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Damping of Coupled-bunch Oscillations with Sub-harmonic RF Voltage?

Damping of Coupled-bunch Oscillations with Sub-harmonic RF Voltage?. H. Damerau LIU-PS Working Group Meeting 4 March 2014. Overview. Introduction Observations in time domain Mode analysis with excitation Possible ingredients for explanation? Summary and outlook. Overview. Introduction

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Damping of Coupled-bunch Oscillations with Sub-harmonic RF Voltage?

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  1. Damping of Coupled-bunch Oscillations with Sub-harmonic RF Voltage? H. Damerau • LIU-PS Working Group Meeting • 4 March 2014

  2. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  3. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  4. Introduction • 1970/71: Issues with longitudinal stability with beam to ISR • ‘Clean oscillations […] are observed soon after transition crossing [...]’ • Coupled-bunch oscillations • Cured by some additional RF voltage below the RF frequency • Only 10 kV (7%) of main 140 kV main RF voltage were sufficient • Today’s instability observations with LHC-type beams similar • 2012: Does the old cure still work? • Easy to test with 10 MHz spare cavity and existing beam control • Main acceleration harmonic (h = 21) not dividable by 2 • Tried harmonic number range hsub = 6…21 h = 20 h = 20 D. Boussard, J. Gareyte, D. Möhl, PAC71, pp. 1073-1074 Without RF/2 With RF/2

  5. Beam conditions and measurements • High intensity 50 ns LHC-type beam: • 18 bunches in h = 21, Nb≈ 1.95 · 1011 ppb, el≈ 0.5 eVs • Reduced longitudinal blow-up to force coupled-bunch instability • Spare cavity started 10 ms after crossing gtr, 50 ms rise time • Kept on until end of acceleration • Voltage ratio: VRF, sub/VRF,h=21 = 5% to 8% Main RF, h = 21, VRF,h=21 = 200 kV Additional RF, VRF,sub= 10 kV gtr gtr

  6. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  7. Very first observations (3 of 18 bunches) No additional RF voltage Additional 10 kV at hsub = 17 • Significantly improved longitudinal stability with additional RF

  8. Harmonic number scan • Harmonic number of additional voltage scanned: hsub = 6…20 8 9 10 11 h = 6 12 13 15 • hsub = 6…16: unstable h = 17 18 19 h = 16 • hsub = 17…20: stable 20

  9. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  10. Dipole oscillations excited by VRF,sub • Data for mode spectra at C1700, 10 ms after full VRF,sub reached • Growth rates faster than usual instability from impedance • Clean single-mode coupled-bunch oscillation • Stable, nothing to analyze

  11. Mode analysis with additional RF voltage hsub = 6 • Analysis of coupled-bunch oscillations excited by hsub = 6…16 • Mode spectra from time domain data immediately after additional cavity switched on hsub = 7 … hsub = 14 • For all unstable cases, excited mode corresponds to frequency of additional cavity • nbatch ≈ 6/7 hsub • No effect with additional cavity just tuned to hsub, but zero voltage program hsub = 15 hsub = 16

  12. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  13. Synchrotron frequency distributions • Calculation of synchrotron frequency distributions for all buckets (at constant energy): • Calculate normalized potential and identify buckets • Calculate normalized area and synchrotron frequency for set of trajectories of each bucket • Bucket area and synchrotron frequency of pure h = 21 bucket: AB0,h=21, wS0,h=21 f

  14. Synchrotron frequency distributions • Accelerating case, 30 synchronous phase: • Synchrotron frequency distributions without and with sub-harmonic RF Accelerating bucket f hsub = 16 hsub = 17 Pure h = 21 • Increased spread compared to stationary buckets

  15. Bucket-by-bucket spread, el ≈ 0.35 AB0 Unstable Stable • Synchrotron frequency spreads of stable and unstable cases similar • Decoupling of synchrotron frequency distributions?

  16. Excited by phase loop? Preliminary • Simple tracking model with single macro-particle per bunch • Toy model of beam phase loop: • Average of bunch phase error with respect to h = 21 bucket centers • Simple moving average (length: ~ ¼ period of fs) loop filter hsub = 16 Without additional RF Unstable hsub = 17 Pure h = 21 Stable Phase jump as test excitation • Phase loop seems not perturbed, independent from hsub

  17. Excited by VRF,sub and impedances? Preliminary • Preliminary tracking studies by M. Migliorati with impedance Bunch oscillation amplitudes Mode oscillation amplitudes hsub = 10 Bunch oscillation amplitude [a.u.] Mode oscillation amplitude [a.u.] 500 kturns 500 kturns hsub = 17 Bunch oscillation amplitude [a.u.] Mode oscillation amplitude [a.u.] • Again no conclusive difference between hsub < 17 or hsub≥17

  18. Overview • Introduction • Observations in time domain • Mode analysis with excitation • Possible ingredients for explanation? • Summary and outlook

  19. Summary of observations • Coupled-bunch oscillation stabilized with 5-10% additional RF voltage at a sub-harmonic of the main RF system • Strong coupled-bunch instability: hsub = 6…16 • Significant stabilization: hsub= 17…20 • Independent from relative phase of main to sub RF system • Excited mode corresponds to additional RF harmonic • Observations reproduced during several MDs • Stability seems to be a threshold effect between hsub= 16 and 17 • How are coupled-bunch oscillations with VRF,sub excited? • What is different between additional voltage at hsub= 16 or 17?

  20. Outlook • In case of no conclusive explanation: beam measurements • Clarify dependence: longitudinal emittance, filling pattern, etc. • Observe initial take-off of excited oscillations • Slightly detune additional cavity to exclude impedance effects • If understood, tentative implementation of damping mechanism with sub-harmonic RF • Flexible use of spare cavity for damping (if not needed otherwise) • Possible with new 10 MHz matrix and spare cavity selection • or/and • Additional drive signal at h – 1 or h – 2 for each cavity • ~1 kV from each of the accelerating cavities • No need for 10 MHz spare cavity

  21. THANK YOU FOR YOUR ATTENTION!

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