The HiSPARC Experiment An Analysis of the MPV and the Number of Events per Unit Time

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The HiSPARC Experiment

An Analysis of the MPV and the Number of Events per Unit Time

Richard T. Bartels 3492907

University College Utrecht UCSCIRES31

December 2011 - February 2012

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Abstract

The research discussed in this report consists out of two parts. The first part is an examination of the most probable value (MPV) of a minimum ionizing particle (MIP) in the HiSPARC pulseheight histogram. Two causes for a shift in the position of the MPV are discerned. Firstly, the MPV will shift due to a change in high voltage causing a change in gain of the photomultiplier tube (PMT). Secondly, the MPV is sensitive to temperature changes. There appears to be a linear anti-correlation between the position of the MPV and the temperature of the PMT. The second part of the research looks into the number of events per unit time. As a result of the shifting MPV, the usefulness of the number of counts per unit time declines. Without a correction for the position of the MPV, no clear correlation is observed between the atmospheric pressure and the number of counts. The research will show that if the position of the MPV is corrected for the number of counts per unit time does become a useful parameter. After the correction, a linear anti-correlation is observed between the number of events per unit time and the atmospheric pressure.

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List of Tables

1.1 Parameters in the Bethe-Bloch Formula . . . 11 2.1 Initial guess of fit parameters . . . 18 2.2 The possibilities for two particles, P1and P2, which are detected by a two detector

station. For our selection we only take those events in which the amount of energy lost by both of the particles is larger or equal to the MPV. . . 27 2.3 All the events that will be kept in a four detector station. A minimum of two

triggers above the MPV is required . . . 28 2.4 Overview of the relation between the atmospheric pressure and the number of events

per unit time. As can be seen from the last column, the number of corrected counts per hour changes with approximately−2 counts/h h⁻¹Pa. . . 31 2.5 Results for the corrected number of counts of station 501 when detectors 1,2 and 4

are considered. A change of 1 hPa in atmospheric pressure will result in approximately 4 corrected counts less per hour . . . 33

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List of Figures

1.1 Hourly counts in the Utrecht cluster . . . 7 1.2 Overview of an extensive air shower triggered by a cosmic particle and its detection.

Picture from [7]. . . 9 1.3 Two detector stations. The distance between the scintillators in a two detector

station is approximately five meters. . . 10 1.4 Stopping power (^dE_dx) as a function of βγ = p/M c and muon kinetic energy (GeV).

M is the incident particle’s mass in MeV c⁻². . . 12 1.5 Schematics of a transmission-type photomultiplier tube [8] . . . 13 1.6 The pulseheight histogram for a two and four detector station. The fit lines in (a)

are fitted to scintillator 1. . . 14 2.1 Gaussian functions fitted to pulseheight histograms . . . 17 2.2 The most probable value (ADC) compared to the ambient temperature (K) from

April 2010 through December 2012. The time bins vary between 1, 4 and 24 hours.

The anti-correlation between the parameters is evident from the seasonal changes that can be observed in figure (b) and the daily fluctuations in (d). The jump in the MPV of detector 2 around 5000 hours is due to an increase of the high voltage on the PMT. The green vertical lines in (c) mark the snapshot that can be observed in (d). . . 19 2.3 Data from the Pierre Auger Cosmic Ray Observatory. On the left, the top figure

shows the VEM value, which is comparable to the MPV. The bottom figure shows the board temperature of one of the photomultipliers. Note the similarity with figure 2.2d. The right figure is a pulseheight histogram, the second peak is the VEM peak [2]. . . 20 2.4 Scatter plots for the MPV of detector 1 and 2 of station 1006 against the KNMI

temperature in de Bilt. The scatters show two blobs, this is due to a change in high voltage which affects the gain of the PMT. As a result, the fits do not match the data. . . 21

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2.5 Scatter diagrams and their respective profile histogram for station 1006. The high voltage for on each PMT is constant according to the database [9]. The linear behaviour of the MPV for changing temperatures is clearly visible in figure 2.5a and 2.5b. The results for detector two are less elegant. When looking in the database at the daily pulseheight histograms, it can be observed how the MPV peak systematically moves to the left in the period April - August 2011. The causes for this left shift have not been investigated. . . 22 2.6 The KNMI temperature at Schiphol compared to that in the Skibox and the tem-

perature of the PMT. Overcast is measured on a 0-9 scale, where 0 means that the sky is completely clear and 9 that the sky is no longer visible. The overcast data is from the KNMI weather station at Schiphol. The time bins in this plot are 4 hours per bin. . . 24 2.7 Scatter plots with their respective profile histogram containing the MPV data from

detector 1 of station 502. The temperature was measured at different positions.

The weighted fit in (a) is most similar to the initial best fit of the data. . . 25 2.8 The uncorrected number of counts per four hours of station 1006 in the period

17 August 2011 through 31 December 2011 compared to the MPV of both of its detectors. Detector 1 had a relatively stable MPV, while there was more fluctuation in the MPV of detector 2. . . 29 2.9 April 2010 through December 2011, the uncorrected number of counts per four

hours of station 1006 compared to the MPV of detector 1. No clear correlation is visible from this graph. . . 29 2.10 The corrected number of counts per four hours against the MPV of station 1006

in the period April 2010 through December 2012. According to the fits there is no correlation between the MPV and the number of counts . . . 30 2.11 As soon as the number of counts is corrected for, the anti-correlation between

atmospheric pressure becomes evident. This correlation is not evident when the number of counts is not corrected for. . . 32 2.12 The number of counts in station 501 at the Science Park in Amsterdam. The time

interval is 24 hours. As can be seen, if there is a malfunctioning detector, meaning that the MPV has fallen of the pulseheight histogram, the number of counts changes.

This results in the lower blob in (a). If this detector is ignored the blob disappears and the linear relation between atmospheric pressure and the number of counts is better visible again, as can be seen in (b). . . 32 2.13 A reproduction of figure 1.1. The timespan is 8 July 2010 through 19 August 2010

for figures 2.13a and 2.13b. The peaks have disappeared and the station 1006 and 1007 now have approximately the same number of counts. . . 34 C.1 An example of a profile histogram. On the x-axis the atmospheric pressure is

displayed, the bins are chosen to be 1 hPa. On the y-axis the mean number of counts of a specific bin is displayed (the red diamonds) with their corresponding standard deviation. The black line is the best fit line, the green line is the weighted fit line. The count data is from station 1006 in the period 2010-2011. . . 43

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Acknowlegdements

I am grateful for having had the opportunity to do my Bachelor’s research thesis on the HiSPARC experiment at FOM-Nikhef and there are a few people I would like to thank, in particular:

Arne de Laat,

for being my supervisor and helping me with every aspect of my thesis.

