CDC Endplate Design

["Curtis A. Meyer" <cmeyer@ernest.phys.cmu.edu>]

Dear Trackers -

    Tim and Slava are currently implementing the 4-4-4 hole pattern
into the CDC endplates. In doing this, Slava noticed a small inconsistency
when one goes from a close-packed stereo to the next layer. In particular,
for several of the innermost transitions, the tubes had a small overlap 
between layers at the endplates. In particular, layers 6+7 8+9 and 10+11
all showed small overlaps.

   Yves and I then carefully looked at the code that did the stereo close pack
and noticed that because the close-pack stereo angle is slightly larger than
6 degrees, the tube moves out in the radial direction at the endplate slightly
more than it would for the nominal 6-degrees. However, the spacing was 
between layers was computed based on the straws at the center of the 
chamber. While our code is different from the code Beni used to generate
the geometry, the two codes produced the same radial positions at the 
center, and the same numbers of tubes per layer. Thus, we suspect that
the same problem exists in the geometry file for the CDC.

    In order to fix this, we now check the gap at both the endplates and at the 
center to make sure that they both work. We then regenerated the hole 
patterns. This very small "fix" had the effect of moving layer 28 out too far
radially. It went from  54.973cm (center) to 56.250cm (center). In fact
layer 27 is now at 54.867cm (center). The easiest way to implement these
close packs is to remove layer 28, leading to a "4-4-4-4-4-4-3" layout.

    We also suspect that the small overlaps that we found exist in the 
version-C CDC geometry and may be contributing to some ineffeciencies.
Layer 6 is at roughly 13.5 degrees and layer 11 is at 18.5 degrees. Hits
that are near the sides of the tubes may have been reconstructed in the 
wrong strawtube, though the overlap is small. The following table gives
the locations of the straws 


          Curtis 
--------------------------------------------------------------------------------------------------------------
Instrumented Layers   is 28
Instrumented Channels is 3580
Instrumented Channels is 3365 excluding layer 28.

layer     number    radius(center) radius(plate)  stereo           gap
  $ 1$ & $ 43$ & $ 10.955$ & $ 10.955$ & $ 0.000$ & $ 10.955$ \\
  $ 2$ & $ 43$ & $ 12.310$ & $ 12.310$ & $ 0.000$ & $  1.356$ \\
  $ 3$ & $ 55$ & $ 14.021$ & $ 14.021$ & $ 0.000$ & $  1.711$ \\
  $ 4$ & $ 55$ & $ 15.385$ & $ 15.385$ & $ 0.000$ & $  1.364$ \\
  $ 5$ & $ 66$ & $ 17.013$ & $ 18.750$ & $ 0.105$ & $  1.628$ \\
  $ 6$ & $ 66$ & $ 18.396$ & $ 20.274$ & $ 0.113$ & $  1.383$ \\
  $ 7$ & $ 80$ & $ 20.627$ & $ 22.081$ & $ 0.105$ & $  2.231$ \\
  $ 8$ & $ 80$ & $ 22.014$ & $ 23.566$ & $ 0.112$ & $  1.387$ \\
  $ 9$ & $ 93$ & $ 23.982$ & $ 25.244$ & $-0.105$ & $  1.968$ \\
  $10$ & $ 93$ & $ 25.371$ & $ 26.706$ & $-0.111$ & $  1.389$ \\
  $11$ & $106$ & $ 27.337$ & $ 28.450$ & $-0.105$ & $  1.965$ \\
  $12$ & $106$ & $ 28.728$ & $ 29.898$ & $-0.110$ & $  1.391$ \\
  $13$ & $125$ & $ 31.895$ & $ 31.895$ & $ 0.000$ & $  3.167$ \\
  $14$ & $125$ & $ 33.273$ & $ 33.273$ & $ 0.000$ & $  1.378$ \\
  $15$ & $137$ & $ 34.958$ & $ 34.958$ & $ 0.000$ & $  1.685$ \\
  $16$ & $137$ & $ 36.337$ & $ 36.337$ & $ 0.000$ & $  1.379$ \\
  $17$ & $148$ & $ 38.174$ & $ 38.979$ & $ 0.105$ & $  1.837$ \\
  $18$ & $148$ & $ 39.569$ & $ 40.403$ & $ 0.108$ & $  1.395$ \\
  $19$ & $161$ & $ 41.528$ & $ 42.269$ & $ 0.105$ & $  1.959$ \\
  $20$ & $161$ & $ 42.924$ & $ 43.690$ & $ 0.108$ & $  1.396$ \\
  $21$ & $173$ & $ 44.624$ & $ 45.315$ & $-0.105$ & $  1.700$ \\
  $22$ & $173$ & $ 46.020$ & $ 46.732$ & $-0.108$ & $  1.396$ \\
  $23$ & $185$ & $ 47.720$ & $ 48.366$ & $-0.105$ & $  1.700$ \\
  $24$ & $185$ & $ 49.117$ & $ 49.782$ & $-0.108$ & $  1.397$ \\
  $25$ & $203$ & $ 51.804$ & $ 51.804$ & $ 0.000$ & $  2.688$ \\
  $26$ & $203$ & $ 53.187$ & $ 53.187$ & $ 0.000$ & $  1.382$ \\
  $27$ & $215$ & $ 54.867$ & $ 54.867$ & $ 0.000$ & $  1.680$ \\
  $28$ & $215$ & $ 56.250$ & $ 56.250$ & $ 0.000$ & $  1.383$ \\

-- 
Professor Curtis A. Meyer        Department of Physics
Phone:  (412) 268-2745          Carnegie Mellon University
Fax:    (412) 681-0648            Pittsburgh PA 15213-3890
cmeyer@ernest.phys.cmu.edu  http://www.curtismeyer.com/