Experiment setup

The JUNO PMT instrumentation group built two independent testing systems for the performance characterization of 20-inch PMTs: The scanning station, which is designed for precise PMT photocathode characterization [22, 24], and a container system that is appropriate for PMT mass testing [23, 24]. Both facilities were capable of measuring afterpulse signals of 20-inch PMTs.

A block diagram of the measurement equipment at the scanning station is presented in Fig. 1. During each afterpulse test, the tested PMTs were installed by an aluminum holder and connected to the JUNO official PMT base [1]. The PMT base provides a positive high voltage (HV) to PMT and couples the PMT signal to a waveform digitizer. A 10-bits fast ADC (analog-to-digital converter, CAEN VME1751) was used for waveform digitization. A 420 nm light-emitting diode (LED) was mounted immediately above the PMT and absorptive ND filter from ThorLab was mounted between the LED and PMT to attenuate the light intensity [25]. The LED has an internal light intensity monitoring and feedback control system to achieve a 1% level of intensity stability. The light intensity can be adjusted using an LED controller from 0 photoelectrons (p.e.) to hundreds of photoelectrons per pulse during one afterpulse measurement. External trigger signals from the pulse generator was used to trigger the LED and digitizer at a frequency of 100 Hz. A previous study has shown that large-size PMTs are sensitive to the Earth’s magnetic field (EMF) owing to its influence on the motion of electrons inside the PMT [26]. To avoid the influence of EMF, a dark room was designed with an Earth magnetic field shielding function using three independent groups of Helmholtz coils [22]. The residual EMF can achieve a 0.5 μT level (~1/10 of the local EMF intensity) at the center of the dark room where the PMT is mounted.

Fig. 1Full-screen View

Schematic overview of the testing system in scanning station.

The container #4 system adopted JUNO electronics for waveform digitization [1], which can capture a 10 μs long PMT waveform frame. Instead of using LED as the light source, the container electronics operate in the self-trigger mode for the afterpulse measurements. A relatively large trigger threshold (with an amplitude approximately 15 times higher than a single p.e.) was used to select events with large primary signals. The possible sources of these large signals (serving as the primary pulse in the afterpulse measurement) in the dark environment could be cosmic rays, radioactive background, etc. [27]. The container afterpulse measurement has independent light source and electronics with the scanning station, thus can double-check the afterpulse timing results.

Afterpulse test method

It has been confirmed that the afterpulse rate and charge depend on primary pulse intensity [8, 29]. Accordingly, for each afterpulse test, we used three different light intensities with average intensities of ~40 p.e., ~80 p.e., and ~120 p.e. to evaluate the final afterpulse level of PMTs. In addition, another test under the same condition but LED turned off is performed to evaluate and subtract the contribution from PMT dark count signals. During one afterpulse measurement, the electronics of the scanning station recorded ~20,000 waveform frames (21 μs period) for each LED light intensity.

As shown in Fig. 2, the two-dimensional contour plot obtained by stacking all 20,000 waveform frames from one measurement displays the general characteristics of afterpulse signals such as time and amplitude distributions. The bottom panel of Fig. 2 shows the afterpulse measurement results from one MCP-PMT with serial number (SN) "PA1804-1066". For this PMT the primary pulse signals arrive at approximately 300 ns, and three afterpulse signal groups (arriving at ∼ 1.2 μs, 3.7 μs, and 5 μs) can be clearly identified. The top panel of Fig. 2 shows the test results of a dynode-PMT (SN: "EA7269"). The primary pulse signals at ∼ 300 ns and afterpulse signals can be identified at ~1 μs, ~4.5 μs, and 15 μs.

Fig. 2Full-screen View

(Color online) The two-dimensional contour plot constructed by stacking 20,000 tested raw waveform frames. The top panel is from one dynode-PMT with SN "EA7269" and bottom panel is from one MCP-PMT with SN "PA1804-1066".

The pulses generated by LED light injection are marked as primary pulses. The pulses arrive 500 ns after the primary pulse are marked as afterpulses. Some previous afterpulse measurements of the 8-inch PMT demonstrated that the H ${}_2^{+}$-induced afterpulse arrival time is ~200 ns, and this time delay is the shortest compared to the time delay of afterpulses caused by other ions [9, 10, 30]. For the 20-inch PMTs, the drift time of ions is much longer than that of the 8-inch PMTs. It is reasonable to address the first group of afterpulses (with a time delay of approximately 900 ns) to an H ${}_2^{+}$ induced afterpulse [8, 9, 29, 31-33]. The pulses after the primary pulse but with a time delay of less than 500 ns (late pulses) were ignored in this study because they are not generated by residual ions.