David Fokkema,

for sharing all his knowledge about the HiSPARC project and Python.

Jos Steijger,

for his extensive and helpful comments on my work.

I would also like to thank the following people:

at Nikhef:

Bob van Eijk, Loran de Vries and the all the Leraren in Onderzoek.

at University College Utrecht:

Filipe Freire, Laura Basu and Cristiane de Morais-Smith

at home:

Tera Pijnacker

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Chapter 1

Introduction

1.1 The HiSPARC Project

HiSPARC stands for the High School Project on Astrophysics and Research with Cosmics. It is a joint outreach project between NIKHEF and Dutch high schools and serves two goals: the study of cosmic rays and to offer high-school students an opportunity to participate in contemporary scientific research in physics. The project was started in Nijmegen in 2002 as The Nijmegen Area High School Array (NAHSA) and established itself as a national project in 2003. High schools can participate by placing a detector station on their roof, the station is installed by the students themselves. At the moment, there are seven clusters of detectors in the Netherlands, with the total number of detector stations exceeding one hundred. Moreover, there is a detection station in Karlsruhe, Germany and the project is being extended to Denmark and England [6].¹

1.2 Motivation

As was mentioned in the previous section, the HiSPARC detector stations are used for the purpose of research and to bridge the gap between high-school physics and actual investigations in the field of physics. The detectors can be used for various purposes, such as the reconstruction of a primary particle’s energy and the composition of the pulseheight spectrum, which has been extensively researched [13]. Moreover, the relation between the observed weather conditions and the number of cosmic particles that reach ground level can be investigated. The latter in particular is something that should appeal to high-school students, as here direct correlations can be found.

However, it is not always possible to straightforwardly obtain these correlations from the HiSPARC data. Various factors can obscure the relation between two observables. For instance, one would expect two stations in each other’s vicinity to approximately record an equal number of events. In addition, on would expect this number of events to be related to the atmospheric pressure, since this influences the mean free path of a particle. However, these relations can be obscured by other, not necessarily to particle physics related, phenomena. In order to have an overview of what influences the spectrum of events recorded by the HiSPARC detectors, it is necessary to investigate the factors that affect the detecting process. This includes the study of the behaviour of the detector itself

1http://www.hisparc.nl/en/about-hisparc/

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under various circumstances. Figure 1.1 provides an example of three detectors all stationed in Utrecht only a couple of hundred of meters apart. The graph shows the number of counts for these three stations, which are clearly varying greatly. Moreover, it shows the atmospheric pressure.

This figure, provided by Dr. Gert-Jan Nooren of Utrecht University, was the initial motivation to look into the relation between the number of events in the various detectors.

Figure 1.1: Hourly counts in the Utrecht cluster

This research looks into external causes for the difference in the events recorded by the HiSPARC detectors. Thereby, it tries to accommodate for the difference in the number of coincidences per unit time for different detectors and calibrate the detectors such that these numbers will be in accordance with what is expected. Moreover, by resolving the excessive difference in the number of coincidences that are detected by stations in each other’s vicinity I hope to provide a clearer correlation between the observables such as the number of coincidences and atmospheric pressure.

1.3 Methods

For this research data from the HiSPARC database will be used, this data can be accessed through the HiSPARC framework. Moreover, data from other sources such as the KNMI [10] and external data loggers will be used. Data analysis will be done through Python, this requires writing and editing Python scripts. More information about the use of Python and specific packages can be found in the corresponding guides [1, 4, 12, 15, 16].

Firstly, the pulseheight histogram will be investigated, in particular the position of the MPV peak (see section 2.1.1). As mentioned above, the pulseheight histogram has been extensively researched [13]. Whereas the theory predicts the position of the MPV to be fixed in an ideal situation, the actual position of the MPV peak appears to shift. This goes hand in hand with a

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shift of the pulseheight histogram in general. Consequently, low energy events will be added to spectrum or a part of the events will fall outside of the observed spectrum. By looking into the relation between the position of the MPV and the temperature I hope to provide an explanation for this shift of the MPV peak and the thereto related shift of the pulseheight histogram in general.

The explanation is likely to be related to the hardware, i.e. the scintillator, photomultiplier tube or electronics box. Moreover, this shift might explain the difference in the number of counts for the different stations.

Secondly, the knowledge gained from the analysis of the position of the MPV peak in relation to the temperature will be used for a renewed analysis of the number of counts per unit of time. This part of the research will look into the relation between atmospheric pressure and the number of counts after correcting for the shift in the pulseheight histogram due to ambient influences on the equipment.

1.4 Background

1.4.1 The Standard Model, Cosmic Rays and Cosmic Showers

Elementary particles are described by the Standard Model. According to this model there are two main types of particles, quarks and leptons. Whereas quarks interact strongly, leptons interact weakly and electromagnetically. Due to quark confinement quarks do not occur in isolation. There are three quark flavours: up (u) and down (d); charm (c) and strange (s); and top (t) and bottom (b). The up and down quarks form the basis of protons (uud) and neutrons (duu). Another particle that consists of quarks is the pion, π. Leptons do occur in isolation, there are three types of leptons to each there is a corresponding neutrino, which is also a lepton itself. All leptons have a charge of

−e, apart from the neutrinos which have no charge. The leptons with their corresponding masses in GeV c⁻² are: the electron, e (5.11· 10⁻⁴ GeV c⁻²); the muon, µ (0.106 GeV c⁻²) and the tau, τ (1.777 GeV c⁻²). Moreover, there exist anti-particles such as the anti-proton (¯p) and positron (e⁺). A particle and its associated anti-particle have the same mass and spin, but opposite charges [7].

