992021 FCC Transverse Feedback FCChh Transverse Feedback System

9/9/2021 FCC Transverse Feedback FCC-hh Transverse Feedback System Wolfgang Hofle for CERN BE-RF 1

Overview q FCC - hh transverse feedback system q Injection damping (dipole modes) q Mitigation of Coupled Bunch Instabilities q Mitigation of Intra-bunch modes FCC Transverse Feedback q q 9/9/2021 Strategy q Plan on strong coupled bunch feedback as in LHC q q q TMCI, Ecloud known territory from LHC (including injection damping) Intra-bunch feedback test in simulation Outlook 2

Principle of Transverse Feedback q Two or more Pick-ups per beam and plane (H and V) 9/9/2021 FCC Transverse Feedback q Extension to four pick-ups under way for LHC Run 2 q Feedback with FIR filters for phase adjustment – multiple turns of delay q Gain limited by type of feedback filter used q Vector sum for more robust phase adjustment q Fractional delay can be explored for very low frequency modes and fast growth rates (FCC) Tsignal = Tbeam + n Trev 3

LHC Transverse Feedback System and Perspectives for FCChh / FCC week Rome 2016 / W. Hofle LHC ADT Design Parameters injection relative emittance increase at injection value energy E 450 Ge. V emittance (norm) e 3. 5 mm injection error ainj 4 mm @ b=185 m increase w/o FB ainj 2/(2 s 2) (5. 92) max increase of e (De/e)max 0. 025 Blow-up factor Fe < 4. 22 x 10 -3 Damping time blow-up factor de-coherence time (in design report due to Q’) Full tune spread 1. 3 x 10 -3 ultimate LHC 1. 7 e 11 ppb nominal LHC 1. 0 e 11 ppb 9/9/2021 EPAC’ 08, THPC 121 LHC Design Report CERN-2004 -003 LHC Run 1 (50 ns): in practice smaller emittances available from injectors LHC Run 2 (25 ns): nominal beam parameters 4

FCC-hh TFB: 25 ns -100 km option FCC tentative parameters FCC Transverse Feedback injection value emittance (norm) e 2. 2 mm injection error ainj 1 mm @ b=185 m increase w/o FB ainj 2/(2 s 2) depends on energy max increase of e (De/e)max 0. 05 FCC injection energy options Injection energy in Ge. V Coupled bunch Instability rise times in turns (O. Boine. Frankenheim et al. ) 450 8 … 16 1500 22 … 47 3300 43 … 91 9/9/2021 Fractional tunes: 0. 72 or 0. 32 FCC versus LHC: • smaller design injection error • 0. 5 mm + 0. 5 mm ripple • slower de-coherence • but faster instability (t. b. c. ) de-coherence time (needs determination) Full simulation at injection In presence of • damping • tune spread • Instabilities desirable 5

FCC injection energy options 450 Ge. V case Blow-up factor limits 450 Ge. V 900 Ge. V FCC Transverse Feedback 20 turns damping 1. 5 Te. V 2 Te. V 3. 3 Te. V (baseline) 5, 5. 5 Te. V 13 turns 10 turns 6. 7 turns 5% emittance blow-up and constant injection error (in mm) 9/9/2021 4 turns 6

Injection Oscillations – LHC time domain ADT response LHC run 1 V-plane (2012) 9/9/2021 FCC Transverse Feedback 50 ns bunch spacing standard + hold 144 bunches (4 x 36) 25 ns bunch spacing enhanced bandwidth 144 bunches (2 x 72) Injection oscillation damping 7 damping at edges of batch slower IPAC’ 13, WEPME 43 7

LHC 2012 Run 1 achievements Damping times as measured on first bunch of batch Beam 2 H: 13 turns V: 26 turns 9/9/2021 FCC Transverse Feedback V H Beam 1 H: 16 turns V: 27 turns LHC, curtesy A. Macpherson See also IPAC’ 13, FRXCA 01 Injection kicker ripple slower V-damping 8

9/9/2021 FCC Transverse Feedback Intra-bunch Motion at LHC M=1 M=2 M=3 M=4 Observed intra-bunch motion T. Levens 9

Mitigation of Intra-bunch motion required bandwidth 0. 5 GHz 9/9/2021 FCC Transverse Feedback 1. 0 GHz 1. 5 GHz 2. 0 GHz Intra-bunch Feedback under study in SPS (LIU) See Talk by K. Li @ CERN Chamonix 2016 Workshop 10

R&D: intra-bunch feedback (SPS) BPM 9/9/2021 FCC Transverse Feedback Analog Front End transverse position q q q pre-processed Kicker Active closed loop Feedback Beam Signal Processing ADC sampled position “slices” Analog Back End DAC calculated correction data correction signal capacity to damp intra-bunch instabilities, 4 -8 GS/s digital feedback started as e-cloud instability feedback in SPS also shown to damp TMCI in simulation if synchrotron tune low closed loop experiments in SPS started milestone to demonstrate feasibility: mid 2016 targeted bandwidth 1 GHz, needed BW scales with bunchlength Power Amp pre-distortion drive signal R&D supported by US-LARP for SPS-LIU J. D. Fox et. al 11

SPS MD Results (single bunch) Feedback off Feedback on 9/9/2021 FCC Transverse Feedback Intra bunch motion Beam losses Kevin Li, Injector MD days 2017, https: //indico. cern. ch/event/609486/ 12

9/9/2021 FCC Transverse Feedback FCC Feedback Simulation Effort q Updated to a recent version of the FCC impedance model q Started studies of single bunch instabilities to evaluate complex tune shifts q Chroma scans, Intensity scans, TMCI thresholds q In conjunction with TMCI, first studies of transverse damper system q looking into impact of transfer functions, delays, system bandwidth q Results are being processed, analyzed and compiled (FCC week, IPAC) q Still need to start deployment of multi bunch simulations for coupled bunch feedback with options for 5 ns and 25 ns bunch spacing (driven by resistive wall instability fast instability rise times at low frequency) Jani Komppula, Kevin Li, Wolfgang Hofle 13

9/9/2021 FCC Transverse Feedback Conclusions q Extensive Experience with LHC Transverse Feedback for 25 ns bunch spacing “cut-and-paste” for baseline q Faster rise-times for lower injection energies require attention and possibly a modified approach q Shorter bunch spacings (5 ns) and intra-bunch feedback require simulation effort followed by R&D for kicker and amplifier technology q SPS experience with Wideband feedback system prototype can serve the needs of FCC if beam dynamics experts request such a system 14