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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

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

H. Damerau

  • LIU-PS Working Group Meeting
  • 4 March 2014
slide3

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide4

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide5

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

slide6

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

slide7

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide8

Very first observations (3 of 18 bunches)

No additional RF voltage

Additional 10 kV at hsub = 17

  • Significantly improved longitudinal stability with additional RF
slide9

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

slide10

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide11

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
slide12

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

slide13

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide14

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

slide15

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
slide16

Bucket-by-bucket spread, el ≈ 0.35 AB0

Unstable

Stable

  • Synchrotron frequency spreads of stable and unstable cases similar
  • Decoupling of synchrotron frequency distributions?
slide17

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
slide18

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
slide19

Overview

  • Introduction
  • Observations in time domain
  • Mode analysis with excitation
  • Possible ingredients for explanation?
  • Summary and outlook
slide20

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?
slide21

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
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