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TDC Information

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 $\sigma_{TR}=510$ ps.

Figure 10: Top panel: Timing jitter as defined by the coincidence of two small finger counters. Bottom panels: Left, timing resolution measurements for all fiber bundles; Right, timing resolution for the horizontal and vertical configurations as well as for different voltages of the Pol.Hi.Tech. multi-clad fibers. The Pol.Hi.Tech. multi-clad curve in the left panel is the one indicated as ``Vertical Positioning (L=2700 V, R=2800 V)'' in the right panel. These PMT high voltage settings were in fact the nominal settings for all the vertical configuration runs.
\includegraphics [height=80.0mm,bbllx=90pt,bblly=350pt,bburx=485pt,bbury=650pt,
angle=0,clip=]{two-fingers.ps} \includegraphics [height=80mm,angle=-90,clip=]{tdc_fits.eps} \includegraphics [height=80mm,angle=-90,clip=]{tdc_fits_9000.eps}

The left panel in Figure 10 shows data for the extracted timing resolution, $\sigma_{L/R}$, 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

\begin{displaymath}
<t_v>=9r\pi/10,
\end{displaymath} (12)

while the average thickness for the horizontal orientation is given by
\begin{displaymath}
<t_h>=9r\pi/4,
\end{displaymath} (13)

where r is the radius of an individual fiber. Hence, we have that
\begin{displaymath}
\frac{\sigma_h}{\sigma_v} = \sqrt{\frac{<t_v>}{<t_h>} } = \sqrt{\frac{2}{5}}
\sim 0.63
\end{displaymath} (14)

It should be noted that this value strongly depends on the angle of the orientation of fibers with respect to the beam line and can be obtained only when fibers are oriented exactly vertical/horizontal to the beam line. In fact, we suspect that the ``Horizontal Positioning (L=2700 V, R=2800 V)'' curve at 550 ps in the right panel was not properly oriented, and as a result the full thickness in equation (13) was not being traversed. By using the average values of the horizontal curve at the (2700 V, 2700 V) high voltage setting and any of the two vertical configuration curves in the right panel of Figure 10, $\sigma_h$/$\sigma_v$ $\sim$ 400 ps/650 ps = 0.62, in excellent agreement with the prediction in equation (14).

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.


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Next: Summary and Conclusions Up: Measurements and Results Previous: ADC Information
Web Master
2001-10-29