1. SPS and LHC Transverse Feedback Parameter Extraction: An Alternative Approach G. Kotzian, D. Valuch LBOC, 08. December 2015 https://indico.cern.ch/event/467428/ This is an internal CERN publication and does not necessarily reflect the views of the CERN management. 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

2. Background 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

3. Kicker Beam Transfer Function - BTF 2 Beam Position Module SUM Signal Processing Unit BPM Power Amp 2.5ns Bunches BBQ Vector Network Analyzer sinusoidal drive signal sinusoidal return signal Sinusoidal excitation: - const. power - swept frequency “The response of a beam to small […] transverse excitation defines its ‘Beam Transfer Function’ (BTF).” [1] [1] J. Borer, G. Guignard, A. Hoffmann, E. Peschardt, F. Sacherer and B. Zotter, “INFORMATION FROM BEAM RESPONSE TO LONGITUDINAL AND TRANSVERSE EXCITATION”, in IEEE Transactions on Nuclear Science, Vol. NS-26, No. 3, June 1979. 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian RXTX dB(RX/TX) frequency

4. Beam Transfer Function: Interpretation 3 Classical method with VNA (Vector Network Analyzer) − VNA excites transverse resonances (sinusoidal excitation) − Narrowband response recorded per frequency, i.e.  Eigenvalues {Magnitude(freq), Phase(freq)} − {Mag(freq), Phase(freq)} represented as POLAR plot Feedback phase and loop delay adjusted – mostly iteratively − Repeated over several frequency bands KNOB 1KNOB 2 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

5. SPS’15: Semi-Auto Parameter Extraction (1) 4 o basis is the classical method with VNA(s) automation with scripts automatic data collection o Measure OL 1 MHz to 20 MHz (here: Meas39, BPCR.221.V  V2) 20 sweeps x SC period … 15-30 min o Post-processing allows parameters to be extracted, e.g. Phase advance PU  Kicker Feedback COARSE + FINE delay Fractional Tune Loop phase response  Loop STABLE (1.. 20 MHz) Note: measurement time >>15 min, not too practical for quick diagnostics PRELIMINARY (Meas39 - 2015/11/04) Open loop response (polar): 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

6. Fractional Tune 5 Open loop response: Mag(f) dB peak(Mag(f)) : Overlay of 20 measurements: from 1 MHz to 20 MHz Feature extraction: blue = q green = (1-q) PRELIMINARY (Meas39 - 2015/11/04) Useful tool for full-blown analysis… 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

7. Motivation Beam transfer function measurements for ADT: Carried out: − per beam = [B1, B2] − per plane = [HOR, VER] − per pickup = [Q7, Q9] + [Q8, Q10] (in 2016) − frequency bands = [0.5, 1.0, 2.0, 4.0, 8.0, 10.0, 15.0, 20.0] MHz  4 PUs x 2 planes x 2 beams = 16 units to be set-up (in 2016) Current method is rather time consuming − 20 measurements [1.. 20 MHz] − 2..3 min/measurement  approx. 1 h per unit = 16 hours in total “Destructive”  sweeps are [moderately] exciting betatron resonances Requires minimum intensity (i.e. several bunches) for the VNA to accurately resolve signal Result depends on − Machine parameters and beam configurations (tunes, chromaticity, octupole settings, etc.) − Instrument setup − Expertise or “interpretation skills” to read these VNA curves … The SPS damper, with at least 40 cycles created and/or maintained during the run 2014 - 2015 would as well benefit from an alternative method. 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

8. Transverse Feedback Parameter Extraction THE QUEST: “Define method to extract feedback parameters.” condition #1 -- SIMPLE (*) condition #2 -- FAST (*) condition #3 -- NON-DESTRUCTIVE (*) (*) with respect to classical method using VNA Objective:Ultimately we were looking for the universal answer to the question: “Can you please check if the damper is working … ?” 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

9. Outline o An alternative approach - the method: Reconstructing transverse phase space Filter kernels: time domain signal processing o Passive Observation  during injection processes Injection damping Fractional tune o Active Excitation Feedback phase Feedback delay o Potential for offline and online analysis LHC Injection kicker waveform SPS Extraction kicker waveform Advanced Feedback Controller 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian This presentation is not aimed at finding correct feedback parameters. --- It rather tries targeting on providing an efficient/ op(era)tional tool.

