Characterizing the KM3NeT 3-inch Hamamatsu Photomultiplier Tube response

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July 11, 2017

Characterizing the KM3NeT 3-inch

Hamamatsu Photomultiplier Tube response

Author:

A. S. Schermer BSc

Supervisors:

dr. R. Bruijn

dr. J. Steijger

First examiner:

dr. R. Bruijn

Second examiner:

Prof. dr. A.P. Colijn

Master Thesis for the Master Physics 60 EC

GRAPPA Track

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Abstract

KM3NeT is a km3 neutrino telescope which is currently under construction at the bottom of the

Mediterranean Sea. KM3NeT aims to pin-point the direction of neutrino sources and measure the neutrino mass hierarchy. Photomultiplier tubes are housed in pressure resistant glass spheres to detect the Cherenkov radiation emitted by charged interaction products of neutrino interactions in Sea-water. The time when the PMT is hit by one or more photons and the size of the signal, encoded in the length of the pulse (time over threshold), in the PMT are measured with ns accuracy. The detailed information of the number and time structure of incoming photons and its relation with the time over threshold is not well understood. In this thesis the relation between the number of photons hitting the photo-cathode of the PMT and the digitized response of the PMT-base is studied. Also measurements of the PMT response to a delay between two incoming photons are done. The relations are studied with the use of a setup consisting of two light sources whose time structure and intensity can be precisely controlled. Model parameters of the PMT response simulations are crosschecked by measurements, such as the default threshold value. The results from this study have lead to a better understanding of the PMT behavior and improvements in the PMT response simulations.

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1 Introduction

KM3NeT (Cubic Kilometre Neutrino Telescope) is a neutrino detection infrastructure which is cur-rently under construction in the Mediterranean Sea. KM3NeT has two main objectives. The first is studying the sources of high energy cosmic neutrinos. The second objective is determining the mass hierarchy of neutrinos. As there are two main objectives in KM3NeT the detector is split into two subdetectors. Each separate part of the detector is optimized to reach one objective. The two respective detector parts are ARCA and ORCA. Where ARCA stands for Astroparticle Research with Cosmics in the Abyss and ORCA for Oscillation Research with Cosmics in the Abyss. In chapter 3.3 the design of KM3NeT will be described in more detail.

Neutrinos are leptonic particles which carry no electric charge and have a small cross-section for the interaction with other particles. Due to the small cross section a big detector is needed.

When a neutrino interacts with the sea water it creates charged particles. These charged particles have a lot of energy and thus will start emitting Cerenkov radiation. In KM3NeT, this radiation is measured using a 3D grid of PMTs contained in pressure resistant glass-spheres called DOMs. An

effective detection volume of approximately 1 km3 is created by deploying a lot of DOMs. Chapter

3.4 elaborates more on the DOMs.

An incoming photon which hits the PMT will create a pulse in it. The leading edge of the PMT signal and the time over threshold, the the time that the signal is over a preset threshold, are registered with a nanosecond accuracy. The non-trivial conversion between the photon flux and the time over threshold (ToT) has been studied in this research. In section 4 the PMTs in general and, the PMTs and its electronics used by KM3NeT will be described in more detail.

To study the stochastic physics processes in KM3NeT, detailed simulations are needed. In this re-search the ingredients used in these simulations are cross-checked with an experimental setup, focusing on the relation between the ToT and the photon flux and their time structure.

The relation between the flux and the ToT is studied to improve the event reconstruction by improving the knowledge of the PMT response. The detailed time structure and the simulations of the PMT response are compared with the data measured in the lab.

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2 Neutrino physics

As stated in the Introduction, KM3NeT aims to study high energy cosmic neutrinos to determine its source and determine the neutrino mass hierarchy. In this chapter a short overview of neutrino physics and cosmic rays will be given, accompanied by a short introduction to particle physics.

2.1 Particle Physics

Particle physics researches the physics of matter and radiation. Matter and radiation are the building blocks of nature and consist of elementary particles. In particle physics the smallest existing particles are studied, in other words point-like particles. Point-like means that there is no internal structure measurable. In physics there are four fundamental forces: the gravitational, weak, strong and electro-magnetic forces.

The currently known elementary particles are dividable into two categories: Fermions and Bosons. This categorization is done according to the spin of the particles. Fermions have half integer spin states and Bosons have integer spin states.

Figure 1 shows an overview of all known elementary particles with on the left side the Fermions and their respective spin and on the right side the Bosons.

Figure 1: Summary of known elementary particles in the Standard Model.

The Fermions are categorized in leptons and quarks where each is dividable into 3 generations. The first generation are the most abundant particle flavours in the universe at the relative lowest energy scale. When, for example in particle colliders, the energy scale is increased the second and

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gluons to the color charge of quarks. All other particles are color neutral so don’t feel the strong force.

2.2 Cosmic rays

The earth is continuously bombarded by cosmic rays. Cosmic rays are discovered in 1912 by Victor Hess. The discovery was done via measuring the ionization rate with respect to the altitude. Charged particles, which come from stars and other sources, e.g. black holes, galaxies or supernovae, in the universe collide with the atmosphere of the Earth. The mechanism that accelerates and shoots the high energy particles into space is still an unknown feature in astro-particle physics.

Figure 2: The energy spectrum of cosmic rays [1].

Cosmic rays mostly consist of protons and heavy nuclei [2]. High energy electrons are also part of cosmic rays only their total contribution to the total amount of cosmic rays is negligible.

When a cosmic ray hits the atmosphere of the Earth, protons and nuclei are hit. The protons and nuclei will create a hadronic shower. In the hadronic showers the decay products are new protons, neutrons and pions. The main production channels are:

p+ p → p + n + π+ or p + p → p + p + π0 (1)

p+ n → 2p + π− or p + n → p + n + π0 or p + n → 2n + π+ (2)

The pions will decay to electrons, muons and their respective neutrinos or photons. For example:

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and

π0 → γ+ γ. (4)

The typical lifetime of a charged pion is 26 ns and for the π0 10−7_{ns. Due to the short life times the}

chance for an interaction with other matter before they decay is minimal. This means they will not lose much energy before decaying so the decay products have a higher chance to be highly energetic.

The resulting muons will thus be relativistic. The lifetime of a muon1 will be prolonged. Because

of the fact that the muon has a high mass the relativistic muon loses a relatively a low amount of energy. Due to the long decay time and the low amount of energy loss atmospheric muons pene-trate deep into the atmosphere and even into the deep sea, where they form a background in KM3NeT. High energy electrons in cosmic rays lose their energy in a different way. When an electron hits the atmosphere, it will start to emit Bremsstrahlung (when it interacts with the electron-magnetic field of the nuclei of atoms). The emitted photons are energetic enough to produce electron positron pairs. Which are in turn able to emit Bremsstrahlung. This process is called a electromagnetic cas-cade. When the electrons and positrons have lost their energy they are absorbed by atomic nuclei. Low energy photons will be absorbed via the photoelectric effect [2, 3, 4].

The position of cosmic ray sources are unknown and cannot be identified from reconstruction of the incoming direction. The cosmic ray charged particles are influenced by intergalactic magnetic fields. Neutrinos however are believed to be produced from cosmic ray sources in the universe and should point in the correct direction. Because of the fact that neutrinos only interact via the weak interaction, are their traveling paths not influenced by the intergalactic magnetic fields. This makes high energy cosmic neutrinos the ideal candidate for finding the position of cosmic ray sources.

