0 1 Studies with the PS coupledbunch feedback

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1 Studies with the PS coupled-bunch feedback and recent simulations H. Damerau, L. Ventura Machine Studies Working Group 03/02/2017 Many thanks to T. Bohl, M. Haase, S. Hancock, M. Migliorati, M. Paoluzzi, D. Perrelet

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 2

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 3

Introduction • Major limitation for LHC-type beams in PS: Longitudinal coupled-bunch instabilities during acceleration and on flat-top • Existing coupled-bunch feedback covers only 2 2 modes • Feedback test system available for MDs in 2016 - Prototype Finemet cavity, up to 5 gaps used so far - Prototype digital LLRF with 10 signal processing chains, covering all possible oscillation modes New range of longitudinal beam parameters accessible Explore performance 4

Timeline 2003/2004 • Coupled-bunch instability with LHC-type beams observed 2005 • Analog feedback covering modes nb = 1/20 and nb = 2/19 • Two accelerating cavities as feedback kickers https: //ab-div. web. cern. ch/ab-div/Meetings/APC/2005/apc 050609/JL_Vallet_slides. pdf 2006/2007 • Study of coupled-bunch oscillations http: //accelconf. web. cern. ch/Accel. Conf/p 07/PAPERS/FRPMN 069. PDF 2008 -2011 • Mode scans along the cycle under various conditions • Instability scales with longitudinal bunch density http: //accelconf. web. cern. ch/Accel. Conf/HB 2010/papers/mopd 52. pdf 2012/2013 • Excitation scans using existing coupled-bunch feedback • All modes are well decoupled from each other • Demonstration of cross-damping (band change) http: //accelconf. web. cern. ch/Accel. Conf/IPAC 2013/papers/tupwa 044. pdf 2014 (LS 1) • Installation of Finemet wide-band kicker • Beam-loading reduction feedback http: //accelconf. web. cern. ch/Accel. Conf/IPAC 2014/papers/tupri 060. pdf 2015 • Excitation of coupled-bunch modes • Damping of all modes simultaneously, 1. 7 · 1011 ppb reached http: //accelconf. web. cern. ch/Accel. Conf/ipac 2016/papers/tupor 028. pdf 2016 • Performance study, 2. 0 · 1011 ppb operationally reached 5

LHC-type beam with 25 ns spacing in the PS Eject 72 bunches h = 21 Controlled blow-ups h = 7 Instability 26 Ge. V/c Split in four at flat top energy Ekin = 2. 5 Ge. V Triple splitting at Ekin = 2. 5 Ge. V 2 nd injection gtr h = 84 Inject 4+2 bunches → Each bunch from the Booster divided by 12 → 6 × 3 × 2 = 72 6

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 7

New 10 MHz cavity impedance model • Studies revealed that 10 MHz cavity four times larger than previously assumed (G. Favia) S of all 10 cavities (real part) Total impedance modelled as three resonators (fit of real part of impedance) Input for Mu. Si. C code (M. Migliorati) 8

Further impedances from RF systems Finemet 20 MHz 40 MHz 80 MHz Little effect in simulations 9

10 Spectrum of coupled-bunch oscillations Typical dipole oscillation, 2 p 10/21 phase advance Corresponding mode spectrum Coupled-bunch oscillations in frequency domain upper lower

11 Simplified mechanism of instability Each dashed line stays for: f 0 - fs f 0 + fs nfrev f • Asymmetry of cavity impedance at synchrotron frequency side-bands of revolution frequency harmonics, e. g. , Impedance h. RF + 2 frev + fs larger than impedance at h. RF - 2 frev - fs Corresponding coupled-bunch mode nb = 2 unstable Smaller impedance asymmetry h. RF ± frev for nb = 1 mode

Simulations with 21 bunches in h = 21 Previous impedance model Single macro-particle per bunch • 1. 3 1011 ppb Updated impedance model Multiple particles per bunch, length ~ 1 m • 2. 6 1011 ppb Mode 2 grows faster than mode 1, as expected Twice shorter rise time when doubling intensity Four times larger impedance translates in three times shorter rise 12

