the HiSPARC-NIKHEF ground array

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Angular Reconstruction and Showerfront Thickness of low energy Air Showers detected at

the HiSPARC-NIKHEF ground array

M.C. Takes

supervisor:

prof. dr. ing. B. van Eijk co supervisor(s):

dr. E. de Wolf dr. H.J. Bulten

Versie 1.4

Master’s Thesis submitted to the University of Amsterdam in fulfilment of the requirements for the CE Degree

of Master of Particle and Astroparticle Physics National Institute for Nuclear and High Energy Physics

February 14, 2007

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Abstract

The underlying report is a final paper describing the performance of the HiSPARC-NIKHEF surface array. This array consist of 2 stations, each with two scintillator detectors operating in a coincidence mode. The total of four detectors can then be seen as four independent triple-stations. The angular reconstruction and angular resolution obtainend by each of these stations is investigated and compared with each other.

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Introduction

The earth’s atmosphere is constantly bombarded by all kinds relativistic particles. The cosmic ray particles that incident the terrestrial atmosphere are devided into primary and secondary particles. Primary particles, such as electrons, protons, helium, carbon, iron and other nuclei, are those particles accelerated at astrophysical sources or other nuclei synthesized in stars. Secondary particles are those particles produced in the interaction of primaries with the interstellar gas such as lithium, beryllium and boron nuclei.

Cosmic rays were discovered by Victor Hess after his balloon experiment in 1912. After the discovery of X-rays by Rntgen in 1895, cosmic rays where seen as radioactive radiation. A survey was done to investigate radioactive substances everywhere; in the crust of the earth, in the seas, etc. Hess ascended in a balloon and took measurements at different altitudes. He found that the background radiation increased as he went higher. From these measurements Hess concluded that the radiation he was studying was coming from outer space. He called it Cosmic Radiation¹ which later evolved into Cosmic Rays. Cosmic Rays became a powerful tool (e.g. discovery of the positron) of research in physics and Hess was rewarded for his work with a nobel prize in 1936.

1.1 High Energy Cosmic Rays

The energy of the cosmic particles can be enormous. In 1991 the Fly’s Eye cosmic ray research group in the USA observed a cosmic ray event with an energy of 3.2·10²⁰ eV, many orders of magnitude larger then the energy of particles produced in the accelerators today.

While the composition of the primary particle was not known with certainty, the best guess is that it was a moderate mass nucleus (something like oxygen).

The energy-flux spectrum of cosmic rays is shown in fig. After the turnover at ∼10¹⁰eV the spectrum behaves as ∼E^−2.7 down to the so-called ’knee’ at ∼3·10¹⁵ eV. After the ’knee’ it then continues with a steeper slope as ∼E^−3.0 up to the ’ankle’ at ∼4·10¹⁸ eV. Results of the KASCADE array [2] shows a substantial difference in the energy spectra of individual nuclear groups around the ’knee’. Today, the change in composition around the ’knee’ is considered to be deeply related to a combined influence of acceleration and diffusion of cosmic rays in our Galaxy.

From fig. [? ] it is clear that the cosmic particle flux decreases rapidly from 1 m⁻² s⁻¹ at

∼10¹¹eV down to 1 km⁻² yr⁻¹at the ’ankle’. Therefore, detection of higher energy particles is more effective by using a ground array of detectors which makes it possible to sample the

1It is important to note that this radiation is not electromagnetic in nature.

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CHAPTER 1. INTRODUCTION

energies from Extensive Air Showers (EAS) and infer the particle energies indirectly.

The major questions in astro-particle physics are; where are these cosmic ray particles coming from and what are their sources responsible for their detected energy. As for the

’low’ energy particles (E < 10¹⁴ eV), their origin and mechanism are fairly well understood.

Most of them are protons and electrons ejected from the sun’s corona causing the aurora phenomenon in the nothern and southern hemisphere.

cosmic rays with energies 10¹¹ < E < 10¹⁴ eV are believed to be mostly due to shock acceleration. In 1949 Enrico Fermi came with an explanation for this acceleration mechanism.