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2.3 Neutrino interactions

As stated in section 2.1 there are three lepton generations with each its own neutrino (νe, νµ, ντ).

Neutrinos do only interact via the weak interaction (no electromagnetic charge and color) and have extremely low masses. Because of the fact that the neutrino only interacts via the weak interaction, the cross-section of a neutrino-matter interaction is small. In figure 3 the cross-section with respect to the energy is shown. Possible cosmic neutrino sources with their expected energy scale are also shown in figure [5].

Figure 3: Cross-section versus the energy scale of the neutrino. The cross-section is extremely small with respect to for example the cross-section of a proton proton collision at 8 TeV which is 96.07±1.34 mb[6]. In the figure are also shows typical energy regimes for different sources [5].

Because of the small cross section to detect the neutrinos a large detection volume, like KM3NeT,

is needed. The large volume increases the σ × Ntargets ratio by using a lot of targets and thus the

chance of a interaction inside the detector.

Neutrino interactions can be categorized into two types interactions, namely neutral current (NC) or charged current (CC) interactions.

Figure 4: The neutral current neutrino interactions on the left side and on the right side the charged current interactions. The l at the bottom stands for the leptonic particle where the neutrino interacts with.

These two type of interactions are important for KM3NeT because they all make a distinct signal in the detector, see section 3.

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neutrino flux there was a large deficit measured in the neutrino flux[7]. The SNO experiment measured that the deficit was caused by the electron neutrino oscillating between the flavours[8]. To be able to oscillate between the flavours, neutrinos have to have a mass and that the mass eigenstate is not equal to the flavour eigenstate. The relation between the mass eigenstates and the flavour eigenstates is given by the PNMS matrix.

The exact masses of neutrinos are still unknown. Even the mass hierarchy between the neutrino flavors is not determined yet. To determine the mass hierarchy between the neutrino flavors are oscillation probabilities used. So when the neutrino propagates through space the probability to measure a certain flavor changes periodically. This probability can be measured by detecting the eigenstates of

atmospheric neutrinos2. Figure 5 illustrates the difference between the two optional hierarchies.

Figure 5: A representation of the neutrino hierarchy possibilities. The lowest mass corresponds with the bottom of the figure and the highest mass with the top of the figure [10].

KM3NeT studies neutrino interactions in sea-water. When a neutrino interacts with the sea-water, secondary charged particles are created. 4 different kind of interactions are distinguishable in the sea water. The neutral current interaction only creates a hadronic shower, while the charged current

interaction creates 3 different signals for each neutrino flavour. The νe creates a hadronic shower and

directly after that electromagnetic shower. The νµ will create a hadronic shower and a muon which

travels a relative long distance, dependent on the energy of the muon. The ντ creates a ”double bang”

interaction, first the hadronic shower and a τ particle are created. The τ particle travels a relatively short distance and then decays, which creates a electromagnetic shower. Figure 6 gives an overview of the neutrino interactions in water.

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Figure 6: Overview of the different neutrino interactions in water. In all interactions is a hadronic shower created, while in the Charged Current interaction are the signals from each individual flavour distinguishable by the shape of the signal.

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2.4 Neutrino Sources

Suspected is that Ultra High Energy Cosmic Rays and high energy cosmic neutrinos share the same origin. Source candidates for the Ultra High Energy Cosmic Rays are shown in the ”Hillas plot”, see figure 7.

Figure 7: The ”Hillas plot” shows candidate sources for the Ultra High Energy Cosmic Rays [11]. Ice cube reported in 2015 about the high energy cosmic neutrino flux but could not determine the position of the sources [12]. The main source candidates for these high energy neutrinos are Active Galactic Nuclei, Gamma-ray Burst or Star Burst galaxies. To locate the high energy neutrino source positions is the main research area for ARCA.

To determine the mass hierarchy are the oscillation probabilities of neutrinos measured. The neutrinos used to determine the mass hierarchy are produced mainly by cosmic rays. These neutrinos are called atmospheric neutrinos. As described in section 2.2 the neutrinos come from the charged pion decay. The study of the atmospheric neutrinos and its oscillations is the main research area for ORCA. Other neutrino sources are for example the sun (Nuclear fusion) or particle accelerators. By studying the neutrinos from the sun was the first prove for neutrino oscillations measured [13].

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3 KM3NeT Detector

In this chapter the experimental principle of large volume water Cherenkov detectors will be explained. This is followed by a description of the KM3NeT detector. As described before in chapter 1, the KM3NeT detector will consist of two sub-detectors. Each of the sub-detectors address different main scientific question. The ARCA detector will search for the cosmic neutrinos and their sources. The ORCA detector will study the atmospheric neutrino oscillation probabilities to determine the mass hierarchy between the neutrinos [14].

3.1 Cherenkov radiation

Cherenkov radiation is emitted by charged particles which surpass the speed of light in a certain medium. This is often seen in water which is transparent to the light emitted. Cherenkov radiation is known for the special property that the light that is emitted by the charged particle is emitted under a certain angle which is dependant on the energy of a particle. The relation between the angle and the energy/velocity is

cos(θ) = 1

nβ. (5)

When the particle has relativistic speeds, so v ≈ c, β will be 1 such that the angle is only dependant

of the refractive index n. nwater ≈ 1.35 and β ≈ 1 thus the Cherenkov angle θ ≈ 42.21◦. The angle

will thus be constant.

The spectrum of Cherenkov light is given by the Frank-Tamm formula, see equation 6. So the number of emitted photons N per unit Energy per unit path length

d2_N dEdx = 2παZ2 λ2 1 − 1 β2_n2(λ) (6) where α is the fine-structure constant, Z number of charged particles of the surrounding matter,

λthe emitted wavelength, β = v_c and n is the refractive index which is dependant on the wavelength.

In the sea water where Z is constant can be deduced that

d2_N

dEdx ∝

1

λ2 (7)

and thus result in a continuous emitted spectrum. This will be important later on for the PMT wavelength sensitivity choice.

3.2 Detecting Neutrinos with KM3NeT

In this section will be discussed what happens in the KM3NeT detector when a neutrino signal occurs in the detector. The principle applies for both ORCA and ARCA.

A passing neutrino interacts with the water. Charged particles are created or even a cascade happens. These charged particles are all relativistic so they will start emitting Cherenkov radiation. This Cherenkov radiation is detected by the PMTs in the DOMs. The signal of the PMT is then processed. KM3NeT uses the all-data-to-shore policy, so all digitized photon-signals are sent to shore via an optical network. On shore the pulses are filtered and analyzed. If the full photon-signals would be digitized in detail, it would use up a lot of data and power in the detector. This is why only the time of arrival of the photon and time over threshold are measured. This reduces the data per hit to 6 bytes per hit. The data is sent to shore by the central logic board (CLB) via the optical network at the bottom of sea. At the shore station the data is collected and processed in real time. After the processing and filtering of the data it is stored for further analysis [14].

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3.3 Detector Design

The detector design is based on the detection of Cherenkov radiation of produced relativistic charged particles when a neutrino interaction occurs. The KM3NeT detector is able to study interactions of GeV order (ORCA) up to PeV and above (ARCA). Both detectors use the same technology, but the density of the instrumentation differs, matching the different energy scales and fluxes of the neutrinos they are aiming to detect. In ARCA is the distance between the detection instrumentation (Digital Optical Modules) bigger than in ORCA.

