Multibunch instabilities from TMBF data at Diamond R. Bartolini Diamond Light Source and John Adams Institute, University of Oxford thanks: R. Fielder, S. Pande, G. Rehm, V. Smalyuk (BNL) Beam dynamics meets diagnostics Firenze, 6 November 2015

Beam dynamics meets diagnostics Outline (Short) review of main results of the theory of multi-bunch instability Data from Diamond TMBF system Impedance analysis and comparison with CST simulations (WIP) Open issues Beam dynamics meets diagnostics Firenze, 6 November 2015

Transverse multibunch oscillations - no wakefields Each bunch oscillates with the betatron frequency x,y In a multi-bunch train without wakefields all bunches are independent The motion can be expanded in Fourier modes, (M bunches = M modes, and in full fill, M = harmonic number) However, without wakefields there is no reason to prefer this set to any other “basis” (i.e. modes are degenerate) Beam dynamics meets diagnostics Firenze, 6 November 2015

Multibunch oscillations - with transverse wakefields Bunches are now coupled by the wakefields Each bunch oscillates with the betatron frequency x,y In the limit of small wakefields (linear wakes) the Fourier modes are eigenvectors of the time evolution, i.e. modes are preserved during the time evolution The betatron oscillation frequency becomes complex Im  damping or anti-damping Re  frequency shift The degeneracy of the Fourier modes is broken, i.e.  = ()

Complex frequency shift and driving impedance For zero length (point-like) bunches (see e.g. A. Chao) e.g. coherent tuneshift (Re = ImZ) growth rate (Im  = ReZ) mode  is driven by the impedance computed at (pM + )0 +  Beam dynamics meets diagnostics Firenze, 6 November 2015

Complex frequency shift and driving impedance For Gaussian rigid bunches with rms bunch duration  e.g. coherent tuneshift (Re = ImZ) growth rate (Im  = ReZ) mode  is driven by the impedance computed at (pM + )0 +  Beam dynamics meets diagnostics Firenze, 6 November 2015

Beam dynamics meets diagnostics Non rigid bunches For bunches with finite length – and internal modes (see e.g. A. Chao) Beam dynamics meets diagnostics Firenze, 6 November 2015

Complex frequency shift and driving Impedance For bunches with finite length – and internal modes (see e.g. A. Chao) e.g. coherent tuneshift (Re = ImZ) growth rate (Im  = ReZ) mode (, l) is driven by the impedance computed at (pM + )0 +  + ls Beam dynamics meets diagnostics Firenze, 6 November 2015

Complex frequency shift and driving Impedance With non-zero chromaticity the bunch frequency spectrum is shifted by  =  / and naming ,l = (pM + )0 +  + ls e.g. coherent tuneshift (Re = ImZ) growth rate (Im  = ReZ) The bunch samples the impedance at ,l but the bunch frequency spectrum is shifted at ,l –  Beam dynamics meets diagnostics Firenze, 6 November 2015

Sampling in time and aliasing in frequency A mode  sampled turn-by-turn corresponds to the frequency frac(x,y) aliased in [0, 0]  frac(x,y) i.e. fractional part of the tune A mode  sampled bunch-by-bunch corresponds to the frequency 0 + x,y aliased in [0, M0]  i.e. baseband of the RF For real signal the spectrum is further folded symmetrically in [0 , M0/2] 1 2 3 Modes  = 0 , 1, , ..., M – 1 Modes  = 0 , 1, , ..., M – 1 folded, i.e. – 1 = M – 1 – 2 = M – 2 ... -1 1 -2 2 -3 3

Beam dynamics meets diagnostics Grow damp experiment 1) Artificially excite mode  by using a stripline driven at the frequency (pM + )0 +  2) Stop the excitation and measure free oscillations (damped or anti damped) 3) Run feedback to damp any unstable mode or any residual oscillation Repeat for all modes  = 0 , 1, ..., M - 1 Beam dynamics meets diagnostics Firenze, 6 November 2015