According to his theory, protons speed up by bouncing off moving magnetic clouds in space.

Exploding stars (supernovae) are believed to act as such cosmic accelerators. Althought these supernovas are capable to give these particles their observed energy, they cannot account for the high-energy cosmic rays (E > 10¹⁴ eV). Cosmic rays in the region 10¹⁴ < E < 10¹⁹ eV are believed to have their energy from pulsars and galactic winds. The Ultra High Energy Cosmic Ray (UHECR) particles (E > 10¹⁹ eV) are believed to be accelerated by enormous electric field, generated by rapidly spinning, magnetized object such as neutron stars or active galactic nuclei (AGN).

1.2 GZK cutoff

Once an UHECR particle is accelerated it will could permeate our surrounding universe.

There are three processes which affect cosmic rays during intergalactic propagation: energy loss by interaction with Cosmic Microwave Background Radiation (CMBR); deflection by magnetic fields; and enery loss by adiabatic expansion of the universum ².

The enery loss with the CMBR can be devided into four prosesses; Compton interaction (negligible); photo-production (only for protons with E > 10²⁰ eV) and pair production (only for protons with E > 5·10¹⁷ eV). In addition to these three interactions K. Greisen, G.

Zatsepin and V. Kuzmin pointed out in 1966 that UHECR would interact with the CMBR according to the reaction pγ → ∆⁺ → π⁰p ending up with a pi zero and a proton. In this proces the proton energy and mean free path length would reduce significantly. This energy loss mechanism is also known as the Greisen Zatsepin Kuzmin (GZK) suppression. It is interesting to look for events above this threshold energy ofaround 5·10¹⁹ eV. If these events occur then we know for sure that their source must local instead of extra-galactic.

1.3 Outline of this thesis

Data collected by the Akeno Air Shower Array (AGASA) experiment showed that the energy spectrum of the primary cosmic rays extents up

2This effect is negligible if the propegationdistance is smaller than 1 Gpc.

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Chapter 2

Air-Shower experiments

2.1 Introduction

There are many Cosmic Ray Shower experiments around the globe. This chapter gives a short overview of the AGASA experiment in Japan and the Fly’s Eye experiment in the USA.

The setup of these experiments, as well as their detection principles are briefly discussed.

Finally an overview of the HiSPARC experiment, along with the NIKHEF ground array itself will be discussed.

As explained in chapter 1? detection of UHECR s can only be done efficiently by making use of large ground arrays of detectors. To infer the energy and direction of the UHECRs currently two methods are used. The generic method is placing a large number of detectors distribute over a large area (ground arrays) to detect only those particles that survive at the detection level. The second method also known as Air Fluorescence makes use of the exitation of nitrogen molecules in air.

2.1.1 Detection with ground arrays

Depending on the energy of the primairy particle a large number of particles will be created and distributed over a large area. Ground detectors, e.g. scintillators, cherenkov detectors are often placed in a regular grid. When looking at small showers, tens or hunderds of detecors with a seperation distance d of 10-30 meters are ussually used. For the much less frequent UCHECRs (large showers), d is typically hunderds of meters.

With an array of particles the direction of the shower axis, hence the primairy particle can be deduced using the relative arrival times of signals at minimum of three noncollinear detectors. Furthermore at each detector the density of charged particles, muons, ”hard” photons and air Cherenkov photons can be measured.

The direction of the shower and the shower lateral (density) distribution function defined in [4] are then used to determine the impact point of the shower (core) on the ground.

Cherenkov light can be used to as an extra tool in measuring the impact piot. Since Cherenkov light is only emitted at a narrow angle to the shower axis, the utility of this method is only possible when the impact point is inside or little (a few hundred meters) outside the ground array.

Finally, with the fit to the lateral distribution function and the particle density at a certain distance from the impact point, the energy can be estimated. For more information about

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CHAPTER 2. AIR-SHOWER EXPERIMENTS

this method see [4].

