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

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

Overview 3 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 h sub = 6…21 D. Boussard, J. Gareyte, D. Möhl, PAC71, pp Without RF/2With RF/2 h = 20

5 Beam conditions and measurements High intensity 50 ns LHC-type beam:  18 bunches in h = 21, N b ≈ 1.95 · ppb,  l ≈ 0.5 eVs  Reduced longitudinal blow-up to force coupled-bunch instability  Spare cavity started 10 ms after crossing  tr, 50 ms rise time  Kept on until end of acceleration  Voltage ratio: V RF, sub /V RF,h=21 = 5% to 8% Main RF, h = 21, V RF,h=21 = 200 kVAdditional RF, V RF,sub = 10 kV  tr

Overview 6 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 voltageAdditional 10 kV at h sub = 17  Significantly improved longitudinal stability with additional RF

Harmonic number scan Harmonic number of additional voltage scanned: h sub = 6…20 h = 6 h = 16 h =  h sub = 6…16: unstable  h sub = 17…20: stable 8

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

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

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

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

Synchrotron frequency distributions Calculation of synchrotron frequency distributions for all buckets (at constant energy): 1.Calculate normalized potential and identify buckets 2.Calculate normalized area and synchrotron frequency for set of trajectories of each bucket Bucket area and synchrotron frequency of pure h = 21 bucket: A B0,h=21,  S0,h=21  13

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

Bucket-by-bucket spread,  l ≈ 0.35 A B0 Unstable Stable  Synchrotron frequency spreads of stable and unstable cases similar  Decoupling of synchrotron frequency distributions? 15

Excited by phase loop? 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 f s ) loop filter 16  Phase loop seems not perturbed, independent from h sub h sub = 16 h sub = 17 Pure h = 21 Unstable Stable Phase jump as test excitation Without additional RF Preliminary

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

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

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: h sub = 6…16 Significant stabilization: h sub = 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 h sub = 16 and 17  How are coupled-bunch oscillations with V RF,sub excited?  What is different between additional voltage at h sub = 16 or 17? 19

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 20

21 THANK YOU FOR YOUR ATTENTION!