Grow damp experiment at Diamond 936 bunches - 2 ns (500 MHz) – full fill M = 936 530 kHz revolution frequency – Current up to 300 mA; bunch length 15-25 ps rms – with current 1) Artificially excite mode  for 250 turns at the frequency (pM + )0 +  p is optimised on the specific stripline design and operating frequency (at Diamond p = 0 corresponding to 0 – 250 MHz band) 2) Stop the excitation and measure free oscillations for 250 turns transfer data *** impossible to transfer fast all bunch-by-bunch turn-by-turn data only the Fourier component (amplitude and phase) at the frequency of interest for mode  is stored 3) Run feedback to damp any unstable mode or any residual oscillation for 250 turns

Grow damp experiment at Diamond Example of mode that is naturally damped: recording the complex amplitude on a turn-by-turn basis only of the mode previously excited Data reduced from 1.3 GB to 5.6 MB (see G. Rehm et al IBIC14) amplitude phase fit slope here 250 turns 250 turns 250 turns Repeat for all modes  = 0 , 1, ..., M – 1 Offline post processing gives the frequency shift and damping or growth rate (take away radiation damping and chromatic damping (if any))

Growth rates of vertical coupled bunch modes Vertical TMF data full fill – zero chromaticity – ID gap open Radiation damping subtracted blu measured – red fit data suggest resistive wall and few high Q resonators 3 4 Resistive Wall 2 β = 12.25 m, b = 13.5 mm, ρ = 7.3·10-7 Ω·m 5 1 Resonator

Search for resonator-like structures

BPM buttons and enclosure 1 2 3 Resonance 1 fr = (19Nb – 22)f0 = 9.4817 GHz Rs = 2.8 MΩ/m Q = 2000 Resonance 1 – mode -22 fr = 9.4200 GHz; Q = 2000; Δf = 61.7 MHz Resonance 2 – mode -64 fr = 8.9081 GHz; Q = 20000; Δf = 51.4 MHz Resonance 2 fr = (18Nb – 64)f0 = 8.9595 GHz Rs = 1.4 MΩ/m Q = 20000 Resonance 3 fr = (13Nb + 119)f0 = 6.5590 GHz Rs = 0.8 MΩ/m Q = 1000 Resonance 3 – mode 119 fr = 6.7578 GHz; Q = 1000; Δf = 198.8 MHz

Effect of closing the IDs Closing the gap of all IDs changes the geometric and RW impedance Vertical coupled bunch modes 3 4 geometry ID res. walls Forest of spikes at modes 100-140 has been associated to IDs

First tentative interpretation of IDs ID gap – I07: CPMU different vessel enclosure ID gap – I04 Phase I - in vacuum ID Changes with gap only in specific modes ID gap – I13: In vacuum ID

More recent measurements Large resonant peak moved in the last months from n = 22 now at n = 81, e.g. Same conditions 150 mA – full fill 936 bunches – 0 chromaticity – IDs open Other peaks (e.g. n = 61) are reproducible through the measurements Investigating causes: unlikely from BPM buttons and enclosures shutdown interventions? septum move; RF cavity swap

Transverse wakefields in the RF cavity Vertical impedance in RF cavities Largest secondary peak at 0.6768 GHz. does not match any of the excited modes Three stub tuners? Different geometry of coupling to waveguides? Issue still unresolved

Further analysis on IDs Occasional jumps in the mode spectrum with ID gap These are however “better understood” as they are clearly correlated to the ID gap changes – jumps of 10 or more modes ! Beam dynamics meets diagnostics Firenze, 6 November 2015

Beam dynamics meets diagnostics ASP CB mode analysis R. Dowd et al., IPAC15 Largest mode number shifts with ID gap Beam dynamics meets diagnostics Firenze, 6 November 2015

Other measurements (WIP) Using the functionality of the TMBF, grow damp measurement can be made on many machine configuration repeatedly with time Different RF i.e. different bunch lengths Different chromaticities i.e. different chromatic damping 2 1

Open issues and conclusions The Diamond TMBF allowed extensive and repetitive grow damp measurements allowing parameter scan and a regular monitoring of the impedance of the machine These studies have produced rather surprising results. Although all coupled bunch modes are eventually stabilised by the TMBF system, it is clear that the machine impedance is changing with time in way that are difficult to interpret and predict. The specific resonances at Diamond will be further investigated to identify possible causes beyond IDs, BPMs and RF cavities (e.g. Collimators, ...) More quantitative evaluation of the impedance – beyond the qualitative identification of the frequency excited in the spectrum – is forthcoming Beam dynamics meets diagnostics Firenze, 6 November 2015