The energy of the neutrinos that ARCA aims to detect is several order of magnitude higher than ORCA thus the charged interaction products also have more energy. This results in longer distances traveled by these interaction products. The sizes of the neutrino fluxes targeted by both detectors impose requirements on the target volume. For ORCA, the required volume to detect sufficient atmospheric neutrinos is a few megaton, while the much lower astrophysical neutrino flux requires ARCA to be of gigaton scale. Because of the lower energy of the interactions in ORCA are the path lengths of the secondary charged particles smaller than at the high energies measured in ARCA. This requires the design of ORCA to be more dense than in ARCA.

To measure the Cherenkov radiation, PMTs housed in a glass sphere, a Digital Optical Module (DOM), are deployed in the sea. 18 DOMs are attached to a vertical structure called a Detection Unit (DU). The vertical space in between the DOMs is 36 meters in ARCA and 9 meters in ORCA. 115 DUs are placed inside a building block. The horizontal space between the DUs is around 95 meters in ARCA and 40 meters for ORCA. ARCA consists of 2 building blocks while ORCA is one building block. The DUs are kept vertical by the buoyancy of the DOMs in combination with a buoy. Each DU is connected to the seafloor network which distributes power and transports data via optical fibers [14]. In figure 8 an overview of one of the building blocks of KM3NeT is shown.

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3.4 Digital optical modules

The DOMs contain the PMTs which are the eyes of the detector. When a particle passes by emitting Cerenkov radiation it will be detected by the PMTs in DOMs. The PMTs are sensitive to Cerenkov light created by the relativistic charged particles produced in the neutrino interaction. Chapter 4 discusses the PMTs used by KM3NeT in detail. A DOM is a transparent glass sphere made out of 2 hemispheres of 17 inches in diameter. It houses in total 31 PMTs and their associated electronics. The reason for using multiple PMTs in the DOM is to increase the photo-cathode area with respect to traditional used designs based on large area PMTs. Other advantages of multiple PMTs is that

it can be used to discriminate on optical backgrounds3, the direction of the incoming photon can be

determined and smaller PMTs have lower transit time spreads. In figure 9 is a DOM shown and a schematic of its components.

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Figure 9: In figure 9a is a fully assembled DOM attached to a part of the Detection Unit. Where in figure 9b is a exploded view of the sub-parts of the DOM. This gives an overview of the internal structure of the DOM.

The PMTs are installed in 5 rings with each containing 6 PMTs and one PMT facing vertically

down. The rings are staggered with a 30◦ angle and the PMTs are spaced with a 60◦ azimuth. 12

PMTs are situated in the upper part of the DOM and the other 19 are in the bottom. The support structure of the PMTs is 3D printed and reflective rings are added around the face of each PMT. This results in an increase of photon collection efficiency of 20-40% with respect to the traditional setups [14]. Optical gel connects the PMTs to the glass sphere. Specifications of the PMTs used in KM3NeT and its properties will discussed in more detail in section 4. The PMTs are connected to a central logic board (CLB). The CLB manages the data collection and transmission to shore over the optical fibre via the optical interface. Furthermore does the DOM contain a piezo sensor, tilt-meter, a nanobeacon and compass which are needed for exact positioning and monitoring [14, 15].

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The DOM is calibrated on shore before deployment. The aim of the on shore calibration is to determine what the timing differences between the individual DOMs and its electronics in a Detection Unit are. When the DOMs are deployed in the sea a White Rabit system monitors and synchronizes the timing between the DOMs. In-situ calibration is also done with the use of nano beacons, muon tracks or data

of 40K decays in water.

3.5 Backgrounds and reduction

The detector has three major optical backgrounds to cope with, bioluminescence,40K decay and

cos-mic muons. The total background rate inside the PMTs is 7-8 kHz.

Bioluminescence is created by organisms which live in the deep sea. When an animal hits a object a light flash can be emitted. Bioluminescence studies were done by H. van Haren et al. [16] and the Antares experiment.

The biggest background in KM3NeT is the abundant radioactive isotope 40K .40K decays into 40Ca

and produces electrons with enough energy to emit Cherenkov radiation. This is a background effect especially for lower energy events but can also be used to perform PMT time calibrations [17]. The

noise rate of40K is around 5 kHz per PMT in the whole detector.

Muons and neutrinos which are produced in cosmic rays, see section 2.2, are the third major back-ground. The signal that comes from the (high energy) atmospheric neutrinos and muons is similar to the signal of cosmic neutrinos when it hits the water in the detector and creates a muon. Just like

40K are cosmic muons used for calibration purposes in the detector. The neutrinos created in these

cosmic rays are indistinguishable from normal neutrino hits.

The biggest background reduction is done by complex trigger algorithms. KM3NeT also makes use of coincidence hits between PMTs in a DOM and between DOMs itself to filter the background. Because of the complex triggering the all-data-to-shore is needed. The cosmic muons coming from above are attenuated by the sea water above the detector which decreases significantly the rate of this background. The neutrino background is reduced by selecting only up going neutrino hits.

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4 Photomultiplier Tubes

Photomultiplier tubes are the eyes of the KM3NeT detector. PMTs are the most essential component of the detector because of that it is crucial to understand their behaviour and characteristics. In this chapter, the working principles of PMTs will be described, followed by details on the PMTs and associated electronics as used in KM3NeT. There will be particular focus on the digitization of the analog PMT signal.

4.1 Properties of the Photomultiplier tubes

A PMT is a light detection device which can be sensitive to even single photons. In figure 10 is schematically shown how a PMT works.

4.7 Photomultiplier tubes

In applications such as scintillation counting, where the light yield is very low, PMTs are the most

common light detectors. PMTs can have a very high gain, high quantum efficiency, low noise and a

fast response, which makes them unsurpassed in many applications. For the X

AMS

TPC, two PMTs

from Hamamatsu Photonics are used.

4.7.1 Working principle

A photomultiplier tube is a vacuum tube that detects light of low intensity down to single photons.

It outputs pulses with a typical duration of tens of nanoseconds. Figure 40 explains the general

principle of PMTs. A photon enters a window, which is coated with a bialkali material. This material

forms the photocathode and emits electrons by the photoelectric effect. The electrons are then

accelerated onto the first dynode by an electric field. When the electrons from the photocathode

(photoelectrons) hit the first dynode, they have gained enough energy to free multiple electrons. If

several dynodes are used, the number of electrons will thus grow at an exponential rate, creating an

avalanche of electrons. Finally, the electrons are focused on the anode, and a small electric current

can be measured at the output using an oscilloscope or a multi-channel analyzer.

Figure 40: Schematic illustration of the working of a photomultiplier tube. Light hits the photocathode,

where a photoelectron is emitted. An electric field accelerates the electron onto the first dynode, where

multiple electrons are emitted by the process of secondary electron emission. After several dynodes, the

signal at the anode is large enough that it can be detected. Image taken from [27].

There are several important figures of merit for PMTs. One of them is the gain. The gain G is

defined as the average multiplication of a photoelectron, or, in other words, the number of electrons

measured at the output divided by the total number of photoelectrons. When a light pulse is

detected, the voltage as a function of time V (t) is usually measured at the output. The voltage is

measured over an internal discharge resistor R

i

of a measurement device such as an oscilloscope.