In 1911-1912 Hess concluded that there must be a source of ionizing radiation coming from outside of the Earth’s atmosphere, for this observation he was given the Nobel Prize in 1936. This ionizing radiation consists of energetic particles and is more commonly known as cosmic radiation. When an energetic particle enters Earth’s atmosphere it can interact with the other particles in the air. This will lead to the production of secondary particles, which can again interact. Ultimately, this will lead to a cascade of secondary particles that is created in the atmosphere. Such a shower of particles is often referred to as an extensive air shower (EAS):

a shower of many particles, some of which may reach ground level. The EAS is initiated by an energetic cosmic particle. A first approximation of the shower front is a flat surface, a pancake in physical slang terms. These secondary particles in the shower front are being measured by the HiSPARC detectors. Primary particles can only be studied indirectly through the secondary particles, because it is unlikely for them to reach the Earth’s surface [5, 7]. Figure 1.2 shows an overview of an extensive air shower. The particles that reach Earth’s surface are mostly muons and electrons.

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7.4 Extensive Air Showers 159

precise. The shower develops in the atmosphere which acts

as a calorimeter of 27 radiation lengths thickness. The infor- energy measurement mation on this shower is sampled in only one, the last layer

of this calorimeter and the coverage of this layer is typically on the order of only 1%. The direction of incidence of the primary particle can be obtained from the arrival times of shower particles in the different sampling counters.

!

! shower axis thickness ~1 m

zenith angle detectors

primary particle

Fig. 7.28

Air-shower measurement with sampling detectors

It would be much more advantageous to measure the total longitudinal development of the cascade in the atmo-

sphere. This can be achieved using the technique of the Fly’s Fly’s Eye Eye (Fig. 7.29). Apart from the directional Cherenkov radi-

ation the shower particles also emit an isotropic scintillation light in the atmosphere.

For particles with energies exceeding 10 ¹⁷ eV the flu- orescence light of nitrogen is sufficiently intense to be recorded at sea level in the presence of the diffuse back- ground of starlight. The actual detector consists of a system

of mirrors and photomultipliers, which view the whole sky. fluorescence technique An air shower passing through the atmosphere near such

a Fly’s Eye detector activates only those photomultipliers whose field of view is hit. The fired photomultipliers allow to reconstruct the longitudinal profile of the air shower.

The total recorded light intensity is used to determine the shower energy. Such a type of detector allows much more

Figure 1.2: Overview of an extensive air shower triggered by a cosmic particle and its detection.

Picture from [7].

1.4.2 The Detector Station

The HiSPARC detector stations consist out of either two or four scintillator detectors with a surface area of 0.5 m² per detector and a GPS antenna for timing. Most detector stations are placed on the roofs of participating high schools. A collection of detector stations is called an array and refers to those detectors that are often used together in analysis. The collection of stations that are in each other’s vicinity are referred to as subclusters. All subclusters in the vicinity of a major city are referred to as a cluster, of which there are seven in the Netherlands [6].

In order to measure the azimuthal angle and the primary particles’ energy three stations with two detectors each are needed. With two stations only the zenith angle can be reconstructed (see figure 1.2). The angles and energy of the primary particle can be reconstructed from the data of the incident secondary particles and the time interval between measurements of the various detectors. Below two images of a two and a four detector station can be found.

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(a) Station 1006: a two detector station (b) A typical four detector station

Figure 1.3: Two detector stations. The distance between the scintillators in a two detector station is approximately five meters.

1.4.3 The Scintillator Plate

When radiation or charged particles pass through the scintillator plate atoms and molecules in the scintillator become excited. When the excited electrons fall back to their original energy level light is emitted and transmitted through the scintillator. This phenomenon of absorbing energy by becoming excited or ionized and then transmitting the absorbed energy is called luminescence [8, 11].

Scintillators can be made out of various materials, the scintillators that are deployed in the HiSPARC stations are so-called plastic scintillators, which means that they are solutions of a plastic scintillator in a solid plastic solvent. In nuclear and particle physics plastic scintillators are most common. The material used in the HiSPARC scintillators is polyvinyltoluene combined with some anthracene

The manufacturer of the HiSPARC scintillators is Saint-Gobain Crystals and the serial number of the scintillator is BC-408. The wavelength of maximum emission is 425 nm. According to the manufacturer the light output of the scintillators is constant in between−60^◦C and +20^◦C.

At +60^◦C the light output is 95% of that at +20^◦C. These values are common for most plastic scintillators as discussed by Leo [11].

Stopping Power and Landau Distribution

Charged particles are generally separated in two classes, the one being electrons and positrons and the other being the heavy charged particles such as the muon. When passing through the scintillator charged particles lose a fraction of their kinetic energy as a result of inelastic collisions with the atoms in the scintillator. In turn, the atoms become ionized or excited, the former case is often referred to as a hard reaction. If enough energy is transferred, the liberated electron can excite or ionize more atoms. Inelastic collisions are statistical in nature, there is a probability of an interaction when a particle passes through a certain medium with a specified thickness.

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Since the total number of interactions of a charged particle is large when traversing a macroscopic medium such as the scintillator, the stopping power becomes a meaningful quantity. The stopping power is the average energy loss per unit path length of a particle and is denoted by ^dE_dx [11]. The quantum-mechanical formula for the stopping power is given by the Bethe-Bloch formula 1.1.

−dE

dx = Kz²Z A

1 β²

1

2ln 2mec²β²γ²Tmax

I²

− β²−δ 2

(1.1)

Here K = 4πNAr²_emec²and Tmax=_m₂ ^2m^e^p²

0+m²_e+2m_e^E

c2

. See table 1.1 for the definition all parameters used in equation 1.1.

Na: Avogadro’s number (6.022· 10²³mol⁻¹) re: Classical electron radius (2.817· 10⁻¹⁵m) mec²: Electron rest energy≈ 511keV I: Average ionization energy of

the absorbing material

Z: Atomic number of absorbing material A: Mass number of absorbing material ρ: Density of absorbing material z: Charge of incident particle in units of (e) β: Velocity (v/c) of incident particle γ: (1− β²)⁻¹²

δ: Density correction m₀: Mass of the incident particle p: Momentum of the incident particle E: Total energy of the incident particle

Table 1.1: Parameters in the Bethe-Bloch Formula

At sea level the kinetic energy of muons is approximately 4.0 GeV. Figure 1.4 gives the stopping power of a muon in copper as a function of the muon energy. An energy of 4.0 GeV corresponds to the horizontal part of the spectrum. At this energy collision interactions, governed by the Bethe-Bloch formula, are the primary phenomena leading to energy transitions from the muon to the molecules in the scintillator. Where the stopping power is minimum the particles are minimum ionizing, meaning that the energy transfer of the particle to scintillator material is minimal. Particles with this energy are referred to as minimum ionizing particles (MIP) [13].

