Damping of coupled bunch oscillations with sub harmonic rf voltage
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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?

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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


Damping of coupled bunch oscillations with sub harmonic rf voltage

Overview

  • Introduction

  • Observations in time domain

  • Mode analysis with excitation

  • Possible ingredients for explanation?

  • Summary and outlook


Damping of coupled bunch oscillations with sub harmonic rf voltage

Overview

  • Introduction

  • Observations in time domain

  • Mode analysis with excitation

  • Possible ingredients for explanation?

  • Summary and outlook


Damping of coupled bunch oscillations with sub harmonic rf voltage

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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Overview

    • Introduction

    • Observations in time domain

    • Mode analysis with excitation

    • Possible ingredients for explanation?

    • Summary and outlook


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Very first observations (3 of 18 bunches)

    No additional RF voltage

    Additional 10 kV at hsub = 17

    • Significantly improved longitudinal stability with additional RF


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Overview

    • Introduction

    • Observations in time domain

    • Mode analysis with excitation

    • Possible ingredients for explanation?

    • Summary and outlook


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Overview

    • Introduction

    • Observations in time domain

    • Mode analysis with excitation

    • Possible ingredients for explanation?

    • Summary and outlook


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Bucket-by-bucket spread, el ≈ 0.35 AB0

    Unstable

    Stable

    • Synchrotron frequency spreads of stable and unstable cases similar

    • Decoupling of synchrotron frequency distributions?


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    Overview

    • Introduction

    • Observations in time domain

    • Mode analysis with excitation

    • Possible ingredients for explanation?

    • Summary and outlook


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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?


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    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


    Damping of coupled bunch oscillations with sub harmonic rf voltage

    THANK YOU FOR YOUR ATTENTION!


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