2.1.2 Detection with fluorescence detectors

Allthough it is a misuse of the term¹, the name Air Fluorescence has been adopted by the astrophysics community to describe the scintillation light from extensive air showers.

When a charged particle traversers the atmosphere it can exite nitrogen molecules, thereby emmiting light isotropically in the 300-450 nm band. In the case of cosmic ray showers, the ionization and excitation are produced by a sort of shock front of secondary particles, mostly electrons, which propagates down through the atmosphere at velocity c, with c the velocity of light.

The detection of cosmic ray showers by this process offers several advantages over conventional (i.e. ground arrays) techniques. First of all the fluorescense detector offers a way to follow the trajectory of the shower. Furthermore the fluorescent intensity as a function of distance along the trajectory yields directly the longitudinal structure of the shower. Com- pared to conventional techniques that only observe a cross section of the shower (at detection level) this technique leaves no questions on whether an observed particle distribution (at detection level) represents a large shower growing towards maximum or smaller showers.

Because the total light output yields the total energy dissipated in the atmosphere, the air fluorescence detector offers us a unique way to infer the primary energy of an UHECR provided that most of the energy has been dissipated before striking the earth.

To detect the isotropic emmission of light the whole sky is viewed by many segmented eyes using photomultipliers. It is collected by mirrors and received by photomultipliers as a time sequence of light. Because the fluorescence light is very weak only the most energetic showers can be detected this way. Furthermore this technique can only be used effectively at places where there is a minimum of background light, e.g. desert, moonless nights. For more information about the fluorescence technique see [3].

2.2 The AGASA experiment

One of the largest ground arrays in world is The Akeno Giant Air Shower Experiment AGASA! located at Akeno. It covers an area of 112 km² (14·8km) and is in operation since february 1990. The array consist of 111 plastic scintillation detectors all with a seperation distance of about 1 km and 27 muon detectors inside concrete bunkers.

In the early stage of the experiment the whole area was devided into four sub-arrays called

”branches” and (for topographical reasons) air showers were observed independently. After the data aquisition system was improved, the four branches were unified into a single detection system in December 1995. The present configuration is shown in Fig. ??. The detector is shut down at the end of 2003 and is not taking data anymore.

1The term fluorescence refers to the process by which atoms absorb photons of one wavelength and emits photons at a longer wavelength. The emmission caused by the exited nitrogen molecules is actually referred to as luminescence or scintillation.

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2.3 The Fly’s Eye experiment

One of the mayor Air Shower experiments using the fluorescent technique today is the Fly’s Eye experiment located in the USA in the West Desert of Utah. The surrounding conditions are ideal for fluorescence observations. The Fly’s eye experiment was in operation for 12 years from 1981 to 1993. The detection of the cosmic ray event with an energy of 3.2·10²⁰on november 15th 1991 had tremendous implications to astrophysics. Because of what we know from the GZK suppression this anomolousparticle should have come from a local source.

However, the arrival direction does not trace back to any known energetic object within the allowed 150 million lightyear radius. The absence of any local source raises the possiblity of new physics.It suggest the possibility of new excotic particles not subjected to the cosmic background radiation.

The Fly’s Eye site comprised of 67 moduls placed within an area of approximatly 10⁴m². Each module consist of a steal barrel with contains a spherical mirror of 1.5m diameter.

Fluorescent light is collected by 12 photomultipliers (PMT) mounted at the focal surface, each of the 12 PMT pixels covering a 5^◦ cone in the sky.The pixels cover the hemisphere in a matter reminiscent to the complex eye of a fly, see fig.2.1a), hence the name Fly’s Eye.

Pointing directions and the arrival times of the PMT hits are used to reconstruct the trajac-

Figure 2.1: left a): PMT track of a Cosmic Ray event at the Fly’s Eye detector. right b):

Shower-plane including the corresponding parameters.

tory of an Air Shower. The procedure can by devided in two steps (1) Detecor-shower plane Fit and (2) Timing Fit. Within pocedure (1) the detector is treated as a single point². We can draw a plane through the detector point and the line given by the PMT hits shown in fig.??a.

