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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?

H. Damerau

- LIU-PS Working Group Meeting
- 4 March 2014

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

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

- 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

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

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

Very 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 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

- 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

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

- 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):
- 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

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

Bucket-by-bucket spread, el ≈ 0.35 AB0

Unstable

Stable

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

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

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

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

- 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?

- 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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