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====== Pulser test ======

In order to investigate the issue of the apparent 7 ms half-life from the 215Po decay,
I acquired some short runs by injecting pulser-generated events directly into the digitizer.
In all cases, the injected signals are square pulses with 1 us duration and negative polarity,
and the acquired windows are 2us long.

The results of the various tests are described below.

=== Single pulses, 1 ms interval ===

In the first test, I acquired about 1 minute of data injecting pulses every 1 ms.
The reconstructed delta-t between subsequent events is shown in the figure, and agrees with the injected value to the 100ns level (compatible with the trigger jitter).

{{:gagg-nd:screenshot_20241025_172819.png?400|}}

=== Single pulses, 100us interval ===

In the second test, I reduced the interval between pulses to 100 us.
In this case, 0.084% of the events reconstruct at a delta-t larger than the injected one, probably due to some dead time.

|{{:gagg-nd:screenshot_20241025_173546.png?400|}}|{{:gagg-nd:screenshot_20241025_173609.png?400|Same as the left plot, but zoomed around 100 us.}}|

=== Single pulses, 10us interval ===

Reducing the interval to 10us, we start to see a larger fraction of events (1.69%) with a timestamp mis-reconstructed by >200us.
Specifically, we have a large distribution of events between 20ms and 150ms, and a more populated region between 400us and 15ms.
About a third of the other 98.31% of the events is reconstructed at the nominal 10us interval,
while the rest is reconstructed at a 20us interval.

This indicates the presence of a significant dead time affecting the acquisition, but this run is taken with a very high count rate,
where we're requiring to digitize 20% of the total acquisition time!

|{{:gagg-nd:screenshot_20241025_174421.png?400|}}|{{:gagg-nd:screenshot_20241025_174613.png?400|Same, but zoomed.}}|{{:gagg-nd:screenshot_20241025_174712.png?400|Even more zoomed.}}|

So far, I always used a readout buffer with a capacity of 1000 events, which is very close to the maximum allowed by the digitizer for 2us-long waveforms.
To check the effect of the readout buffer length on the dead-time, I shortened it capacity to 100 events.
The situation is similar as before, with 2% of the events reconstructed with a delta-t >200us, with most of them around 700us.

At this point, I decided to move back to a buffer capacity of 1000 events, and send bursts of a handful of signals in order not to saturate the digitizer.

|{{:gagg-nd:screenshot_20241025_175555.png?400|}}|{{:gagg-nd:screenshot_20241025_175757.png?400|}}|{{:gagg-nd:screenshot_20241025_175936.png?400|}}|

=== Pulses bursts ===

As a first attempt, I injected bursts of 2 pulses distanced by 10us. The distance between bursts is 1 ms.
The reconstructed delta-t shows a double peak, centered at 10us and 0.990ms, as expected.
Each of them has a standard deviation of 100ns. I guess there's no surprise here.

{{:gagg-nd:screenshot_20241025_180711.png?400|}}

At this point I kept the distance between bursts fixed to 1ms, and changed the number of pulses in the burst, or the distance between pulses.
In particular, I run the following tests:
  * Delta-T=1ms, delta-t=10us, 5 pulses per burst
  * Delta-T=1ms, delta-t=4us, 4 pulses per burst
  * Delta-t=1ms, delta-t=2.5us, 2 pulses per burst

In all cases, the distribution of the short and large delta-t are consistent with the injected values down to 100ns.

=== Conclusion ===

I'd conclude that the event timing is correct, unless we're running in conditions of very high count rate.
Notice however that the average count rate registered with the GAGG detector is around 15 Hz, while these tests proved that we are safe up to 10Khz.
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