The resulting plane is defined as the Detecor-shower plane and is shown in fig.2.1b.

Procedure (2) is used to determine the trajectory of the shower within the shower plane.

Both the arrivel times ti and angles χi between the ground and PMT hits are measured and fitted with a simple trigonometric formula [5].

In 1986 a second Fly’s Eye side was completed with 36 mirrors. This side (Fly’s Eye I)

2Detector size is negligible at distances of a few km or more

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was located 3.4km from the old side (Fly’s Eye II). Stereoscopic obeservation made it possible to determine the shower trajectory more acurately as the trajectory was given by the intersection of the two reconstructed shower planes

The successor of Fly’s Eye is the HiRes experiment wich is still taking data. The first side (HiRes I) was completed in 1997 and has 22 mirrors. The second (HiRes II) was completed in 1999, consist of 42 mirrors and is separated from HiRes I by 12.4km.

Each mirror is equipt with 256 PMT’s, therefore each pixel cover a smaller 1^◦ angular cone of the sky. Consequently, the new camera’s have a much better angular resolution than Fly’s Eye hence the name HiRes.

Data taken from AGASA and HiRes show a different energy spectrum above the GZK cutoff. HiRes data proclaimed less events above 10²⁰. While AGASA claimed to see a continue power law type of flux. Recent results from HiRes [6] have failed to confirm this and are consistent with the expected GZK cutoff, see fig.2.2. The disagreement between AGASA and HiRes may be due to different energy scales. Ground arrays as AGASA uses Monte Carlo calculation of shower development to relate the particle density on the ground to the primary energy. This requires knowledge of hadronic and nuclear physics beyond what is observed in accelerator experiments today. Air fluorescent experiments are much more direct. The most recent experiment a hybryd (both ground array as fluoresence detectors) is the Pierre Auger experiment in Argentina. Data however is still to preliminary to participate in the GZK debate.

Figure 2.2: High energy part of the Cosmic Ray spectrum. Clearly visible the continous flux obtained by AGASA vs the negative slope from HiRes. Picture taken from [7].

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2.4 The HiSPARC project

There are many ground arrays around the world. Beside their scientific value, some of these experiments were also set up for educational purposes. In the last few years more and more research institutes around the world started working together with local high schools by ini- tiating so called Cosmic Ray hands on projects. Within these projects high school students are builiding, analysing, and taking care of their own cosmic ray detector station with the help of a research facility nearby.

One of these projects is HiSPARC [8] (High School Project on Astrophysics Research with Cosmics) in the Netherlands. The first initiative came from the University of Nijmegen.

It began his first (pilot) stage in the fall of 2001 under the name of NAHSA (Nijmegen Area High School Array). In this stage, a prototype detector was placed on the roof of the university and two local³high schools. Beside the scientific goal, NAHSA’s secondary mission was to strengthening the links between high schools and university and to increase the interest of high school students in exact sciences. An important factor considering the decrease of the number of first year physics students in the Netherlands. It is the latter what provided the extrinsic motivation⁴ for the HiSPARC project. Nowedays the HiSPARC network consist of five fully (independent) operational clusters, see fig.6.4, distributed troughout the country with a total of 39 detectors (32 placed on high schools).

Amsterdam

Groningen

40 km

Nijmegen(NAHSA) Utrecht

Leiden

Figure 2.3: The HiSPARC network in the Netherlands (nov.2006). Clusters are located around the universities of Amsterdam, Utrecht, Nijmegen, Groningen and Leiden. Each of the dots in the figure correspont to a detector station.

3Taking into account a certain distance ( 1km) from each other.

4Intrinsic motivation for the HiSPARC project is the investigation of the nature, flux and origin of UHECR.

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NIKHEF 1

Entries 32508

Mean 245.6

RMS 194.5

Underflow 0

Abs. Voltage (mV)

0 200 400 600 800 1000

eventsN

0 50 100 150 200 250 300

350

NIKHEF 1

Entries 32508

Mean 245.6

RMS 194.5

Underflow 0 = 13809

γ Integral

= 17681 µ

Integral

= 31453 µ

γ + Integral

detector 1 detector 2

Figure 2.4: Voltage distribution between detector 1 and 2.

