[BDXlist] Calorimeter saturation effect

Tue Mar 29 17:39:19 EDT 2016

Dear all,
I investigated the saturation effect as seen in the calorimeter, and I'd 
like to share with you what I found.

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.

1B) The single-phe amplitude measured by DAQ (i.e. after splitting) is:
- For the 25 um MPPC: 12 mV
- For the 50 um MPPC: 9.7 mV
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)

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:

- For the 25 um MPPC: 62.5 phe
- For the 50 um MPPC: 77 phe

*Important:* 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.

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.

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:

Nphe =  Ncells * (1-exp(-N0*PDE / Ncells))

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.

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)

- For the 25 um MPPC: 9.73 phe/MeV
- For the 50 um MPPC: 19.67 phe/MeV

Note that these two numbers were derived without correcting for the 
intrinsic MPPC saturation.

4) I took run 1338 and plotted, for all the events, the two MPPC 
charges, one against the other, in phe.
Attached is the result.
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:

- Completely ignoring saturation, Q(50) = Q(25) * 19.67 / 9.73
- 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))

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.
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.
At higher charge neither curve reproduces data - but here also the 
amplifier saturation is important too..

Bottom-line messages:
- 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
- I'd suggest to use the two MPPCs to measure different energy regions:
--Low energy measured by the 50 um MPPC (higher PDE)
--High energy measured by the 25 um MPPC (higher number of cells)

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?

Please, let me know what you think about.

Bests,
Andrea

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