Advanced Topics of Cavity BPM Simulation and Analysis

1. Advanced Topics of Cavity BPMSimulation and Analysis Nquestions > Nanswers ΔNquestions ~ eNanswers • Lyapin, S. Boogert, G. Boorman, F. Cullinan, N. Joshi (JAI/RHUL, UK) • A. Morgan, G. Rehm (Diamond Light Source, UK) • M. Ross (Fermilab, USA) • A. Aryshev, Y. Honda, T. Tauchi, N. Terunuma, J. Urakawa (KEK, Japan) • A.-Y. Heo, E.-S. Kim, H.-S. Kim, Y. I. Kim (KNU, Korea) • J. Frisch, D. McCormick, J. Nelson, T. Smith, G. White (SLAC, USA) A. Lyapin et al, BPM workshop

2. What this talk is about • Some problems we encountered while working at the ATF/ATF2, none of which are of a deciding importance, but taken together define the performance of a CBPM system • Tuning, timing and thermal variations • Calibration and beam jitter • Timing and gain variations and long-term stability • Non-linearities and electronics noise • Closely spaced bunches • Will try demonstrating the importance of system simulations, including the whole chain • Beam motion • Cavity • Electronics • Digitisers • Digital processing A. Lyapin et al, BPM workshop

3. Accelerator test facility • Low-emittance facility, test system for 35 nm beam size next LC beam delivery system • Very dense with instrumentation: wire scanners, OTRs, laserwires, laser interference BSM • Relies mainly on cavity BPMs, currently ~ 40 in total A. Lyapin et al, BPM workshop

4. Cavity beam position monitor system IP region (4 BPMs) S-band BPMs (movers) C-band BPMs (mounted on movers) BPM test area Strip line/Cavity BPMs (mounted rigidly) A. Lyapin et al, BPM workshop

5. System resolution • SVD using a few BPMs surrounding the one of interest and calculate the residual • Usually a high residual signals for a re-calibration • In some cases it indicates more fundamental problems • Large offsets (between the BPM and quad) and consequent saturation • This display is now an online tool for operators Lines indicate cut, at which BPM is labelled bad x y SFs, Large BBA offset IP1 200 nm IP1 No attenuators in this region 40 nm A. Lyapin et al, BPM workshop

6. Cavities+Electronics • C and S-band cylindrical cavities with 4 symmetric couplers • Slot-coupled structure for monopole mode rejection, based on cavities previously used in NanoBPM experiment • Tuners for adjusting x-y coupling • Single stage image reject mixer, converting down to 20-30 MHz • Front-end LNA in C-band, all but 3 attenuated • Digitise at ~100 MHz C-band S-band A. Lyapin et al, BPM workshop

7. Digital processing • Digitised signal is processed • Digital IQ mixer • Digital filtering (Gaussian filter) • LO frequency tuned to IF frequency for each channel • Same processing for position and reference • Amplitude and phase are sampled at one point • Position phasor normalised by the reference to remove the charge and length dependency, and reference the phase to the beam arrival • The real and the imaginary parts of the resulting phasor are referred to as I’s and Q’s (in phase and in quadrature phase with the reference) • I and Q carry information on position, angle and tilt (separated using calibration) Amplitude Phase A. Lyapin et al, BPM workshop

8. Tuning and timing • The frequency of the LO signal used in digital demodulation needs to be tuned precisely to the frequency of the cavity • Set a relatively large offset to make S/N high • Look at the phase of the demodulated signal trying to flatten it adjusting the LO frequency • If the signal is saturated, the sampling point slides to the right, the amplitude must be extrapolated, but the phase apparently stays the same A. Lyapin et al, BPM workshop

9. Trigger jitter/drift • Due to small differences between the position and reference cavities, changes of the trigger timing cause changes of the phase, even when the phase is flattened along the waveform • Measuring the beam arrival time for each beam pass and referring the sampling point to the arrival time, it’s possible to compensate for this effect ts t0 A. Lyapin et al, BPM workshop

10. RF/trigger adjustments S. Boogert, RHUL • Problem when using DR RF ramp for dispersion measurements • Both the accelerator RF-derived LO (locked to 714 MHz) and the beam trigger change when activating the ramp • Problem exaggerated by a large frequency difference between the position and reference cavities in the S-band system (~50 MHz) • Less pronounced, but still visible in C-band system (Δf~1-2 MHz) A. Lyapin et al, BPM workshop

