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Photomultiplier tube performance of the WCDA++ in the LHAASO experiment
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Photomultiplier tube performance of the WCDA++ in the LHAASO experiment Hengying Zhang a , Yanhong Yu a , Khuram Tariq a , Zongkang Zeng b,c , Xiurong Li b , Cheng Liu b , Dong Liu a , Cunfeng Feng a ,∗, For the LHAASO Collaboration a
Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China c University of Chinese Academy of Sciences, Beijing 100049, China b
ARTICLE
INFO
Keywords: LHAASO PMT Non-linearity Bi-readout Water Cherenkov detector array
ABSTRACT In the Large High Altitude Air Shower Observatory (LHAASO), the main physics objective of the water Cherenkov detector array (WCDA) is to survey the sky for gamma-ray sources in the energy range of 100 GeV to 30 TeV. In order to extend the dynamic range of the WCDA, a 1.5-inch photomultiplier tube (PMT) is placed aside the 8-inch PMT in each cell of the WCDA. All of these 1.5-inch PMTs (900 in total) consist of the WCDA dynamic extended system (WCDA++). These PMTs are required to maintain linearity within four orders of magnitude. The performance of the 1.5-inch PMTs with a specially designed bi-readout voltage divider is tested with a PMT test system. Accordingly, the effects of the working high voltage and signal width on the dynamic range of the PMTs are studied. The test results show that the dynamic range with a 5% non-linearity for a driven signal width of 5.5 ns is more than 200 kPEs (photoelectrons). The dark noise count rate is less than 200 Hz for a 1 mV threshold at a PMT gain of 2 × 105 . These results confirm that the PMT performance meets the WCDA++ requirements.
1. Introduction The Large High Altitude Air Shower Observatory (LHAASO) is a hybrid extensive air shower (EAS) array in Sichuan Province (P.R. China) 4410 m above sea level. The observatory consists of an EAS array covering an area of 1.3 km2 (KM2A), a 78,000 m2 water Cherenkov detector array (WCDA) and 12 wide-field air Cherenkov/fluorescence telescopes (WFCTAs) [1,2], as shown in Fig. 1. The WCDA is one of the major components of the LHAASO. The main physics objective is to survey the sky for gamma-ray sources in the energy range of 100 GeV to 30 TeV [3]. In order to extend the dynamic range to PeV, one 1.5-in. photomultiplier tube (PMT) is placed aside the 8-in. PMT in each cell of the WCDA, as shown in Fig. 2. All(900) 1.5-in. PMTs constitute the WCDA dynamic extended system (WCDA++). The WCDA++ experiment requires that the operational gain of the PMT is 2 × 105 , and the corresponding high voltage is called the working high voltage. The performance parameters of the designed photomultiplier at the working high voltage are as follows: (1) the linear maximum number of photoelectrons (PEs) is more than 200 kPEs within a 5% non-linearity, (2) the dark noise count rate is less than 200 Hz at a 1 mV threshold, and (3) the gain ratio of the anode to the dynode (called ADratio) is between 90 and 150. The XP3960 photomultiplier tube is manufactured by Hainan Zhanchuang Photonics ∗
Technology Co., Ltd (HZC). This PMT has nine dynode stages. Because of the space charge effect, it is impossible to maintain the linearity of the PMT output with only anode signal readout. A bi-readout divider circuit of the anode and 6th dynode is designed. The special divider circuit and readout circuit is developed by using the design of a special ladder circuit, as shown in Fig. 3. This paper is organized as follows. In Section 2, the PMT test bench is introduced, and the PMT test items are mentioned. In Section 3, the PMT batch test results are given. 2. PMT test 2.1. The PMT test bench The main characteristics of the PMTs for the LHAASO-WCDA++ experiment, such as the Single Photoelectron (SPE) spectrum, the high voltage response and the dark noise count rate, are tested using the test bench shown in Fig. 4. In a light-tight box, an LED is driven by a pulse generator (BNC-575) as a pulse source. The high-voltage power supply is CAEN SY1527. The PMT’s anode output charge is calculated by the QDC and recorded by a computer. The detailed information can
Corresponding author. E-mail address: [email protected] (C. Feng).
https://doi.org/10.1016/j.nima.2019.04.033 Received 18 March 2019; Received in revised form 4 April 2019; Accepted 7 April 2019 Available online xxxx 0168-9002/© 2019 Published by Elsevier B.V.