From the measurement of V (t), the total charge at the output signal can be determined. If n

out

is the total number of electrons at the output of the PMT, then

n

out

=

Q

e

=

s

I

(t)dt

e

=

s

V

(t)dt

R

i

e

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where Q is the total charge, I(t) is the current and e is the elementary charge. From the definition

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Figure 10: Working schematic of a PMT. A photon hits the photo-cathode. The photon liberates a photo-electron at the photo-cathode. The electron is multiplied. The avalanche of electrons is caught by the anode which emits the current pulse [18].

The PMTs photo sensitive area is the photo-cathode. The photo-cathode is damped onto the transparent glass window from the inside of the PMT. As a photon hits the photo-cathode an electron is liberated via the photoelectric effect. The efficiency of liberating an electron is called the quantum efficiency. The quantum efficiency is a strong indication for the performance of a PMT. The typical quantum efficiency for the PMTs used at KM3NeT is measured and shown in figure 11.

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Figure 11: The quantum efficiency measurement of the KM3NeT Hamamatsu PMT done by S. Aiello et al. [19].

When the photo-electron (p.e.) is liberated from the cathode it is accelerated to the first dynode. This is done with the help of applying a high voltage between the cathode and the first dynode. When the p.e.hits the first dynode a certain amount electrons will be liberated. This is a Poisson statistical process. The newly liberated electrons are then attracted to the next dynode by a high voltage and this is repeated till the anode. Each dynode multiplies via the Poisson process the amount of electrons. The total amount of electrons liberated after the multiplication of one p.e. is called the gain. The

gain is often of the order 106₋108, this depends on the high voltage settings, amount of dynodes and

the geometry of the PMT.

The PMT signal, the electrical pulse measured at the anode, is characterized by the rise time (tr), full

width at half maximum t(fwhm) and the transit time (tt). The rise time is the time the signal needs

to reach the maximum voltage. The transit time is the time between the moment of the photon hitting the photo-cathode and the moment that the signal is measured. The spread on the transit time (TTS) is important for the determination of the accuracy of the PMT regarding timing measurements. In figure 12 an example of a PMT output pulse which is measured at the anode is shown.

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important to have an really low dark rate. Most of the dark rate is generated by thermal fluctuations which liberate an electron in the cathode. Other possibilities are that the gas in the PMT is ionized or a dynode loses an electron [21].

4.2 KM3NeT Photomultiplier Tubes

The PMTs of KM3NeT are placed in the DOM connected to a base. The base controls and reads out the PMT. The base will be discussed in section 4.2.1 KM3NeT has some strict specifications, see table 1 which have to be fulfilled by the PMTs.

Parameter Requirement

Optical sensitivity range 400-500 nm Photo cathode diameter > 72 mm

Length < 12 cm

Nominal Voltage for Gain 3 × 106 900-1300 V

Gain Slope 6.5 - 8 ns

Quantum Efficiency at 404 nm > 23%

Quantum Efficiency at 470 nm > 18%

transit time spread < 5 ns

Dark count at threshold < 2 kHz

Pre-pulses < 1%

Delayed pulses < 3.5%

Early after pulses < 2%

Late after pulses < 10%

Table 1: Main requirements of the characteristics for the 3-inch PMT of KM3NeT [22]. The choice for the wavelength range of the PMT sensitivity is dictated by the combination of the Cherenkov light spectrum and absorption length in the Sea-water. The absorption length in water is the largest in the region of 400 - 500 nm. In figure 13 is the absorption length spectrum shown for the Mediterranean Sea,

Figure 13: Measured absorption spectrum in the Mediterranean Sea by [23]

To detect the neutrino interactions and reconstruct their energies nanosecond accurate timing is needed from the PMTs. To achieve this, the strict requirements on the transit time spread and gain

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slope must be met. To have the optimal PMT setup and being able to distinguish signals from noise the dark count has to be as low as possible and the random background effects as pre-, delayed and after pulses have to be reduced as much as possible. The requirements set a limit on these background factors [22].

The PMTs used in the current phase of KM3NeT, and which is used in this study, are manufactured by Hamamatsu. Other manufacturers such as ETEL and HZC have provided candidate PMTs which are also considered for the next phase of KM3NeT. One of the Hamamatsu PMTs used by KM3NeT, and in this study, is shown in figure 14

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4.2.1 PMT-Base

The base of a PMT contains electronics to generate the required high voltage, and to amplify and digitize the signal. The base is connected to the bottom part of the PMT, see figure 14. In figure 15 is schematically the working and parts of the PMT shown.

Figure 15: The electronic parts of the base schematically shown. Schematic from D. Real [24]. The base is powered by a 3.3 V power supply which comes from the CLB. The electronic noise level, base line, is at 1 V. When a signal arrives in the base the signal will be on top of the 1 V baseline.

The signal from the PMT needs to be amplified by a pre-amplifier because of the low gain. The pre-amplifier is designed in such a way that when a low amount of incoming photons, the response is linear with the amount photons. The amplified signal is then compared to the threshold by the comparator. The comparator gives a high or a low signal dependant on the fact if the amplified signal is above or below the set threshold. When the signal thus passes the threshold value the comparator gives a high in the out coming LVDS signal. The rising flank, when the signal switches from low to high, is the time of arrival of the signal which indicates the arrival of a photon. The time between the rising edge and the falling edge corresponds with the ToT. The LVDS signal is processed by the CLB or other DAQ like a oscilloscope as used in this study. In figure 16 the process of amplification and comparison with the threshold is shown.

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Figure 16: The processing of the incoming signal from the PMT schematically shown in this figure. First the raw signal is amplified where after the signal is compared with a preset threshold. The comparator gives a low signal when the PMT signal is below threshold and a high signal when the PMT signal is above threshold. The rising flank is where the arrival moment of the incoming photon is registered. The time between the rising and falling edge is the ToT.

The analog pre-amplified pulse is optionally available, but this feature is by default disabled and not used in the read out. This is done to keep the data volume as small as possible and the power usage of the CLB low.

The base settings are controlled by a I2C controller. The threshold settings are sent via the I2C to the

Threshold DAC. The threshold range can be set from 0.8-2.4 V and has 256 intermediate steps. The HV DAC controls the high voltage in the PMT in a range between 700 - 1300 V and has 256 steps. All settings are sent in hexadecimal numbers to the base. Each PMT can be separately controlled from shore by calling onto their PMT ID. This can be needed for (high voltage) calibration purposes or threshold changes in-situ.

4.2.2 Relation between the photon flux and ToT

As stated in the introduction not all information of the hits is used. The photon flux which is translated in a ToT by the base is measured but not used in the default event reconstruction algorithms of KM3NeT. Also the detailed time structure of the incoming photons is not used.

The ToT is not used because of the fact that the translation between the photon flux and the ToT is not well understood. The detailed time structure has never been studied in detail yet, so if the

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cathode is studied to find the relation between the photon flux and the ToT. The time structure of the incoming photons and their relation with the ToT is measured by studying the time of arrival of the photons in the setup. By studying this relation is looked into effects that happen in the PMT when a photon hits the photo-cathode. Examples of these effects are pre and after pulses which come together with the real photon signal. Furthermore, the effects of a delay between photons are studied. Finally a threshold scan is done to determine the relation between the settings and the threshold expressed in units of photo-electrons. In this way, it can be cross-checked if the default value used corresponds with the intended 0.3 p.e.

