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Dear all,<br>
I investigated the saturation effect as seen in the calorimeter, and
I'd like to share with you what I found.<br>
<br>
1A) The single-phe charge, for both MPPC mounted on the crystal, is
~ 712 pVs. This is consistent with the measurement that was
performed in Genova, where we found 1.4 nVs for both: in Catania
there is a x2 splitter between each MPPC and the DAQ.<br>
<br>
1B) The single-phe amplitude measured by DAQ (i.e. after splitting)
is:<br>
- For the 25 um MPPC: 12 mV<br>
- For the 50 um MPPC: 9.7 mV<br>
The two are different, but the area is the same, since the single
phe-signal has a slightly different shape between the two, the 50 um
is longer (it is reasonable: for the same total MPPC capacitance,
the 50 um capacitance per cell is larger, hence the single phe
signal is longer)<br>
<br>
1C) Our amplifiers are really NOT optimized for output dynamic
range. According to the schematic (attached), the last stage is
OPA694-based. This has an output dynamics of 3V. However, there's
also a 50 Ohm-50 Ohm x2 voltage divider, between the output resistor
(R12) AND the 50 Ohm impedance of the splitter. It means the maximum
output voltage MEASURED by the DAQ is 750 mV for both channels (3 V
of OPA 694 -> 1.5 V after voltage divider-> 750 mV out of
splitter). This means that the maximum number of phe is:<br>
<br>
- For the 25 um MPPC: 62.5 phe<br>
- For the 50 um MPPC: 77 phe<br>
<br>
<b>Important:</b> this limit holds for a signal where all the phe
are syncronous, i.e. detected almost at the same time, such as a
fast plastic scintillator. For a CsI detector, that has a very long
decay time compared to the amplifier response time, the actual
MAXIMUM number of measurable phe is much larger (since they arrive
at different times). If I consider the single-phe signal time ~ 100
ns, and the CsI(Tl) decay time ~ 1 us, the ratio x10 suggests that
AT LEAST we can measure 10x phe than the two numbers above.<br>
<br>
2) Other than the amplifiers saturation, there's the intrinsic
saturation of the MPPC, that can't fire more than Ncells, where
Ncells=3600 for the 50 um MPPC, and Ncells=14400 for the 25 um MPPC.
<br>
<br>
IF all the incoming photons were hitting the two MPPCs in a time
interval shorter than the MPPC-cell recovery time (~10 ns?), then,
for a input signal of N0 photons, the response of the MPPCs would
be:<br>
<br>
Nphe = Ncells * (1-exp(-N0*PDE / Ncells))<br>
<br>
Here, the situation is again more complicated, since photons ARE NOT
hitting the MPPCs at the same time, given the long CsI(Tl) decay
time.<br>
<br>
3) From cosmics-ray calibrations, the two MPPCs have a different
overall gain, i.e. the number of phe seen per MeV is different,
probably due to a different optical coupling / PDE (Hamamatsu quotes
25% for 25um and 40% for 50um)<br>
<br>
- For the 25 um MPPC: 9.73 phe/MeV<br>
- For the 50 um MPPC: 19.67 phe/MeV<br>
<br>
Note that these two numbers were derived without correcting for the
intrinsic MPPC saturation.<br>
<br>
4) I took run 1338 and plotted, for all the events, the two MPPC
charges, one against the other, in phe. <br>
Attached is the result.<br>
Using the two cal. constants before *assuming cosmics are in a
low-charge area, where saturation can be neglected*, one can derive
the expected charge of MPPC 50 um as a function of the measured
charge of MPPC 25 um:<br>
<br>
- Completely ignoring saturation, Q(50) = Q(25) * 19.67 / 9.73 <br>
- Ignoring saturation for 25 um (since Ncells is "large"), but
considering for 50 um saturation-for the case of all photons hitting
the MPPC together: Q(50) = Ncells(50) * (1 - exp(-(Q(25) * 19.67 /
9.73)/Ncells(50))<br>
<br>
The two super-imposed curves refer to the two above scenarios. One
can see that, although the two curves reproduce the order of
magnitude of the data, neither agree with it well.<br>
It seems that the "no-saturation" curve is better at low charge -
because photons hitting the MPPC are distributed in time, hence for
a single event the SAME MPPC cell can fire twice.<br>
At higher charge neither curve reproduces data - but here also the
amplifier saturation is important too.. <br>
<br>
Bottom-line messages:<br>
- Saturation and non-linearity effects in the crystal are very
complicate - analytical formula we are used to do not apply so
easily, given the fact CsI(Tl) photons hit the MPPCs in a longer
time than the MPPC intrinsic one<br>
- I'd suggest to use the two MPPCs to measure different energy
regions: <br>
--Low energy measured by the 50 um MPPC (higher PDE)<br>
--High energy measured by the 25 um MPPC (higher number of cells)<br>
<br>
To do so, it would be good to increase the dynamic range of the 25
um amplifier: this can be done by changing, in amplifier n.10,
resistor R11 from 270 Ohm to ~ 100 Ohm, thus decreasing the
amplifier gain by a factor of ~3. Marzio, Mariangela, can you do so?<br>
<br>
Please, let me know what you think about.<br>
<br>
Bests,<br>
Andrea <br>
<br>
<br>
<br>
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