1. NanoBPM Status and Multibunch Mark Slater, Cambridge University
WP 4.2 Meeting – 13/09/06
Mark Slater, Cambridge University

2. NanoBPM Results – Calibration Stability (1)
I have spent some time looking at the stability of the calibrations at ATF, specifically, the frequencies and decay constants of the cavities
First, I examined the short term stability (~12mins) by fitting the waveform of BPM X1 (thus avoiding cross talk) with an unknown frequency and decay constant
The dependence with time and amplitude is shown:

3. NanoBPM Results – Calibration Stability (2)
In order to try to understand the systematic drift and RMS of the distribution, I produced some Monte Carlo pulses and ran the same fitting code over them
After adding in a band pass filter to the Monte Carlo, I could get the generated distributions to produce similar systematics and RMS values
However, both the systematic drift and RMS were very dependent on the shape and size of the filter
More investigation would be required to fully recreate the observed distributions

4. NanoBPM Results – Calibration Stability (3)
I have also looked at the long term stability of the frequencies and decay constants over the period of an entire shift
By taking average values of from the fit over 100 pulses, taken from runs throughout the shift, the long term behaviour of the cavities could be seen:

5. NanoBPM Results – Calibration Stability (4)
The decay constant seems to just have random variation during this time period but the frequency decreases with time during the shift
Believing this may be associated with temperature, I examined the data recorded by the temperature sensors and a similar trend was found:

6. NanoBPM Results – Calibration Stability (5)
The recorded temperature change (~0.25C) produces a change in frequency of ~65kHz which agrees reasonably well with that predicted by Alexei
This frequency change alters the scale factor by ~0.5% as the DDC is no longer extracting the same amount of power
Assuming a typical offset of 10m, this indicates a systematic change of ~50nm

7. NanoBPM Results – Resolutions with Tilt
In June, Stewart and Alexei took data at ATF where the BPMs were tilted
The first check was to see if the resolution changed between tilt setting of -1000rad and +1000rad
It was found that there was no significant difference in resolution between the two settings:

8. NanoBPM Results – Calibrations with Tilt
However, the calibrations changed significantly with the different tilt settings
Using the data taken during the whole day, I could plot the change in IQ Phase and Scale vs. tilt setting
It appears that there is a gradual change in IQ Phase through the day (Note: the data was taken in the order it was plotted – hence the discontinuity)
There is however, a noticeable dependence of the scale on the tilt
The reason for this systematic effect is not currently known

9. Multibunch (1)
Also in June, Stewart and Alexei took some multibunch data (3 bunchs, 150ns separation)
Unfortunately, it was almost impossible to steer down and so the data is too saturated to be used
Consequently, I have done preliminary analysis of some simulated multibunch data
I first tried to fit bunches from the beginning of a bunch train and see if, by subtracting the fitted waveform, the amplitudes and phases could be adequately extracted from each bunch
This seemed to be possible with only a slight addition of noise:

10. Multibunch (2)
The algorithm shows good linear behaviour until the saturation becomes too much and there aren't enough unsaturated points to perform a good fit
Doing a crude calculation using just an exponential decay and assuming the fit requires 10 points to perform an accurate fit indicates that the maximum amplitude for a 300ns bunch spacing is ~15000 counts
The fit was also performed in the middle of the bunch train to see if it was possible to recover resolution/accuracy after a significantly saturated pulse
It appears that it requires only a single bunch to return to a stable state, though this is assumed to be amplitude dependent
There is a slight systematic drift over the next 5 or so bunches as the system settles down

11. Multibunch (3)
On the request of Alexei, I then started to look at the energy build up in the cavities during long bunch trains
By summing a series of exponentials and applying a phase factor (assuming that the start of a bunch will be the maximum amplitude), it was possible to find the steady state reached by the BPM as a fraction of the actual set amplitude
I investigated the response as a function of decay constant and phase for both 300ns and 150ns bunch spacings

12. Multibunch (4)
Finally, I investigated what effect altering the coupling would have on the resolution
Altering the coupling will not only change the decay constant but also the amplitude as the amount of power extracted is the same
It turns out that the amplitude is proportional to the square root of the decay constant
There does seem to be a significant dependence of the RMS (which is effectively resolution) on the coupling, but it remains to be seen whether the larger dynamic range gained from a shorter decay time would outweigh the loss in sensitivty

13. Multibunch Conclusions
The fitting algorithm seems able to extract both amplitude and phase from a multibunch waveform with minimal addition of noise
This seems to be the case even when starting the fit from the middle of the bunch train
There is a limitation on the dynamic range as a result of the saturation and the number of unsaturated points required to fit the waveform
One of the significant issues still to be resolved is that of t0 fitting
If the bunch spacing is constant to within a few ns, the initial t0 can be found from fitting and then then the t0's of the following bunches found just by the addition of this bunch spacing
If this is not the case though, a more complicated system would need to be developed as the trigger pulse for multibunch is no longer a simple rising and falling curve
I still need to try a similar analysis using the DDC algorithm