[esa-t474] spectrometer calculations

[Bino Maiheu]

	Dear all,

For the purpose on converging on a sort of operational scheme of the
spectrometer, I think it is useful to have a central set of functions
which encode how we calculate the energy from the BPM and magnet data. 
This will make future simulations based on an agreed upon methodology.
Please find the set of functions I have so far are reasonably well
documented in :

http://www.hep.ucl.ac.uk/~bino/spectrometer/doc/index.html

I have implemented an abstract spectrometer class which can be fitted to
work with all the ROOT trees that we have currently in circulation
(Yury-style, Mark/Stewart-style and my simulation) so they will all use
the same routines to do the energy calculation.

Okay, on the procedure itself. 

I'm working on implementing 3 methods to obtain the residual offset at
the center of the chicane ( and thus the energy ). One method is to use
correlation coefficients between what I define as "Orbit BPMs" (think
BPMs 1,2,3,5,9,10,11) and what I define as "Chicane BPMs" (think BPM4)
by the SVD method. The other two methods are having a linear or
parabolic fit to the orbit BPMs and extrapolating to Chicane BPM
locations. For the latter method we will need to subtract the alignment.
I have discussed a bit with Yury but from simulations I'm not convinced
we can use an SVD method to obtain correlation coefficients with the
field on. It should work with the field off. In any case we will also
need to establish some alignment if we want to use a linear or parabolic
fit. 

So having this in mind, I think each time we operate the chicane at zero
field, we should get these alignment constants, be it the offsets from a
linear or parabolic fit trough the orbit BPMs or the correlation
coefficients between the orbit and chicane BPMs. Once these are
established, we can say the spectrometer is "aligned" and we can then
measure at +/- B fields. 
Off course the matter or residual field becomes important there and I
will try to simulate this.

In the virtual spectrometer class I have implemented this in the 
alignSystem() method. 

Comments and criticism are welcome.

Cheers,
     bino 



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