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
H. Zhang, Y. Yu, K. Tariq et al.
Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx
Fig. 4. The schematic of the PMT test bench.
Fig. 1. Layout of the LHAASO experiment.
Fig. 5. The schematic of the non-linearity test.
charge of the anode or dynode, so in this paper we use nPEs to represent the output charge of the anode or dynode. In order to study the effect of the pulse width on linear maximum nPEs, the pulse width of the signal generator is set to 5.5 ns, 15 ns and 30 ns and the frequency is kept at 5 kHz during the test process. In Section 2.3.2, a detailed introduction to non-linearity testing is given. The linear maximum nPEs increases with an increase in the pulse width, as shown in Fig. 6. Since the arrival time of Cherenkov light is very narrow [5], a 5.5 ns pulse width was selected for the bench test process.
Fig. 2. Profile of two adjacent WCDA cells.
be found in [4]. The stability of the system was periodically calibrated with a standard PMT throughout the test period. The dynamic linearity ranges of the anode and 6th dynode were measured by the bi-distance method. A non-linearity test system was set up as shown in Fig. 5. The LED can be moved to a far or near position. Both the anode and 6th dynode output charges are measured by an oscilloscope and recorded by the computer.
2.2.2. The effect of the LED light intensity on the relation between the gain and the working high voltage The exponential relationship between the anode or dynode output charge with different working high voltages agrees with Eqs. (1) (2), )( ( )𝑘 ∏ 𝑉𝑖 ∏ ∏ 𝑐𝑖 𝑎𝑛 𝑉 𝑛𝑘 = 𝐴𝑉 𝛽 (1) 𝑐𝑖 𝛿𝑖 = 𝐺= 𝑉 𝑖=1,𝑛 𝑖=1,𝑛 𝑖=1,𝑛
2.2. PMT test condition 2.2.1. The effect of the pulse signal width on the linear maximum number of photoelectrons A test schematic for the linear maximum number of photoelectrons (nPEs) is shown in Fig. 5. An AFG3252C pulse signal generator is used to test the charge non-linearity. The nPEs is proportional to the output
where 𝐺 is the gain of the PMT, 𝑉 is the sum of the working high voltages supplied to the PMT, 𝑐𝑖 is the collection efficiency of the 𝑖th dynode, and 𝑛 is the number of dynodes. For this type of PMT, when 𝑛 = 10, it is an anode; when 𝑚 = 6, it is the 6th dynode. The parameters
Fig. 3. Diagram of the divider circuit.
2
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Fig. 6. Non-linearity curves for one PMT with pulse widths of 5.5 ns, 15 ns and 30 ns. Fig. 9. Non-linearity curves measured for the PMT at a gain of 2 × 105 .
𝑎 and 𝑘 depend on the performance of the dynode, where 𝑘 is in the where 𝐺𝑑 is the dynode gain of the PMT. As expected, there is the similar exponential relationship between the gain and working high voltage for the anode and dynode. When testing the relation between gain and working high voltage, both the anode and dynode cannot be saturated. Different light intensities are selected for the anode and the dynode during the test. In the PMT linear region, the relation between gain and the working high voltage does not change with the LED light intensity within the margin of error, as shown in Fig. 7(a)(b). 𝑝0 represents 𝐴 and 𝐴′ , 𝑝1 represents 𝛽 and 𝛽 ′ , and all parameters are the same within the error for different light intensities. Thus, in the PMT linear region, the light intensity does not affect the relation between
range of 0.7–0.8. We assume here that 𝑎 and 𝑘 are constant for all the dynodes. 𝛿𝑖 = 𝑎𝑉𝑖𝑘 is the secondary electron emission coefficient of the 𝑖th dynode. Thus, 𝛽 is proportional to the number of dynodes. For the output charge of a dynode 𝑄 = 𝑄𝑜𝑢𝑡 − 𝑄𝑖𝑛 , 𝐺𝑑 =
∏ (
∏
𝑖=1,𝑚
= 𝐴′ 𝑉 𝛽
𝑐𝑖 𝛿𝑖
𝑖=1,𝑚−1
𝑖=1,𝑚
=
∏
𝑐𝑖 𝛿𝑖 −
′
)( 𝑐𝑖
1−
1 𝑐𝑚 𝑎𝑉𝑚𝑘
)(
∏ 𝑉𝑖 𝑉 𝑖=1,𝑚
)𝑘 𝑎𝑚 𝑉 𝑚𝑘 (2)
Fig. 7. (a) The anode and (b) dynode output charge is linear for the different working high voltages.
