1 Damping of Coupledbunch Oscillations with Subharmonic RF

1 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 2

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

4 • 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 k. V (7%) of main 140 k. V main RF voltage were sufficient h = 20 Without RF/2 With RF/2 ® 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 D. Boussard, J. Gareyte, D. Möhl, PAC 71, pp. 1073 -1074 Introduction

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 e. Vs ® 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 Main RF, h = 21, VRF, h=21 = 200 k. V Additional RF, VRF, sub = 10 k. V gtr ® Voltage ratio: VRF, sub/VRF, h=21 = 5% to 8% gtr

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

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

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

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

10 Dipole oscillations excited by VRF, sub • Data for mode spectra at C 1700, 10 ms after full VRF, sub reached • Growth rates faster than usual instability from impedance ® Clean single-mode coupledbunch 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

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

13 Synchrotron frequency distributions • Calculation of synchrotron frequency distributions for all buckets (at constant energy): 1. Calculate normalized potential and identify buckets f 2. Calculate normalized area and synchrotron frequency for set of trajectories of each bucket Bucket area and synchrotron frequency of pure h = 21 bucket: AB 0, h=21, w. S 0, h=21

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

15 Stable Unstable Bucket-by-bucket spread, el ≈ 0. 35 AB 0 ® Synchrotron frequency spreads of stable and unstable cases similar ® Decoupling of synchrotron frequency distributions?

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

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

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

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 k. V from each of the accelerating cavities ® No need for 10 MHz spare cavity •

21 THANK YOU FOR YOUR ATTENTION!