[esa-t474] Energy resolution for the ESA spectrometer

[Yury Kolomensky]

	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