Fig. 8. The gain ratio of the anode to the dynode varies with the working high voltage (left). The working high voltage difference of three adjacent PMTs (right).
3
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Fig. 10. The distribution of the gain, beta, working high voltage and dark noise rate.
is denoted as 𝐶. As the light intensity increasing, the output charge of the PMT enters the non-linear region. The non-linearity is defined as ( ) 𝑄𝑛𝑒𝑎𝑟 − 𝐶 ∕𝐶 (4) 𝜆= 𝑄𝑓 𝑎𝑟
gain and the working high voltage. We chose a suitable light intensity to test the high voltage response curve. 2.2.3. The effect of the working high voltage on the ADratio Eq. (3) is the ratio of Eqs. (1) to (2), which is called the gain ratio of the anode to the dynode (ADratio).
(
∏
𝐴𝐷𝑟𝑎𝑡𝑖𝑜 =
)( 𝑐𝑖
𝑖=𝑚+1,𝑛 ′′
= 𝐴 𝑉 (𝑛−𝑚)𝑘
∏ 𝑉𝑖 𝑉 𝑖=𝑚+1,𝑛
)𝑘
( 𝑎𝑛−𝑚 𝑉 𝑛−𝑚𝑘 ∕ 1 −
1 𝑐𝑚 𝑎𝑉𝑚𝑘
where 𝑄𝑛𝑒𝑎𝑟 and 𝑄𝑓 𝑎𝑟 are the output charges measured at the near position and far position, respectively. The non-linearity curve of one PMT is shown in Fig. 9. Suppose that the PMT is linear, varying uniformly between the last point (𝑄𝑎 , 𝜆𝑎 ) that is greater than -5% and the first point (𝑄𝑏 , 𝜆𝑏 ) that is less than −5%. Accordingly, we can obtain the maximum charge at point 𝜆𝑠𝑡𝑑 =−5% with 𝑄𝑎 − 𝑄𝑚𝑎𝑥 𝜆 − 𝜆𝑠𝑡𝑑 = 𝑎 (5) 𝑄𝑎 − 𝑄𝑏 𝜆𝑎 − 𝜆𝑏
)
(3)
The ADratio is varied with the working high voltage, as shown in Fig. 8 (left). The ADratio should be measured for the working high voltage. There is a linear relation between log10(ADratio) and log10(high voltage). In the WCDA++ experiment, three adjacent PMTs share one power supply. The working high voltage difference of three adjacent PMTs is within 3 V, as shown in Fig. 8 (right). The average of the difference is less than 0.5 V, and the effect on the ADratio is less than 0.1%.