4.2.3 Photon flux to ToT models

The simplest model is that the ToT depends linearly on the number of photons. This motivated by the design of the pre-amplifier which gives a linear response with respect to the amount of incoming photons. Because of the fact that the charge of the incoming photons is Gaussian distributed, with

a width that Poisson like behaves 4 and a mean that is linear dependent on the amount of incoming

photons, a first educated guess is that the ToT distributions are also Gaussian. This model was first put to the test in this study. First results showed that this model breaks down in the single photon region so more sophisticated models are needed.

Two other more complex optional models are suggested to describe the relation between the charge. The need for a more complex model results from the fact that the signal has to pas first a threshold before it is registered. This results in a non-linear relation between the ToT and charge in the lower range around and below the charge of single incoming photons. At higher numbers of incoming photons is a linear relation expected because of the design of the amplifier on the PMT base. Two models are suggested, where as a result from this study the last model is currently used in the PMT response simulations of KM3NeT. In this study both models are tested.

The first model, equation 8, takes in account the structure of signal which comes out of the PMT. The relation between the charge and the ToT can be derived from the shape of the PMT signal, see figure 12. The signal is composed of a rise time, which is the time it takes the signal to rise from 0 to the maximum, and a down fall which is described by an exponential decay.

T oT(x) = A + B × x + C ln(x) (8)

σ(n) = √Q

x + P

√

x (9)

Where A represents the rise time, B the increase in rise time which is dependant on the number of incoming photons, C the time it takes for the signal to decay, P and Q are constants of the width. The width of the ToT distributions is derived from the width of the Gaussian charge distributions and transform it via the same translation as the ToT. The number of photons are represented by x which is also equal to the charge via a linear transformation. In this models is the threshold value not taken into account yet.

The second model tested in this study takes the threshold value into account. Other important input parameters for this model are the gain spread and the rise time of the signal. In this model is taken into account that in the higher photon flux range the ToT will relate linearly with the charge. This is the first part of equation 10. The second part of the equation controls the relation in the lowest parts of the photon flux and the threshold cut of on the ToT.

T oT(x) = (A + B × x) r x − xT hres x (10) σ(n) = √Q n (11)

4The width of the charge distributions is given by σ

N =

√

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where A, B are the constants which hold the gain spread and the rise time of the signal, xT hres is the

threshold value and Q is the width of the distribution constant. In figure 17 a representation of the model, which takes the threshold into account, is shown.

charge

(m

e

ov

er

th

re

sh

ol

d

𝑔(𝑥)=𝑎+𝑏𝑥

1

𝑥↓1 

ℎ(𝑥)=√⁠𝑥−𝑥↓1 /𝑥  

𝑓(𝑥)≡𝑔(𝑥)×ℎ(𝑥)

speciﬁca(on

𝑓(1)

Schema(c behavior of the ToT vs Charge

Figure 17: The relation between the charge and the ToT is shown as the red line. The model translate the ToT cuts off at a certain point in the charge space which is the set threshold. So the derivative of the relation goes to infinite. In the higher charge region a linear relation is expected to occur. So at the point of one is the mean charge of 1 p.e. is expected to be in the near linear region but if the charge becomes a little bit less there will be a non-linear translation between the ToT and the charge. The used model translation is given as f(x). Maarten de Jong [2017]

The non-linear relation between the ToT and the number of photons (charge) implicates that there is a transformation between the ToT distributions and the Gaussian charge distributions. To translate the Gaussian charge distribution into the ToT distribution via a non-linear relation the following transformation method has to be used:

g(T oT ) = f(x(T oT )) dx_{dT oT}(T oT (12)

where x is the charge, f(x) is the Gaussian charge distribution and |dx(T oT )

dT oT |is the Jaccobian. The

Jacobian (dT oT

dx ) gives the non-trivial shape of the ToT distribution which can be seen in figure 41

in chapter 7. It is not yet proven that one of these models is the completely correct model for the translation between the photon flux and the ToT. The results of testing the models to the data are

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4.2.4 PMT Calibration

PMTs are not all completely identical thus to get the same response from each PMT to a signal the PMT needs to be calibrated. PMT calibration in KM3NeT is done on the high voltage with a preset

default threshold at 2F which corresponds with 1.09375 V. The PMT is calibrated to a gain of 3 × 106

which corresponds with a ToT of 26.4 ns.

The calibration procedure uses several steps. Multiple high voltages are applied and the ToT

distri-bution is measured. A Gaussian fit is made to determine the 1 photon peak position5. The program

used for this is MRunAnalyser.

A linear fit is then made through the data of HV vs ToT. An important assumption for the calibration is thus that the ToT scales linearly with the HV. After that the correct value is found for the PMT, it is set and measured again to confirm that the ToT is at 26.4 ns.

An example of the calibration is the calibration of the PMT used in this thesis. The calibration method as in-situ was used. In figure 18 is the HV vs the TOT shown with the linear fit. The error bars are the width of the Gaussian fits (σ). The error values on the fit parameters as the mean and the width are not available anymore. During the measurement was made sure that the data had enough statistics to do the calibration. The blue horizontal line shows the 26.4 ns ToT line and the vertical line the corresponding HV. The HV is 1172 V.

High Voltage (V) 1100 1120 1140 1160 1180 1200 1220 1240 1260 ToT (ns) 15 20 25 30 35

Calibration Hamamatsu AB1510

Figure 18: Calibration plot of the PMT used in the setup. The calibration is done with a constant threshold and a variable High Voltage to find the correct HV which gives a ToT for 1 p.e. of 26.4 ns. The error bars are the widths of the fitted Gaussian peaks. The blue horizontal line is at 26.4 ns and the vertical line is the found HV of 1172 V.

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5 Nanosecond interval PMT test setup

To measure the PMT properties and test the suggested models discussed in section 4.2.2 a table top setup is build. The objective of this setup is to precisely measure the photon flux, delay between the photons and its relation with the ToT. With the setup a PMT can be tested in a completely dark environment and shoot a controlled amount of photons with a sub ns accurate preset delay at the PMT. First in this section the setup design will be discussed and later on will be elaborated on the measurement techniques used with the setup.

5.1 Setup description

The setup is developed and built at the Nikhef. The setup consists of two photon sources, electronics which pulses the sources, a PMT in a dark box and a digital scope which acts as the data-acquisition. In figure 19 is an overview shown of all external parts of the experiment. Where in figure 20 is the inside of the dark box shown.

Figure 19: Nanosecond interval PMT test setup. Where on the right (C) is the control electronics which provide the high voltages of the PMT and the pulse generator which initiate the signal for the LEDs. On the top with the green lights are the generators of the LEDs. The laptop (E) has the control software for the PMT base to for example adjust the Threshold or High Voltage. The big metallic box is a dark box (A) where in the PMT is installed. The inside is coated with neoprene. On the left is the digital oscilloscope (D) which acts as data-acquisition. The light sources are at the white boxes (B).

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Figure 20: The inside of the PMT dark box. The PMT is situated at F and is resting on foam cushion such that it is at the right height for the incoming light sources. The light will be incoming from the point of the arrow. The distance between the fibre-ends and the PMT is around 5 cm.

