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1 BROOKHAVEN SCIENCE ASSOCIATES FCC Week 2016 Rome, 11-15 April 2016 Collective Effects in Low-Emittance Rings: Projection for FCC Victor Smaluk NSLS-II,

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Presentation on theme: "1 BROOKHAVEN SCIENCE ASSOCIATES FCC Week 2016 Rome, 11-15 April 2016 Collective Effects in Low-Emittance Rings: Projection for FCC Victor Smaluk NSLS-II,"— Presentation transcript:

1 1 BROOKHAVEN SCIENCE ASSOCIATES FCC Week 2016 Rome, 11-15 April 2016 Collective Effects in Low-Emittance Rings: Projection for FCC Victor Smaluk NSLS-II, BNL, New York

2 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, 11-15 April 2016

3 3 BROOKHAVEN SCIENCE ASSOCIATES Low Emittance Rings ε x (nm) E (GeV) C (km) MAX IV 0.33 0.528 NSLS II 0.93 0.792 PETRA III 16 2.3 ALS 21.9 0.197 APS 2.57 1.104 DLS 2.73 0.562 SSRF 33.5 432 SPRING-8 3.48 1.436 SOLEIL 3.92.75 0.354 ESRF 4 6 0.844 ALBA 4.5 3 0.269 ELETTRA 7 2 0.259 LEP 20100 27 PEP e+ 243.1 2.2 PEP e- 48 9 2.2 KEKB e+ 183.5 3.016 KEKB e- 248 3.016 CESR 2106 0.768 VEPP-4M 301.8 0.366 VEPP-2000 2501 0.024 FCCee Z 0.0945.6 100 FCCee W 0.26 80 100 FCCee H 0.61120 100 FCCee tt 1.3175 100 colliders light sources FCC Week 2016 Rome, 11-15 April 2016

4 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 4015015 NSLS II 1230024 PETRA III 441007.2 ALS 2550017 APS 2015035 DLS 1130023 SSRF 1420012 SPRING-8 1310018 SOLEIL 1850042 ESRF 2020011 ALBA 161208.5 ELETTRA 1832014 LEP 383694 PEP e+ 333026153 PEP e- 37196090 KEKB e+ 131637310 KEKB e- 131188225 CESR 60340129 VEPP-4M 1662029 VEPP-2000 13315036 FCCee Z 131450166 FCCee W 10152372 FCCee H 850539 FCCee tt 86.61300 colliders light sources FCC Week 2016 Rome, 11-15 April 2016

5 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, 11-15 April 2016

6 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, 11-15 April 2016

7 7 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening (measured) ImZ || /n 2a 2b Ω mm mm MAX IV0.27 22 22 Cu NSLS II0.12 63 24 Al PETRA III0.14 80 4 Al ALS0.39 66 46 Al APS0.17 84 42 Al DLS0.23 80 24 SS SPRING-80.09 70 40 Al SOLEIL0.29 80 25 SS/Al ESRF0.22 74 33 SS ELETTRA0.41 82 53 SS PEP e+0.08 95 55 Cu PEP e- 0.09 95 55 Cu KEKB e+0.06 94 94 Cu KEKB e- 0.06 104 50 Cu VEPP-4M 3.9 60 30 SS FCC Week 2016 Rome, 11-15 April 2016

8 8 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Bunch lengthening (measured) L eff| 2a 2b nH mm mm MAX IV 76 22 22 Cu NSLS II 52 63 24 Al PETRA III 169 80 4 Al ALS 41 66 46 Al APS 100 84 42 Al DLS 69 80 24 SS SPRING-8 71 70 40 Al SOLEIL 54 80 25 SS/Al ESRF 98 74 33 SS ELETTRA 57 82 53 SS PEP e+ 90 95 55 Cu PEP e- 103 95 55 Cu KEKB e+ 115 94 94 Cu KEKB e- 122 104 50 Cu VEPP-4M 766 60 30 SS FCC Week 2016 Rome, 11-15 April 2016

9 9 BROOKHAVEN SCIENCE ASSOCIATES Longitudinal Broad-band Impedance Z || /n : measurement vs impedance budget Z || /n calc Z || /n meas ( Ω) (Ω) NSLS II0.120.19 PETRA III0.130.14 APS0.420.17 DLS0.40.23 SPRING-80.100.09 SOLEIL0.210.29 ESRF 0.50.22 ELETTRA 0.60.41 PEP e+ 0.070.08 PEP e- 0.070.09 KEKB e+0.0150.072 KEKB e- 0.0150.076 FCC Week 2016 Rome, 11-15 April 2016

10 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, 11-15 April 2016

11 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, 11-15 April 2016

12 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, 11-15 April 2016

13 13 BROOKHAVEN SCIENCE ASSOCIATES Transverse Broad-band Impedance Kick factor: measurement vs impedance budget kV/(pC m) kV/(pC m) A -1 MAX IV2.1 1.4 -0.63 NSLS II6.9 5.4 -6.6 PETRA III 3.9 3.0 -7.91 ALS1.2 1.9 -0.26 APS 3.7 1.8 -2.5 DLS* 6.2 6.4 -3.75 SPRING-8 3.1 4.6 -2.19 SOLEIL 5.4 2.4 -1.67 ESRF 7.1 3.8 -6.67 ALBA* 3.0 3.3 -0.57 ELETTRA 3.2 2.0 -0.78 PEP e+*1.1 0.6 -3.0 KEKB e+1.7 1.6 -3.6 * No transverse impedance budget, rough formula is used: FCC Week 2016 Rome, 11-15 April 2016

14 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, 11-15 April 2016

15 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, 11-15 April 2016

16 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, 11-15 April 2016

17 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, 054401 (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, 11-15 April 2016

18 18 BROOKHAVEN SCIENCE ASSOCIATES Transverse Instabilities Local impedance contribution TMBI: TMCI: NSLS IIFCC ee FCC Week 2016 Rome, 11-15 April 2016

19 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, 11-15 April 2016

20 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, 11-15 April 2016

21 21 BROOKHAVEN SCIENCE ASSOCIATES Thank you for your attention! FCC Week 2016 Rome, 11-15 April 2016

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