[esa-t474] Energy resolution for the ESA spectrometer

[Alexey Lyapin]

Dear All,

There have been some developments on our energy measurements in the ESA 
recently, so I thought some of you might still be interested.

First of all, Michele has done some interesting analysis. He wrote a 
note on it, and I am hoping to forward this note to everyone once I gain 
the adequate control over this mailing list. Basically, what he was 
trying to do is some abstraction from BPMs with their micrometers and 
microradians etc. just trying to estimate the noise on top of the energy 
measurement. The note he wrote is also a part of his thesis, which was 
published last month.

Once I've read Michele's note, I started thinking that there should be 
an easy way of estimating the resolution of our spectrometer without 
going into all the trouble of BPM calibration, magnets etc. (Note that I 
am really talking about the resolution here, NOT precision, and, by far, 
NOT accuracy.) In the past couple of days I've done some analysis to try 
that. So, what I did was:

* take the same data as Michele used, run 2743 (energy scan with magnets on)
* take I's and Q's from BPMs 1,2,3,5 and regress them against I's and 
Q's from BPM 4 for a "quiet" period, where the energy does not jump 
(magnets are on!)
* use the constants to predict the I's and Q's in BPM4 during the energy 
scan, get dI and dQ, which means jitter-subtracted measurements of BPM4
* 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
* go to dAmp and dPhase in order to do the phase rotation and projection 
on that straight line in the IQ plane
* get the energy scale for the resulting value from the energy scan with 
known steps (see plots in bpmPlot.pdf)
* the resulting plot of the energy scan is very clean, so I again took 
some data from the quiet piece to estimate the resolution (see 
enePlot.pdf), it turned out to be about 0.73 MeV, but this measurement 
still included the energy jitter of the beam itself
* 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
* there is a clear visual improvement when one looks at the plots, 
although the resolution is still about 0.63 MeV
* now, 0.63 MeV/28.5 GeV = 2.2e-5, which is still not bad!

Please, let me know what you think about all that. Personally, I believe 
this may be worth a short paper wrapping up our ESA work nicely...

Cheers,
Alexey


-- 
Dr. Alexey Lyapin

Applied Physicist
Physics and Astronomy
University College London
Gower Street
London WC1E 6BT
UK

Tel. +44 (0)20 7679 3454
Fax  +44 (0)20 7679 7145
Mob. +44 (0)79 2965 1821
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