Sensitivity of LHC ADT to intra-bunch motion

1. WORK IN PROGRESS Sensitivity of LHC ADT to intra-bunch motion Gerd Kotzian, Wolfgang Hofle, Daniel Valuch HSC meeting, 22. January 2014 Sensitivity of LHC ADT to intra-bunch motion

2. Transverse Damper in General • The transverse damper is a feedback system: it measures the bunch-by-bunch oscillations and damps them by fast electrostatic kickers. • Key elements: • Beam position monitor(s) • Signal processing system • Power amplifiers • Electrostatic kickers • Key parameters: • Feedback loop gain, phase, and total loop delay • Kick strength • System bandwidth D. Valuch, “TRANSVERSE FEEDBACK: HIGH INTENSITY OPERATION, ABORT GAP CLEANING, INJECTION GAP CLEANING AND LESSONS FOR 2012”, in LHC Beam Operations Workshop, Evian 2011. Sensitivity of LHC ADT to intra-bunch motion

3. LHC Transverse Damper (ADT) Sensitivity of LHC ADT to intra-bunch motion

4. Analog Front-End • Apply and test various input combinations and evaluate the output responses. long. profile sym asym no internal saturation allowed Analog Processing Digital Processing norm. transverse position trans. oscillation pattern movement of centre-of-charges even sym odd sym Sensitivity of LHC ADT to intra-bunch motion

5. Analog Front-End GOAL: • to have 1 position reading per bunch • bunch-synchronous digitization, sampling frequency fs = 40.08 MHz • no cross-talk between adjacent bunches (a.k.a. ISI – Inter-Symbol-Interference) at the ADC input • time-domain response: Sampling points (40 MHz) no cross-talk to adjacent bunches Sensitivity of LHC ADT to intra-bunch motion

6. Analog input signal to the sampling ADC: Discrete-time sequence of bunch-to-bunch positions as seen by the damper signal processing Sensitivity of LHC ADT to intra-bunch motion

7. Beam Position Module (BPos) – Current HW Calculates normalized beam position bunch by bunch, independent of intensity Sensitivity of LHC ADT to intra-bunch motion

8. BPMC – Coupler Type Pick-ups logarithmic scale: dBMax(1V/m), 70 dB range Frequency Domain |ZT (w)| ^ ZT (w) = ZT j sin(wT0/2) e -jwt/2 t ^ ZT … load or short Beam L=150 mm … assuming w f=1/(2t) T0 = 2 L/c PU output voltage, matched in 50 Ω notches in freq. response direct representation of the bunch profile Sensitivity of LHC ADT to intra-bunch motion

9. BPMC – Coupler Type Pick-Ups … transverse offset • Peak voltage (beam centered) for ultimate beam @ collision: ~140 V  very large • Position information encoded in the signal amplitude: AM-modulated! • Strong common signal (Σ), with (ideally) only small contribution by difference signal (Δ) • Why not sample and digitize & directly?  limited dynamic range • most of the of the ADC input range would be consumed by common signal Sensitivity of LHC ADT to intra-bunch motion

10. Coaxial Transmission Lines max. PU response @ 500 MHz max. PU output (σ=0.375 ns) @ 320 MHz max. signal outputafter 650m COAX @ 180 MHz (σ=0.375 ns) • cable attenuates to levels acceptable to hybrid(signal transmission over 500 – 700m) • Coaxial transmission line adds dispersion to pulse response: • Frequency domain: maximum from PU output @ 500 MHz • after the cable the Frequency maximum lowered to approx. 180 MHz Sensitivity of LHC ADT to intra-bunch motion

11. 180o – Hybrid: Sum & Delta Coax line Tunnel-SR4 (500-700m, 7/8” Flexwell) CONVOLUTION A 0o 0o B 0o 180o MODULATION CONVOLUTION • Hybrid calculates from and two signals: • Assuming ideal Hybrid, i.e. no cross-talk between and . • Combine to eliminate-dependence of position For a set of Hybrids (M/A-COM H9) the average cross-talk at 400 MHz was found to be better than -40 dB. For more details see IBIC 2013, WEPC12 Sensitivity of LHC ADT to intra-bunch motion

12. Intra-Bunch Excitation = Modulation here with Sensitivity of LHC ADT to intra-bunch motion

13. 180o – Hybrid Output: Time and Freq. Domain CONVOLUTION MULTIPLICATION …Fourier transform and its inverse, MODULATION CONVOLUTION Transverse oscillation causes shift in the spectrum … Sensitivity of LHC ADT to intra-bunch motion