Simulations with 18 bunches in h = 21 Single macro-particle per bunch • 1. 3 1011 ppb • 2. 6 1011 ppb Updated impedance model Multiple particles per bunch, length ~ 1 m Mode amplitude [ns] Previous impedance model Mode nb = 1 Mode nb = 2 Mode nb = 3 Cycle time [s] Rise times not well defined Stays of the order of ~50 ms 13

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 14

Filtering of fs sidebands Transfer function measurements for one signal processing chain • fcenter = 10 MHz corresponding to h. CB = 20 at frev = 500 k. Hz Harmonic of frev attenuated by more than 40 d. B compared to sidebands at ± fs (~300 Hz) Precise 180° phase jump at center frequency Notches covering all other frev multiples and their fs sidebands 15

Tracking filters – coupled-bunch damping sin(hdown frevt + f) cos(h Wall current monitor sin(hup frevt) fs side-band filter ADC DAC fs side-band filter cos(hdown t + f) sin(h f frev t + f) down rev fs side-band filter • • • hdown + huph = h = 21 down. RF up = 3 rd order deep CIC Cavity drive cos(hup frevt) df/dt Gain control Leaky integrator Sharp attenuation to separate ± fs of sidebands from frev harmonics Sharp 180° phase jump at center frequency Programmable gain, delay and phase Demodulation (at hdown)/modulation (at hup) at different harmonics Sideband inversion for cross-damping 16

Extension to multiple harmonics 17 Straight-forward extension to multiple harmonics Cavity return ADC Wall current monitor ADC DAC Single harmonics signal processing EDA-2175, D. Perrelet • • PS 1 -turn delay feedback hardware (4 modules) 3 harmonics per board 12 harmonics to reduce beam induced voltage Beam synchronous clock Cavity drive

PS coupled-bunch feedback overview Single LLRF driving all six cells 6 Wall current monitor Coupledbunch feedback Splitter + amp. -3 d. B fclk = 256 frev Originally: 2 nd feedback loop reducing beam-induced voltage Not needed so far, no effect of Finemet cavity impedance on longitudinal stability observed 18

19 Cross-damping • Profit from spectral symmetry: Avoid detection at low harmonics Detect at f. RF/2…f. RF Use maximum impedance of Finemet damper cavity Apply correction at frev…f. RF/2 Network From beam analyzer induced voltage (low intensity) frf Inversion of side-bands Must lock all numerical local oscillators to frev With all RF sources synchronized cross-damping works as expected

Cross-damping • Successfully commissioned with new hardware in 2015 • Synchronization of all RF sources for down- and up-conversion with respect to h = 1 (frev) Feedback on and off In phase /anti-phase Intermittent state when synchronization missing 20

Measured transfer function of all harmonics • Difficult to measure due to freq. conversion: fout = h. RF fclk/256 - fin Excitation sweeps upwards from 10. 5 frev to 20. 5 frev Detection sweeps downwards from 10. 5 frev to 0. 5 frev fs/frev 0. 0006 Feedback design fully validated All 10 signal processing channels operational 21

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 22

Transition to start of blow-up • First 50 ms after transition crossing crucial Blow-up with 200 MHz only ~40 ms after transition due to frev sweep rate Equivalent intensity: 1. 8 · 1011 ppb Start blow-up Start coupled-bunch feedback Transition Longitudinal emittance at transition as large as possible 23

Quadrupolar coupled-bunch oscillations • Mode analysis of bunch length oscillations (after transition) Average mode pattern Total spread Std. dev Systematic measurements difficult Damping system would need to separate fs from 2 fs side-bands 24

Flat-top • Arrival at flat-top and high-energy splittings • Mode pattern changes due to impedance Feedback off (Nb = 1. 8 · 1011 ppb) Feedback on (Nb = 1. 8 · 1011 ppb) • Previous coupled-bunch feedback did not cover dominant modes No effect Significant improvement of longitudinal stability due to feedback 25

