Introduction

Recently we received a new MCP-PMT of type PP2365AC manufactured by Photonis . We plan to use it as a timing reference for beta particles, as has been done by others , , , . The device is currently operating in our lab, but what is its time resolution for tagging beta particles from a radioactive Sr-90 source? To address this question I performed the "triple beta scan method", described below, to determine its time resolution.

The triple beta scan method

The triple beta scan method allows to determine the time resolution of three devices without knowing any of them beforehand. The method consists on performing three different beta scans combining each pair of detectors. Each of these three beta scans is an "ordinary beta scan" as the one described in  § 4.4. In an ordinary beta scan two detectors are employed, one with known time resolution used as a reference and one with unknown time resolution to be characterized. The time resolution of each detector contributes in quadrature to the total dispersion observed in the measurement: $$\sigma_\text{device 1}^2 + \sigma_\text{device 2}^2 = \sigma_\text{measurement}^2$$ where $\sigma_\text{measurement}$ is the value of the fluctuations of the time difference between the time tagged by device 1 and the time tagged by device 2. If there are three devices and three scans are performed combining two devices in each measurement, we then have the following system of equations $$ \left\{ \begin{aligned} & \sigma_{\text{device 1}}^{2}+\sigma_{\text{device 2}}^{2}=\sigma_{\text{measurement 1}}^{2}\\ & \sigma_{\text{device 1}}^{2}+\sigma_{\text{device 3}}^{2}=\sigma_{\text{measurement 2}}^{2}\\ & \sigma_{\text{device 2}}^{2}+\sigma_{\text{device 3}}^{2}=\sigma_{\text{measurement 3}}^{2} \end{aligned} \right. $$ where $\sigma_{\text{device }i}$ is the time resolution of each device and $\sigma_{\text{measurement }i}$ the dispersion of the $\Delta t$ between the pulses in each beta scan. This system can be inverted to obtain $$ \left\{ \begin{aligned} & \sigma_{d1}=\sqrt{\frac{\sigma_{m1}^{2}+\sigma_{m2}^{2}-\sigma_{m3}^{2}}{2}}\\ & \sigma_{d2}=\sqrt{\frac{\sigma_{m1}^{2}+\sigma_{m3}^{2}-\sigma_{m2}^{2}}{2}}\\ & \sigma_{d3}=\sqrt{\frac{\sigma_{m2}^{2}+\sigma_{m3}^{2}-\sigma_{m1}^{2}}{2}} \end{aligned} \right. $$ where $\sigma_{di} \equiv \sigma_{\text{device }i}$ and $\sigma_{mi} \equiv \sigma_{\text{measurement }i}$. Here we see that the time resolution of each device can be determined without prior information or the need of a time reference.

Setup, analysis and results

The three devices used for this experiment were:

1. LGAD "Speedy Gonzalez 11", AIDA-2020 V1 RUN 11478 W5-DA11.
   • Mounted in Chubut board.
   • No second stage amplifier.
2. LGAD "Speedy Gonzalez 12", AIDA-2020 V1 RUN 11478 W5-DA12.
   • Mounted in Chubut board.
   • No second stage amplifier.
3. Photonis MCP-PMT PP2365AC.
   • Connected straight to the 50 Ω input of the oscilloscope without any amplification at all.

The window of the MCP-PMT was covered with thin aluminum adhesive tape to prevent ambient photons to enter into the device. This proved to be enough shielding to allow the device to be used under ambient light conditions without issues .

In some pictures of the setup are shown.

Pictures of the setup used for the measurements. The first picture shows two Chubut boards where the LGAD devices were mounted, and the radioactive beta source on top. The second picture shows one of the Chubut boards mounted in a 3D-printed structure that holds the MCP-PMT inside, and the beta source on top.

Each of the three beta scans collected a total of 3333 events in coincidence of the two respective detectors. Each signal was then individually processed to extract its features using the lgadtools package for Python . An example of such processing is shown in .

The values of the "time at $x$ %" extracted from the analysis shown in were used to perform a timing analysis using the constant fraction discriminator method. The value of each $\sigma_{mi}$ from was determined as the median absolute deviation of the time difference between pulse 1 and pulse 2 choosing the "constant fraction discriminator constants" $k_i$ at the value where this quantity was minimized. displays an example of the method applied to one of the beta scans performed. Here we see in the color map the dispersion of the time difference for different values of the constant fraction discriminator threshold $k_i$ for each detector. For example the point where $k_1=10\%$ and $k_2=50\%$ is showing the dispersion of $\Delta t = t_{10 \%}^\text{device 1} - t_{50 \%}^\text{device 2}$ where each $t_{\%}^{\text{device }i}$ is given by the value as shown in for the respective detector. At each value of $k_1,k_2$ the distribution of $\Delta t$ is Gaussian, an example is shown in at the right.

The final values reported (later on) for each $\sigma_\text{measurement}$ were obtained as $$ \sigma = 1.4826 \times \text{MAD} $$ where $\text{MAD}$ is the median absolute deviation. This estimator is practically equivalent to the standard deviation but more robust against outliers . The Gaussian fit as the one shown in was used as a cross check for the value of $\sigma$.

Results

The results obtained from 5 beta scans are summarized in . The uncertainty in each measured σ was obtained by bootstrapping. We see that the scan with the "worse time resolution" is that performed with the two LGADs, while those in which one of the devices was the MCP-PMT have smaller values of σ. This is consistent with the MCP-PMT being better for time tagging, as expected.

Using this data and the time resolution of each device can be computed. Specifically we can distinguish two cases:

1. Using beta scans 1, 2 and 3: characterize the MCP-PMT at 2650 V, which is the nominal voltage.
2. Using beta scans 1, 4 and 5: characterize the MCP-PMT at 3000 V, which is the maximum voltage.

We see that the time resolution for both of the Speedy Gonzalez devices is on the order of 38 ps. Using the measured σ from the beta scan 1 alone and assuming that the two devices are identical (which should be the case) a value of $\frac{53.1\text{ ps}}{\sqrt{2}}\approx 37.5\text{ ps}$ which is consistent. For the MCP-PMT the time resolution is on the order of 22-24 ps at the two different voltages. There seems to be a slight improvement with increasing the bias voltage but it is not important.

Conclusions and discussion

The time resolution of two LGADs and our new MCP-PMT was determined by means of the "three beta scans method". For the two LGADs a time resolution of 37 ps was obtained while for the MCP-PMT a value of 22-24 ps was determined. These values are not in perfect agreement with the expected ones. For the two Speedy Gonzalez LGADs a value of 27 ps was determined in the past  while for the Photonis PP2365AC MCP-PMT a value of the order of 10-15 ps was expected. It has to be noted, however, that for a similar device of the same manufacturer a value at the level of 35-40 ps was reported for MIPs . With respect to the two Speedy Gonzalez LGADs, in the past they were mounted in Santa Cruz boards and a second stage amplifier was also used, this may be the difference.