Afterpulses of different populations are caused by ions with different time delays; therefore, it is convenient to divide them into groups according to their different time delays. Four groups of afterpulse are confirmed for 20-inch MCP-PMTs, tagged M0, M1, M2 and M3; three groups of afterpulse are confirmed for 20-inch dynode-PMTs, tagged D0, D1, and D2. The time windows for the searching of these afterpulses in data analysis are summarized in Table 1.

The method to classify afterpulses into groups by their arrival time is not perfect because, in one time window, there could be multiple sources of afterpulses with different amplitudes or charge distributions but with similar time delays [9]. In this study, we only focused on the dominant afterpulse signals in one selected time window and ignored the non-significant components that may occur when a much higher HV is applied to PMTs.

Afterpulse waveform analysis

Figure 3 shows a typical single waveform captured for afterpulse analysis. The primary pulse arrives at approximately 280 ns on the time axis; subseqeubtly, two afterpulse signals appear at ~1300 ns and ~3100 ns. In the zoom-in section of Fig. 3, it is shown that the baseline around primary pulse is distorted by the pre-pulses, late pulses, and potential EM noise [18]. Therefore, the baseline of primary pulse is calculated as the mean value of waveform from 10 μs to 20 μs where the waveform is less affected by LED induced signals. The charge of the primary pulse (afterpulse) is integrated from -25 ns to +50 ns from the peak position of the primary pulse (afterpulse). A 3 mV threshold is used to seek afterpulse signals; the charge of one afterpulse signal must be larger than 0.25 single p.e. charge to exclude negligible signals or low-frequency noise.

Fig. 3Full-screen View

A tested waveform with 21 μs length.

For each primary pulse, all afterpulse signals in the time range [T_PP+500, 21000] ns was recorded for analysis, where T_PP is the arrival time of the primary pulse. For the baseline calculation of afterpulses, we used the average value over a 50 ns time interval before the threshold-cross time of one afterpulse signal. The arrival time of one afterpulse (primary pulse) signal T_AP (T_PP) was calculated based on the threshold cross time of its leading edge. If one afterpulse is detected at Ti, we search for the next afterpulse from Ti+50 ns. Accordingly, the minimum time interval between two adjacent afterpulses belonging to one primary pulse is 50 ns in this study.

Timing of afterpulse signals

The afterpulse time is defined as the delay between one afterpulse signal and its corresponding primary pulse signal, $t_{\text{AP}}=T_{\text{AP}}-T_{\text{PP}}$, where T_AP (T_PP) denotes the arrival time of afterpulse (primary pulse). For one PMT, the afterpulse time of each waveform is filled into a histogram and then fitted using a Gaussian function. Accordingly, the fitted mean value $t_{\text{AP}}^i$ is referred to as the time for a group i (i=D0, D1,...) of afterpulses.

The afterpulse time distribution histograms and fitting results of one dynode-PMT (SN: "EA7217") are plotted in Fig. 4; the afterpulse time distribution histograms and fitting results of one MCP-PMT (SN: "PA1906-2539") are plotted in Fig. 5. For the MCP-PMT, the fitted afterpulse times of M0, M1, M2, and M3 are $t_{\text{AP}}^{\text{M0}}=906\pm 1\text{ns}$, $t_{\text{AP}}^{\text{M1}}=3209\pm 3\text{ns}$, $t_{\text{AP}}^{\text{M2}}=4669\pm 2\text{ns}$, and $t_{\text{AP}}^{\text{M3}}=16.57\pm 0.13\mu \text{s}$, respectively. For the dynode-PMT, the fitted afterpulse times of D0, D1, and D2 are $t_{\text{AP}}^{\text{D0}}=837\pm 1\text{ns}$, $t_{\text{AP}}^{\text{D1}}=3651\pm 14\text{ns}$, and $t_{\text{AP}}^{\text{D2}}=13990\pm 14\text{ns}$, respectively. The uncertainty of $t_{\text{AP}}^i$ is estimated considering both the contribution from the primary pulse and afterpulse.

Fig. 4Full-screen View

Gaussian fitting of afterpulse time distribution for one dynode-PMT, SN: "EA7217".

Fig. 5Full-screen View

Gaussian fitting of afterpulse time distribution for one MCP-PMT, SN: "PA1906-2539".

As mentioned in Sect. 2, the container #4 PMT test system is also used for the afterpulse timing study to cross-check the scanning station measurement. Owing to the limitation of the hardware configuration, the electronics of the container #4 system can only record a 10 μs long waveform for afterpulse measurement [28]. Figures 6 and 7 plot the testing results for one dynode-PMT and one MCP-PMT, respectively, obtained using the container system. The top panel is a two-dimensional stacking contour plot of 20,000 waveform frames, and the bottom panel is the histogram of the afterpulse time distribution and fitting results. There is some extra noise in the self-trigger mode afterpulse measurement of the MCP-PMTs. This type of signal-induced pulse starts near the end of the primary pulse signal and is distributed exponentially.

