Although the results obtained using equations (5) or
(6) were found to be consistent with one another,
equation (6) is more robust since it does not
require information about the timing resolution of the trigger/finger
counter PMT. Nevertheless, the timing resolution of the finger
counter was determined using the data from a separate run where two
finger counters of similar characteristics were used. The TDC
spectrum for the second finger counter triggered by the TR counter is
shown in Figure 10. The Gaussian fit gives a sigma of
14.44 channels, or 722 ps (the TDC conversion factor for the TRIUMF
tests was 50 ps/channel). From this value and
equation (6) the trigger jitter was extracted to be
ps.
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The left panel in Figure 10 shows data for the extracted
timing resolution, , for several positions along the
fiber. Our suspicion of breakage in the Pol.Hi.Tech. single-clad
fiber bundle is supported also by the timing resolution for this
bundle which is poorer compared to the other fiber bundles. This can
be explained in part by lower light collection due to the breaks in
the fibers and also possibly by the increased number of reflections
within each fiber. Statistically it appears that Kuraray fibers have
superior timing resolution to the Pol.Hi.Tech. fibers. This implies
that Kuraray fibers have better light production and light collection
capabilities compare to the Pol.Hi.Tech. fibers.
The right panel in Figure 10 shows the timing resolution for the Pol.Hi.Tech. multi-clad bundle in the horizontal and vertical configurations, as shown in Figure 8, and for different high voltage values. It is immediately noticable that the timing resolution is much better when the fiber bundles are oriented horizontally with respect to the beam. This can be explained by the difference in the average thickness of fiber material that the pion traverses for these two orientations.
The amount of light produced is proportional to the thickness of
material, and the timing resolution is inversely proportional to the
square root of the number of photons produced. The average thickness
for vertical orientation is given by
Next, the curves in the right panel of Figure 10, for the different HV's applied, can be understood as follows. The different bias had essentially no effect for the vertical configuration, since in this mode the average thickness of fibers traversed depends very little on the precise vertical alignment. However, the sensitivity to the alignment is much more critical in the horizontal case, which may explain the large effect of the bias change.
Finally, the timing resolution was unaffected by the Group 3 and 4 configurations of the fiber bundles, as compared to the standard vertical configuration of a single bundle. The Group 5 results were consistent with expectations on the timing resolution from the effective doubling of the traversed fiber thickness.