10. Transverse Phase Space 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian POSITION SLOPE xnxn x n+1 2πq2πq Analytic signal (time domain = complex valued): Z n = x n + i y n = A n exp(jα n ) Z n+1 = x n+1 + i y n+1 = Z n r exp(j2πq) Z n = A n exp(j2πq * n + φ 0 ) In general: “damping”, “decoherence” fractional tune “feedback phase” Decay factor r: r < 1 … stable r > 1 … unstable r = 1 … steady Need to know also y n …

11. Phase Space Reconstruction 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Phase Shift 1 Phase Shift 2 Analytic signal (complex valued time sequence):

12. Filter Kernels 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

13. 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Time domain …

14. Damping Times per bunch [1] “EMITTANCE GROWTH AT LHC INJECTION FROM SPS AND LHC KICKER RIPPLE“, G. Kotzian, EPAC’08, 2008 Witness bunches low gain  inc. damping Trains with 72 bunches/batch, nominal gain  nom. damping Factor 2 between bunches in the centre an the edge of trains > 12 bunches B2 All bunches excited coherently during one turn. Transverse deflection by ADT << 1 mm.  expected blow-up less than 1 %. Damper was originally designed to counteract maximum injection errors of 3.3sigma corresponding to 4 mm at beta=185m, with an estimated emittance blow-up better than 2% [1]

15. Pathological Case: Over-Damping 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian [1] “TOO MUCH LOVE WILL KILL YOU”, Queen, in ‘Made in Heaven’, 6 Nov. 1995. See also: “MARGINS TO INCREASE ADT GAIN AT INJECTION”, W. Hofle, LBOC 49, 6 Oct. 2015 https://indico.cern.ch/event/451051/

16. 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Initial condition

17. Witness bunches Fractional Tune per Bunch 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Trains with 72 bunches/batch, nominal gain  nom. damping All bunches excited coherently during one turn. B2

18. Kick by ADT: Feedback Phase (1) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Initial condition NB: bunch3 oscillating in counter-phase due to bipolar excitation waveform (kick) All bunches excited coherently during one turn. The kick waveform in use is a bipolar pulse (50% duty cycle) for DC suppression.

19. Kick by ADT: Feedback Phase (2) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Values in GRAD. Measured for injection tunes. This list is not exhaustive. H1B1V1B1V2B1H1B2V2B2 Q7Q9Q7 Q9Q7Q9 160.0-73.553.055.3143.4-86.990.539.7 161.2-74.156.654.6141.5-88.191.242.1 161.3-75.4143.0-87.892.742.6 161.2-74.9141.5-88.192.643.0 161.2-74.554.855.0142.4-87.791.241.2 1.Feedback Phase as measured with transverse kick and analyzed in time domain (26-Jun-2015, injection tunes): H1B1V1B1V2B1H1B2V2B2 Q7Q9Q7 Q9Q7Q9 155-8055 155-809045 2.Feedback Phase as set up (26-Apr-2015, injection tunes): To be noted: 28 measurements < 10 min (!) Values in GRAD. Measured for injection tunes. This list is not exhaustive.

20. Kick by ADT: Loop Delay (1) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Batches of 24 bunches COSINE, or in-phase term N = 2 periods per revolution ADTmDSPUVerM2B1 Acquisition date: 26-Jun-2015 15:48:13.9542 SINE, or quadrature term N = 2 periods per revolution ADTmDSPUVerM2B1 Acquisition date: 26-Jun-2015 15:50:03.9640 Two consecutive measurements: 1)COSINE, N periods per revolution, 1 turn excitation + record oscillation 2)SINE, N periods per revolution, 1 turn excitation + record oscillation

