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 and Detection

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

• 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%
• Frequency-dependent efficiency functions must be taken into account. Using nominal efficiency specifications, SiPM PDE distribution weighted by scintillator (BCF-10 or BCF-20) emission and BCF-98 waveguide transmission spectra is integrated over all wavelengths. These distributions are shown in adjacent figures.
• Assuming for simplicity a uniform light beam profile emerging from the waveguide, the output is rescaled according to active area available on the SiPM (e.g. 1 mm² for Hamamatsu MPPC compared to 4 mm² waveguide cross-section)
• Correction introduced for the saturation effect of the firing pixel population. When an appreciable fraction of available pixels are firing, the possibility of a photon hitting a firing pixel can no longer be neglected. This can be expressed as hollows:

$N_{fired}=N_{total}\left(1-e^{\frac {-N_{\gamma }\cdot PDE}{N_{total}}}\right)$

Actual number of pixels fired BCF-10 BCF-20 MPPC 180 149 SSPM~06 192 393

Leading to time resolution:

Time resolution (ps) BCF-10 BCF-20 MPPC 201 221 SSPM~06 195 136