5 th Low Emittance Rings Workshop Grenoble 15

5 th Low Emittance Rings Workshop Grenoble, 15 -17 September 2015 Collective Effects in Low Emittance Rings Victor Smaluk NSLS II, BNL, New York 1 BROOKHAVEN SCIENCE

Outline • Lattice parameters of operating low-emittance rings (MAX IV*, NSLS II, KEK ATF DR, PETRA III, ALS, APS, DLS, SSRF, SPRING-8, SOLEIL, ESRF, ALBA , ELETTRA) * 1 st beam 25 Aug 2015 • Broad-band impedance – single-bunch collective effects: - bunch lengthening - microwave instability - betatron tune shift & chromatic damping - TMCI (fast head-tail) • Narrow-band impedance – multi-bunch collective effects: - longitudinal coupled-bunch instability - transverse coupled-bunch instability - betatron tune shift – dipole and quadrupole impedance • Ion-related effects • Beam lifetime – Touschek and vacuum • IBS • Summary 2 BROOKHAVEN SCIENCE

Wake fields and impedances Wake function d–function response Wake potential l(t) beam response Impedance Frequency-domain transfer function (Fourier transform of wake function) Impedance contributions • resistive walls • steps and tapers • button-electrode BPMs • strip-lines • high-order modes (HOM) of RF cavities • flanges • bellows • beam scrapers • openings, slots, RF shields • … Broad-band impedance – short-range wake • non-resonance behavior (inductive at low frequencies) • short rising/damping time τ • single-bunch instabilities Narrow-band impedance – long-range wake • narrow resonance peaks in spectra • long rising/damping time τ • multi-bunch instabilities 3 BROOKHAVEN SCIENCE

Low Emittance Lattices DBA (NSLS II) 7 BA (MAX IV) For low emittance: • increase ρ – number of dipoles; • minimize Hx – dispersion; • use damping wigglers. 4 BROOKHAVEN SCIENCE

Low Emittance Rings εx (nm) E (Ge. V) MAX IV 0. 3* 3 7 BA NSLS II 0. 9 3 2 BA KEK ATF DR FOBODO 1 1. 5 PETRA III 1 6 2 BA (1/8), FODO ALS 2 1. 9 3 BA APS 2. 5 7 2 BA DLS 2. 7 3 2 BA SSRF 3 3. 5 2 BA 8 2 BA SPRING-8 3. 4** SOLEIL 3. 9 2. 75 2 BA ESRF 4 6 2 BA ALBA 4. 58 3 2 BA ELETTRA 7 2 2 BA * design value ** 2. 4 from 2013 5 BROOKHAVEN SCIENCE

Parameters of Low Emittance Rings Beam intensity Beam current for regular operation Iaver (m. A) number of bunches MAX IV 500* 176 NSLS II 300 (500*) KEK ATF DR 100 1080 300 PETRA III 100 960 ALS 500 300 APS 150 324 (24) DLS 300 900 SSRF 200 720 SPRING-8 100 812 ü Higher bunch charge SOLEIL 500 312 ESRF 200 992 ALBA 120 320 higher peak current ELETTRA 300 432 stronger collective effects 6 BROOKHAVEN SCIENCE

Parameters of Low Emittance Rings Energy spread 7 BROOKHAVEN SCIENCE

Parameters of Low Emittance Rings Bunch length Momentum compaction factor: Synchrotron tune: Energy loss per turn: ü Shorter bunch higher peak current stronger collective effects 8 BROOKHAVEN SCIENCE

Parameters of Low Emittance Rings Betatron tunes ü Stronger focusing ü horizontal - higher betatron tunes; - higher beta function variation; - higher natural chromaticity stronger sextupoles vertical 9 BROOKHAVEN SCIENCE

Parameters of Low Emittance Rings Vacuum chamber aperture ü Smaller aperture • • higher resistive-wall and geometric impedance; difficult vacuum conditioning; higher probability of ion instabilities; shorter lifetime (gas scattering). horizontal MAX IV NSLS II vertical 10 BROOKHAVEN SCIENCE

Longitudinal Broad-band Impedance Bunch lengthening Ibops σt 0 Measured data σtops (m. A) (ps) MAX IV* 2. 84 TUPWA 005 40 47. 6 IPAC 2013 NSLS II TUAB 2 0. 28 20 22. 2 IPAC 2015 PETRA III MOPS 055 0. 20 40 40. 8 IPAC 2011 ALS WXE 06 1. 69 15 17. 8 PAC 1995 APS TPPH 068 6. 25 16 39 PAC 2001 DLS 0. 33 TUPWA 052 11 16 IPAC 2013 SSRF WEPH 13 15 15. 3 SAP 2014 SPRING-8 WEPRI 013 0. 28 0. 12 13 13. 4 EPAC 2002 * estimation SOLEIL WEOBC 01 1. 60 18 22. 5 PAC 2007 11 BROOKHAVEN SCIENCE