There is still a substantial discrepancy of the number of detectors per cluster between each cluster. The ultimate goal is to increase this number to at least 15-20 det./clust. in a cluster area of about 100 km² which is quit realistic since the number of participating schools is still growing. Each detector consist of two scintillator plates of 0,5 m², seperated with a distance of about 8 m. The scintillator detectors are operating in a coincidence mode. When both of the detectors receive a signal within a time window of 2 µs, a trigger is send to a GPS antenne which provide the trigger with a corresponding time stamp. Beside the time stamp more information such as PMT pulshigh, trace samples, etc is send and saved in a database at a local server. One of these is the HiSPARC-NIKHEF ground array in which two detector units are placed close to each other. For more about the mechanical and electronic setup of this ground array and the detector itself, read capter 3.

On June 15, 2004, the HiSPARC project received the Altran Foundation Award⁵ for actively engaging high school students and teachers with scientific research. The price award money was one million euro.

5ALtran Foundation for Innovation: Award winner HiSPARC, first prize, June 15 (2004) (http://http:

//www.altran-foundation.com/DevSite/index.jsp?id=000001087245346781/).

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NIKHEF 19

Entries 29568

Mean 258.7

RMS 201.3

Underflow 0

Abs. Voltage (mV)

0 200 400 600 800 1000

eventsN

0 50 100 150 200 250

300

NIKHEF 19

Entries 29568

Mean 258.7

RMS 201.3

Underflow 0 = 12114

γ Integral

= 16623 µ

Integral

= 28712 µ

γ + Integral

detector 3 detector 4

Figure 2.5: Voltage distribution between detector 3 and 4.

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Chapter 3

The HiSPARC-NIKHEF ground array

In this chapter we discuss the HiSPARC-NIKHEF architecture and data aquisition in more detail. The ground array consist of two detectors units thus with a total of 4 scintillator plates, placed on the roof of the NIKHEF¹ institute in Amsterdam. The detectors used in this configuration are not unique in the HiSPARC network. Both hard- and software, apart from some small exceptions, are the same as in any other detector unit used in the network.

For simplicity, in this chapter, we name each of the 4 scintillator plates in this ground array a detector.

3.1 Detector architecture

The detectors are placed fairly close to each other. All 4 detectors are basicly forming 5 triangles where the lapla in the shape of a triangle with a fourth detector in the center, see fig.??. Detectors 2,3 and 4 are placed in an almost equilateral triangle.

3.2 Data acquisition

3.2.1 GPS Resolution

1NIKHEF - National Institute for Nuclear and High Energy Physics - Amsterdam (http://www.nikhef.nl/).

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CHAPTER 3. THE HISPARC-NIKHEF GROUND ARRAY

det. 1

det. 2

det. 3 det. 4

DAC1 DAC2 DAC3 DAC4

8.9 m 8.7 m 9.2 m

8.2 m A

0.5 m

1.0 m

PMT

A

Figure 3.1: A schematic view of the HiSPARC-NIKHEF array. The complete configuration comprises 4 scintillator detectors. The sensitive elements of the detector are the scintillator plates and the photo-multiplier tubes (PMTs). To protect them against external influences they are housed inside a ski box (part A) normally used for housing ski equipment on top of a car. All 4 PMT signals are send to their corresponding Analog Digital Convertor (ADCs) using a coaxial cable (RG-58 BNC) of approximately 25 m long. The effective area of the scintillator is 0.5 m² and the thickness is 2 cm.

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Time (ns)

1600 1700 1800 1900 2000 2100 2200

Time (ns)

1600 1700 1800 1900 2000 2100 2200

Voltage (mV)

-400 -350 -300 -250 -200 -150 -100 -50

0 Scintillator 1

Scintillator 2 Scintillator 3 Scintillator 4

Figure 3.2: Detector readout, 4 traces.