and we can calculate 𝑛𝑝𝑒 = 𝑄𝑚𝑎𝑥 ∕(𝑔𝑎𝑖𝑛 × 𝑒), where 𝑒 is the electron charge. The equivalent maximum number of photoelectrons is calculated according to the maximum charge of the dynode 𝑁𝑝𝑒 = (𝑄𝑑𝑦𝑚𝑎𝑥 × 𝐴𝐷𝑟𝑎𝑡𝑖𝑜)∕(𝑔𝑎𝑖𝑛 × 𝑒), where 𝑄𝑑𝑦𝑚𝑎𝑥 is the linear maximum charge of the dynode calculated by Eq. (5). 3. Batch test results
2.3. PMT test items
Each PMT has been tested, and 900 PMTs have been selected. Unqualified PMTs were returned to the manufacturer. Figs. 10 and 11 show the final statistical results. In Fig. 10, the upper left figure presents the distribution of the gain, and the average gain of the PMTs measured at a 2000 V high voltage is 3.9 × 106 . Some PMTs were rejected due to low gain. The upper right figure shows the distribution of 𝛽, and the average 𝛽 of the PMTs measured at the high voltages of 2000 V to 1100 V is 6.02. The lower left figure is the working high voltage distribution with a gain of 2 × 105 based on the formula of the relationship between gain and the high voltage. The average working high voltage is 1230 V. One group of three PMTs with similar working voltages are placed in adjacent cells and share one power supply. The average of the difference in the working high voltages is approximately 0.5 V, as shown in Fig. 8 (right). The lower right figure shows the distribution of the dark noise count rate of the PMTs, and the average value is only 3.58 Hz, far lower than 200 Hz. Fig. 11 shows the statistical results of the charge non-linearity test of the PMTs. The upper left figure presents the distribution of the number of anode photoelectrons. For the working voltage of each PMT,
2.3.1. General test For this type of PMT, the SPE spectrum is tested at a 2000 V positive voltage, and the selected gain of the PMT is greater than 2 × 106 . The anode output charge is measured at different working high voltages that vary from 2000 V to 1100 V with a step of 100 V. 𝛽 can be obtained from the high voltage response curve. Then, the working high voltage can be deduced for a PMT gain of 2 × 105 . The dark noise count rate is tested for a 1 mV threshold at the working high voltage. The test methods for the above measurements can be found in [4]. 2.3.2. Charge non-linearity For the charge non-linearity measurement, the pulse signal generator it used to set the pulse width to 5.5 ns, and the frequency is 5 kHz in the test process. The steps of the test are as follows. First, keeping the LED light intensity constant, the PMT output charge is measured at far and near positions. Then, the light intensity is gradually increased, and the above test is repeated. In the linear region, the ratio of the PMT output charges for the near and far positions is constant, which 4
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Fig. 11. Distribution diagram of the charge non-linearity test.
the average number of maximum anode photoelectrons is 1.47 × 104 . The upper right figure shows the distribution of the ADratio, which is the charge output ratio between the anode and the dynode, and the mean value is 122. The lower left figure shows the maximum number of photoelectrons of the equivalent anode distribution, and the average number is 3.0 × 105 . The WCDA++ experiment requires that the number of photoelectrons of the equivalent anode should be greater than 2 × 105 . All 900 PMTs selected meet the experimental requirements.
Acknowledgment This work is supported by National Science Foundation of China (NSFC) (Grant No. 11775131). References [1] Cao Zhen, A future project at Tibet: The large high altitude air shower observatory (LHAASO), Chin. Phys. C 34 (2010) 249. [2] He Huihai, Design of the LHAASO detectors, Radiat. Detect. Technol. Methods 2 (2018). [3] Yao Zhiguo, Design & Performance of LHAASO-WCDA in: Proceedings of the 32nd International Cosmic Ray Conference (ICRC 2011). [4] Wang Xu, et al., Setup a photomultiplier tube test bench for use at LHAASO-KM2A, Chin. Phys. C 40 (2015). [5] X. Zhao, et al., Characterization of HZC XP1805 photomultiplier tube for LHAASO-WCDA with a high dynamic range base, J. Instrum. 11 (2016).
4. Conclusions The performance of 1.5-inch PMTs with a specially designed bireadout voltage divider is tested. The effects of the working high voltage and signal width on the dynamic range of the PMTs are studied. The results show that the dynamic range with a 5% charge non-linearity for a signal width of 5.5 ns is more than 200 kPEs. The dark noise count rate is less than 200 Hz for a 1 mV threshold. These results confirm that the PMT performance meets the requirements of the WCDA++ experiment.