Fig. 6Full-screen View

(Color online) The two-dimensional waveform stacking contour histogram of dynode-PMT "EA1500" (top panel) and histogram of afterpulse arrival time (t_AP) distribution (bottom panel), measured using the container system.

Fig. 7Full-screen View

(Color online) The two-dimensional waveform stacking contour histogram of MCP-PMT "PA2003-1034" (top panel) and histogram of afterpulse arrival time (t_AP) distribution (bottom panel), measured using the container system.

An exponential background and three Gaussian functions were used to achieve a global fitting of the afterpulse time histogram for the MCP-PMT; two Gaussian functions were used to fit the afterpulse time histogram of the dynode-PMT. For MCP-PMT ("PA2003-1034"), the fitted afterpulse time of M0, M1, and M2 are 896± 2 ns, 3259± 8 ns, and 4705±9 ns, respectively; for dynode-PMT (“EA1500”), the afterpulse time of D0 (D1) is 1018±8 ns (3879±26 ns).

The results obtained from the scanning station and container system confirmed the timing features of the three groups of MCP-PMT’s afterpulse and two groups of dynode-PMT’s afterpulse. These two PMT testing systems have independent light sources and electronics, thus can exclude potential flaws in light sources or electronics problems.

The afterpulse timing features of JUNO 20-inch dynode-PMTs are similar to the results obtained with smaller dynode-PMTs [10, 11]; the afterpulse timing results of MCP-PMTs are consistent with data published by vendors [35]. For each afterpulse component, a weighted average over all tested PMTs (150 MCP-PMTs and 11 dynode-PMTs) is calculated as the final afterpulse delay time ${\overline{t}}_{\text{AP}}^i$ and their uncertainties are listed in Table 2.

Charge distribution of afterpulse signals

Afterpulses with different time delays are caused by different types of ions, each of which having a different capability of generating secondary electrons from the photocathode.

Fig. 8 plots the typical charge distribution of each group of afterpulse when the primary pulse light intensity is ~120 photoelectrons. The top panel is obtained from one MCP-PMT (SN: "PA1804-1066"), while the bottom panel is obtained from one dynode-PMT (SN: "EA7269"). The afterpulse charge of each event is normalized to the primary pulse charge with 100 photoelectrons in the histograms, assuming that the afterpulses’ charge is proportional to the charge of the primary pulse.

Fig. 8Full-screen View

(Color online) Charge distribution of different afterpulse groups in a number of photoelectrons, the primary pulse intensity is ~120 photoelectrons. Top panel: MCP-PMT. Bottom panel: dynode-PMT.

The charge distribution histograms of MCP-PMT show that afterpulse M0 contains more average photoelectrons than the others, which could be a feature of hydrogen-induced afterpulses [30].

The charges of afterpulses M1 and M2 are approximately at the level of tens of photoelectrons; however, most of the M3 afterpulses are single p.e. signals. For dynode-PMT, afterpulse D0 has more average photoelectrons than the others; D1 and D2 mostly contain single photoelectron signals. Comparing the results of the MCP-PMT and dynode-PMT in Fig. 8a-b, we observe that the afterpulse charges of dynode-PMT are less than 25 photoelectrons when the PMT is illuminated by a primary pulse of 100 photoelectrons, while afterpulses of MCP-PMT have more average photoelectrons for each event. The difference in afterpulse charge (time) distribution between these two types of PMTs is related to their different photocathode materials, geometry design, and electron multiplication mechanisms. A detailed discussion about the charge response of MCP-PMT and dynode-PMT can be found in Ref. [34].

The charge distributions of different groups of afterpulses when the PMT is illuminated by different LED intensities are shown in Fig. 9 (a-c) and Fig. 10 (a-d). For both dynode-PMT and MCP-PMT, the total afterpulse rate (with dark count rate removed) of all afterpulse components grow with a higher primary pulse intensity, which is consistent with the results obtained in previous studies [11, 31, 35, 36].

Fig. 9Full-screen View

(Color online) Charge distribution of different group of afterpulses of one dynode-PMT "EA7269" in number of photoelectrons, the three LED intensities are plotted in different colors. The primary pulse intensity corresponding to light intensity 1 (2, 3) is 19.1 (43.7, 68.9) photoelectrons.

Fig. 10Full-screen View

(Color online) Charge distribution of different afterpulse groups for one MCP-PMT "PA1808-2151" in number of photoelectrons; the three LED intensities are plotted in different colors. The primary pulse intensity corresponding to light intensity 1 (2, 3) is 39.7 (84.1, 128.2) photoelectrons.

The afterpulse charge distribution and dependency of afterpulse rate on the primary pulse charge vary for different afterpulse groups. Subsequently, the total charge ratio between all afterpulses and primary pulse is defined to describe the total afterpulse level for JUNO 20-inch PMTs.