Figure 21 shows the flow of the signal and processes in the setup.

Pulse

generator Sub ns delay regulator

LED 1 470 nm 470 nm LED 2 PMT + standard base Photon Photon pulse (delayed) pulse DAQ/ Scope LVDS signal ToT spectrum Toa spectrum HV and Threshold controller Histograms Raw data Thres 2F HV = 1172V Trigger

Flow chart of the setup

Figure 21: Flowchart of the setup used in the measurements. The pulse generator generates a pulse which leads to the sub ns delay regulator. Also the pulse of the generator is used as trigger for the DAQ. The signal travels by the delay regulator which delays LED 2 to the preset delay with ns accuracy. The LEDs pulse switch on and off and sent out a photon. The Photons are collected by the PMT. The PMT is calibrated by the KM3NeT standard calibration procedure. The PMT is connected to a normal base and gives out a LVDS signal. The signal travels to an oscilloscope/data acquisition. The DAQ is able to do basic analysis on the data or is able to put out raw data files.

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de-lay regulator which creates the dede-lay, (∆t), between the signals. The output signal is then typically 100 ns wide block pulse. The pulse arrives then at the LED generators. The LED generators are adjustable in intensity such that the amount of emitted photons per trigger is controlled this is a Poisson statistical process. The generator are able to switch the LEDs on and off within 1 ns. The photons are emitted by blue LEDs, λ = 470 nm, which has around the same wavelength as the part of the Cherenkov radiation which propagates long distances through the seawater. The capacity of the LEDs is 17 pF and of the brand VCC. The LEDs have a rise and fall time of 1 ns. This results in a total switching time of around 1.5 ns at the minimum intensity. When the intensity is increased the total switching time might go up to around 2 ns. This increase might have an increasing effect on the TTS. The photons travels through optical fibers into the dark box. When the PMT is hit by the photon the cascade happens and signal is created and processed by the base. The output signal of the base is then sent to the DAQ/scope The total transit time of the system is around 70 ns per pulse.

Data acquisition

The scope, a waverunner HRO 66Zi, acts as the data acquisition. It is able to sample at a rate of 2GS/s and has an internal frequency of 600 MHz. The PMT is coupled to the PMT via LEMO cables and gets an input of the LVDS signal. Due to the up going and down going of the signal the PMT has to be connected to the scope via 2 cables, in figure 19 the left two cables with the red markers. To reduce the dark rate in the system is the scope triggered by the pulse generator at the beginning of the system. After the trigger there is a 1 µs window where in the pulse can arrive.

The scope can directly analyze the hit or is able to output raw data files. Analyzing or outputting the raw data files result in dead time for the scope. This reduces the processing rate to around 100 triggers per second. The optimal triggering rate is determined by a quick measurement of the data taking rate.

To speed up the data taking rate so called sequence triggering is used. Sequence triggering works like first taking a sequence of a preset amount of trigger windows, for example 100 trigger windows. The windows are then put after each other an then all in one go analyzed. This speeds the data taking rate up to around 150 Hz.

The data acquisition thus outputs raw data or is able to give analyzed data. The analysis functions used in this thesis are the pulse width analysis (ToT) and the time of arrival determination. The data is then put into a histogram which gives for a example a ToT distribution or a time of arrival distribution.

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6 Measurements and Results

In this section the measurements of the PMT response and the corresponding results are described in detail. All measurements are done with the setup described in section 5.1. For each individual measurement first the measurement methods are discussed, then the results.

In all measurements, unless stated otherwise, the following settings are used:

• Same PMT used in all measurements

• PMT calibrated according to the KM3NeT calibration protocol

• Trigger rate LEDs = 150 Hz

• PMT high voltage = 1172 V

• PMT threshold = 1.09375 V (Default KM3NeT Threshold)

• The hits are measured by the scope as described in 5.1

6.1 Single photon PMT response

Single photons are the dominant signal in KM3NeT, so the PMT response to single photon hits is important to characterize. Also with single photons it is possible to determine several PMT properties. The PMT properties determined in this study are discussed in chapter 6.4.

Method

By using a single LED set to the minimum intensity, the ToT response of the PMT to the single

photon hits is measured. The minimal intensity of the LED source is that around 1

180 triggers results

in a hit. The down side of using such a low intensity is that the required time to gather enough statistics is of the order of several days.

The configuration inside the dark-box is exactly the same as in figure 20. To characterize the PMT response and cross-check if there are source dependent effects, both sources are individually measured. This single photon flux measurement is also used as a cross-check of the PMT High Voltage calibration procedure used in KM3NeT.

Result

The ToT distributions of both sources at the low intensity are shown in figure 22.

ToT (ns) 0 10 20 30 40 50 60 70 80 90 Events/second 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Photon source 1 (a) ToT (ns) 0 10 20 30 40 50 60 70 80 90 Events/second 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Photon source 2 (b)

Figure 22: In figure 22a and 22b the ToT distributions obtained with the two individual sources are shown.

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Figure 23: Both ToT distributions overlapped with each other to control if both spectra are the same. From these distributions it can be concluded that the ToT distribution obtained with both sources are similar, as expected. No source dependent effects are measured. The asymmetric shape of the single photon distribution is caused by the fact that the relation between the ToT and the charge, is not linear, see section 4.2.3. This results in a tail to the left side, lower ToT values, in the ToT distribu-tion. The low ToT hits on the left side of the distribution will be discussed in more detail in section 6.5

Conclusions

The single photon ToT is determined by doing a Gaussian fit at the peak position. The mean of the fit is then the ToT. The ToT of a single incoming photon is 27.10 ± 0.09 ns for source 1 with a σ of 3.08 ± 0.1 ns. The ToT of a single incoming photon for source 2 is 27.02 ± 0.15 ns and the width of the distribution is 3.17 ± 0.08 ns. This is slightly higher than the calibrated ToT of 26.4 ns, see section 4.2.4. This small offset can be explained by the fact that different fit range is used. In this study a fit range of 4 ns instead of 8 ns, in the official procedure, is used. When the official calibration fit procedure is used the ToT positions of the single photon peaks are consistent with the calibration to 26.4 ns, namely 26.6 ± 0.15 ns. This indicates that the official fit procedure systematically underestimates the peak position of the single photon peak. The errors on the values are the fit parameter errors.

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6.2 PMT response to multiple incoming photons

The multiple photon measurements, also referred to in this thesis as ”high intensity” measurements, are important to determine the accuracy with which the number of incoming photons can be interped from the PMT response. The amount of emitted photons by the secondary charged particles increases with the increasing energy of the neutrino interactions. So the number of incoming photons is a measure for the energy neutrino interactions. As stated in chapter 4.2.2, by studying the PMT response to multiple incoming photons and testing the suggested models(see chapter 4.2.3) for the relation between the ToT and the number of incoming photons, the energy resolution and event reconstruction can be improved.

Method

To study the relation between the number of incoming photons and the ToT a single LED is used. This is done so that all photons will arrive at the same moment at the PMT. The intensity of the LED is set to its maximum, around 2.5 hits are detected per trigger. With the scope are the pulses registered and the ToT distribution measured.

