[Halld-tagger] analytical model of tagger optics

[Richard Jones]

Colleagues,

Please find attached the excel spreadsheet that contains my analytical 
model of the tagger optics and focal plane position as a function of 
numerous inputs.  All of these inputs can be tweaked there at the top of 
the spreadsheet, and the figure updates immediately.  The graph shows 
the outline of the uniform field region, the nominal beam axis, and the 
"focal curve" computed for a uniform field and sharp boundaries.  The 
position of Yang's focal plane, taken from two sources I found, are 
shown as Yang(1) and Yang(2).   Parameters that are intended for user 
modification are highlighted in green.  Note that if you vary the 
parameters outside of reasonable limits, the results are unpredictable, 
so start with the nominal settings and go from there in small steps.  In 
this version I have added the nominal beam trajectory (brown line) to 
the graph so that you can verify that the beam exits through the end of 
the magnet and does not get to close to the back edge of the pole.

Note that the focus in the analytical model is the "point-to-point", 
which is not exactly what Yang used to position his focal plane, but it 
is not far away.

-Richard Jones
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