Particles with similar βγ factors have the same stopping power. The βγ factor of electrons at sea level corresponds to that of muons. Therefore, both electrons and muons are minimum ionizing particles that lose approximately the same amount of energy to the scintillator plate. Consequently, electrons and muons yield similar light intensities in the scintillator and therefore similar resulting pulses. The electron and muon spectrum overlap in the pulseheight spectrum [13].

In thin absorbers where the number of collisions, N , is relatively small the fluctuations in energy loss are described by the Landau distribution. Landau statistics holds in case the ratio κ = ¯∆/Wmax≤ 0.01, where ¯∆ is the mean energy loss calculated from the Bethe-Bloch formula and Wmaxthe maximum allowable energy transfer in a single collision. A small κ value means that there is large probability of single collision taking place that transfers more energy than calculated from the Bethe-Bloch formula. Unlike the symmetric Gaussian distribution, the most probable energy loss and mean energy loss are not the same for the asymmetric Landau distribution. The mean energy loss is higher than the most probable energy loss because of possible single collisions in which a large amount of energy is transferred [11]. Pennick determined the κ of a HiSPARC scintillator to be 5.57· 10⁻⁴, thus the energy loss adheres to Landau statistics. The most probable value (MPV) for the energy loss was determined to be 3.38 MeV [13].

Moreover, Pennick states that due to inaccuracies in the photomultiplier tube, which measures the light yield in the scintillator, an additional normal distribution should be considered

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Figure 1.4: Stopping power (^dE_dx) as a function of βγ = p/M c and muon kinetic energy (GeV). M is the incident particle’s mass in MeV c⁻².

for the resultant current. Therefore, the final energy distribution for MIPs is a convolution of a Landau and a Gaussian function. The peak corresponding to the most probable value can be seen in figure 1.6 in section 1.4.5. It is important to realize that most particle events are to the right of the MPV (or MIP) peak [6, 13].

1.4.4 Photo Multiplier Tube

The Photo Multiplier Tube (PMT) is the device that turns the photon stream coming from the scintillator plate into an electric current. Each event will thus be related to a specific current and voltage, and this is what can be observed in the pulseheight histogram.

Figure 1.5 shows a schematic overview of a photomultiplier tube. The PMT consists out of three main parts. Firstly, the photon coming from the scintillator is incident on the photocathode. The incident photon releases an electron from the photocathode through a process called the photoelectric effect. This electron is called the primary electron and its initial kinetic energy depends on the energy of the incident photon. A potential difference in the PMT then accelerates the electron and an electric field ensures that it is focussed on the dynodes. When the electron hits the dynodes the signal is amplified, which means that for every incident primary electron a few secondary electrons will be produced, typically around five. These secondary electrons are then focussed on a second dynode where the same process will repeat itself. The gain of the PMT specifies how many secondary electrons are produced by a single primary electron. This gain depends on several factors, such as the high voltage on the PMT and the material of the dynodes.

Peter Krizan [8] gives the following equation for the gain of the PMT, G = AU^kn, where G is the gain, n is the number of dynodes, U the high voltage, k ≈ 0.7 − 0.8 depending on the dynode material and A is a constant which depends on n. Moreover, magnetic fields can be of influence on the PMTs efficiency. Krizan mentions that the geomagnetic field can deflect the electrons, leading

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Figure 1.5: Schematics of a transmission-type photomultiplier tube [8]

to a loss in efficiency.

HiSPARC uses an ETEnterprises 9125B 29mm photomultiplier, with a bialkali cathode and 11 SbCs dynodes with a total gain of 10⁶. The temperature coefficient of the PMT as specified by the manufacturer is−0.5%^◦C⁻¹, as a result a change in the ambient temperature of 1K will lead to a change in gain with respect to the calibrated gain at +20^◦C. However the literature does not specify by how much this gain will change and what exactly constitutes the temperature coefficient. In a 1963 research Young gives values between -0.7% and -1% for the temperature coefficient. Moreover, Leo also gives a temperature coefficient of -0.5% due to changes in the Fermi levels and resistance in the cathode and a few hundredths of a percent for the dynodes.

Young gives an average of -0.04% per stage for the temperature coefficient of the dynodes, but he mentions this may vary between 0 and -0.1% [18]. Both Young and Leo mention that these values may vary between different types of photomultipliers, but also among similar PMTs. Moreover, under constant illumination and constant high voltage small changes in gain can occur, these are called shift changes².

Singh and Wright separate the temperature coefficient into two components, the spectral sensitivity coefficient of the cathode, α(λ), and the multiplier gain coefficient, αm [17]. This research seems to suggest that the temperature coefficient is in fact a measure of the fluctuations in output current with changing temperatures and that two factors influence these fluctuations, namely the spectral sensitivity coefficient and the multiplier gain coefficient. Moreover, they point out that most literature only looks at the temperature coefficient as a whole and not at the individual components. They give a value of −0.2%^◦C⁻¹ for the multiplier gain coefficient of, amongst others, SbCs dynodes. This indicates that the gain will decrease with increasing temperature. For wavelengths of 425 nm they give 0%^◦C⁻¹ for the spectral sensitivity coefficient of bialkali cathodes. This would mean that temperature changes have a negligible effect on the efficiency of the cathode and that the differences in the output current with varying temperature

2Note that this is not the same as the shift in the MPV to which this report commonly refers.

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are mainly due to changes in the gain coefficient of the dynodes. However, the multiplier gain coefficient of−0.2%^◦C⁻¹does not match the temperature coefficient of−0.5%^◦C⁻¹given by the manufacturer.

The Electronics Box

The PMTs are connected to an electronics box. The Electronics box contains Analog to Digital Converters which turns the analog current of the PMT into a digital signal. The voltage resolution of the ADC is 0.57 mV [6]. It is relevant to mention that the electronics boxes are positioned indoors and therefore only exposed to small temperature changes. The electronics box also provides the high voltage on the PMT, this might differ slightly as well with temperature changes, resulting in a change in gain. However, this has not been looked into in this research.