Results

The relation between the ToT and number of incoming photons is best approximated by the model described in equation 10. The model fits the single photon ToT distribution very well. Therefore this model is used in the multiple photon distribution fit to constrain the single photon peak. This is done

by fitting the model first to a single photon spectrum and using the resulting fit parameters6 in the

multiple photon distribution fit. From 2nd_{till the 7}th _{a Gaussian distribution for the ToT is assumed.}

This is motivated from the linear behavior of the amplifier on the base of the PMT, see chapter 4.2.1, which allows a linear translation between the ToT and charge distributions in the region above the charge of 1 pe.

To measure the ToT versus the number of photons without assuming a model beforehand, the means and widths of the Gaussian distributions are not constrained. The mean of the underlying Gaussian distributions is the ToT of the corresponding number of photons. Because of the fact that no con-straints on the means are imposed, the assumption of the linearity of the amplifier is cross-checked. The only constraint on the fit is that, due to the Poisson-like behaving setup, the integrals of the Gaussian distributions (which are linear with the heights of Gaussian distributions) has to be Poisson distributed. The fit function used to fit the multiple incoming photon ToT distribution is:

f(T oT ) = √ 1 2πσcharge · C1· e −0.5 _x−µcharge σcharge 2 · _{dT oT}_(x) dx −1 + CP ois· N =7_X N =2 P ois(λ, N) ·√ 1 2πσN · e −0.5 T oT −µN σN 2 (13)

f(ToT) describes the hit rate for a certain ToT in events/second, where C1 is the constant that

determines the height of the 1 p.e. peak and has units of events/second. σcharge is the width of the

charge distribution, µcharge is the mean charge of the Gaussian charge distribution both are fitted in

the single photon distribution and fixed in the multiple photon distribution fit. The Jacobian at the end of the first line comes from the relation in equation 12, with ToT(x) is equation 10 and x is the

charge. CP oiss is the constant which scales with the Poisson function for each individual photon-peak.

The sum of the individual Gaussian are representing the underlying distributions of the individual

photon peaks. µN and σN are free variables and both have the units nanoseconds. The resulting best

fit of the multiple incoming photon distribution is shown in figure 24.

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ToT (ns)

0 10 20 30 40 50 60 70 80 90

number of events per second

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Figure 24: The free Gaussian fit for the analysis of the ToT and sigma correlation. The only constraint

for the 2nd _{till the 7}th _{photo peak is that the height of the peaks has to be Poisson distributed .}

The measured values of the means (ToT(pe)) and the widths of the fitted Gaussian distributions are shown in figure 25.

Number of p.e. 2 3 4 5 6 7 Peak ToT [ns] 35 40 45 50 55 60 65 70 (a) (b)

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because the the spread on the charge distributions increase withpNp.e.. Further studies are needed

to investigate this.

Conclusions

All different suggested models of the relation between ToT and number of p.e. were tested but non was found to completely describe the data. The model equation 10 in chapter 4.2.3, is the best approxima-tion so far. The models were tested by fitting them to data and compare the chi-square, convergence and the reasonableness of the individual underlying distributions. The best found model is now used in the default PMT response simulations of KM3NeT. The model still needs improvements to better match the ToT distributions in the higher number of photon range, because still a Gaussian approach

for the 2nd ToT peak and higher is used in the fit. Where actually also these distributions has to

transformed according to 12.

The hypothesized linear relation between the ToT and number of p.e. has been observed in the data. The irregular behavior of the widths of the distributions might be the lack of a strong restricting model, so that they might interfere with each other. To confirm this further studies are needed.

The result of the fit is also given in table 2. The result of the single photon peak measurement added to complete the full ToT peak position from the 1st till the 7th photon peak.

p.e. ToT (ns) σ (ns) 1 27.02 ± 0.15 3.17 ± 0.08 2 34.97 ± 0.04 2.79 ± 0.02 3 41.60 ± 0.03 3.17 ± 0.02 4 48.60 ± 0.05 3.27 ± 0.01 5 55.46 ± 0.06 3.16 ± 0.03 6 61.38 ± 0.08 3.64 ± 0.06 7 68.93 ± 0.11 4.62 ± 0.15

Table 2: The best fit values of equation 13, as shown in figure 24 The errors on the values are the fit errors.

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6.3 ∆T in between photons and time of arrival distributions

Photons arriving at the PMTs of the KM3NeT detector are distributed in time, reflecting the properties of the emitting source and the effects of propagation through water. The arrival times of photons are well understood, demonstrated by various studies in which data is confronted with simulation. The response of the PMT to consecutive photons, reflected in the resulting ToT is not well understood and not extensively studied. A systematic study of the response of a KM3NeT PMT to photons arriving with a variable time delay at the photo-cathode has been done for the first time in this work. This section describes these studies.

Method

To measure the relation between the ToT and the time difference between consecutive photons the next steps are followed:

• Measure the ToT distribution for each source individually

• Measure at the same time the time of arrival distributions.

An example of a arrival time distribution of single source is shown in figure 26. The shape of the time of arrival distributions is compatible with transit time measurements done on a large batch of PMTs by the KM3NeT collaboration.

Time of arrival [ns] 40 60 80 100 120 140 160 180 Number of Hits 0 10000 20000 30000 40000 50000 60000 70000 80000 (a) Time of arrival [ns] 40 60 80 100 120 140 160 180 Number of Hits 1 10 2 10 3 10 4 10 5 10 (b)

Figure 26: In figure a) and b) show the same Toa distribution on a linear and a logarithmic scale, respectively. The peak of around 70 ns is the moment when the incoming photons arrive. This plot clearly shows the other populations of arrival times. Just before the large peak at 70 ns is a small population which can be characterized as pre-pulses. The tail to the right side is the contribution of delayed pulses. The pulses even further to the right are after pulses which are uniformly distributed. The peak position is determined with a Gaussian fit where the mean is the peak position and the width is the transit time spread (TTS).

• Determine the delay between the hits.

To determine the delay between the hits on the PMT for each individual source the time of arrival distributions are measured. The average delay between the two photon arrival times are determined with sub-nanosecond accuracy

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order to calculate the rate of 1 p.e. hits expected, the following reasoning can be followed:

P(X = 0) = 1 − P (X > 0) (14)

Where X is the amount of photons in a trigger. P (X > 0) is the integral of the total spectrum normalized to the total amount of triggers.

P(X = k) = λ

k_e−λ

k! (15)

With these measurements it is then possible to determine λ for each distribution:

λ= − ln(1 − P (X > 0)) → λ = − ln

1 −_{number of triggers}number of hits (16)

The rate (λ in hits per trigger) of each measurement is determined with this method. The rates then are used to determine the ratio of how much hits in the simultaneous measured ToT distribution come from a single source. With this ratio the individually measured spectra are re-scaled and then subtracted from the simultaneous measured ToT distribution. So in formula form:

λ2hits= λs1+ λs2− λs1+s2 (17)

gives the amount of hits per trigger which are simultaneous hits, where λs1 is the rate of source

1. λs2 the rate of source 2 and λs1+s2 is the rate when both sources are triggered at the same

time. The scaling factors of the individual ToT distributions are:

Scale1= 1 − λ2hits λs1 (18) Scale2= 1 − λ2hits λs2 (19)

• Find the 2 p.e. peak created by coincident hits of the two sources

• Gaussian fit to 2 p.e. to determine ToT peak position

• Repeat with a relative offset between the two sources

Figure 27 shows an example of the the individual measured ToT distribution of both sources (a and b), the measurement of the combined sources (c) and the extracted result (d).