5
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
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Photomultiplier tube performance of the WCDA++ in the LHAASO experiment Hengying Zhang a , Yanhong Yu a , Khuram Tariq a , Zongkang Zeng b,c , Xiurong Li b , Cheng Liu b , Dong Liu a , Cunfeng Feng a ,∗, For the LHAASO Collaboration a
Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China c University of Chinese Academy of Sciences, Beijing 100049, China b
ARTICLE
INFO
Keywords: LHAASO PMT Non-linearity Bi-readout Water Cherenkov detector array
ABSTRACT In the Large High Altitude Air Shower Observatory (LHAASO), the main physics objective of the water Cherenkov detector array (WCDA) is to survey the sky for gamma-ray sources in the energy range of 100 GeV to 30 TeV. In order to extend the dynamic range of the WCDA, a 1.5-inch photomultiplier tube (PMT) is placed aside the 8-inch PMT in each cell of the WCDA. All of these 1.5-inch PMTs (900 in total) consist of the WCDA dynamic extended system (WCDA++). These PMTs are required to maintain linearity within four orders of magnitude. The performance of the 1.5-inch PMTs with a specially designed bi-readout voltage divider is tested with a PMT test system. Accordingly, the effects of the working high voltage and signal width on the dynamic range of the PMTs are studied. The test results show that the dynamic range with a 5% non-linearity for a driven signal width of 5.5 ns is more than 200 kPEs (photoelectrons). The dark noise count rate is less than 200 Hz for a 1 mV threshold at a PMT gain of 2 × 105 . These results confirm that the PMT performance meets the WCDA++ requirements.
1. Introduction The Large High Altitude Air Shower Observatory (LHAASO) is a hybrid extensive air shower (EAS) array in Sichuan Province (P.R. China) 4410 m above sea level. The observatory consists of an EAS array covering an area of 1.3 km2 (KM2A), a 78,000 m2 water Cherenkov detector array (WCDA) and 12 wide-field air Cherenkov/fluorescence telescopes (WFCTAs) [1,2], as shown in Fig. 1. The WCDA is one of the major components of the LHAASO. The main physics objective is to survey the sky for gamma-ray sources in the energy range of 100 GeV to 30 TeV [3]. In order to extend the dynamic range to PeV, one 1.5-in. photomultiplier tube (PMT) is placed aside the 8-in. PMT in each cell of the WCDA, as shown in Fig. 2. All(900) 1.5-in. PMTs constitute the WCDA dynamic extended system (WCDA++). The WCDA++ experiment requires that the operational gain of the PMT is 2 × 105 , and the corresponding high voltage is called the working high voltage. The performance parameters of the designed photomultiplier at the working high voltage are as follows: (1) the linear maximum number of photoelectrons (PEs) is more than 200 kPEs within a 5% non-linearity, (2) the dark noise count rate is less than 200 Hz at a 1 mV threshold, and (3) the gain ratio of the anode to the dynode (called ADratio) is between 90 and 150. The XP3960 photomultiplier tube is manufactured by Hainan Zhanchuang Photonics ∗
Technology Co., Ltd (HZC). This PMT has nine dynode stages. Because of the space charge effect, it is impossible to maintain the linearity of the PMT output with only anode signal readout. A bi-readout divider circuit of the anode and 6th dynode is designed. The special divider circuit and readout circuit is developed by using the design of a special ladder circuit, as shown in Fig. 3. This paper is organized as follows. In Section 2, the PMT test bench is introduced, and the PMT test items are mentioned. In Section 3, the PMT batch test results are given. 2. PMT test 2.1. The PMT test bench The main characteristics of the PMTs for the LHAASO-WCDA++ experiment, such as the Single Photoelectron (SPE) spectrum, the high voltage response and the dark noise count rate, are tested using the test bench shown in Fig. 4. In a light-tight box, an LED is driven by a pulse generator (BNC-575) as a pulse source. The high-voltage power supply is CAEN SY1527. The PMT’s anode output charge is calculated by the QDC and recorded by a computer. The detailed information can
Corresponding author. E-mail address: [email protected] (C. Feng).
https://doi.org/10.1016/j.nima.2019.04.033 Received 18 March 2019; Received in revised form 4 April 2019; Accepted 7 April 2019 Available online xxxx 0168-9002/© 2019 Published by Elsevier B.V.
