1 BROOKHAVEN SCIENCE ASSOCIATES FCC Week 2016 Rome, April 2016 Collective Effects in Low-Emittance Rings: Projection for FCC Victor Smaluk NSLS-II, BNL, New York

2 BROOKHAVEN SCIENCE ASSOCIATES Wake Fields and Impedances Impedance: frequency-domain transfer function Wake function: point charge (  –function) response Wake potential: (t) beam response Broad-band impedance – short-range wake non-resonance behavior (inductive at low frequencies) short rising/damping time single-bunch effects: - bunch lengthening, microwave instability - coherent energy loss – heat load - coherent tune shift, TMCI - chromatic head-tail – fast damping Narrow-band impedance – long-range wake resonance peaks in spectra long rising/damping time multi-bunch effects: - longitudinal/transverse multi-bunch instabilities FCC Week 2016 Rome, April 2016

3 BROOKHAVEN SCIENCE ASSOCIATES Low Emittance Rings ε x (nm) E (GeV) C (km) MAX IV NSLS II PETRA III ALS APS DLS SSRF SPRING SOLEIL ESRF ALBA ELETTRA LEP PEP e PEP e KEKB e KEKB e CESR VEPP-4M VEPP FCCee Z FCCee W FCCee H FCCee tt colliders light sources FCC Week 2016 Rome, April 2016

4 BROOKHAVEN SCIENCE ASSOCIATES Higher bunch charge + shorter bunch  higher peak current  stronger wake fields Peak current σ t (ps) I aver (mA) I peak (A) MAX IV NSLS II PETRA III ALS APS DLS SSRF SPRING SOLEIL ESRF ALBA ELETTRA LEP PEP e PEP e KEKB e KEKB e CESR VEPP-4M VEPP FCCee Z FCCee W FCCee H FCCee tt colliders light sources FCC Week 2016 Rome, April 2016

5 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening and coherent energy loss further increase of bunch length energy spread growth synchrotron sidebands in beam spectrum no beam loss threshold bunch current Haissinski equation (potential well distortion) 3-rd order equation (approx.) Coherent energy loss Microwave instability Loss factor Example: DLS (model: resistive wall + broad-band resonator) FCC Week 2016 Rome, April 2016

6 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening and coherent energy loss Example: DIAMOND Light Source (model impedance: resistive wall + broad-band resonator) = 40 mm, = 12 mm, ρ = 7.3  10 –7 (st. steel) f r = 22GHz, Rs = 8 kΩ FCC Week 2016 Rome, April 2016

7 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening (measured) ImZ || /n 2a 2b Ω mm mm MAX IV Cu NSLS II Al PETRA III Al ALS Al APS Al DLS SS SPRING Al SOLEIL SS/Al ESRF SS ELETTRA SS PEP e Cu PEP e Cu KEKB e Cu KEKB e Cu VEPP-4M SS FCC Week 2016 Rome, April 2016

8 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening (measured) L eff| 2a 2b nH mm mm MAX IV Cu NSLS II Al PETRA III Al ALS Al APS Al DLS SS SPRING Al SOLEIL SS/Al ESRF SS ELETTRA SS PEP e Cu PEP e Cu KEKB e Cu KEKB e Cu VEPP-4M SS FCC Week 2016 Rome, April 2016

9 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Z || /n : measurement vs impedance budget Z || /n calc Z || /n meas ( Ω) (Ω) NSLS II PETRA III APS DLS SPRING SOLEIL ESRF ELETTRA PEP e PEP e KEKB e KEKB e FCC Week 2016 Rome, April 2016

10 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Narrow-band Impedance Multi-bunch instability coherent bunch-by-bunch longitudinal oscillations, usually no beam loss driven by HOMs of RF cavities or trapped high-Q modes of other vacuum components: resonance condition: growth rate: no threshold bunch current stability condition: Possible cures: HOM dampers, HOM frequency shifters; precise control of RF cavity temperature (moving away from a resonance); longitudinal feedback. Example: normal-conductive RF cavity superconducting cavities have much better spectra FCC Week 2016 Rome, April 2016

11 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance Coherent tune shift and chromatic damping – bunch spectrum Eigenvalue problem for head-tail modes: for Gaussian bunch: FCC Week 2016 Rome, April 2016