14. Band Pass Filter 400 MHz IN OUT • Why Band Pass Filter? • Look only at 400 MHz component • Harmonic chosen for simplicity: less complexity in terms of HW • “Sampled line” type comb filter (9 sections) D. Valuch and P. Baudrenghien “Beam Phase Measurement and Transverse Position Measurement Module for the LHC”, in LLRF07 Workshop, Knoxville TN, USA, October 2007. Sensitivity of LHC ADT to intra-bunch motion

15. Band Pass Filter 400 MHz “Analogue version of digital FIR filter” 1st replica 2nd replica 3rd replica 9th replica • where is the response of the directional coupler: • bipolar pulse (same shape as ) Filter response designed for time-limited impulse response Tresp < 25 ns:  rectangular window shorter than bunch spacing  no mixing between adjacent bunch signals Sensitivity of LHC ADT to intra-bunch motion

16. Band Pass Filter response BP directional coupler response: Delay-line response: side lobes due to rect. window Band Pass filter response: phase zero at DC, 800 MHz, etc. max. at 400 MHz, 1200 MHz, etc. Sensitivity of LHC ADT to intra-bunch motion

17. Band Pass Filter output: Signal Sensitivity of LHC ADT to intra-bunch motion

18. Band Pass Filter output: Signal “Deformations” in wavelet mostly due to asymmetries around 400 MHz, i.e. dispersion of cable Sensitivity of LHC ADT to intra-bunch motion

19. I/Q – Demodulator and Baseband Sampling D. Valuch and P. Baudrenghien “Beam Phase Measurement and Transverse Position Measurement Module for the LHC”, in LLRF07 Workshop, Knoxville TN, USA, October 2007. Designed in 2006 information encoded in the envelope for the RF signal “RF” domain Base-band (DC domain) Demodulation Sensitivity of LHC ADT to intra-bunch motion

20. I/Q – Demodulator: Signal DEMOD examine in base-band (around DC) with: In-phase component of 400 MHz = real part  symmetric; cosine Quadrature component of 400 MHz = imaginary part  anti-symmetric; sine Sensitivity of LHC ADT to intra-bunch motion

21. I/Q – Demodulation: Signal DEMOD DEMOD Sensitivity of LHC ADT to intra-bunch motion

22. RECAP: on Mixing & Convolution only Sensitivity of LHC ADT to intra-bunch motion

23. RECAP: on Mixing & Convolution Sensitivity of LHC ADT to intra-bunch motion

24. I/Q – Demodulation: Signal In-phase component (even sym.): DEMOD Quadrature component (odd sym.): where room to play Sampling point • Flat plateau (= stretched pulse) for sampling with ADC • Possibility – to some extend – to shift hardware complexity between and Sensitivity of LHC ADT to intra-bunch motion

25. I/Q – Demodulation: Signal long. bunch profile DEMOD baseband bunch signal (400 MHz comp.) Sampling • Adjacent bunch signals are well separated (some overlap in the tails, but has no influence on the sampled values) Sensitivity of LHC ADT to intra-bunch motion

26. I/Q – Demodulation: Signal MOD DEMOD In-phase component: Shifting the spectrum … and down by … up by Quadrature component: MOD DEMOD with • Order of multiplication is important! • Transverse position modulation • demodulation with Sensitivity of LHC ADT to intra-bunch motion

27. Sampling of I/Q in and Out of a continuous-time signal one value is picked: The discrete-time representation of the continuous-time signal through periodic sampling is obtained from the relation Since we have no cross-talk, i.e. it follows for : masking / sifting property Sampling point Sensitivity of LHC ADT to intra-bunch motion

28. Beam Position Module (BPos) – Current HW Normalized bunch position calculation angle fDS determined during setting-up, different settings required for different gains in pre-amplification chain this factor becomes one if properly adjusted – will be assumed in the following Sensitivity of LHC ADT to intra-bunch motion

29. NUMERICAL SIMULATIONS • MATLAB SIMULINK model (reference) • all blocks included • simulations are time-consuming • exploit the analytical approach and verify versus MATLAB SIMULINK Sensitivity of LHC ADT to intra-bunch motion

30. 25 ns Bunch Spacing (HW “as is”) 25 ns 1e11 ppb, σ=0.375 ns @ INJ Beam current (blue), Bunch position modulation, e.g. 1mm / 20 MHz (red) Pick-up electrode voltages: VA (blue), VB(red) sign flip Hybrid output voltage (after 650 m transmission line) 10x DELTA (blue), SUM (red) sign flip Band Pass filtered output (400.8 MHz) 10x DELTA (blue), SUM (red) Baseband Magnitude () 10x abs{DELTA} (blue), abs{SUM} (red) flat top for sampling Normalized Position (UNSAMPLED) in mm (blue) x10-7 Special e-cloud bunch spacing: ADT compatibility

