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Procedure 1:
Measure inital amplitude of BPM oscillations
Measure 50 kV kicker signal without beam
See how long 50kV kicker signal takes to decay to original level
Measure amplitude of BPM oscillation for a few turns after this point at all kicker voltages
Normalise by initial amplitude
40kV:
10kV:
Tiny increase can be seen in amplitude in 10kV case over initial amplitude (horizontal blue line) -- is it enough?
Procedure 2: use Hilbert transform: (?)
Example (David Posthuma de Boer)
Blue line: original signal
Orange line: transformed signal
Green line: sqrt(blue^2+green^2)
Gives envelope of function
Below: comparison of short window FFT spectra
Normalise by height of rev. freq. peak?
Need to be cautious of overlap between main peak and sidebands when measuring amplitude of sidebands.
This may be less of an issue at higher harmonics.
Taken data of sum of 2bpms and difference of 2bpms
NAFF behaviour:
blue is fft
purple points are NAFF
Plot from Shinji's NAFF using small window
Discussion with David PdB
compare pre-kick and post-kick spectra
NAFF is able to identify baseband signal; however calculated tune from baseband peak is c.0.89 vs c.0.81 of my measurements
Is this strong baseband peak just the kicker CT signal?
Suggested use of NAFF is:
Determine peak position using FFT
Apply bandpass filter to data to effectively 'window' the frequency region where NAFF will find peaks
Use NAFF to refine peak finding from FFT
NAFF may be less accurate than FFT for damped signal
Hi Max and Carl,
I found this comparison[1] of NAFF vs. interpolation methods[2] using generated "kicked" beam data rather than just a sinusoidal signal. This seems to suggest that NAFF might not offer the same improvement in frequency resolution for a damped sinusoidal signal as it does for a pure sinusoidal signal.
Cheers,
Dave
[1] - https://rstein.web.cern.ch/sites/test-static-05.web.cern.ch/files/Presentations/2007-12-18_TuneResolution/2007-12-18_TuneResolution.pdf
[2] - https://cds.cern.ch/record/720344/files/ab-note-2004-021.pdf
Note: how do I get uncertainty from NAFF?
need to modify code for uncertainty in lsq (/whatever) fit ?
Compare pre-kick and post-kick spectra. Sidebands around revolution harmonics only appear post-kick. Post-kick data shows two large baseband peaks. The second one is approximately the right position for the horizontal tune. The first one does not correspond to machine tune.
Beam off data, kicker CT only. RF and magnets on.
Large baseband peak can be seen in beam off data. Suggests that this frequency may be associated with kicker ringing. An interesting feature is that it looks like a double peak -- this is contrary to what I expected.
A broad peak can be seen at c 3.9MHz. This could be RF noise due to wire crosstalk. Similarly, narrower peaks corresponding to higher harmonics of the revolution frequency also seem to be apparent in the spectrum. These peaks are stronger and sharper in the beam on BPM data.
I think it is probably justified to measure tune from revolution harmonic sidebands. These are not apparent in beam off data and clearly only appear after the kick.
3BPM test:
Can oscillations be seen on innermost bpm?
If so, is sum of 3bpms ~constant?
middle BPM (please ignore labels. This is 30kV using only one BPM):
Inner BPM (please ignore labels. This is 30kV using only one BPM):
No sidebands in post-kick spectra of inner BPM. Try 55 kV result.
Clear sidebands in BPM7 spectrum, none in BPM6.
n.b. sidebands are very sensitive to windowing, . (Cannot say with 100% confidence that they do not exist in BPM6 data?)
However, oscilloscope picture above leads me to believe that beam is at boundary of BPM7 and BPM8. Transverse size of BPM triangle is measured at 10cm.
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