1.4.5 The Pulseheight Spectrum

0 500 1000 1500 2000

Pulseheight (ADC)

10⁰ 10¹ 10² 10³

Count

Gammas Particles Sum Scin. 1 Scin. 2

(a) Station 1006 (two detectors) - 20 January 2012

0 500 1000 1500 2000

Pulseheight (ADC)

10⁰ 10¹ 10² 10³ 10⁴

Count

Scin. 1 Scin. 2 Scin. 3 Scin. 4

(b) Station 501 (four detectors) - 20 January 2012

Figure 1.6: The pulseheight histogram for a two and four detector station. The fit lines in (a) are fitted to scintillator 1.

Figure 1.6 shows typical pulseheight spectra for respectively a four and a two detector HiSPARC station. There are several features which these two spectra have in common, but also some features which are different for the four plate station and the two plate station.

On the x-axis the pulseheight is displayed, by default the energy scale is in Analog to Digital Conversion (ADC) counts. The energy scale is in bins of 1 ADC. The ADC scale is related to millivolts (mV) by the following ratio, 0.57 mV ADC⁻¹. On the y-axis the number of events in a given timespan that correspond to a particular ADC bin is shown.

The two detector station (figure 1.6a) has a peak around 53 ADC (30 mV), to the left the count is zero and to the right the number of counts fall exponentially. 53 ADC is the trigger level for a HiSPARC detector, therefore, only when two detectors measure a signal above 53 ADC an event will be reported, this explains why no counts can be found to the left of the this peak.

53 ADC is above the noise level of the detector, the exponentially falling part at low pulseheights is caused by gamma radiation. High energy photons such as gamma rays interact with the scintillator

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through the Compton effect, in which the photons ionize the scintillation material and the resultant electrons will in return interact with the material in the scintillator producing scintillation light.

The counts in a four detector station are decreasing at low pulseheights. For a four detector station there are two trigger levels. The low threshold, approximately 53 ADC, is for a coincidence in three detectors. The high threshold, approximately 120 ADC (68 mV), is for a coincidence in two detectors. However, this means that one or two detectors can measure a lower pulseheight which is nevertheless stored. This results in the peak to the left of 120 ADC.

At 120 ADC there is a sudden increase in the number of events, because here most events are detected and the actual pulseheight histogram starts.

The pulseheight spectra of the two and four detector stations are similar at the higher pulseheights, generally above a 120 ADC. This part of the spectrum belongs to charged particles, electrons and muons, which interact with the scintillator. The charged particle part of the pulseheight spectrum is characterized by a maximum with a long tail at the right. This maximum is the Most Probable Value (MPV) and will be further discussed in section 2.1.

In short, the pulseheight spectrum of the HiSPARC detector is characterized by two regions, the lower energies belong to gamma rays, and is approximated by the exponential blue line in figure 1.6a. The gold line indicates the contribution of the charged particles to the pulseheight histogram, which is a convoluted Landau function. Finally, the green line is an approximation of the resultant pulseheight spectrum and consists of the sum of the blue and the gold line. It should be mentioned that to the far right the observed spectrum differs from the spectrum that the theory predicts. These high energy pulses are likely to be caused by multiple particles simultaneously interacting with the scintillator, resulting in a higher pulse [6, 13].

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Chapter 2

Results

2.1 The Most Probable Value

2.1.1 Determining the MPV

In section 1.4.3 it was discussed that the most probable value of a muon’s energy loss in the scintillator plate is 3.38 MeV. Fluctuations around this value are negligible for muons that reach sea level. Therefore, if the experimental setup and the hardware are all ideal or have a fixed deviation, one would expect to find a Landau distribution for the muons with a constant position of the MPV peak in the pulseheight histogram of a specific detector. From now on MPV will refer to the most probable value of the current detected and not to the energy loss of 3.38 MeV of a muon in the scintillator.

However, the pulseheight histogram appears to shift to the left or right. This effect is also observed by Buisman in his study of the photomultiplier tube [3]. In order to find the most probable value for a specific detector at a specified time we can fit a Landau or Gaussian to the pulseheight histogram and determine the peak of the fit. The ADC for which the fit peaks corresponds to the MPV. A change in the x-position of the MPV can be used as a measure of the left and right shift of the pulseheight histogram. The cause of this shift should be sought in the detector, since the theory predicts a constant MPV.

In order to determine the position of the MPV peak a Gaussian function is fitted to the bump in the pulseheight histogram. It was decided to use a Gaussian because of its similarity to the convolution of the Landau and Gaussian function. Figure 2.1 shows the plot of a Gaussian function fitted to the pulseheight histogram.

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0 200 400 600 800 1000

Pulseheight (ADC)

10⁰ 10¹ 10² 10³

Count

Gaussian Fit Appr. max Appr. min Fit bounds Scin. 1

(a) Station 1006 - 20 January 2012 (one day): MPV at 297 ADC

0 200 400 600 800 1000

Pulseheight (ADC) 10⁰

10¹ 10²

Count

(b) Station 1006 - 20 January 2012 00:00 - 04:00 (4 hours): MPV at 289 ADC

0 200 400 600 800 1000

Pulseheight (ADC) 10⁰

10¹ 10²

Count

(c) Station 1006 - 20 January 2012 00:00 - 01:00 (1 hour): MPV at 296 ADC

Figure 2.1: Gaussian functions fitted to pulseheight histograms

The fit parameters are set as follows. First, the position of the MPV is approximated by looking at the bin with the largest number of counts in the region 150 ≤ ADC < 410 using the SciPy option ndimage.extrema() [16]. This function returns the position of the maximum and minimum value in an array. Next, the minimum in between the gamma peak and the first guess of the maximum is approximated using the same function. The bounds are based on the difference between the first guess of the maximum (Xmax) and minimum (Xmin). The left bound is:

bound1 = Xmax− (X^max− X^min)· 0.75 (2.1) For the right bound there are two possibilities. If Xmax− X^min≤ 50:

bound2 = Xmax+ (Xmax− X^min)· 1.5 (2.2) else:

bound2 = X_max+ (X_max− X^min) (2.3)

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Since the right side of the Landau function is more similar to a Gaussian function than the quickly falling left side and because the gamma contribution to the left of the peak can hamper the fit, a larger section of the pulseheight histogram on the right of the approximated MIP peak is used.