Quadrupolar oscillations at flat-top • Dipole oscillations very well stabilized by feedback • No effect of feedback expected for high order oscillations First measurements in 2015 at start of flat-top C 2595 Feedback on C 2595 Feedback off Quadrupolar coupled-bunch oscillation (2015 data) 26

Coupled-bunch mode comparison • Mode pattern changes at flat-top, as observed for dipole oscillations Flat-top Dipole (2011 data) Acceleration Quadrupole (2016 data) Total spread Std. dev 27

Effect of 80 MHz cavity impedance • 80 MHz cavity for lead ions tuned to 135 k. Hz below proton frequency, but 3 d. B bandwidth about 0. 7 MHz 80 MHz structure during h = 42 84 splitting Gap C 80 -08 closed Gap C 80 -08 open • Perturbation visible at 1. 6 · 1011 ppb Effect on beam quality at extraction? Averaged difference, with and without effect of 80 MHz ion cavity 28

29 Emittance at arrival on flat-top (4 final bunches) Cavities with gap open e. RMS [e. Vs] C 40 -78, C 80 -89 0. 231 C 40 -78, C 80 -89 and C 80 -08 (at ion frequency) 0. 238 Average bunch length at extraction Cavities with gap open 4 s. Gauss [ns] C 40 -78, C 80 -89 4. 03 C 40 -78, C 80 -89 and C 80 -08 (ion frequency) 4. 34 Bunch length at extraction C 80 -08 gap open closed http: //cds. cern. ch/record/1141522/files/AB-Note-2008 -052 -MD. pdf 80 MHz cavity impedance Minor emittance blow-up at arrival on flat-top, but ~0. 3 ns longer bunches due to impedance of additional 80 MHz cavity Expect improvement with new multi-harmonic feedbacks

Maximum intensity at extraction • Coupled-bunch feedback significantly improves beam stability Regularly delivered ~2 · 1011 ppb with nominal longitudinal emittance of el = 0. 35 e. Vs with gaps of unused 40/80 MHz cavities closed Beam quality as at ~1. 3 · 1011 ppb without feedback Feedback off Feedback on 30

Higher intensity? Pushing intensity at expense of larger longitudinal emittance Bare minimum of 40/80 MHz cavities with gap open (C 40 -78, C 80 -89) Trips of remaining cavities C 40 -78 and C 80 -08 due to beam loading Intensity ramp up Overall transmission Nej/(Ninj 1+Ninj 2) Excellent transmission up to 2. 6 · 1011 ppb, even with el > 0. 35 e. Vs No further RF issues related to high intensity 31

Longitudinal beam quality Longitudinal parameters at LIU/HL-LHC baseline intensity: 2. 6 · 10 11 ppb Additional longitudinal blow-up • • • Bunch length increase along the batch Onset of instability Average el at arrival on flat-top: 0. 3 e. Vs (RMS, 4 final bunches) Corresponds to ~0. 45. . . 0. 5 e. Vs per bunch in usual convention 32

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 33

Beam loading in 10 MHz RF cavities Above Nb = ~2 · 1011 ppb: • • 10 MHz cavities tripping due to beam-loading at flat-bottom Before start of voltage program Explanation: • • Six cavities detuned to h = 20 tuned back to h = 7 at end of flat-bottom Fine tuning loop closes with RF voltage, cavity off-frequency before Feedbacks working against beam and cavity off-resonance wrt beam Trips due to amplifier over-current Initial condition h(t) Delay 1 -turn FB start h(t) Fine tuning loop closes IA, C 36, IA, C 46, IA, C 51 50 ms Quick and dirty fix Considering improved pre-tuning of cavities 34

Tripping of Finemet cavity 35 Frequent trips of Finemet cavity, especially with 48 bunch beams 1. Spikes on drive signal 2. Insufficient attenuation of from LLRF revolution frequency harmonics Feedback 21 bunches, h = 21 Feedback 18 bunches, h Beam spectrum (LHC 50 ns) Drive RF to Finemet cav. Total/driven gap voltage Glitches on beam phase loop move nfrev into filter pass-band for short time 21, 18 and 12 bunches in h = 21 Larger harmonic content of beam at 20 frev Reduce gain of FB branch Better interlock logic (PLC) to make power system more robust

