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

H. Damerau

LIU-PS Working Group Meeting

4 March 2014

3

Overview

• Introduction

• Observations in time domain

• Mode analysis with excitation

• Possible ingredients for explanation?

• Summary and outlook

4

Overview

• Introduction

• Observations in time domain

• Mode analysis with excitation

• Possible ingredients for explanation?

• Summary and outlook

5

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

D.

Bou

ssard

, J.

Gare

yte,

D.

Möh

l, P

AC

71,

pp

. 1073-1

074

Without RF/2 With RF/2

h = 20 h = 20

6Beam 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

gt

r

gt

r

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Overview

• Introduction

• Observations in time domain

• Mode analysis with excitation

• Possible ingredients for explanation?

• Summary and outlook

8Very first observations (3 of 18 bunches)

No additional RF voltage Additional 10 kV at hsub = 17

® Significantly improved longitudinal stability with additional RF

Harmonic number scan• Harmonic number of additional voltage scanned:

hsub = 6…20h = 6

h = 16

h = 17

8 9 10

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12

13

15

18

19

20

® hsub = 6…16: unstable

® hsub = 17…20: stable

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Overview

• Introduction

• Observations in time domain

• Mode analysis with excitation

• Possible ingredients for explanation?

• Summary and outlook

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

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Mode analysis with additional RF voltage

• Analysis of coupled-bunch oscillations excited by hsub = 6…16

• Mode spectra from time domain data immediately after additional cavity switched on

hsub = 6

hsub = 7

hsub = 14

hsub = 15

hsub = 16

…

® 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

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Overview

• 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: AB0,h=21, wS0,h=21

f

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Synchrotron frequency distributions

• Accelerating case, 30 synchronous phase:

Synchrotron frequency distributions without and with sub-harmonic RF

Accelerating bucket

hsub = 16

hsub = 17

Pure h = 21

f

® Increased spread compared to stationary buckets

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Bucket-by-bucket spread, el ≈ 0.35 AB0

Un

stab

leS

tab

le

® Synchrotron frequency spreads of stable and unstable cases similar

® Decoupling of synchrotron frequency distributions?

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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 fs) loop filter

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® Phase loop seems not perturbed, independent from hsub

hsub = 16

hsub = 17

Pure h = 21

Un

stab

leS

tab

lePhase jump as test excitation

Without additional RF

Preliminary

Excited by VRF,sub and impedances?

Bunch oscillation amplitudes

Mode oscillation amplitudes

500 kturns 500 kturns

Bu

nch

osc

illa

tion

am

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e [

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.]B

un

ch

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.]

Mod

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.]M

od

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a.u

.]

• Preliminary tracking studies by M. Migliorati with impedance

hsu

b =

10

hsu

b =

17

18

® Again no conclusive difference between hsub < 17 or hsub ≥ 17

Preliminary

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Overview

• 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: 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?

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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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THANK YOU FOR YOUR ATTENTION!