Tagger Time Resolution

The Tagger Microscope is expected to have a time resolution of 200 ps or better. This specification imposes a strict demand on the light pulse rise time uncertainty because it introduces trigger time uncertainty when Constant Fraction Trigger (CFT) point is used.

Scintillation Pulse Time Uncertainty

The scintillations in the fiber are distributed exponentially with a characteristic decay time $\tau$ = 2.7  for BCF-10/20. Since the variance is $\tau ^{2}$ (and is additive over independent events) the time uncertainty for N generated photons becomes $\tau /N^{1/2}$. Thus, in order of priority, this relation implies

1. scintillating fiber with smallest decay time must be procured
2. photon capture and detection efficiency must be optimized

Photon Capture

Taking the accepted photon yield in plastic scintillator to be 8000γ/MeV, the following considerations control the total photon capture:

• taking the energy deposition in plastic (~1 $g/cm^{3}$) to saturate at ~2 MeV/cm with 2 cm length of scintillator yields 4 MeV
• The critical angle in multi-clad BCF scintillating fibers is 27.4^o C resulting in forward capture of 5.6%
• Lastly, frequency-dependent efficiencies must be taken into account. Using nominal efficiency specifications, SiPM PDE distribution weighted by scintillator (BCF-10 or BCF-20) emission and BCF-98 transmission spectra is integrated over all wavelengths. These distributions are shown in adjacent figures.