Longitudinal Broad-band Impedance Bunch lengthening and centroid shift Example: DLS (PRSTAB 18, 064401 (2015)) Model impedance: resistive wall + broad-band (Q = 1) resonator Potential well distortion Haissinski equation Multi-particle tracking – wake-field kick 12 BROOKHAVEN SCIENCE

Longitudinal Broad-band Impedance Microwave instability • • • Example: APS (PAC 2001 TPPH 068) further increase of bunch length energy spread growth synchrotron sidebands in beam spectrum no beam loss threshold bunch current Ibops (m. A) Ithmwi (m. A) MAX IV* 2. 84 3. 5 ALS 1. 69 2. 2 APS 6. 25 7. 5 DLS 0. 33 1. 0 SSRF 0. 28 2. 5 SPRING-8 0. 12 * estimation Example: DLS (EPAC 2008 TUPP 020) Example: ELETTRA (PAC 2003 WPAG 018) 5. 0 SOLEIL 1. 12 10. 0 ESRF 0. 20 7. 1 ELETTRA 0. 69 1. 4 13 BROOKHAVEN SCIENCE

Transverse Broad-band Impedance Betatron tune shift – single bunch For accurate estimation of the tune shift, take into account: – bunch spectrum • local impedances and beta functions; • current-dependent bunch lengthening. horizontal vertical Measured data 14 BROOKHAVEN SCIENCE

Transverse Broad-band Impedance Betatron tune shift – single bunch Measurement vs impedance budget measurement impedance budget NSLS II IPAC 2015, TUAB 2 from A. Blednykh PETRA III IPAC 2010, WEPEA 018 EPAC 2004, THPKF 021 APS ASD/APG/2007 -08 PAC 2003, RPPB 004 DLS* PRSTAB 18, 064401 TUPWA 052 IPAC 2013, SPRING-8 EPAC 2002, WEPRI 013 [7] EPAC 1996, WEP 103 G SOLEIL PAC 2007, WEOBC 01 EPAC 2004, WEPLT 081 * No transverse impedance ESRF EPAC 98, THP 05 G EPAC 2002, budget, WEPRI 010 rough formula is used: ALBA* IPAC 2014, TUPRI 052 IPAC 2011, MOPS 064 ELETTRA PRSTAB 6, 030703 ST/M-TN-90/14 15 BROOKHAVEN SCIENCE

Transverse Broad-band Impedance Betatron tune shift and chromatic damping – single bunch Example: DLS (PRSTAB 18, 064401 (2015)) Model impedance: resistive wall + broad-band (Q = 1) resonator Head-tail mode coupling Eigenvalue problem for Gaussian bunch Multi-particle tracking – wake-field kick 16 BROOKHAVEN SCIENCE

Transverse Broad-band Impedance TMC (fast head-tail) instability • 0 th and – 1 st head-tail modes coupling: • high betatron sidebands in beam spectrum; • rise time about ½ period of synchrotron oscillation; • beam loss; • threshold bunch current (zero chromaticity): ; Measured data – bunch spectrum Possible cures: • bunch lengthening; • chromaticity increase; • feedback. 17 BROOKHAVEN SCIENCE

Transverse Broad-band Impedance TMC (fast head-tail) instability Example: NSLS II (IPAC 2015 TUAB 2) ξx = 0, ξy = 0; Ith = 0. 95 m. A ξx = 5, ξy = 5; Ith = 3. 2 m. A 18 BROOKHAVEN SCIENCE

Longitudinal Narrow-band Impedance Multi-bunch instability • • coherent bunch-by-bunch oscillations driven by HOMs of RF cavities: • resonance condition: • • no threshold bunch current growth rate: Example: ELETTRA (EPAC 1998 THP 03 E) Possible cures: • • HOM dampers; HOM frequency shifters; precise control of RF cavity temperature (moving ωHOM away from a resonance); longitudinal feedback. 19 BROOKHAVEN SCIENCE