21. Loop Delay (2) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian DELAY ADTmDSPUVerM2B1 Acquisition date: 26-Jun-2015 15:48:13.9542 26-Jun-2015 15:50:03.9640 Measurement and analysis: 1)COSINE, N periods per revolution, 1 turn excitation + record oscillation 2)SINE, N periods per revolution, 1 turn excitation + record oscillation 3)Polar plot of data in the same turn  Loop Delay 0

22. COARSE Loop Delay 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian ADTmDSPUVerM2B1 Acquisition date: 26-Jun-2015 15:48:13.9542 26-Jun-2015 15:50:03.9640  Coarse Delay OK For this measurement N=2. By increasing N, i.e. the number of excitation periods per revolution the time resolution can be further refined.  FINE DELAY

23. FINE Delay Measurement (1) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian If we excite with N = 891 then every other bunch should be kicked, i.e. 10 MHz (Note that the excitation frequency is locked to the RF frequency/10 or 40 MHz): However: increasing N results in a reduced excitation due to limited BW of the ADT power amplifier + kicker (fc = 1 MHz). COSINE, or in-phase term N = 891 periods per revolution:  Exciting EVEN bunch numbers SINE, or quadrature term N = 891 periods per revolution:  exciting ODD bunch numbers  The combination of the two results in a 4-QAM, a.k.a. QPSK

24. FINE Delay Measurement (2) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Evaluate the damping evolution:  During the damping the excitation pattern (SIN + COS) is preserved Shown in this example are the subsequent 25 turns after excitation with N=2 Oscillation damping after excitationFootprint (I/Q) ADTmDSPUVerM2B1 Acquisition date: 26-Jun-2015 15:48:13.9542 26-Jun-2015 15:50:03.9640

25. FINE Delay Measurement (3) 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian  Make use of information content in subsequent decay turns Subsequent turns after excitation with N=891 (10 MHz) Each circle = average over 72 bunches Results of two Pickups (blue Q7, red Q9) ADTmDSPUVerM1B1 Acquisition date: 26-Jun-2015 16:10:17.0775 26-Jun-2015 15:50:03.9640

26. Potential for offline analysis 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian Injection steering Incoming batch 12x2 bunches (Ions) Circulating bunch being “tickled” at injection Reconstructed transverse phase space at MKI as seen by the damper:

27. Potential for offline analysis 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian http://indico.cern.ch/event/398182/contribution/3/attachments/798590/1094540/LHC_commissioning_status.pdf “LHC COMMISSIONING STATUS – MKI”, L. Stoel et.al., LHC Injection and Beam Dump Meetings (LIBD), 9 June 2015 Injection steering

28. 08. Dec 2015 SPS  LHC BEAM1 SPS  LHC BEAM2 SPS Extraction B1 LHC Injection B1 SPS Extraction B2 LHC Injection B2 FOR DISCUSSION LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

29. Advanced Feedback Controller 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian POSITION SLOPE xnxn x n+1 2πq2πq TUNE LINE Kick 1 Kick 2 "So much for theory.“  SPS Test bed 2016

30. Summary and Conclusions Alternative method for feedback parameter extraction − Single transverse excitation, generated by ADT − Data acquisition provided by ADT BeamPos Modules − Analysis carried out solely in time domain – no FFT-ing − Impact on emittance marginal Tests can be carried out as routine health checks − Measure all PUs at once (notifications scheduled in parallel) Ready-to-use for ObsBox data processing (single PU) Allows data processing for − Feedback parameters (gain, phase, delay) − Beam parameters (tune, damping time/decoherence time) − Kicker waveforms (SPS extraction / LHC injection kickers) Novel ideas for alternative feedback controllers − New inputs: tune, oscillation amplitude, phase advance 08. Dec 2015 LBOC / Feedback parameter extraction: an alternative approach – G. Kotzian

31. THANK YOU 03. Dec 2015 SPS Damper - Gerd Kotzian30 Questions? Many thanks to: W. Hofle, E. Jensen, V. Kain, M. Kuhn, F. Velotti, for fruitful discussions