Saturation effect (binning width)

Introduction

The saturation effect of PMT is one of the important thing to be handled well in simulation especially for EHE analysis. It can bias our results.

Kotoyo and Alex have studied the effect. You can see their results from below links.

* Kotoyo's page * Alex's page 1 2

The PMT saturation occures when there are many input photo-electrons. Those photo-electrons are multiplied by getting energy by applied high voltage. Although, the effective voltage between dynodes decreases when there are many multiplied electrons between dynodes. Therefore, the saturation effect depends on the input current.

We binned input photon timing by 10 ns to speed up simulation processing time. This is done in brutus (EHE hit-constructor). Although Kotoyo and Alex have checked that 10 ns binning will be probably fine for EHE analysis by using MC test beams, I just wanted to check the effect by using the full MC data where an EHE muon and full detector response is simulated.

Procedure

As I said, the current default binning for input photons in brutus (EHE hit-constructor) is 10 ns. I have just changed the value to 5 ns, and change a parameter of RomeoOutputTimeResolution to 5ns, too. The script I used is here.

Results

Event-wise total Npe Vs energy

The current default binning width (10 ns) The statistics is ~50k.

binning width 5 ns The statistics is 10k. The distribution is quite similar to 10 ns binning.

Typical saturated waveform (ATWD)

The current default binning width (10 ns) The waveform is a bit jaggy. This is consistent with Kotoyo's result. (Sorry that the plot is not in high resolution. I have just get this from the event-viewer.)

binning width 5 ns The waveform is smoother.

other parameters

DOM number distribution black: 10ns, red: 5ns They are almost identical.	channel-wise atwd npe distributions black: 10ns, red: 5ns They are almost identical.	channel-wise fadc npe distributions black: 10ns, red: 5ns They are almost identical.
channel-wise atwd peak amplitude distributions black: 10ns, red: 5ns They are almost identical.	channel-wise fadc peak amplitude distributions black: 10ns, red: 5ns They are almost identical.

processing time

I have just checked the processing time with fixed geometry (horizontal) and energy (10^8 GeV) for the relatively fair comparison. (Note that the random seed for interactions changes with time, so the events are not identical.)

I didn't try so many events because I just did like to know the rough number. The event statistics is just 20 events.

The results are the follwings.

• 10ns: 856 sec (with optimized mode)
• 5ns: 1164 sec (with optimized mode)
• (10ns: 1145 sec (with debug mode))

Though the statistics is not enough, the 5ns binning seems to be still torelable.

Summary

• As far as working on npe base, the results doesn't change at all between 5ns and 10ns binning.
• For the waveform based analysis, the 5ns binning would be better (but need to be checked).
• The processing time doesn't seem so bad for finer binning of 5ns.