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
H. Zhang, Y. Yu, K. Tariq et al.
Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx
Fig. 4. The schematic of the PMT test bench.
Fig. 1. Layout of the LHAASO experiment.
Fig. 5. The schematic of the non-linearity test.
charge of the anode or dynode, so in this paper we use nPEs to represent the output charge of the anode or dynode. In order to study the effect of the pulse width on linear maximum nPEs, the pulse width of the signal generator is set to 5.5 ns, 15 ns and 30 ns and the frequency is kept at 5 kHz during the test process. In Section 2.3.2, a detailed introduction to non-linearity testing is given. The linear maximum nPEs increases with an increase in the pulse width, as shown in Fig. 6. Since the arrival time of Cherenkov light is very narrow [5], a 5.5 ns pulse width was selected for the bench test process.
Fig. 2. Profile of two adjacent WCDA cells.
be found in [4]. The stability of the system was periodically calibrated with a standard PMT throughout the test period. The dynamic linearity ranges of the anode and 6th dynode were measured by the bi-distance method. A non-linearity test system was set up as shown in Fig. 5. The LED can be moved to a far or near position. Both the anode and 6th dynode output charges are measured by an oscilloscope and recorded by the computer.
2.2.2. The effect of the LED light intensity on the relation between the gain and the working high voltage The exponential relationship between the anode or dynode output charge with different working high voltages agrees with Eqs. (1) (2), )( ( )𝑘 ∏ 𝑉𝑖 ∏ ∏ 𝑐𝑖 𝑎𝑛 𝑉 𝑛𝑘 = 𝐴𝑉 𝛽 (1) 𝑐𝑖 𝛿𝑖 = 𝐺= 𝑉 𝑖=1,𝑛 𝑖=1,𝑛 𝑖=1,𝑛
2.2. PMT test condition 2.2.1. The effect of the pulse signal width on the linear maximum number of photoelectrons A test schematic for the linear maximum number of photoelectrons (nPEs) is shown in Fig. 5. An AFG3252C pulse signal generator is used to test the charge non-linearity. The nPEs is proportional to the output
where 𝐺 is the gain of the PMT, 𝑉 is the sum of the working high voltages supplied to the PMT, 𝑐𝑖 is the collection efficiency of the 𝑖th dynode, and 𝑛 is the number of dynodes. For this type of PMT, when 𝑛 = 10, it is an anode; when 𝑚 = 6, it is the 6th dynode. The parameters
Fig. 3. Diagram of the divider circuit.
2
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
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Fig. 6. Non-linearity curves for one PMT with pulse widths of 5.5 ns, 15 ns and 30 ns. Fig. 9. Non-linearity curves measured for the PMT at a gain of 2 × 105 .
𝑎 and 𝑘 depend on the performance of the dynode, where 𝑘 is in the where 𝐺𝑑 is the dynode gain of the PMT. As expected, there is the similar exponential relationship between the gain and working high voltage for the anode and dynode. When testing the relation between gain and working high voltage, both the anode and dynode cannot be saturated. Different light intensities are selected for the anode and the dynode during the test. In the PMT linear region, the relation between gain and the working high voltage does not change with the LED light intensity within the margin of error, as shown in Fig. 7(a)(b). 𝑝0 represents 𝐴 and 𝐴′ , 𝑝1 represents 𝛽 and 𝛽 ′ , and all parameters are the same within the error for different light intensities. Thus, in the PMT linear region, the light intensity does not affect the relation between
range of 0.7–0.8. We assume here that 𝑎 and 𝑘 are constant for all the dynodes. 𝛿𝑖 = 𝑎𝑉𝑖𝑘 is the secondary electron emission coefficient of the 𝑖th dynode. Thus, 𝛽 is proportional to the number of dynodes. For the output charge of a dynode 𝑄 = 𝑄𝑜𝑢𝑡 − 𝑄𝑖𝑛 , 𝐺𝑑 =
∏ (
∏
𝑖=1,𝑚
= 𝐴′ 𝑉 𝛽
𝑐𝑖 𝛿𝑖
𝑖=1,𝑚−1
𝑖=1,𝑚
=
∏
𝑐𝑖 𝛿𝑖 −
′
)( 𝑐𝑖
1−
1 𝑐𝑚 𝑎𝑉𝑚𝑘
)(
∏ 𝑉𝑖 𝑉 𝑖=1,𝑚
)𝑘 𝑎𝑚 𝑉 𝑚𝑘 (2)
Fig. 7. (a) The anode and (b) dynode output charge is linear for the different working high voltages.