In case the difference between the approximated minimum and maximum becomes small the right bound is moved further to the right. This ensures that enough bins are present on the right side to fit a Gaussian function.

The number of ADC per bin in figure 2.1 is twenty, if ten bins would have been used the ditch near the MIP peak spoils the fit for the one and four hour fits. The right bound would now be positioned in the ditch itself, consequently leading to a too low MPV. Therefore, the bins should not be too small.

Fitting the function is done using the SciPy function optimize.curve fit(), which makes a least-squares fit of the data [16]. The first step is to define a Gaussian function:

f = lambda x, a, b, c : a∗ exp(−((x − b) ∗ ∗2)/c) (Python code) (2.4)

= a e^−(x−b)²^/c (2.5)

The x in the function f is the independent variable a, b and c are the other parameters of the function. Computation will be faster and better when an approximation of the parameters is given.

See table 2.1 for the approximations used when fitting a Gaussian function to the pulseheight histogram.

Parameter Represents Approximated by

a Maximum of the Gaussian in counts Counts at the approximated maximum

b ADC value of the mean ADC of the approximated maximum

c Spread of the Gaussian 1

Table 2.1: Initial guess of fit parameters

The curve fit function returns an array containing the values a, b and c of the fit. The second element of this array, b, is used as the MPV in ADC counts of the pulseheight histogram for which the fit is made.

2.1.2 Temperature Dependence of the MPV

According to Leo, the cathodes in the photomultiplier tube have a negative temperature coefficient of approximately −0.5%^◦C⁻¹ [11]. The negative temperature coefficient was confirmed by Buisman, who observed a left shift of the pulseheight histogram at high temperatures and a right shift at low temperatures. An explanation of this shift can be in the gain of the photomultiplier tube, as discussed in section 1.4.4. An increase in gain means a larger current is generated and a related right shift of the spectrum.

In the analysis of the correlation between the temperature and the MPV multiple detector stations were considered. Moreover, for detector 1 of station 502 (Anton Pannekoek) various temperature measuring devices were considered. All ambient temperature data comes from the

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KNMI database, which provides hourly data [10]. The temperature in the skibox and the temperature of the PMT was measured using two Lascar data loggers. For a more elaborate discussion on the temperature data see appendix A and B.

A first impression

Station 1006 is situated at University College Utrecht. Data from April 2010 through December 2011 is used in the analysis of the relation between temperature and the MPV. Figure 2.2 shows the MPV in ADC counts on the left y-axis and the temperature in Kelvin on the right y-axis. The weather data is from the KNMI station in de Bilt [10]. The different graphs are for different time intervals over which the MPV and the average temperature were determined.

0 2000 4000 6000 8000 10000 12000 14000 16000 Time (h)

100 150 200 250 300 350 400 450 500 550

MPV(ADC)

Scin. 1 Scin. 2

260 270 280 290 300 310 320

Temperature(K)

KNMI

(a) MPV determined per hour

0 2000 4000 6000 8000 10000 12000 14000 16000 Time (h)

100 150 200 250 300 350 400 450 500 550

MPV(ADC)

260 270 280 290 300 310 320

Temperature(K)

(b) MPV determined per 24 hours

0 2000 4000 6000 8000 10000 12000 14000 16000 Time (h)

100 150 200 250 300 350 400 450 500 550

MPV(ADC)

260 270 280 290 300 310 320

Temperature(K)

(c) MPV determined per 4 hours

11400 11450 11500 11550 11600 11650 Time (h)

100 150 200 250 300 350 400 450 500 550

MPV(ADC)

Scin. 1 Scin. 2

260 270 280 290 300 310 320

Temperature(K)

KNMI Midnight

(d) MPV determined per 4 hours - fragment

Figure 2.2: The most probable value (ADC) compared to the ambient temperature (K) from April 2010 through December 2012. The time bins vary between 1, 4 and 24 hours. The anti-correlation between the parameters is evident from the seasonal changes that can be observed in figure (b) and the daily fluctuations in (d). The jump in the MPV of detector 2 around 5000 hours is due to an increase of the high voltage on the PMT. The green vertical lines in (c) mark the snapshot that can be observed in (d).

Two things come to mind when looking at figure 2.2. Firstly, a large fluctuation of the

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MPV is observed in figure 2.2a, whereas this is not the case in figures 2.2c and 2.2b. The simplest explanation for the fluctuations is that it is due to inaccuracies in the fit. In order to make a first selection of the useful MPV data only the data for which 120≤ MP V ≤ 550 is used. All MPVs with a different value are considered bad data. The MPVs of one hour are in the entire range from 120 to 550. In section 2.1.1 the determination of the MPV was discussed, deviations are likely to occur when there is little data. Therefore, the MPV of an hour will be less accurate than that of a longer time interval. Then again, daily fluctuations will be overlooked if we only consider daily data. Thus the time interval should not be too large.

Secondly, figure 2.2 gives a first indication of an anti-correlation between the MPV and the temperature. 2.2d clearly shows that every temperature valley corresponds to a peak in the value of the MPV. An anti-correlation corresponds to the expected behaviour of the photomultiplier tube, which has a temperature coefficient of approximately −0.5%^◦C. The negative temperature coefficient implies a loss in gain with rising temperatures, meaning a lower MPV.

A similar effect has been observed in the Pierre Auger Cosmic Ray Observatory (figure 2.3a) [2]. The experimental setup at the Auger observatory is different from that of HiSPARC.

Whereas HiSPARC makes use of scintillator plates, Auger uses Cherenkov tanks. Grossly oversim- plified, these tanks are basically big containers with purified water. When a muon passes through the tank, Cherenkov light is emitted, which is measured by photomultipliers. Three different photomultiplier tubes were used in the Auger experiment, namely an Hamamatsu R5912 (202 mm diameter), an ETL 9353 (200 mm diameter) and a Photonis XP1802 (230 mm). Finally, verical equivalent muons or VEMs are the Auger equivalent of the MIPs. The VEM is the average energy loss of a high energy muon passing the tank perpendicular to the water surface and in the center of the tank. Figure 2.3b shows a graph of the VEM peak, note the similarity with figure 1.6.

