[esa-t474] Energy resolution for the ESA spectrometer

[Mike Hildreth]

Hi Yury,

	Interesting question.  The NMRs we used at CERN to map the LEP 
spectrometer dipole were better than 1e-4, but that was also at much 
higher field. We had reproducibility on the integral of the central field 
where the NMRs locked to a few 1e-6, where the integral was calculated as 
the piecewise area between successive measurements using the NMR values as 
the corners of the trapezoid and a precision rule for the distance.  The 
field itself had fluctuations along the length of almost 1e-3, so it was 
definitely not a case of averaging out fluctuations.
	
	cheers,

		mike

On Thu, 11 Mar 2010, Yury Kolomensky wrote:

> 	Hi Alexey and Michele,
> 
> On Mar 9, 2010, at 5:36 AM, Alexey Lyapin wrote:
> 
> >Dear Michele et al,
> >
> >Thank you for the comments! Let me answer some of them...
> >
> > >If you look at the NMR data (only for magnet 2&3) we see that we have
> > >fluctuations of the magnetic field in the order of 10^{-4}. I was always
> > >believing that this is a kind of lower limit for our resolution, since we
> > >cannot correct for it (at least not bunch by bunch).
> >
> >This is a very good question. I was looking at 1000 events/10 Hz = 100 s = ~2
> >min of data. If the magnetic field changed by ~10e-4 on that time scale no
> >way I would get 2.2e-5. I don't think I have an answer to that yet.
> >
> 
> What is the expected noise in the NMR probes ? I would be very surprised if it
> was smaller than 1e-4 (that's about 0.1 G). So I bet the observed fluctuations
> of the field are representative of the measurement noise, not the actual
> variation of the B field.
> 
> One way to check if the B field variation is significant is to compute the
> pulse-pair energy resolution. In other words, do the analysis like Alexey did,
> and write out the resolution values to a file (i.e. values from top-right plot
> in Alexey's enePlot.pdf). Then divide this file into a set of consecutive
> pairs, and compute the pair difference of resolutions E_i-E_{i+1}. This
> difference will subtract out the long-timescale drifts (e.g. B field drifts),
> and will leave you true pulse-to-pulse resolution representative of the
> electronics noise (the RMS of E_i-E_{i+1} is sqrt(2) times the single pulse
> resolution).
> 
> Looking at Alexey's plot, it's already clear that the pulse-pair resolution
> would be better -- probably by a factor of 2 or so -- than the RMS displayed
> in bottom-right plot. In the top-right plot, you can see some saw-tooth
> oscillations with a timescale of about 200 pulses (20 sec) -- my guess this is
> the effect of the current feedback on the magnet power supplies. There is also
> a long-term drift with a timescale of a min or so -- probably temperature
> related (BPM position or magnet current readout).
> 
> 
> >I little walk through the plots:
> >
> >bpmPlot.pdf
> >
> >top left: x4dAmp = sqrt(dI^2 + dQ^2), dI = x4iPred - x4iMeas, dQ = x4qPred -
> >x4qMeas, so it's the change of the amplitude of the signal in BPM4 during the
> >energy scan
> >
> >top right: dQ vs dI during the energy scan. This establishes the IQ rotation
> >of the line on which points (dI,dQ) would lie in the absence of noise. For
> >any measured (dI,dQ) I then take a projection on that line, because whatever
> >moves the point off the line is not the energy.
> >
> >bottom left: rawEnergy = x4dAmp * cos( x4dPhase - iqRotEnergy ) -- (dI,dQ)
> >points projected on the line in the previous plot and averaged for every step
> >of the scan, they form a calibration line
> >
> >bottom right: BPM4 data translated into the energy with the rotations and
> >scales applied
> >
> 
> Did you do the regression with Bino's and Mark's SVD ?
> 
> >enePlot.pdf
> >
> >top left: data from a quiet period processed in the same way to extract the
> >energy and (bottom left) its distribution
> >
> >top right: same data regressed to BPM12 and BPM24 to remove the energy jitter
> >and (bottom right) its distribution
> >
> > > >* establish the IQ rotation from the energy scan - all the points lie
> > > >on a straight line in the IQ space, any offset means some change not
> > > >related to energy
> > >I dont understand this: I guess you are talking about the top right
> > >figure in file bpmPlot.pdf. For DeltaE = 0 (no change in energy), I
> > >should expect both value of I/Q in 0 with no offset (which seems to be
> > >the case in figure), since this corresponds to the situation where you
> > >made you regression between I/Q from BPM 4 and I/Q of the other BPMs.
> >
> >Some of the points lie a little off the line. Whatever the cause of the
> >offset, it's not the change of the energy, so I want to ignore it and project
> >the measured point on the calibration line
> >
> > > >* so, in the next step I regressed the energy against the I's and Q's
> > > >of BPMs 12 and 24 to exclude the energy jitter and expose the noise of
> > > >the spectrometer system
> > >Why dont you try to regress and subtract during the energy scan, where
> > >any relation between "Amplitude" of BPM4 and I/Q values from BPM12 and
> > >BPM24 appears more clearly?
> >
> >Ultimately, you're right. The best thing would be to "remove" the energy scan
> >from the scan data using BPMs 12 and 24. I haven't had luck with this yet,
> >but will try again. For now, I used the quiet period as it is easy to remove
> >small variations and get a resolution estimate.
> >
> 
> For estimating the resolution, focusing on the quiet period with 0 energy
> offset is the right thing to do. The problem with looking at the entire energy
> scan is that it moves the beam by a significant fraction of the dynamic range
> in BPMs 12 and 28. So any nonlinearity in those devices will show up as a
> broadening of the resolution.
> 
> Yury
> 
> 
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