Bunch-by-Bunch Broadband Feedback for the ESRF ESLS RF meeting / Aarhus 21-09-2005 J. Jacob, E. Plouviez, J.-M. Koch, G. Naylor, V. Serrière Goal: Active damping of longitudinal and transverse multibunch instabilities by means of a broadband bunch-by-bunch feedback ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 1
LFB: what for? HOM driven LCBI for I beam > 50 ma stabilized by Landau damping from transient beam loading in fractional SR filling (200 ma in non symmetric 1/3, later 2/3 filling) 1998: new cavity temperature regulation to ± 0.05ºC, for precise control of HOM frequencies: stable up to 200 ma in uniform and 2 x 1/3 filling However, no cavity temperature settings found to escape HOM driven LCBI over full 0 to 250 ma range Longitudinal Feedback LFB: will allow to Increase instability thresholds by a factor up to about 5, thereby: Damp HOM driven LCBI for 250 ma. 300 ma Less sensitivity to RF parameters for normal operation at 200 ma (tuning angles, power distribution, cavity voltages, transmitter phasing and associated detectors) RF working points easier to tune and more reliable Possible tests at 5 GeV with 400 ma (factor 4 more instable) ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 2
TFB: what for? Transverse instabilities: Resistive wall instability Ion trapping instability No HOM driven TCBI observed, since thresholds above RW instabilities and therefore hidden mastered by increasing the chromaticity At expense of dynamic aperture Transverse Feedback TFB will provide: Same stability at reduced chromaticity Increase in current at reasonable chromaticity Effectiveness against Ion trapping to be checked ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 3
LFB / TFB This talk: principle and design of bunch-by-bunch feedback explained in detail for LFB LFB & TFB developed in parallel LFB & TFB will make use of identical Digital Signal Processor hardware ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 4
Synchrotron equation - HOM / LFB τ = ˆ τ e jωt ˆ τ e jωt ω 2 s0 + 2 jω τ s 2 ω = αv ( t) T E / e 0 0 HOM with ω pω + nω + ω HOM RF 0 s0 External Perturbation V ( t) = ω I ( jr HOM beam HOM X HOM ) ˆ τ e jωt R HOM produces anti-damping, which cancels natural damping for Coupled Bunch Mode of order n when: I beam 2ω st0 E0 / e = τ αω R Feedback: must provide voltage to re-establish sufficient damping j t Pick up + detector: measure ˆe ω j t τ (easy) or ˆ ε e ω (difficult) s HOM HOM Calculate kick: V ( t) = j[ ω V ( t) = [ ω HOM HOM Apply the kick via an adequate kicker I I beam beam R R HOM HOM ] ] Adjustable GAIN MAX MAX ˆ τ e α ω E s 0 jωt, ˆ ε e jωt, differentiation! no differentiation! ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 5
LFB Gain? The natural damping time at the ESRF is τ s = 3.6 ms As shown later, the digital processing will allow an active damping time of down to about τ damp = 0.5 ms τ s /7 for which the gain will have to be: Vˆ ˆ τ kick = [ ω HOM I beam R HOM ] MAX = 7 2ωsT E0 τ α / e 0 = s 4.7 V/fs or NB: this has nothing to do with: dτ/dt α ε /E 0 ˆ ε / ˆ τ = Δε / ΔΦ 352 MHz = 3.3 MeV/ 0. 4 kev / fs ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 6
LFB - Longitudinal feedback - principle Bandwidth: f RF /2 = 176 MHz Strength will depend on quality of phase signal measurement: Resolution (S/N, ADC, ) Spurious signals: RF transmitter noise, Injection glitch, beam loading phase transients Phase detection at 1.4 GHz Σ 200 MHz BW low pass ADC in FPGA processor DAC out RF clock 1.2 GHz to 1.4GHz BW cavity RF clock 1.4 GHz power amplifier 4 x 50 W = 200 W QPSK modulator [ inspired from PEP II, ALS, DAΦNE, ELETTRA, design ] ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 7