(a) VEM - temperature correlation (b) VEM peak for a single muon

Figure 2.3: Data from the Pierre Auger Cosmic Ray Observatory. On the left, the top figure shows the VEM value, which is comparable to the MPV. The bottom figure shows the board temperature of one of the photomultipliers. Note the similarity with figure 2.2d. The right figure is a pulseheight histogram, the second peak is the VEM peak [2].

A More Accurate Analysis

There appears to be a linear anti-correlation between the temperature of the PMT and the MPV value. In the following section the anti-correlation will be investigated in more details using scatter plots and profile histograms.

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Again, the analysis will start with an observation of the data of station 1006. Making a scatter plot for station 1006 does not immediately yield an obvious correlation between temperature and the MPV. Figure 2.4 shows a scatter plot with a best fit line, for which the numpy option polyfit is used, and a weighted fit on the basis of the profile histogram (see appendix C). If there is a linear correlation, a scatter plot ought to display something resembling an inclined line.

Different, non-linear, correlations will have scatter plots resembling the shape of the function. A cloud is an indication that there is no correlation.

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350 400

MPV(ADC)

W. fit fit Scin. 1

(a) Detector 1: April 2010 - December 2011

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350 400

MPV(ADC)

W. fit fit Scin. 2

(b) Detector 2: April 2010 - December 2011

Figure 2.4: Scatter plots for the MPV of detector 1 and 2 of station 1006 against the KNMI temperature in de Bilt. The scatters show two blobs, this is due to a change in high voltage which affects the gain of the PMT. As a result, the fits do not match the data.

In figure 2.4 two inclined blobs are observed. As a result the fits do not run nicely through the data. These blobs are the result of a change in high voltage on both the PMT of detector 1 and detector 2. In the period between 15 April, 2010, when the station was put into use, and 17 August, 2011 the high voltage was changed multiple times [9]. By taking a period in which the high voltage remains constant a more accurate observation can be done. Detector 1 had a stable high voltage of 1232 V between 2 November, 2010 and 31 December, 2011. Detector 2 had a stable high voltage of 780 V between 3 November, 2010 and 16 August, 2011.

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260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 1

(a) Detector 1 (high voltage - 1296 V): 3 November 2010 - 31 December 2011

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 1

(b) Weighted fit: −2.31 ADC K⁻¹; best fit:

−2.27 ADC K⁻¹

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 2

(c) Detector 2 (high voltage - 780 V): 3 November 2010 - 15 August 2011

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 2

(d) Weighted fit: −4.04 ADC K⁻¹; best fit: =

−3.41 ADC K⁻¹

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 2

(e) Detector 2 (high voltage - 780 V): 3 November 2010 - 31 March 2011

260 270 280 290 300 310 320 Temperature (K)

150 200 250 300 350

MPV(ADC)

W. fit fit Scin. 2

(f) Weighted fit: −2.20 ADC K⁻¹; best fit:

−2.18 ADC K⁻¹

Figure 2.5: Scatter diagrams and their respective profile histogram for station 1006. The high voltage for on each PMT is constant according to the database [9]. The linear behaviour of the MPV for changing temperatures is clearly visible in figure 2.5a and 2.5b. The results for detector two are less elegant. When looking in the database at the daily pulseheight histograms, it can be observed how the MPV peak systematically moves to the left in the period April - August 2011.

The causes for this left shift have not been investigated.

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When the changes in high voltage and the thereto related changes in gain are filtered out the linear anti-correlation between temperature and MPV starts to become evident. Figure 2.5 shows the resultant scatter plots and profile histograms. The fact that the weighted fit lines closely match the best fit lines indicates that these are a good approximation of the behaviour the data.

The behaviour of detector 2 is a bit out of line with the expectations. At higher temperatures the MPV value starts to drop faster. This is not completely at odds with the expectations (see section 2.1.2), but the effect is rather extreme. Moreover, detector 1 also slightly shows this behaviour, but less extreme. According to the pulseheight histograms in the database the MPV peak of detector 2 starts to systematically move to the left from April 2011 onwards, whereas the peak of detector 1 stays behind. This shift explains the lower MPV values of detector 2. The causes of this shift have not been investigated.

The Climate in the Skibox

Station 502, Anton Pannekoek, is situated at the Science Park in Amsterdam. Detector 1 of this station contained two USB data loggers. One has an internal sensor and was used to measure the temperature at the bottom of the skibox. The other data logger has an external sensor which was connected to the PMT. For more details on the USB data loggers see appendix B.

Since the data loggers have only been used in detector 1, we will only look into the behaviour of this detector. The data logger attached to the PMT captured data from 27 May through 26 November, 2011. The data logger at the bottom of the skibox captured data from 27 May until 1 November, 2011. However, the high voltage in this period was not constant. From 27 May through 18 October, the high voltage on the PMT of detector 1 was 752 V, this is the period that is used in the analysis. After 18 October the high voltage was 747 V.

During the day the temperature in the skibox and that of the PMT are higher than the temperature measured by the KNMI at Schiphol. At night the temperature in the skibox follows the ambient temperature, as mentioned by Buisman [3]. This effect can be observed in figure 2.6, moreover, the temperature in the skibox and the temperature of the PMT rise even further when it is sunny.

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1350 1400 1450 1500 1550 1600

Time (h)

270 280 290 300 310 320

T emp erature (K)

KNMI PMT Skibox

0 3 6 9

Ov ercast

Overcast Midnight

Figure 2.6: The KNMI temperature at Schiphol compared to that in the Skibox and the temperature of the PMT. Overcast is measured on a 0-9 scale, where 0 means that the sky is completely clear and 9 that the sky is no longer visible. The overcast data is from the KNMI weather station at Schiphol. The time bins in this plot are 4 hours per bin.

The results of the temperature analysis of station 502 show that a linear fit between the MPV of detector 1 and the temperature of the PMT is better than one between the MPV and the temperature given by the KNMI. In figure 2.7 the results of the analysis are displayed. Bins which contain less than 5 bins are discarded when making a weighted fit and do not show up in the figure. The limitation of the analysis is the relatively short time period, from the end of May until half October and the fact that only one detector could be used. Nevertheless, the result indicates that there is a linear anti-correlation between the temperature of the PMT and the most probable value.