Overview • Introduction • Simulations (Mu. Si. C) • New impedance model of accelerating cavities • Coupled-bunch feedback • Results from 2016 beam studies • • • Quadrupole coupled-bunch oscillations Residual impedance of 80 MHz cavities Higher intensity? • Technical issues • Summary and outlook 36

Summary and outlook • Extensive studies with Finemet coupled-bunch feedback Dipolar oscillations well handled Bunch intensity of 2. 0 · 1011 ppb regularly delivered with excellent longitudinal beam quality • Effects at high intensity Quadrupolar coupled-bunch instabilities Not covered by feedback Uncontrolled blow-up due to residual impedance of 40/80 MHz cavities Future 1 -turn delay feedbacks should improve 2. 6· 1011 ppb tested at el ~ 0. 45 e. Vs, very good transmission No other show-stopper than longitudinal stability • Technical issues to be resolved Trips of cavities due to beam loading and reliability of Finemet cavity • Studies in 2017 Make coupled-bunch feedback fully operational (remote control, FESA) Continue study of quadrupolar coupled-bunch oscillations Feedback? Complementary stabilization techniques (Landau cavity, etc. )? 37

38 38 THANK YOU FOR YOUR ATTENTION! H. Damerau, S. Hancock, CERN/GSI Meeting on RF Manipulations and LLRF in Hadron Synchrotrons

39 Spare slides

Choice of frequency ranges: cross-damping Impedance per cell with amplifier Best shunt impedance: 0. 4 to 5 MHz Kick Network analyzer From beam induced voltage (low intensity) Correction frf Preferred detection Measure Detect at 8 frev, damp at 13 frev (2012 test) 1. Detect fs sidebands at 11… 20 frev 2. Correct beam at 1… 10 frev 20 modes 10 signal processing chains 40

Numerical oscillators with azimuth register • Beam synchronous numerical RF sources for down/up-conversion h. RF Reset fclk f sin Counter h. RFF + f F CORDIC cos F F h = 1 t h. RF F h. RF t t Generates any (non-)integer harmonic of frev Programmable harmonic, phase and (virtual) delay Automatically synchronous to common h = 1, no ‘tagged’ clock required Easy synchronization with any other synchronous RF source system Clock frequency choice: 28 frev = 256 frev 111. 7 MHz to 122. 1 MHz 41

Both feedbacks together (1 harmonic) 42 sin(h. BL frevt) sin(h. BL frevt + f) Low-pass Cavity return ADC DAC Low-pass cos(h. BL frevt + f) cos(h. BL frevt) cos(h. CBfrevt + f) h. CB + h. BL = h. RF = 21 Wall current monitor fs side-band filter ADC fs side-band filter sin(h. CBfrevt + f) Signal processing for single harmonic Needed 10 times Cavity drive

First damping of coupled-bunch oscillations • Single signal processing chain at 20 frev, digital LLRF + Finemet cavity • Nominal LHC 25 ns beam, 18 bunches, 1. 3 1011 ppb, reduced el Feedback off unstable Feedback on stable 20 ms/div fs sideband amplitude at 20 frev Drive signal to Finemet cavity 43

Observations along the cycle Mode spectrum during acceleration (~10 cycle average): 21 bunches in h = 21 18 bunches in h = 21 Clean mode spectra for full ring with 21 bunches in h = 21 Mode n = 2 strongest, as independently found in simulations More complicated spectra with 18 bunches (filling pattern) 44

Mode scan with 18 bunches in h = 21 New coupled-bunch feedback LLRF, excitation of each mode All 18 modes can be excited 45

Mode scan with 21 bunches in h = 21 New coupled-bunch feedback LLRF, excitation of each mode Upper side-band: n = nexc Lower side-band: n = 21 - nexc Every oscillation mode from n = 1… 21 can be excited on both side-bands 46