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Entries 60307 Mean -23.3 RMS 130.5

t (ns)

-400 -300 -200 -100 0 100 200 300∆ 400

eventsN

0 20 40 60 80 100 120 140 160 180 200 220

240 Entries 60307

Mean -23.3 RMS 130.5 Time difference GPS1-GPS19 04/09/2005

Figure 3.3: Time diference between the time of GPS1 and GPS19. With GPS1 and GPS19 the GPS antenna of NIKHEF 1 and 19 respectively. Data is taken on september 4, 2005.

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Chapter 4

Theoretical overview of Cosmic Ray Air Showers

Basically the cosmic radiation is integrated by atomic nuclei (96 H, 3 He, 1 C,N,O,Fe), -rays, electrons and positrons, neutrinos and other types of elemental particles.

The cosmic radiation travels from the emission source until it reaches the Earth. On its way through the outer space some interactions with the intergalactic or interstellar medium can take place, as for example fragmentation of the nuclei, ionization, particle production and many more. This sub-products of the original cosmic particles are the ones that reaches the earth’s atmosphere. When the cosmic rays enter the earth’s atmosphere they have extremely high energy and give rise to a number of complicated processes through the interaction with an atmospheric nuclei that gives rise to a certain number of secondary particles turning into what is called Extensive Air Shower or EAS.

The primary particles in the EAS at upper atmosphere are, in the main, nuclei, essen- tially photons and -nucleus, and, in smaller number, heavier nuclei. The distribution of the incidence direction is basically isotropic, and its spectrum is extended in energy up to, at least, eV.

Primaire deeltjes kunnen 1 bestaan uit een enkel zwaar nucleon of 2 uit een nucleon met atoomnummer A. De resulterende shower van (2) kan dan gezien worden als een superpositite van A subshowers elk met een energiefractie van E/A van de beginshower.

Disagreement between AGASA and HiRes paragraaf 6.

Het grootste deel van de primaire energie wordt ’gedragen’ door elek(posi)tronen.

4.1 Time structure of the front of an air shower

A proper understanding of the shower disc thickness is important for several reasons. Mainly the thickness determines the accuracy at wich we can determine the shower direction. Larger disc thickness gives us a whider spread in arrival times thereby making the approximation of a planar disc less accurate.

4.2 Simulation

In order to give a good estimate of the showerthickness and therefore the resolution of our detector it is nessesary to compare the data with a data from a small simultation. A

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CHAPTER 4. THEORETICAL OVERVIEW OF COSMIC RAY AIR SHOWERS

verry small and simple simulation is made. The events were generated with two fluxes and compared with each other. The first events flux spectra is given by:

dN₂

dθ = cos²θ (4.1)

This distribution is also known as the cosmic ray muon PDG (Particle Data Group) flux [7]. Most of the primary particles will arive the earth with zero inclination. However, an air shower experiment in Turku, Finland [9] has shown that because of detection limitations most of the air showers we detect have a arrivel distribution given by

dN₁ dθ = 1

N1

sinθcosⁿθ (4.2)

where n = 8.9 ± 0.2

N1= sinθ0cosⁿθ0 (4.3)

with

θ0 = arctan(

r1 n)

both eq. 4.1as eq. 4.3are plotted in figure 4.1. There is a clear distinction between the PDF flux4.1and the flux given by4.3. The PDF flux is the measured muon distribution at sea level. The flux given by4.3however is the air shower distribution at sea level. Compared with other secondary particles, muons have a small deviation from the arival direction of the primary particle. Therefore as an approximation, both spectra can be compared with each other.

The simulation

4.3 Shower development

4.4 Summary

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CHAPTER 4. THEORETICAL OVERVIEW OF COSMIC RAY AIR SHOWERS

(rad)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 θ1.6

(rad)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 θ1.6

θdN/d

0 0.2 0.4 0.6 0.8 1

Flux 1

Flux 2 Flux spectra

Figure 4.1: Flux spectra of flux 1 and 2 used in the simulation. Flux 1 corresponts to

dN1

dθ = cos²θ and flux 2 with ^dN_dθ² = N₂cosθsinⁿθ where n = 8.9 ± 0.2.