Transverse Narrow-band Impedance Multi-bunch instability • • coherent bunch-by-bunch oscillations resonance condition: resistive wall • complex tune shift (point bunches, ξ = 0): resonances • • no threshold bunch current growth rate: 3 Example: DLS (thanks to G. Rehm, R. Fidler, R. Bartolini) 1 growth rates of coupled-bunch modes: measurement and model 4 impedance of BPMs (CST) 2 2 5 5 1 20 BROOKHAVEN SCIENCE

Transverse Narrow-band Impedance Multi-bunch instability Possible cures: • • Stabilizing effect of chromaticity Example: NSLS II (thanks to A. Blednykh) bunch lengthening; chromatic head-tail damping; non-linear decoherence; feedback. Stabilizing effect of harmonic sextupoles Example: ELETTRA (PRSTAB 6, 054401 (2003)) Time of decoherence vs harmonic sextupole strength Example: SOLEIL (thanks to R. Nagaoka, F. Cullinan) Amplitude of unstable mode vs harmonic sextupole strength 21 BROOKHAVEN SCIENCE

Transverse Narrow-band Impedance Betatron tune shift – dipole and quadrupole impedance Complex frequency shift is derived from PRSTAB 5, 111001 (2002). betatron frequencies in these equations have been replaced with local beta functions. Measured data – skin depth at revolution frequency Sb – bunch separation; C – circumference t – vacuum chamber thickness b – vacuum chamber half-aperture d – distance to outer wall for perfect magnet for perfect conductor 22 BROOKHAVEN SCIENCE

Transverse Narrow-band Impedance Betatron tune shift – dipole and quadrupole impedance Example: ESRF (PAC 2001 TPPH 112) betatron tune shift in multi-bunch mode Example: NSLS II (thanks to A. Blednykh, G. Bassi) betatron tune shift in multi-bunch mode ξx = 2, ξy = 2 ESRF “achromat” chamber profile NSLS II dipole chamber profile 23 BROOKHAVEN SCIENCE

Ion-related effects Fast ion instability Ion oscillation frequency: Example: KEK ATF DR (EPAC 2008, MOPP 066) Example: NSLS II (thanks to W. Cheng) vertical instability, streak camera observation Ion accumulation condition: Rise time, linear theory: vertical emittance growth along the bunch train Rise time with decoherence and variation of beta functions: Example: SOLEIL (IPAC 2010, TUPD 028) oscillation amplitude along the bunch train Emittance perturbation: 24 BROOKHAVEN SCIENCE

Beam Lifetime Gas scattering Touschek effect (large angle scattering) Particle loss rate (inverse lifetime): Bremsstrahlung (inelastic scattering) Elastic scattering acceptance at the dominant aperture ax, y(s) – transverse aperture n – residual gas ion concentration Example: NSLS II (thanks to B. Podobedov) 25 BROOKHAVEN SCIENCE

Beam Lifetime Measured operation lifetime Ib (m. A) τ (hours) MAX IV 2. 84 15 NSLS II 0. 28 6. 5 PETRA III 0. 20 7. 4 ALS 1. 69 6. 5 APS 6. 25 20 DLS 0. 33 15 SSRF 0. 28 9 SPRING-8 0. 12 25 SOLEIL 1. 60 11. 5 ESRF 0. 20 18 ALBA 0. 38 26 ELETTRA 0. 69 15 26 BROOKHAVEN SCIENCE

Intra-beam Scattering IBS (small angle scattering) • no particle loss; • 3 D emittance growth. 27 BROOKHAVEN SCIENCE

Intra-beam Scattering Example: KEK ATF (PRL 92, 054802 (2004) ) Example: PETRA III @ 3 Ge. V (thanks to R. Wanzenberg) 28 BROOKHAVEN SCIENCE

Summary Impedance Beam effects Possible cures longitudinal broad-band impedance microwave instability • bunch lengthening (harmonic cavities) transverse broad-band impedance transverse mode coupling • (fast head-tail) instability • bunch lengthening longitudinal narrowband impedance transverse narrow-band impedance ion-related effects longitudinal coupledbunch instability • feedback • HOM dampers • HOM frequency shifters • control of RF cavity temperature • feedback transverse coupled-bunch • instability • bunch lengthening chromatic head-tail damping • non-linear decoherence • feedback transverse coupled-bunch • instability • emittance growth • 29 chromatic head-tail damping better vacuum bunch train splitting feedback BROOKHAVEN SCIENCE

Acknowledgements Thanks to A. Blednykh, G. Bassi, B. Podobedov, W. Cheng, B. Bacha (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) I appreciate your help! 30 BROOKHAVEN SCIENCE

Thank you for your attention! 31 BROOKHAVEN SCIENCE