Coupled-bunch oscillation feedback studies 1 H. Damerau LIU-PS Working Group Meeting 20 February 2013 Many thanks to R. Garoby, S. Gilardoni, S. Hancock, M. Migliorati, E. Shaposhnikova, L.Ventura

Overview 2 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Overview 3 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

4 Introduction To control longitudinal coupled-bunch oscillations, a new wide- band kicker cavity will be installed during LS1 For MD studies, the spare 10 MHz cavity C10-11 can be used as kicker cavity for the feedback  Tuned to the modes to be damped, low bandwidth  But huge kick voltage available for MDs Difficult to perform tests in 2012 as the coupled-bunch feedback was required for high-intensity beams to the LHC  Extensive studies during this year’s short run  Summary of few measurements, >80% of data yet to be analyzed  All results are still preliminary

Coupled-bunch oscillations, time domain 5 Bunches oscillate with different phases (and amplitudes) Example of an n = 12 mode (  ≈ 206  ) Mode number defined by phase advance from bunch-to-bunch: Additionally the bunches may oscillate dipolar (m = 1), quadrupolar (m = 2), sextupolar (m = 3), etc. Present analysis: dipolar modes, m = 1  How does this look like in frequency domain?  = 2  n/h

Coupled-bunch oscillations, freq. domain 6  Synchrotron frequency sidebands of the f rev harmonics: F. Pedersen, F. Sacherer, PAC77, pp  In the case of LHC-type beams in the PS (h = 21) upper lower

Coupled-bunch oscillations, freq. domain 7 upper lower  Each mode n is observable as an upper side-band of n f 0 or as a lower sideband of (h - n)f 0  Damper: Suppress synchrotron frequency side-bands  Damping and excitation of mode n may be achieved at: DetectionExcitation harmonicSide-bandharmonicSide-band nuppern h - nlowerh - nlower h - nlowernupper n h - nlower normal cross f rf 2f rf

Frequency domain feedback system 8 + Filter + + h 1 f 0 (sin) h 1 f 0 (cos) h 1 f 0 (sin) h 1 f 0 (cos) Beam signal (WCM) Longitudinal kicker Test Perturb. Up-conversionDown-conversionFilter and perturbation Filter J.-L. Vallet Test Perturb.

Overview 9 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Measurements (1/2) 10 1.Feedback in anti-phase to adjust optimum phase 2.Inject perturbation close to f s (max. at ~ 395 Hz) Beam energy, E13 GeV(C1800) - 15 GeV(C1850), or scan 9 to 26 GeV RF voltage~165 kV Synchrotron frequency, f s ~400 Hz Longitudinal emittance<0.7 eVs, pushed to stab. limit Feedback in anti-phase Excitation

Measurements (2/2) 11 3.Excite with perturbation and observe natural decay 4.Time domain mountain range data for analysis 5.Long. emittance

Mode analysis 12 → 18 oscillation amplitudes  n, 18 phases  n + f s 3.Discrete Fourier transformation → 18 mode amplitudes  k, 18 mode phases  k 1.Fit position of each bunch during each frame 2.Dipole oscillations: fit sinusoidal function to motion of bunch Why not measuring in frequency domain with a spectrum analyzer? Revolution frequency f rev sweeps along the cycle Spurious f rev lines due to 6/7 filling (18 bunches in h = 21) Synchrotron side-bands very close to strong f rev lines Measurement in time domain: Example with old data

Overview 13 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Injection of perturbation 14 + Filter + + h 1 f 0 (sin) h 1 f 0 (cos) h 1 f 0 (sin) h 1 f 0 (cos) Beam signal (WCM) Longitudinal kicker Test Up-conversionDown-conversionFilter and perturbation Filter Test Perturb. (norm. sin) Perturb. (norm. cos)  Swap phasing of injected perturbation, perturb only sin/cos

Excitation (feedback at h FB = 14, 18b) 15 Single side-band  single mode

Overview 16 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Mode scan with 18 bunches in h = Excite each mode individually and measure mode spectrum  Some modes can be excited very cleanly, others as a mixture; artefact? n

Mode scan with 21 bunches in h = n 21 - n Excite each mode individually and measure mode spectrum 2n2n 2n - 21  Clean observation of all possible modes

Overview 19 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Kick voltage measurement 20 1.Time resolved spectrum of C10-11 cavity return Time Excitation 2.Extract an normalize relevant harmonic Excitation Damping  Amplitude modulation from carrier (at hf 0 ) and f s side-band (hf 0 ± f s )  Fit gives initial damping amplitude and time (+ f s and phase)

Damping time/kick strength 21 Anti-phase excitation Perturbation excitation Not corrected for natural damping time Damping time from kick voltageMax. kick voltage vs. mode ampl.  About 1 kV/ns for the given damping times  Little dependence from mode number or gain  Damping time and feedback gain changes with frequency Very preliminary!

Residual carrier at f 0 harmonic (1/2) 22 Feedback out: 100 mV/div Due to an offset problem with the up conversion mixers, a spurious carrier is generated at the revolution frequency harmonic  Significant power need from kicker cavity  No contribution to feedback action Offset well compensatedNormal operating condition  Will be resolved with digital low-level hardware for the coupled bunch feedback after h = 14 Feedback out: 200 mV/div

Residual carrier and f 0 harmonic (2/2) 23 Offset well compensatedNormal operating condition Try anti-phase excitation with well compensated offset: Feedback out: 100 mV/div h = 14 Feedback out: 200 mV/div  Residual carrier at revolution frequency harmonic excites the corresponding coupled-bunch mode For h = 14, this confirms earlier measurements, driving instabilities Unfortunately no data taken for h = 17…20; expect improved stability …too late…

Overview 24 Introduction Measurements and mode analysis Excitation, symmetry of modes Mode scans Kick voltage Cross damping Preliminary summary

Cross-damping 25 upper lower  Each mode n is observable as an upper side-band of n f 0 or as a lower sideband of (h - n)f 0  Important for PS longitudinal feedback:  Detection easier at h FB = 10…20  Longitudinal kicker easier at h FB = 1…11 f rf 2f rf Kick Measure  How can this be checked with the existing feedback?

Cross-damping, h 1 + h 2 = Filter + + h 1 f 0 (sin) h 1 f 0 (cos) h 2 f 0 (cos) h 2 f 0 (sin) Beam signal (WCM) Longitudinal kicker Perturb. Up-conversionDown-conversionFilter and perturbation Filter Need to flip side-bands: lower  upper  Swap sin/cos of LO signals to down- or up-conversion mixers

Test with feedback crossed 27 Tested combinations h = 8/13, 9/12 and 10/11  Feedback behaviour as expected Detect at h = 13  damp with C10-11 at h = 8 Detect at h = 8  damp with C10-11 at h = 13

What remains to be analyzed… 28 Mode scans with 50 ns and 25 ns beams Damping times for modes around h = 19 and 20 along the cycle Damping times versus longitudinal emittance, intensity and feedback gain Coupled-bunch mode spectra without feedback nor excitation  Extract relevant voltage requirement and estimate performance of new longitudinal damper

Preliminary (qualitative) summary run: excellent opportunity for tests  No need for very high intensity beams to LHC  Coupled-bunch feedback and the spare cavity available Clean mode scans: modes are well decoupled Shown that spurious mixer offsets with existing hardware do not contribute to feedback action Demonstrated working feedback with detection and excitation at different harmonics  Lots of interesting data yet to be analyzed

30 THANK YOU FOR YOUR ATTENTION!