[d2n-analysis-talk] The Affect of Transversity's Optics Matrix on z_react

[David Flay]

Hi Brad,

Attached are the plots of z_react with various adjustments: our original
optics matrix -- that is, what we had before I started looking at the
optics; z_react with Transversity's Optics Matrix (with no mis-pointing
values); z_react with Transversity's Optics Matrix with our mis-pointing
values in; then finally, z_react with Transversity's Optics Matrix and
mis-pointing values in.  Each in the sequence of z_react with just the
survey values in (red lines), then with survey values + focal plane cuts.

It can be seen in the focal plane cut plots, there seems to be a small
dependence on the cut position (see last plot for the color coding).  It
appears to be ~1-2mm for the cut regions in the center; the cut regions on
the edges appear to differ by ~3-4mm (zooming in on the plot in ROOT).

One can see that when the mis-pointing values are in, the peaks are aligned.

This is "different" from last meeting, in that I did not realize at the
time, but I had utilized the mis-pointing values in the <incorrect>
manner.

Initially, I had used:

L.off_x = +/- Hmisptg*\cos \theta_0
L.off_y = Vmisptg
L.off_z = -/+ Hmisptg*\sin \theta_0

While L.off_y is correct, I was not comfortable with the x and z values
(in the first place).  So, I drew it out, and one can show the results I
display in spectrometer_mispointing.jpg.  It turns out that there was a
factor of 2 missing on the z offset.

It should be noted that in the diagram, the lowermost line to the
spectrometer is the reference point -- that is, it would be the 'true'
spectrometer line, if everything were aligned properly.  Further, the
Hmisptg (horizontal mis-pointing) is defined as the <horizontal
perpendicular distance from the spectrometer (ideal) central line>. 
Knowing this, it is fairly straight forward to work out the angles and the
geometric quantities as I show. (The diagram does not show the
perpendiculars, and I did not scrutinize over making those angles perfect
in the drawing, but I'm certain that the angles are right here -- given we
take the angle between the true [optimum] position and the 'real' position
to be small -- which is true, as the horizontal mis-pointing is 1.01 mm =>
angular displacement ~ 0.05 deg. if we consider the distance to the
spectrometer to be ~1m, so I think this is valid.  I only solve for x and
z in the drawing -- x' = x-offset; z' = z-offset.) Once I take this into
account, the mis-pointing values work.  The (+/-) appears due to whether
or not the mis-pointing value is upstream (+) or downstream (-).

For d2n, \theta_0 = 44.985 deg.; Hmisptg = +1.01 mm (upstream); Vmisptg =
-0.15 mm (down) from the survey. The reason why z' is -/+ is because it
points in the opposite direction of the z-direction in the HCS.

Dave

-------------------------------------------------
David Flay
Physics Department
Temple University
Philadelphia, PA 19122

office: Barton Hall, BA319
phone: (215) 204-1331

e-mail: flay at jlab.org
            flay at temple.edu

website: http://www.jlab.org/~flay
              http://quarks.temple.edu
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