possible mitigation strategiesOne method that can be used to mitigate the TMCI instability exploits the chromaticity.Nonzero lattice chromaticity induces a spread in the betatron tunes, which could stabilise the beam.Simulations indicate a slight improvement with a positive chromaticity, but the threshold remainsbelow the nominal beam intensity.The long-range transverse wakefield due to the RW also produces a coupled bunch instabilitywith a rise time that depends on the fractional part of the tune. For the parameter list of Table 1,the rise time of this instability is about 2 ms, corresponding to 6 revolutions, and it can be curedwith a robust bunch-by-bunch feedback system. The same feedback system also affects the TMCI.Indeed, by acting on the centre of mass of each bunch, the feedback counteracts the shift of the 0mode toward the −1 one. On the other hand, the same feedback could induce an instability of the4PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation4 Emanuela CarideoFigure 3: Mode analysis considering, on the top, only the transverse wakefield with resistive feedback havinga damping time of 10 turns, on the bottom, transverse and longitudinal wakefield with resistive feedbackhaving a damping time of 4 turns.−1 mode [15], with a threshold depending on the complex phase of the feedback itself. For a purereactive feedback, with only the effect of the transverse wakefield, the instability threshold is evenlower than that of TMCI, as shown on the top of Fig. 3.However, this instability of the −1 mode, or ITSR [15], has a growth rate not as dramaticas that of the TMCI, and it can rather easily be cured by means of Landau damping. Indeed,the synchrotron tune spread due to the longitudinal wakefield suffices to increase the instabilitythreshold from 18×1010 to 46×1010 particles per bunch, as is illustrated in the bottom part of Fig. 3.Finally, we note that these results were obtained for a single beam without beamstrahlung. Fora self-consistent evaluation, simulations which also include the beam-beam effects are necessary.In general, the increased energy spread due to beamstrahlung helps to stabilize the beam.6. ConclusionConsidering an updated model of the FCC-ee machine impedance, we simulated single bunchcollective effects in the transverse and longitudinal planes for the main ring of the Z pole machine.At nominal intensity, the longitudinal beam dynamics is stable only in collisions, thanks to thebeamstrahlung effect. Otherwise, because of the longitudinal wakefields, we are in the microwaveinstability regime, which manifests itself through an anomalous increase of bunch length and energyspread. The longitudinal wakefield also has a profound impact on the transverse dynamics. In fact,its inclusion in the simulations decreases the TMCI threshold. However, this instability is keptunder control by a strong resistive transverse feedback, used to mitigate the transverse coupledbunch instability. In this case the longitudinal wakefields seem to play a beneficial role suppressingthe eventual ITSR instability, as discussed in Sec. 5.In future work, the FCC-ee machine impedance model will need to be further extended toinclude other important impedance sources, as those due to the collimation system, while examiningany consequent changes in instability thresholds and beam dynamics.5PoS(ICHEP2022)046FCC-ee Collective Effects and Their Mitigation5 Emanuela CarideoAcknowledgementsThis work was supported by the European Union’s Horizon 2020 Research and Innovationprogramme under grant no. 951754 (FCCIS).References[1] A. Abada, et al., FCC-ee: the lepton collider: future circular collider conceptual design reportvolume 2. Eur. Phys. J. Spec. Top. 2019;228(2):261–623.[2] A. W. Chao, “Physics of collective beam instabilities in high energy accelerators”, New York,USA: Wiley (1993).[3] M. Migliorati, E. Belli, M. Zobov, Impact of the resistive wall impedance on beam dynamicsin the Future Circular e+ e- Collider, Physical Review Accelerators and Beams, 21, 041001(2018).[4] E. Belli, et al, Electron cloud buildup and impedance effects on beam dynamics in the FutureCircular e+ e- Collider and experimental characterization of thin TiZrV vacuum chambercoatings, Physical Review Accelerators and Beams, 21, 111002 (2018).[5] Nicolas Mounet, https://gitlab.cern.ch/IRIS/IW2D[6] M. Migliorati, et al, Resistive wall impedance in elliptical multilayer vacuum chambers,Physical Review Accelerators and Beams, 22, 121001 (2019).[7] https://www.3ds.com/products-services/simulia/products/cst-studio-suite/[8] Carideo E., et al, Transverse and longitudinal single bunch instabilities in FCC-ee, IPAC 2021,pp. 3153-3156. https://doi.org/10.18429/JACoW-IPAC2021-WEPAB225.[9] A. Oeftiger, Rep. CERN-ACC-NOTE-2019-0013, 2019.[10] PyHEADTAIL, https://github.com/PyCOMPLETE/ PyHEADTAIL[11] M. Migliorati, et al, An interplay between beam–beam and beam coupling impedance effectsin the Future Circular e+e- Collider, The European Physical Journal Plus, (2021) 136:1190[12] M. Migliorati, et al, Impedance modelling and collective effects in the Future Circular e+e-Collider with 4 IPs, The European Physical Journal Techn Instrum 9, 10 (2022).[13] Amorim, David et al, Simulation and Measurement of the TMCI Threshold in the LHC, Proc.HB, 2018,[14] E. Métral, M. Migliorati, Longitudinal and transverse mode coupling instability: Vlasovsolvers and tracking codes, Physical Review Accelerators and Beams, 23, 071001 (2020).[15] Métral, E, “Imaginary tune split and repulsion single-bunch instability mechanism in thepresence of a resistive transverse damper and its mitigation”, Physical Review Acceleratorsand Beams, 24, 041003 (2021).6

FCC-ee Collective Effects and Their Mitigation

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FCC-ee Collective Effects and Their Mitigation

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