[esa-t474] Energy resolution for the ESA spectrometer

[Alexey Lyapin]

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.

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

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.

Cheers,

Alex