11. RF/trigger adjustments S. Boogert, RHUL • Investigated several filters and chose the one providing a few points on the front of the pulse for the t0 reconstruction while not smoothing it (10 MHz) • Correction works a lot better but much worse than wished for • Thinking of replacing the reference! A. Lyapin et al, BPM workshop

12. Temperature changes N. Joshi, RHUL • CBPMs are mounted on the quads in ATF2, so where the current is high, temperature variations can be considerable • Gradients of tens of kHz/0C are expected, in this example 48 kHz for a 2.9 GHz BPM • Eventually, can use cavity’s phase gradient for the temperature measurement, but need to have an idea of the scale of the variations A. Lyapin et al, BPM workshop

13. Calibration • Cavity BPMs need to be calibrated in order to determine: • position scale • IQ rotation of the position signal • suppress angle/tilt • Can calibrate by either: • moving the beam • may introduce angle • moving the BPM • more precise • need precision movers • Calibration: • position changed in steps • I and Q averaged over several beam passes • fit Q vs I to get the rotation • fit rotated I (I’-position) to get the scale A. Lyapin et al, BPM workshop

14. Calibration and long-term stability 2010: A. Lyapin et al, BPM workshop

15. Calibration and jitter subtraction F. Cullinan, RHUL • Easiest approach – collect multiple pulses, average for each step • Works well, until you face large excursions • Can collect some pulses before doing the calibration to establish correlations with the BPMs upstream, and then subtract the jitter • Even better results when running the correlations on the calibration data including the mover/bump position in the matrix A. Lyapin et al, BPM workshop

16. Calibration stability - Scale F. Cullinan, RHUL • Histograms for repeated calibrations processed using all three approaches • Clearly, using the SVD directly on the calibration gives the best results • Going down from 10-15% in X and 5% in Y to <1% A. Lyapin et al, BPM workshop

17. Calibration stability – IQ rotation F. Cullinan, RHUL • Similar results for the IQ rotation • The improvement is not as impressive as for jitter, if mainly positional, does not affect the rotation as much, and the large variations due to timing had been fixed A. Lyapin et al, BPM workshop

18. Calibration stability - Summary F. Cullinan, RHUL • Scales vary by less than 1% - is that enough? • Measuring 100 μmx 0.01 = 1 μm precision. Limited by movers? • Probably need to calibrate each BPM several times • Use the active gain/phase monitoring system at that level A. Lyapin et al, BPM workshop

19. Non-linearities and electronics noise • Electronics noise well understood • Need to keep in mind the digitisers are noisy too • Non-linearities are less well explored, even the cavity is not perfectly linear when it comes to measuring nm • A measurement of resolution as f(x,y) across the dynamic range would be interesting, and can be done at ATF, so we should probably include it in our program A. Lyapin et al, BPM workshop

20. Closely spaced bunches N.Joshi, RHUL • 2 bunches separated by 182 ns • BPM moved in 100 um steps • Contribution from the 1st bunch is propagated to the sampling point of the 2nd and phasors are subtracted A. Lyapin et al, BPM workshop

21. System simulations • Hopefully, it is clear by now that in systems aiming at high resolution, precision and accuracy all the elements of the processing chain need to be analysed at least at a basic level • Not always there is an obvious “bottleneck” issue limiting the resolution, but a number of factors contributing • Propagating the signal through the whole system looks like the right idea • Depending on the aim of a simulation, the models included may be less sophisticated Beam dynamics Analog processing Digital processing modes, sensitivities granularity, noise calibration errors position, size, length gain, NF, non-linearity non-linearity, sensitivity BPM response Digitisation Conversion to position A. Lyapin et al, BPM workshop

22. System simulations: Example 1 F. Cullinan, RHUL • Beam is tracked using a lightweight tracker code (Serpentine) • Beam jitter is calculated at each CBPM location and its effect on the calibration is estimated A. Lyapin et al, BPM workshop

23. System simulations: Example 2 Y.I.Kim, KNU Without electronics noise • Start with the beam optics and get bunch position at each BPM • Propagate the errors and noise (without doing the full signal simulation) • Do resolution calculation as for the beam data • Describes the system’s behavior pretty well… With electronics noise Beam measurement A. Lyapin et al, BPM workshop

24. Diagnostic simulation package? • Probably all beam diagnostics work in a similar way: certain properties of the beam are transformed into electrical signals • There are certain sensitivity, noise and background signals • The output is digitised at some point • Additional digital processing and calibration may be applied to provide the actual measurement • Maybe we should think of a package simulating diagnostic tools? • A lightweight version of it could be useful for beam dynamics simulations • Anyway, just a thought… A. Lyapin et al, BPM workshop