# A method to measure transit time spread of photomultiplier tubes with Cherenkov light

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3 346 WU Chong et al. / Nuclear Science and Techniques 20 (2009) Fig.2 Divider circuit of PMT2. the two H6533, σ 1XP is the standard deviation of the time walk between the H65331 and XP2020, and σ 2XP is the standard deviation of the time walk between the H65332 and XP2020. All the standard deviations of the time walks included the scintillators. The time resolution of electronics was about 20 ps (r.m.s). Solving the equations, σ H65331 is 76 9 ps. It is the standard deviation of the time walk of PMT1 used. 3.2 TTS measurement Fig.3 Self-gated spectra of the PMT under test. The solid line is the fit with Eq.(7). 3 Results and discussion 3.1 Measurement of time resolution of the start signals The time walk of start signal affects the TTS measurement of PMT2, and it should be eliminated from TTS. Three PMTs, one XP2020 and two H6533, called H65331 and H65332, were coupled with scintillators. In the experimental setup in Fig.1, three PMTs were used as the PMT1 and PMT2. Thus, three time resolutions could be obtained as Eqs.(4 6): σ 2 H σ 2 H65332= σ 2 12 (4) σ 2 H σ 2 XP2020= σ 2 1XP (5) σ 2 H σ 2 XP2020= σ 2 2XP (6) where σ H65331 and σ H65332 are the standard deviations of the time walk of the H65331 and H65332, σ XP2020 is the standard deviation of the time walk of the XP2020, σ 12 is the standard deviation of the time walk between With the experimental setup, the TTSs of XP2020 and XP2020Q were obtained. Fig.4 is the amplitude distribution of XP2020 under 60 Co γ-rays. The background distribution was obtained without 60 Co source. The structures of the two amplitude spectra and time spectra (Fig.5) are similar. It means that the background is contributed by cosmic rays. Compared with Fig.3, the amplitude spectra of Fig.4 is mainly from the contribution of the single photonelectron (SPE). However, there are obvious multiphotoelectron contributions which will affect the TTS measurement. In order to eliminate the effect, the distribution was fitted by the convolution of a Poisson and a Gaussian: n 1 n Npe pee /2 ( x nc) /(2 n ) N f( x) (2π n ) e (7) n! where N pe is the number of average photoelectrons, is the standard deviation of the distribution of SPE, and C is the peak position of SPE. In the fitting to distributions, pedestals were subtracted. The fitted curve is shown in Fig.4 with a solid line. The other lines show the contributions of

4 WU Chong et al. / Nuclear Science and Techniques 20 (2009) the numbers of different photoelectrons. The contribution of multi-photoelectron can be observed. To get the TTS, a cut to amplitude distribution was chosen as from Ch.140 to Ch The time spectrum is shown in Fig.5a. With the fit of Gaussian distribution function and the subtracting of time walk, the TTS was obtained. Figs.5b and c show the time spectra of double and triple photoelectrons with different cuts. Table 2 lists the TTSs of different number of photoelectrons with two PMTs. There are two errors. The first is statistical error, and the second is the contributions of other photoelectrons. It can be seen that TTSs are almost the same with Philips data of 250 ps [8]. In the last column, the TTSs were obtained without any cut to channels. They are also similar to the Philips data. The reason is that the contribution of SPE is dominant from the amplitude spectrum. But they are not TTSs. Fig.4 Amplitude spectra of Cherenkov light of XP2020 with 60 Co γ-rays. The relations between number of photoelectrons and TTSs are shown in Fig.6. The fit lines reveal TTS is inversely proportional to the square root of number of photoelectrons. The same result can be found in Ref.[9]. With Eq.(7), the contributions of different photoelectrons can be obtained. They are listed in Table 3 which is similar with the simulation results shown in Table1. Fig.5 Time spectra of different numbers of photoelectrons of XP2020, P1=amplitude, P2=centroid and P3=width, (a) SPE with a cut from Ch.140 to Ch.200; (b) Double photoelectrons with a cut from Ch.300 to Ch.370; (c) Triple photoelectrons with a cut from Ch.460 to Ch.580.

5 348 WU Chong et al. / Nuclear Science and Techniques 20 (2009) Table 2 Transit time spreads (in ps) with different number of photoelectrons with different PMTs PMT Single photoelectron Double photoelectrons Triple photoelectrons No cut to channel XP XP2020Q Table 3 Ratios of three photoelectrons of Cherenkov light of PMTs in experiments with 60 Co source PMT source Ratio of SPE / % Ratio of two photoelectrons / % Ratio of three photoelectrons / % XP2020 XP2020Q 60 Co Co PMTs of XP2020 and XP2020Q are consistent with data supplied by Philips. And TTSs are inversely proportional to the square root of number of photoelectrons. References Fig.6 Relation between TTS and number of photoelectrons. 4 Conclusion Using coincidence method, it is feasible to measure TTS of a PMT with Cherenkov light on the photocathode window of PMT produced by cascade radiation source, when the amplitude of single and multi-photoelectrons can be distinguished. The convolution of Poisson and Gaussian can fit the amplitude of Cherenkov radiation well. The TTSs of 1 Tsagli S, Aggouras G, Anassontzis E G, et al. Nucl Instrum Methods A, 2006, 567: Cherenkov P A, Doklady Akad. Nauk SSSR, 1934, 2: Ypsilantis T and Seguinot T, Nucl. Nucl Instrum Methods A, 1994, 343: Ratcliff B N, Nucl Instrum Methods A, 2003, 502: Artuso M, Ayad R, Bukin K, et al. Nucl Instrum Methods A, 2005, 554: Allkofer Y, Amsler C, Horikawa S, et al. Nucl Instrum Methods A, 2007, 582: Wu C, Wang Z M, Xu Z Z. Nucl Nucl Instrum Methods A, 1998, 405: Photo and electron multipliers (Netherlands: Phillips Electronic Components and Materials Division), 1985, Matsui S, Akatsu M, Enari Y, et al. Nucl Instrum Methods A, 2001, 463:

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