Afterpulse model of 20-inch JUNO PMTs

The charge and arrival time distributions of afterpulses from all the tested PMTs are plotted in two-dimensional contour plots, as shown in Fig. 11 (a-b) (with a primary pulse ~120 p.e.). Because all the PMTs were manufactured using the same technology, the afterpulse timing features are preserved even after the averaging process. Four (three) groups of afterpulse signals of MCP-PMTs (dynode-PMTs) can still be identified.

Fig. 11Full-screen View

(Color online) The two-dimensional contour plot of the charge-time (t_AP) distribution of afterpulses for dynode-PMTs (top panel) and MCP-PMTs (bottom panel) with light intensity 120 p.e. per trigger.

For one PMT, the charge ratio of group i afterpulse $R_{\text{AP}}^i$ is defined as follows: $R_{\text{AP}}^i=\frac{{\displaystyle {\sum }_j{Q}_{\text{AP}}^{ij}-Q_{\text{dark}}^i}}{{\displaystyle {\sum }_j{Q}_{\text{PP}}^{ij}}}\mathrm{,}$ (1) where $Q_{\text{AP}}^{ij}$ denotes the total charge of group i afterpulse signal in frame j and $Q_{\text{PP}}^{ij}$ denotes the charge of the primary pulse signal in frame j. $Q_{\text{dark}}^i$ denotes the total charge contribution from the dark signal in the time window of the afterpulse group i. Subsequently, $Q_{\text{dark}}^i$ is calculated as $Q_{\text{dark}}^i={{\displaystyle {\sum }_j\frac{w_i}{W}}}_j{Q}_{\text{dark}}^j$, where $Q_{\text{dark}}^j$ is the total charge for frame j in the dark test, wi is the width of the selection time window for afterpulse group i and W is the total length of the wave frame. Then, the total charge ratio R_AP of one tested PMT is defined as the sum of all afterpulse components, $R_{\text{AP}}={\displaystyle \sum _i}{R}_{\text{AP}}^i\mathrm{.}$ (2) For one PMT, R_AP represents the ratio of the total charge induced by afterpulses to the total charge induced by the primary pulses. This value R_AP is treated as the afterpulse occurrence probability of one PMT. The afterpulse charge ratio of each afterpulse group and total charge ratio R_AP are averaged over all the tested PMTs, which are summarized in Table 3.

The stability of the LED light intensity, afterpulse searching threshold, and dark count of PMT are considered when calculating the systematics. The uncertainties of the charge ratio calculation are estimated considering both the experimental and statistical errors using conservative values.

A simplified afterpulse model can be built for JUNO 20-inch PMTs based on the afterpulse testing data with the following two assumptions: only the dominant components of afterpulse in one time region are considered, and the total charge ratio between afterpulses and primary pulse is calculated as the probability of occurrence for each afterpulse component. In this model, the afterpulse time distribution is described by a Gaussian function; the corresponding charge probability is a coefficient, as shown in Eq. (3) and Eq. (4): $\begin{array}{c}{P}_{\text{AP}}^{\text{MCP-PMT}}=0.019\times G(\mathrm{0.91,0.069})\\ +0.016\times G(\mathrm{3.134,0.154})\\ +0.018\times G(\mathrm{4.579,0.125})\\ +0.007\times G(\mathrm{17.731,3.896}),\end{array}$ (3) $\begin{array}{c}{P}_{\text{AP}}^{\text{dynode-PMT}}=0.007\times G(\mathrm{1.067,0.075})\\ +0.065\times G(\mathrm{4.239,1.312})\\ +0.06\times G(\mathrm{15.081,2.602}),\end{array}$ (4) where $G(\mu \mathrm{,}\sigma )=\frac{1}{\sigma \sqrt{2\pi }}\cdot \text{exp}\left(-\frac{{(t-\mu )}^2}{2{\sigma }^2}\right)$ denotes a normal distribution. The coefficient before each Gaussian function denotes the occurrence probability of one afterpulse component when there is a primary pulse with a charge of 1 p.e., μ denotes the average time of one group of afterpulses, and σ denotes the standard deviation of the time distribution of one afterpulse component. Considering all the confirmed afterpulse components, the final afterpulse charge ratio of the JUNO MCP-PMT (dynode-PMT) is 5.7% (13.2%), which is consistent with previous measurements [35-37].

The afterpulse model defined in Eqs. (3) and (4) are based on testing data with a primary pulse intensity of 100 p.e.. It is not clear whether this model still works when the primary pulse is several p.e. levels because the dependency of afterpulse charge and rate on primary charge intensity could be different at very low primary pulse intensity owing to the complex structure and manufacturing technology of these large-size PMTs [7, 35, 9, 11, 37].