Phase measurement - Principle RF mixer (phase detector) Beam pick up Σ 200MHz BW output 14 bits ADC RF combiner RF clock Phase detector sensitivity [ f(freq) ] Thermal noise (R = 50Ω, B = 176 MHz) Phase detector turn by turn resolution: Work at 4 frf = 1.4 GHz τ resolution: 14 bit ADC, LSB = δφ, usable range ± 8000 LSB V noise 10 mv / = ktbr 6μV 5 10-4 4 fs @350 MHz δτ 1 fs / turn Δτ detect-range ±8 ps Suppression of spurious signal (RF noise, transients) below ±8 ps! ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 8
Phase measurement - spurious mode 0 level 1V/ RF degree 7ps/degree Will not saturate the ADC (<8ps), but would result in a too high correction signal 2.5ps rms.4ps rms ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 9
Phase measurement - beam loading transients 2 x 1/3 filling Would put +/-15 V at the input of the ADC Must be reduced by 30dB (or 31) in the analog front end. ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 10
Phase measurement - pick-up and RF front end RF mixer Beam pick up Σ Comb Generator filter 200MHz BW output 10 KHz BW output FPGA RF combiner The comb generator turns each pulse induced by the bunch in 4 pulses, improving the sensitivity of the phase detection The reference signal of the mixer is the 4th harmonic of the RF frequency in order to multiply the phase resolution by 4 X 4 Φ RF clock PLL The PLL keeps the mixer low frequency output level equal to 0V The RF transformer bandwidth is 0.1 MHz to 200 MHz, attenuating the 0 mode signal by an extra 30 db To cope with the phase shits due to the beam loading in the non uniform filling mode, a more sophisticated PLL able to compensate for the average phase drift of individual bunches, will be added in addition to the mode 0 suppression ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 11
Output dynamic range: kicker strength Remember: ˆ ˆ τ V kick = 4.7 V/fs for 0.5 ms damping time So, without safety margin: φ detector sensitivity 1 fs/turn Vˆ min kick = 4.7V ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 12
Longitudinal Kicker Design: DAΦNE / SLS kicker adapted to ESRF frequencies HFSS simulation S21 3.5 frf / 3.75 frf / 4 frf 1 0.95 S21 0.9 0.85 0.8 f rf /2 R s loaded Vˆ kick =1700 Ω = P 2R incident s loaded 0.75 1.2 1.3 1.4 1.5 frequency [GHz] V ˆ kick > 600V for P = amplifier 200W Measurement at ESRF: 500 V kick have been verified ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 13
QPSK modulator: bunch by bunch & BW= f rf /2 2 carriers in quadrature at 3.75 f rf : 1 for the even order bunches (176 MHz) 1 for the odd order bunches (176 MHz) The combination of 2 modulated carriers will still use only 176 MHz because they are in quadrature. Σ f RF X15 PLL Π/2 Σ 0 Σ φ f RF /4 in 3.75 f RF Phase trim 4 V bias Bias tee Bias tee Bias tee Bias tee t t t t Fast PDU signals at f RF /4, T RF wide QPSK built up in house using components of the ESRF fast timing system FPGA test out DAC out To kicker amp in ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 14
QPSK modulator - Bunch by bunch kick QPSK scheme for bunch-by-bunch LFB 1.5 1 Kicker signal [a.u.] 0.5 0-2 -1 0 1 2 3 4 5-0.5 Bunches Bunch 0 Bunch 1-1 -1.5 t / Trf ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 15
FPGA digital processor Phase detection at 1.4 GHz Σ 200 MHz BW low pass ADC in FPGA processor DAC out RF clock 1.2 GHz to 1.4GHz BW cavity RF clock QPSK modulator Bunch by bunch feedback: 1.4 GHz power amplifier 4 x 50 W = 200 W parallel processing of all 992 bunches processes shifted by T rf = 2.84 ns Each process sequenced at T 0 = 2.8 μs ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 16