Fig. 8. The gain ratio of the anode to the dynode varies with the working high voltage (left). The working high voltage difference of three adjacent PMTs (right).
3
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
H. Zhang, Y. Yu, K. Tariq et al.
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Fig. 10. The distribution of the gain, beta, working high voltage and dark noise rate.
is denoted as 𝐶. As the light intensity increasing, the output charge of the PMT enters the non-linear region. The non-linearity is defined as ( ) 𝑄𝑛𝑒𝑎𝑟 − 𝐶 ∕𝐶 (4) 𝜆= 𝑄𝑓 𝑎𝑟
gain and the working high voltage. We chose a suitable light intensity to test the high voltage response curve. 2.2.3. The effect of the working high voltage on the ADratio Eq. (3) is the ratio of Eqs. (1) to (2), which is called the gain ratio of the anode to the dynode (ADratio).
(
∏
𝐴𝐷𝑟𝑎𝑡𝑖𝑜 =
)( 𝑐𝑖
𝑖=𝑚+1,𝑛 ′′
= 𝐴 𝑉 (𝑛−𝑚)𝑘
∏ 𝑉𝑖 𝑉 𝑖=𝑚+1,𝑛
)𝑘
( 𝑎𝑛−𝑚 𝑉 𝑛−𝑚𝑘 ∕ 1 −
1 𝑐𝑚 𝑎𝑉𝑚𝑘
where 𝑄𝑛𝑒𝑎𝑟 and 𝑄𝑓 𝑎𝑟 are the output charges measured at the near position and far position, respectively. The non-linearity curve of one PMT is shown in Fig. 9. Suppose that the PMT is linear, varying uniformly between the last point (𝑄𝑎 , 𝜆𝑎 ) that is greater than -5% and the first point (𝑄𝑏 , 𝜆𝑏 ) that is less than −5%. Accordingly, we can obtain the maximum charge at point 𝜆𝑠𝑡𝑑 =−5% with 𝑄𝑎 − 𝑄𝑚𝑎𝑥 𝜆 − 𝜆𝑠𝑡𝑑 = 𝑎 (5) 𝑄𝑎 − 𝑄𝑏 𝜆𝑎 − 𝜆𝑏
)
(3)
The ADratio is varied with the working high voltage, as shown in Fig. 8 (left). The ADratio should be measured for the working high voltage. There is a linear relation between log10(ADratio) and log10(high voltage). In the WCDA++ experiment, three adjacent PMTs share one power supply. The working high voltage difference of three adjacent PMTs is within 3 V, as shown in Fig. 8 (right). The average of the difference is less than 0.5 V, and the effect on the ADratio is less than 0.1%.