θ d

dϕ θ

ϕ

∆t d/c

−d/c x

y

z

Figure 4.2: Flux spectra of flux 1 and 2 used in the simulation. Flux 1 corresponts to

dN1

dθ = cos²θ and flux 2 with ^dN_dθ² = N₂cosθsinⁿθ where n = 8.9 ± 0.2.

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Chapter 5

Data analysis

In this chapter we discribe the operations required to extract background, pulshight and time information of all four traces.

5.1 Background 5.2 Pulshight

5.3 Time Reconstruction

In this section we discuss the methods that are used to extract time information from all four detectors. It is important to reconstruct the time t_q (q = 1, 2, 3, 4) of each trace q accurately because time will be the main parameter for all the variables in chapter 6. The time resolution for all four ADC channels is 20 ns. Thus, for an accurate estimation of t_q it is necessary to make an interpolated between the data points. To reconstructed the time t_q of trace q we make use of the Lagrange interpolation. For every function f (x) we can make a Lagrange interpolation P (x) of degree (n − 1) that passes through n points ((x₁, y₁), · · · , (x_n, y_n) where y_n= f (x_n). The Lagrange polynomial of degree n is given by

P_n(x) =

n

X

j=1

P_j(x) (5.1)

where

P_j(x) = y_j

n

Y

k=1

k6=j

x − x_k

xj− x_k (5.2)

Two methods A and B are used and compared with each other. Method A makes use of a Lagrange interpolation through two points n = 2. Method B uses a Lagrange interpolation through three points n = 3. In general, a high-degree interpolation will give an high accuracy at the data points (xq[i], yq[i]) but a poor prediction of the trace function between points.

Therefore in our case a large number n must be avoided.

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CHAPTER 5. DATA ANALYSIS

5.3.1 Lagrange Interpolation 2points - Method A

Before we make a Lagrange interpolation P₂(x) through two points we first need to determine wich two data points we can use. In both cases (method A and B) this will be the data points in the downgoing flank of trace q. The method itself is pretty straightforward and simpel. After we have determined the maximum V^max^q of trace q we will calculate the threshold level δV . This threshold level is defined as δV = ₁₀₀^p V^max^q where p the fraction in %. Once the threshold is set the data point (xq[i2], y[i2]) is calculated where i2 is given by δV > y_q[i₂]. Then an interpolation is made through the points (x_q[i₂− 1], y_q[i₂− 1]) and (xq[i2], yq[i2]) which is shown by the straight red line in figure 5.1.

V_max

Voltage

Threshold

t_s

x[i+1], y[i+1]

x[i], y[i]

x[i−1], y[i−1]

Time

PMT signal (integrated) 20 ns

Figure 5.1: Schematic picture of the Lagrange interpolation through two data points After we have determined the polynomial P₂(x) we calculate the corresponding time t_q of trace q by solving P₂(t_q) = δV . The solution can than be written as

tq = δV (x_q[i₂] − x_q[i₂− 1]) + x_q[i₂− 1]y_q[i₂] − x_q[i₂]y_q[i₂− 1]

yq[i2] − yq[i2− 1] (5.3)

5.3.2 Lagrange Interpolation 3points - Method B

Kort wat over methode B: tijdbepaling aan de hand van een Lagrange fit door drie datapun- ten.

V_max

Voltage

PMT signal (integrated) Threshold

t_s

x[i+1], y[i+1]

x[i], y[i]

x[i−1], y[i−1]

Time 20 ns

Figure 5.2: Three points method. Red line shows the curve through the points xq[i − 1], xq[i]

and xq[i + 1].

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5.4 Calibration data

In this section we determine the time ofset values δt₂₁, δt₃₁ and δt₄₁ between detector 1,2,3 and 4. Also we investigate the optimized threshold level for both methods. In general the offset values are the sum of two parts.