12 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance Coherent tune shift and chromatic damping Example: DIAMOND Light Source (model impedance: resistive wall + broad-band resonator) = 40 mm, = 12 mm, ρ = 7.3  10 –7 (st. steel) f r = 30GHz, Rs = 0.31MΩ/m FCC Week 2016 Rome, April 2016

13 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance Kick factor: measurement vs impedance budget kV/(pC m) kV/(pC m) A -1 MAX IV NSLS II PETRA III ALS APS DLS* SPRING SOLEIL ESRF ALBA* ELETTRA PEP e+* KEKB e * No transverse impedance budget, rough formula is used: FCC Week 2016 Rome, April 2016

14 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance TMC (fast head-tail) instability coupling of 0 th and –1 st head-tail modes : ; high betatron sidebands in beam spectrum; rise time about ½ period of synchrotron oscillation; beam loss; threshold bunch current (zero chromaticity): Head-tail modes: – bunch spectrum Possible cures: bunch lengthening; chromatic head-tail damping; non-linear decoherence; feedback. FCC Week 2016 Rome, April 2016

15 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance TMC (fast head-tail) instability Example: NSLS II ξ x = 0, ξ y = 0; I th = 0.95 mA ξ x = 5, ξ y = 5; I th = 3.2 mA FCC Week 2016 Rome, April 2016

16 BROOKHAVEN SCIENCE ASSOCIATES Transverse Narrow-band Impedance Multi-bunch instability coherent bunch-by-bunch transverse oscillations driven by HOMs of RF cavities, trapped high-Q modes of other vacuum components, or low-frequency resistive-wall impedance ( ) : resonance condition: growth rate (imaginary part of complex tune shift): no threshold bunch current stability condition: resonances res. wall growth rates of coupled-bunch modes: measurement and model Example: DLS (thanks to G.Rehm, R.Fidler, R.Bartolini) FCC Week 2016 Rome, April 2016

17 BROOKHAVEN SCIENCE ASSOCIATES Transverse Narrow-band Impedance Multi-bunch instability Example: NSLS II (thanks to A.Blednykh) Possible cures: bunch lengthening; chromatic head-tail damping; non-linear decoherence; feedback. Decoherence rate vs harmonic sextupole strength Example: ELETTRA (PRSTAB 6, (2003)) Amplitude of unstable mode vs harmonic sextupole strength Example: SOLEIL (thanks to R.Nagaoka, F. Cullinan) Stabilizing effect of chromaticity Stabilizing effect of harmonic sextupoles FCC Week 2016 Rome, April 2016

18 BROOKHAVEN SCIENCE ASSOCIATES Transverse Instabilities Local impedance contribution TMBI: TMCI: NSLS IIFCC ee FCC Week 2016 Rome, April 2016

19 BROOKHAVEN SCIENCE ASSOCIATES Summary ImpedancePossible problemsPossible cures longitudinal broad-band impedance microwave instability; coherent energy loss bunch lengthening (lower RF frequency of harmonic cavities) longitudinal narrow-band impedance longitudinal coupled-bunch instability; trapped modes HOM dampers/frequency shifters control of RF cavity temperature feedback “low-impedance” design of vacuum components transverse broad-band impedance transverse mode coupling (fast head-tail) instability bunch lengthening chromatic head-tail damping non-linear decoherence feedback transverse narrow-band impedance transverse coupled-bunch instability FCC Week 2016 Rome, April 2016

20 BROOKHAVEN SCIENCE ASSOCIATES Acknowledgements Thanks to F.Zimmermann (CERN) A.Bogomyagkov, E.Levichev (BINP) A.Blednykh, G.Bassi, T.Shaftan (NSLS II) G.Rehm, R.Bartolini, R.Fidler (DIAMOND) E.Karantzoulis (ELETTRA) V.Sajaev (APS) R.Nagaoka, F.Cullinan (SOLEIL) R.Wanzenberg (PETRA III) F.Perez, T.Gunzel (ALBA) S.Liuzzo, J.-L.Revol (ESRF) FCC Week 2016 Rome, April 2016

21 BROOKHAVEN SCIENCE ASSOCIATES Thank you for your attention! FCC Week 2016 Rome, April 2016