and we can calculate 𝑛𝑝𝑒 = 𝑄𝑚𝑎𝑥 ∕(𝑔𝑎𝑖𝑛 × 𝑒), where 𝑒 is the electron charge. The equivalent maximum number of photoelectrons is calculated according to the maximum charge of the dynode 𝑁𝑝𝑒 = (𝑄𝑑𝑦𝑚𝑎𝑥 × 𝐴𝐷𝑟𝑎𝑡𝑖𝑜)∕(𝑔𝑎𝑖𝑛 × 𝑒), where 𝑄𝑑𝑦𝑚𝑎𝑥 is the linear maximum charge of the dynode calculated by Eq. (5). 3. Batch test results
2.3. PMT test items
Each PMT has been tested, and 900 PMTs have been selected. Unqualified PMTs were returned to the manufacturer. Figs. 10 and 11 show the final statistical results. In Fig. 10, the upper left figure presents the distribution of the gain, and the average gain of the PMTs measured at a 2000 V high voltage is 3.9 × 106 . Some PMTs were rejected due to low gain. The upper right figure shows the distribution of 𝛽, and the average 𝛽 of the PMTs measured at the high voltages of 2000 V to 1100 V is 6.02. The lower left figure is the working high voltage distribution with a gain of 2 × 105 based on the formula of the relationship between gain and the high voltage. The average working high voltage is 1230 V. One group of three PMTs with similar working voltages are placed in adjacent cells and share one power supply. The average of the difference in the working high voltages is approximately 0.5 V, as shown in Fig. 8 (right). The lower right figure shows the distribution of the dark noise count rate of the PMTs, and the average value is only 3.58 Hz, far lower than 200 Hz. Fig. 11 shows the statistical results of the charge non-linearity test of the PMTs. The upper left figure presents the distribution of the number of anode photoelectrons. For the working voltage of each PMT,
2.3.1. General test For this type of PMT, the SPE spectrum is tested at a 2000 V positive voltage, and the selected gain of the PMT is greater than 2 × 106 . The anode output charge is measured at different working high voltages that vary from 2000 V to 1100 V with a step of 100 V. 𝛽 can be obtained from the high voltage response curve. Then, the working high voltage can be deduced for a PMT gain of 2 × 105 . The dark noise count rate is tested for a 1 mV threshold at the working high voltage. The test methods for the above measurements can be found in [4]. 2.3.2. Charge non-linearity For the charge non-linearity measurement, the pulse signal generator it used to set the pulse width to 5.5 ns, and the frequency is 5 kHz in the test process. The steps of the test are as follows. First, keeping the LED light intensity constant, the PMT output charge is measured at far and near positions. Then, the light intensity is gradually increased, and the above test is repeated. In the linear region, the ratio of the PMT output charges for the near and far positions is constant, which 4
Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.
H. Zhang, Y. Yu, K. Tariq et al.
Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx
Fig. 11. Distribution diagram of the charge non-linearity test.
the average number of maximum anode photoelectrons is 1.47 × 104 . The upper right figure shows the distribution of the ADratio, which is the charge output ratio between the anode and the dynode, and the mean value is 122. The lower left figure shows the maximum number of photoelectrons of the equivalent anode distribution, and the average number is 3.0 × 105 . The WCDA++ experiment requires that the number of photoelectrons of the equivalent anode should be greater than 2 × 105 . All 900 PMTs selected meet the experimental requirements.
Acknowledgment This work is supported by National Science Foundation of China (NSFC) (Grant No. 11775131). References [1] Cao Zhen, A future project at Tibet: The large high altitude air shower observatory (LHAASO), Chin. Phys. C 34 (2010) 249. [2] He Huihai, Design of the LHAASO detectors, Radiat. Detect. Technol. Methods 2 (2018). [3] Yao Zhiguo, Design & Performance of LHAASO-WCDA in: Proceedings of the 32nd International Cosmic Ray Conference (ICRC 2011). [4] Wang Xu, et al., Setup a photomultiplier tube test bench for use at LHAASO-KM2A, Chin. Phys. C 40 (2015). [5] X. Zhao, et al., Characterization of HZC XP1805 photomultiplier tube for LHAASO-WCDA with a high dynamic range base, J. Instrum. 11 (2016).
4. Conclusions The performance of 1.5-inch PMTs with a specially designed bireadout voltage divider is tested. The effects of the working high voltage and signal width on the dynamic range of the PMTs are studied. The results show that the dynamic range with a 5% charge non-linearity for a signal width of 5.5 ns is more than 200 kPEs. The dark noise count rate is less than 200 Hz for a 1 mV threshold. These results confirm that the PMT performance meets the requirements of the WCDA++ experiment.
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Please cite this article as: H. Zhang, Y. Yu, K. Tariq et al., Photomultiplier tube performance of the WCDA++ in the LHAASO experiment, Nuclear Inst. and Methods in Physics Research, A (2019), https://doi.org/10.1016/j.nima.2019.04.033.