PMT Calibration

PMTs are crucial components of the anti-neutrino detectors. Daya Bay experiment has a good process to monitor PMT quality, which includes PMT gain, relative efficiency and channel linearity. In addition, PMT ringing and flashing have been understood.

3.1.1 Gain

The PMT gain is the conversion constant from ADC to PMT output charge in p.e.

(photoelectron). We use two photon sources, low intensity LED and PMT dark noise, to measure the single photoelectron (SPE) spectrum. Three functions, simple gauss function, full model and simple full model, are used for the SPE fit. The full model is described in the later subsection, which discusses PMT pedestal, noise, SPE and multi PEs. The simple full model only considers the SPE and multi PEs.

PMT dark noise

PMT dark noises are caused by the leakage current between the electrodes and the PMT surface or the thermal emission of single electron from the cathode. They exist in the normal data taking, so this calibration process can be performed any time and it does not need to stop a run.

The signal range is for TDC value larger than 1070, as shown in Fig 3.3. First, it requires the removal of 40 MHz noise and the peak-cycle¹are between 4 and 6. The criteria for signal selection are as follows:

• Time to previous trigger is larger than 20 µs.

• Only one hit per channel.

• Signals must be in fine gain range.

• |preAdc − avePreAdc| is less than 20.

Low intensity LED

The LED calibration is performed once a week. It is an independent process for obtaining the PMT conversion constant. To reduce the double or multiple photoelectron hits on PMT, the first criteria is that the occupancy of the PMT hits should be lower than 13%

of the total triggers. The signal range is located at TDC values between 950 and 1050, which separates the signal from the dark noise and after-pulses, as shown in Fig 3.4.

The peak-cycles are between 3 and 8 and it requires the removal of 40 MHz noise. The disadvantage of this method is the need to stop the physics run, so it cannot monitor the gain fluctuation during the data taking. Therefore, this method only be used for cross check.

Figure 3.3: TDC distribution from the normal data taking run.

3.1.1.1 Single Photo-Electron (SPE) Fitting Model: Full Model

The fitting model for single photo-electron is from Ref. [26]. Here, we can treat the photomultiplier as an instrument with two parts, photo-electron detector and amplifier.

For simplicity, the light source illuminating on the photo-electron detector can be treated as stable, so the average number of photons hitting on PMT is a constant. How-ever, not every photon hitting on the PMT can be converted into electron. Only part of those photons are collected by PMT, which is referred to as quantum efficiency. The process is a random binary process. The convolution of Poisson and binary processes

1Peak-cycle: When a channel has a hit, it starts to look for a ’peak’ in the ADC. It will look at each ADC (every 25ns) in a window from 0 to 350ns. The peak cycle is the time of the peak; with each count equals to 25ns.

Figure 3.4: TDC distribution from the LED trigger events.

gives rise to a Poisson distribution,

P (n; µ) = µⁿe^−µ

n! , (3.1)

where µ is the mean value of the photo-electrons collected by the first dynode and P (n; µ) is the probability that n photo-electrons are observed when the mean value is µ.

In the amplifier part of the PMT, the charge amplification by the dynode system follows Poisson distribution. However, if the first dynode is large (more than 4), the response function can be approximated by a Gaussian distribution:

G₁(x) = 1 σ₁√

2πexp(−(x − Q₁)²

2σ₁² ), (3.2)

where x is the charge variable, Q₁ is the average charge of the PMT output when one electron is collected by the first dynode, and σ₁ is the corresponding standard deviation of the charge distribution.

When more than one photo-electron are collected by the first dynode, the response function is a convolution of n single electron case:

G_n(x) = 1 σ₁√

2nπexp(−(x − nQ₁)²

2nσ₁² ) (3.3)

Combining these two parts, the response of an ideal noiseless PMT is given by For the real PMT, the noise has to be taken into account. The noise sources include thermo-electric emissions from the photocathode or dynode, leakage current in the PMT, electron auto-emission of the electrodes, etc. There are two contributions to the back-ground term. The first one is known as ’pedestal’, which can be approximated as Gaussian function. The second contribution is the noise background. One can parameterize the background term as

B(x) = 1 − w σ₀√

2πexp(− x²

2σ₀²) + wθ(x)αexp(−αx). (3.5) where σ₀ is the standard deviation for the pedestal, w, α and θ describe the background noise. w is the probability and α is the coefficient of the exponential, θ is the step function.

In Daya Bay experiment, the simple full model is the current official method for the PMT gain fit. The pedestal was first subtracted from the SPE spectrum and fitted with the simple full model. Figures 3.5 and 3.6 are the fitted PMT responses from the single photon-electron (SPE) measurement with dark noise and LED light source, respectively.

h_Adc_DayaBayAD1_R01_C19

Figure 3.5: Fitting to the distribution of ADC-preADC from the PMT dark noise events with Eq. (3.4).

Figure 3.6: Fitting to the distribution of ADC-preADC from the LED events with Eq. (3.4).

3.1.1.2 Monitoring the conversion constant

PMT gain (ADC/SPE) is determined and monitored by the dark noise results and cross-checked with the LED calibration. Figs 3.7 and 3.8 show the current status of conversion constant.

3.1.2 Linearity

The PMT hit charge is measured by the FEE and recorded as ADC value. There are two ADC ranges, low charge (”fine”) range and higher charge (”coarse”) range. The channel charges of the former is up to about 200 p.e. at a gain of 1 × 10⁷ and the later is from 200 p.e. up to 3000 p.e. The IBD events are in the fine gain range and the higher energy events, like muon, are in the coarse gain range.

3.1.3 Ringing

The large signals induces a large noise in the electronic response after the primary pulse, called ringing. It could effects the experimental results; such as the fake signals or dupli-cated hits. One example is given in Fig 3.11.

Date, UTC Jul13 Oct12 Jan12 Apr13 Jul13 Oct12 Jan12 Apr13 Jul13 Oct12 Jan12

Gains’ average [ADC]

18 18.5 19 19.5 20

ALL Water Pool

DYB-AD1 DYB-AD2 LA-AD1 LA-AD2 Far-AD1 Far-AD2 Far-AD3 Far-AD4

ALL AD

Figure 3.7: PMT gain for all ADs via the dark noise measurement from Aug 24, 2011 to Dec 31, 2013.

Date, UTC Jul14 Oct13 Jan13 Apr14 Jul14 Oct13 Jan12 Apr13 Jul13 Oct13 Jan12

Gains’ average [ADC]

19 19.5 20 20.5 21

ALL Water Pool

EH1-OWS