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Cathode flatness and readout accuracy




A local tilt of the cathode plane leads to a shift of the centroid.
The order of magnitude of the shift is simple to evaluate:
delta(x)=alpha*5mm, where alpha is the cathode angle.

However, more accurate calculations show that the effect is
only a half of that:
delta(x)=alpha*2.5mm

The cathode readout resolution is supposed to be about 0.1mm.
Limiting the shift to 0.05mm we limit the plane angle to 0.02
(20 mrad).
The largest gradient measured by Micah was about 0.1mm/2cm=0.005.
It ocurred just across the sticky tape which glued the pieces together.

Therefore, from just the accuracy considerations, we can tolerate
0.4mm deviations on the width of the tape.

I would limit the smooth gap variations to about +/-1mm for esthetical
reasons, even if the gain and drift time variations are not significant
for larger deviations (both are largely defined by the field wires).

The electrostatic pressure of 0.022Pa on the foil has been calculated by Simon
within a certain approximation. I recalculated this pressure numerically and
obtained a close value of 0.015Pa, which leads to a foil deflection of about 0.003mm
at a 300N/m tension. It can be neglected.

There are a couple os slides on this matter in:
http://www.jlab.org/~gen/gluex/talk_fdc_1.pdf

Eugene