FPGA digital processor Virtex-II from Xilinx 100 Gops Development with System Generator (Xilinx / The MathWorks) Demultiplexer and multiplexer can be synthesized inside the FPGA Data transfer in and out: Required LVDS lines (low voltage differential signals) available on FPGA Ios Four 14 bit ADC channels x 125 MS/s max per channel (ESRF: 4 x 88 MHz) One 14 bit DAC (DDR) at 500 MS/s (ESRF: 352 MS/s) Fast DDR2 RAM 64 MB ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 17
FPGA Filter block: decimation + FIR + mode 0 removal Factor 11 decimation: 11 T 0 = 31 μs 16 TAP FIR: 16 x 31 μs = 0.5 ms = T synchrotron BP filter at fs Differentiation (V kick jτ): phase shift by 90 Total averaging 176, sensitivity: 1fs -> 0.08 fs FIR: (a,b,c,1,c,b,a,0,-a,-b,-c,-1,-c,-b,-a,0) Mode 0 removal ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 18
FPGA Simulation - Decimation & FIR ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 19
FPGA Simulation: Mode 0 and Phase transient suppression Input Signal Output correction Correction with Mode 0 removed Input Signal with phase dift during a turn Output correction ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 20
FPGA Simulation: Damping of instability No feedback Feedback turned on after a delay (effective damping time = 500μs) ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 21
Transverse feedback issues Kicker design: stripline (straightforward) Kicker strength: low (we do the 24x8 bunches cleaning with 2 x 50 W) Signal processing : processing speed and power similar to the longitudinal case. Position measurement resolution: The vertical position measurement is demanding; if we do not want to spoil the emittance we need to achieve a resolution of 1μm over a 200 MHz bandwidth ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 22
Transverse feedback Position detection Σ Σ Δ 200 MHz BW low pass ADC in FPGA processor DAC out RF clock Stripline kicker RF clock Ο/π splitter 0.1 to 200 MHz 100 W power amplifiers ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 23
Correction signal calculation (vertical TFB) Bunch by bunch digital signal processing We assume that the instability signal is an oscillation at the betatron frequency, so we can write: Z = j.g. e jφ ΔZ with Z = correction signal and φ = betatron phase difference between the BPM and the corrector For each bunch, every turn, we derive Z from the ΔZ signal by a FIR band pass filtering centered around qf 0 which provides also the φ phase shift We apply the G. Z correction kick to this bunch at every turn ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 24
Horizontal kicker layout Half view: Stripline U shape to increase the shunt impedance ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 25
Vertical kicker layout ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 26
Status of Multibunch Feedback Most of the hardware installed and tested FPGA system: - 1 st unit expected in October 2005 Software design and writing: - Structure designed and simulated - Tests done with prototype FPGA - First beam data collected - Final software in progress LFB commissioning 1 st tests scheduled in Autumn 2005, now waiting for FPGA Full commissioning in 2006, expected to be operational end of 2006 Protection of amplifier against beam induced peak voltage: Isolator ordered RF switches connected on loads for single bunch currents > 5 ma TFB commissioning: all milestones only a few months after LFB ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 27
Beam power load of amplifier and loads Beam power coupled to each Kicker cable and amplifier Average Power [W] 200.0 180.0 160.0 140.0 120.0 100.0 80.0 60.0 40.0 20.0 0.0 15 ma 16x5.6 ma 4x10 ma Aver Pw - f-domain calc Aver Pw - t-domain calc Peak voltage 200 ma 4500 4000 3500 3000 2500 2000 1500 1000 500 0 Peak Voltage [V] sb 4b 16b 24 x 8 1 third 2 third uniform Fill pattern ESLS RF meeting, Aarhus 21/09/2005 Bunch-by-Bunch Feedback J. Jacob et al., ESRF, Slide 28