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Figure 27: An overview of the extraction method used to the determine the 2 photon peak position. a) and b) show the results for the individual sources. Figure c) shows the ToT distribution with both sources activate simultaneously and d) shows the extracted result. In c) the 2 photon peak position is already visible at around 50-60 ns.

The fluctuations in the beginning of the extracted distribution (d) are the result of small shifts in the ToT distributions, which cannot be corrected for.

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Results

In figure 28 the relation between the ∆t and the 2 p.e. ToT peak position of the simultaneous hits is shown.

Figure 28: The ToT vs ∆t relation is shown. The bigger uncertainties in the beginning, with respect of the other data points, come from fluctuations in the extracted distribution, see figure 27. When the delay increase the 2 p.e. peak position shifts away from the 1 p.e. region so become better distinguishable. In the beginning only a slow increase in the ToT with respect to the ∆T is measured. With a delay bigger than 5 ns, the ToT and delay relate linearly with each other. The slow increase in the beginning can be explained by the fact that this is still within the range of the TTS.

On the left side of the plot the relation between the ToT and ∆T is slowly rising to the linear behavior on the right side of the distribution. This ”slow” start at the beginning of the figure can be explained by the fact that the ∆t is partially absorbed in the width of the Toa distribution (TTS). The TTS of the setup used in this thesis is between 1.1-1.9 ns. The linear behavior at the right side of the distribution is just as expected because of the fact that the ∆t will dominate the change in position of the mean ToT of the 2 p.e. peak.

When the delay between the individual photons reaches the ToT of the 1 p.e. peak (≈ 26.4 ns) there would be expected that the height/area of the 2 p.e. peak decreases. Because that the chance of the second photon hitting the PMT in time, such that the signal of the first hitting photon is not fallen below the threshold again, becomes smaller. The results are shown in figure 29.

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Figure 29: Peak height of the 2 p.e. peak measured in the ∆T measurement. The fluctuation on the left side are systematic fluctuations. On the right side the clear decrease of the 2 p.e. peak height measured around the ToT of the 1 p.e.

Conclusions

From the time of arrival spectra the transition time spread is determined at 1.359 ± 0.21 ns. This is the TTS of the whole setup including the triggering electronics and the LEDs. The TTS of only the PMT cannot be measured with the current setup, because the transit time of the setup itself is not well defined.

The relation between the delay and the ToT is linear, especially in the region with delays bigger than 5 ns. When the delay becomes smaller than 5 ns it converges back to the ToT of the two photon peak. The 2 p.e. ToT in the ∆T measurement with a ∆T = 0 is cross-checked with the 2 p.e. ToT of the multiple incoming photon measurement. The ToT of the 2 p.e. in the ∆T measurement is 34.76 ± 0.22 ns with respect to the 34.97 ± 0.04 from the multiple incoming photon measurement.

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6.4 Threshold Scan

The threshold is an important feature of the PMT-readout. The threshold controls the amount of hits that are seen from the PMT but also the noise rate. In other words the signal to noise ratio depends on the threshold settings.

With a threshold scan the integrated charge distribution of the 1 p.e. peak can be measured. From the integrated charge distribution, the mean charge of 1 p.e. and the gain spread on the 1 p.e. signal are determined. With the mean of the charge distribution the assumed default threshold in KM3NeT is determined in units of p.e. and cross-checked with the assumed value of 0.3 p.e.

Method

Several steps are followed in a threshold scan. A single LED at the lowest intensity is used so that only single photons are emitted and thus the effects of 2,3,4... p.e. can be neglected. The LED is then triggered at a high rate so that the rate of incoming photons is above the dark rate. The dark rate is around 1 kHz. The threshold scan is done on one Hamamatsu PMT which is calibrated according to the KM3NeT calibration protocol. Keep the HV to the constant and then the next procedure is followed:

1. Set Threshold value

2. Take count rate of Source + Dark rate (Total count rate) 3. Take count rate of Dark rate only

4. Set New threshold value

5. repeat for different threshold values

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Results

The threshold and the gain spread are important parameters for the KM3NeT detector simulations. The currently used default threshold is set in Hexadecimal numbers: 2F. This corresponds to a voltage of 1.09375 V where each individual step in the threshold range is 0.00625 V. In figure 30 the result of the threshold scan is shown.

Threshold (V) 1 1.2 1.4 1.6 1.8 2 2.2 Count rate (kHz) 2 − 10 1 − 10 1 10 2 10 3 10 4 10 _Legend Total rate Dark rate

Threshold Scan

Figure 30: The result of the threshold scan. The total count rate is indicated by the black data points, the dark rate by the red data points and the default threshold value used by KM3NeT is indicated by the blue line.

The steep rise in the left of the figure is caused by the fact that the threshold reaches the electronic noise level. The result of subtracting the dark rate from the total count rate is shown in figure 31.

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Threshold (V) 1 1.2 1.4 1.6 1.8 2 2.2 Count rate (kHz) 0 5 10 15 20 25 30 35 Threshold Scan Threshold Scan (a) Threshold (V) 1 1.2 1.4 1.6 1.8 2 2.2 Count rate (kHz) 1 − 0 1 2 3 4 5 Threshold Scan (b)

Figure 31: In a) the result of the threshold scan after subtracting the dark rate. In b) is zoomed in at the region from 0-5 kHz and a error-function fitted to the data.

The charge distribution of the 1 p.e. peak is assumed to be approximated by a Gaussian distri-bution. Assumed in this measurement is that the height of the 1 p.e. PMT signal scales with the total charge of a 1 p.e. hit. In this threshold scan is integrated over the Gaussian distribution in the following way:

Rate = CZ ∞

T hresGaussian(q)dq (20)

Thus the relation between the threshold and the count rate can be described by an error-function, which is the integral of a Gaussian distribution. The error-function is fitted in 31b. The steep rise on

the left and the points where the count rate equals 0 give an indication of the base line7. The baseline

is expected to be 1 V.

To verify the baseline a second threshold scan was done but then with the high voltage of the PMT at the minimum such that effectively no signal will come through. Because of the low HV the electrons in the PMT are not accelerated enough to create a cascade. The result of the scan is shown in figure 32.

7The baseline is the point where the electronic noise is. This point is determined by the electronics. When the Threshold

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Threshold (V) 1 1.02 1.04 1.06 1.08 1.1 Count rate (Hz) 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10

Baseline Thresholdscan

Figure 32: The baseline threshold scan, where the baseline is determined at 1V.

The baseline is at the asymptotic line where the trigger rate rises to the maximum. In figure 32 the asymptote is at 1 V. The point on the left holds no relation with real signals because the threshold is below the baseline.

Conclusions

The default threshold used by KM3NeT is 1.09375V and assumed to be equal to 0.3 p.e. The height of the 1 p.e. peak is 1.43674 V with a baseline at 1 V. The threshold of 1.09375 V corresponds with 0.2147 ± 0.003 p.e. This is lower than the assumed threshold. This influences the PMT efficiency in the simulations positively with around 5%. The gain spread, in other words the width of the 1 p.e. peak, is equal to 0.202 V which is 0.462 ± 0.002 p.e. instead of the assumed 0.55 p.e.

Characterizing the KM3NeT 3-inch Hamamatsu Photomultiplier Tube response

July 11, 2017