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270 280 290 300 310 320 Temperature (K)

150 160 170 180 190 200 210

MPV(ADC)

W. fit fit PMT

(a) PMT temperature: 27 June - October 17

270 280 290 300 310 320

Temperature (K) 150

160 170 180 190 200 210

MPV(ADC)

W. fit fit PMT

(b) Weighted fit: −0.742 ADC K⁻¹; best fit:

−0.667 ADC K⁻¹

270 280 290 300 310 320

Temperature (K) 150

160 170 180 190 200 210

MPV(ADC)

W. fit fit KNMI

(c) KNMI temperature: 1 June - October 17

270 280 290 300 310 320

Temperature (K) 150

160 170 180 190 200 210

MPV(ADC)

W. fit fit KNMI

(d) Weighted fit: −1.05 ADC K⁻¹; best fit:

−1.26 ADC K⁻¹

270 280 290 300 310 320

Temperature (K) 150

160 170 180 190 200 210

MPV(ADC)

W. fit fit Ski

(e) Skibox temperature: 27 June - October 1

270 280 290 300 310 320

Temperature (K) 150

160 170 180 190 200 210

MPV(ADC)

W. fit fit Ski

(f) Weighted fit: −0.866 ADC K⁻¹; best fit:

−0.639 ADC K⁻¹

Figure 2.7: Scatter plots with their respective profile histogram containing the MPV data from detector 1 of station 502. The temperature was measured at different positions. The weighted fit in (a) is most similar to the initial best fit of the data.

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2.2 Counts per Unit Time

The final part of the research consists of an investigation into the counts per unit time. Counts per unit time means the number of events recorded by the HiSPARC detector per unit time. In this research an event corresponds to a coincidence. Using the number of coincidences does not provide any information about the number of events in which two, three or four detectors are triggered in a four detector station. As mentioned in the discussion of the detector station, there are different thresholds in a four detector station. However, this does not imply a loss in generality, since every event is supposed to represent a shower, irrespective of whether two, three or four detectors are triggered.

Figure 1.1 was the original motivation to investigate the counts per unit time. As can be seen, two stations, 1006 and 1007, separated only a couple of hundred meter, have a very different count rate. This section offers an explanation for the difference in counts, a correction and relates the number of counts to the atmospheric pressure. The correction model that is suggested is for a two detector station, it can also be used for a four detector station with some minor adaptations.

2.2.1 An Explanation for the Difference in Counts per Hour

As was discussed in the previous section on the most probable value, the pulseheight histogram can shift to the left or to right, due to various causes. One of the causes is a change in the high voltage on the PMT, which leads to a larger or smaller gain. Another cause is a change in temperature, which can be seen from the results of the previous section.

As we know, the pulseheight spectrum consists of a gamma part and a charged particle part which slightly overlap. The gamma part is exponentially increasing towards the left end of the spectrum. If there is an increase in gain of the photomultiplier tube the entire spectrum will be shifted towards the right. Moreover, events that used to fall just outside of the spectrum, will now be strengthened slightly more with the result that they will make it past the trigger level and are recorded. Of course, the opposite holds for a decrease in gain. On the exponential slope of the gammas an increase or decrease in gain can mean a large difference in the total number of events per unit time. Since the results of the previous section imply that the gain is temperature dependent, there will be daily and seasonal fluctuations in the total number of counts. The position of the MIP peak gives an indication of the right or left shift of the spectrum, since the behaviour of the muons has not changed. In the following subsection, a correction model is suggested on the basis of the position of the MIP peak.

2.2.2 Proposed Correction for the Counts per Unit Time

As a correction for the number of counts per unit time one can make an artificial trigger at the MPV. Although the position of the MPV will change, the total number of events at the right of the MPV will not change with an increase or decrease in gain. What will change is the number of events on the left of the MPV. Therefore, the MPV is a good candidate for an artificial trigger when investigating the number of events. The downside of using the MPV as a cut-off point is that some particle events will now be discarded. However, the ratio of particle events kept and particle events discarded will be fixed and depends on the details of the convolution of the Landau

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and the Gaussian distribution. Fact is that the mean of a Landau distribution is to the left of the median, thus more than half of the particle events will be considered. Another limitation is that this technique will only work if the MPV is visible on the pulseheight histogram. However, it is not supposed to be the case that the MIP peak is not visible in a well functioning detector.

A Two Detector Station

In a two detector station there are three possibilities that can trigger an event. The possibilities for two particles, P1 and P2, which are incident on scintillator 1 and 2 respectively are shown in table 2.2

Scin. 1 Scin. 2

1 MPV≤ P¹ MPV ≤ P² kept 2 MPV≤ P¹ P₂< MPV discarded 3 P1< MPV MPV ≤ P² discarded 4 P₁< MPV P₂< MPV discarded

Table 2.2: The possibilities for two particles, P1 and P2, which are detected by a two detector station. For our selection we only take those events in which the amount of energy lost by both of the particles is larger or equal to the MPV.

We are only interested in those cases in which the energy lost by both particles is at least equal to the MPV, possibility 1 in table ??. This ensures that all the events that are considered towards the total number of counts are independent of any shift in temperature, gain or whatever else can shift the pulseheight histogram. In case we would also consider events to left, and only one particle above the MPV peak, so also option 2 and 3, the technique becomes flawed. Because then the particle with the lower energy might only just be on the pulseheight histogram, which means it could also just be off the pulseheight histogram. A fixed portion of the particle event spectrum ought to belong to possibility 1, therefore by filtering out these events we have a relative measure of the number of counts per unit time.

A Four Detector Station

In principle this method is the same for a four detector station, apart from the fact that a four detector station has more possibilities to be triggered. A four detector station has two trigger levels. It can either be triggered by three particles above the lower trigger level, or two above the higher trigger level. However, this does not change anything about the position of the MIP peak and its usability to filter events. This report proposes the following filtering method: two events above the MIP peak. Unlike the two detector station, is does not matter that two signals can be smaller than the MPV, because the coincidence would have been recorded nevertheless. Thus if we use the number of coincidences as measure of the counts, which is in fact already the case for the count histogram on the HiSPARC website, then two signals above the MPV peak is enough.

The possibilities that are kept are given in table 2.3

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The HiSPARC Experiment An Analysis of the MPV and the Number of Events per Unit Time