31. 5-20 ns from SPS 20 MHz “even mode” 5 ns 5 ns 2x 5e10 ppb, σ=0.375 ns @ INJ Beam current (blue), Bunch position modulation, e.g. 1mm / 20 MHz (red) lower peak voltage electrode voltages: VA (blue), VB(red) Hybrid output voltage (after 650 m transmission line) 10x DELTA (blue), SUM (red) “stepped onset” same peak voltage as in the 25 ns case Band Pass filtered output (400.8 MHz) 10x DELTA (blue), SUM (red) Baseband Magnitude () 10x abs{DELTA} (blue), abs{SUM} (red) reduced flat top Normalized Position (UNSAMPLED) in mm (blue) x10-7 Special e-cloud bunch spacing: ADT compatibility

32. 5-20 ns from SPS 20 MHz odd mode: no movement of COG 2x 2e11 ppb, 4σ=2.5 ns @ INJ Beam current (blue), Bunch position modulation, e.g. 1mm / 20 MHz (red) up down Pick-up electrode voltages: VA (blue), VB(red) up Hybrid output voltage (after 650 m transmission line) 10x DELTA (blue), SUM (red) leads to cancelation down Band Pass filtered output (400.8 MHz) 10x DELTA (blue), SUM (red) Baseband Magnitude () 10x abs{DELTA} (blue), abs{SUM} (red) odd mode invisible Normalized Position (UNSAMPLED) in mm (blue) … sensitive to beam profiles and symmetries x10-7 Special e-cloud bunch spacing: ADT compatibility

33. Transverse Excitations (Intra-bunch) • for a given longitudinal profile • apply transverse excitation of 1 mm peak oscillation: • for various frequencies • in even mode: symmetric case • in odd mode: anti-symmetric case • in both even and odd the excitation is aligned with the centre of the long. profile • record the normalized position as implemented in the BeamPos HW • plot the movement of the centre of charges • the longitudinal profile is considered to be symmetric (asymmetric longitudinal profiles convert modes from symmetric to asymmetric and vice versa) Sensitivity of LHC ADT to intra-bunch motion

34. Longitudinal Profile From measurement: Numerical input for simulation: Taken from: “UPDATE ON BEAM INDUCED RF HEATING IN THE LHC”, B. Salvant et.al., IPAC’13, May 12-17, 2012, Shanghai, China: Fig. 2: Effect of reducing bunch length on measured LHC beam spectrum (in dB) from 1.2 ns (in blue) to 1.04 ns (in red). The first notch of the distribution is observed to shift from 1.5 GHz to 1.7 GHz. The peaks beyond 2.7 GHz are believed to be due to the acquisition system bandwidth. Sensitivity of LHC ADT to intra-bunch motion

35. Simulation Results: Symmetric Excitation • Analytical and numerical results are in agreement. • Damper sensitivity on symmetric intra-bunch motion is a function of the longitudinal beam spectra • For the anti-symmetric excitation no movement of the centre of charges, hence • for the anti-symmetric case no oscillation amplitude is detected by the current normalization algorithm  odd modes not visible to the damper • Alternate beam position processing scheme for odd modes… movement of centre-of-charges normalized position as implemented in the BeamPos HW NB: although higher even modes visible the damper is acting only in baseband up to 20 MHz – for damping of higher frequencies  wideband transverse feedback Sensitivity of LHC ADT to intra-bunch motion

36. Simulation Results: Anti-Symmetric Excitation alternate processing scheme to detect and indicate anti-sym. oscillations: • indication of odd-mode oscillations! • Question: since asym. oscillations are detectable by HW, could a narrow-band high freq. damper @ 400 MHz counteract this? Sensitivity of LHC ADT to intra-bunch motion

37. Summary and Conclusions • Signals from even-symmetric intra-bunch movement > 20 MHz seen by damper  corrective measure applied in baseband (up to 20 MHz) • Signal from anti-symmetric (odd-symmetric) intra-bunch movement can be made accessible with only minor firmware update diagnostics indicator • Information on excitation frequency lost  only indication on the presence of instability (transverse) • Damper sensitivity is a function of the longitudinal bunch spectrum (and the oscillation frequency) • Notches in the beam spectra will render the damper blind for certain frequencies • [notches in bunch spectrum ≠ blind frequencies] • mode conversion: even – odd, requires precise adjustment of I/Q coordinate rotation, done during setting up: align Coordinate systems of - and -pairs • even/odd signals visible for asymmetric bunch profiles: • practical implementation: even odd Sensitivity of LHC ADT to intra-bunch motion

38. Questions? THANK YOU Sensitivity of LHC ADT to intra-bunch motion