δt = δt_hardware+ δt_cable (5.4)

with δt_hardware the time offset introduced by the hardware and δt_cable the time offset introduced by the cablelength. In practice the latter will be the same in all cases because all cablelengths are approximately the same. To collect calibration data we must give all 4 detectors the same input signal. We have generated a block pulse of -1 V with a length of 20 ns and a frequency of 3 Hz. This main signal is then splitted in four signals by using a T-splitter and fed to the input of cable 1,2,3 and 4. If all the pulses are integrated and amplified in the same way we expect an output of -250 mV at all four ADCdisplays. First we determine the best threshold level.

5.4.1 Optimized Resolution and Threshold level

We have investigate which method for both methods. The results are shown below in the table 5.1 and 5.2.

Threshold (%) 5 8 10 15 20 30 40 55

RMS 6.522 5.711 5.866 7.047 7.952 8.631 8.918 9.28

Mean -20.56 -20.74 -20.76 -20.62 -20.32 -19.68 -19.41 -19.26 Table 5.1: Time resolution of ∆32 = t3 − t₂ at different threshold levels determind with method A. Threshold levels are given as fractions of V_max.

Threshold (%) 5 8 10 15 20 30 40 55

RMS 6.626 7.170 7.512 8.246 8.727 9.135 9.289 9.341

Mean -20.81 -20.58 -20.44 -20.10 -19.79 -19.32 -19.20 -19.33 Table 5.2: Time resolution of ∆₃₂= t₃− t₂ determind with method B.

From table 5.1 and 5.2 we conclude that the time reconstruction performance is much better when using method A in stead of B.

Hieronder (tabel5.3) wordt met methode A tevens de resolutie bekeken van het tijdver- schil tussen detector 1 en 2 (∆₂₁= t₂− t₁).

Threshold (%) 5 8 10 20 30 40 50 70 80

RMS 0.707 0.788 0.710 0.38 0.268 0.318 0.374 0.449 0.709 Mean 20.36 20.49 20.44 20.38 20.37 20.43 20.48 20.53 20.59 Table 5.3: Mean and RMS values of ∆21= t2− t₁ determind by using the 2 points method.

Op basis van de resultaten uit tabel 5.1 en 5.3 kies ik bij het bepalen van de tijdstempels voor methode A en een threshold van 10%. Zie figuur ??.

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Threshold (%) 5 8 10 20 30 40 50 70 80

RMS 0.494 0.446 0.4276 0.355 0.354 0.297 0.359 0.489 0.626 Mean 20.37 20.39 20.40 20.43 20.44 20.45 20.47 20.44 20.44 Table 5.4: Mean and RMS values of ∆₂₁= t₂− t₁ determind by using the 3 points method.

Entries 24517

Mean 20.37

RMS 0.2018

/ ndf

χ2 41.39 / 43

Prob 0.5413

Constant 532.8 ± 5.4 Mean 20.33 ± 0.00 Sigma 0.1712 ± 0.0026

(ns) t21

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 100 200 300 400 500

600 Entries 24517

Mean 20.37

RMS 0.2018

/ ndf

χ2 41.39 / 43

Prob 0.5413

Constant 532.8 ± 5.4 Mean 20.33 ± 0.00 Sigma 0.1712 ± 0.0026 (2points 30%)

-t1

t2

Entries 24517

Mean 20.41

RMS 0.2498

/ ndf

χ2 37.14 / 39

Prob 0.5552

(ns) t21

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 100 200 300 400 500

Entries 24517

Mean 20.41

RMS 0.2498

/ ndf

χ2 37.14 / 39

Prob 0.5552

Constant 545.9 ± 5.8 Mean 20.32 ± 0.00 Sigma 0.151 ± 0.002 (3points 30%)

-t1

t2

Figure 5.3: left : (a) Distribution of ∆t21 = t2 − t1 analized with method A. Data is fitted with a gaussian with a binsize is 0.01 ns. Results of the fit show a resolution of σ21= 0.17ns and an average ofset of δt₂₁= 20.33ns with a chi-square probability of P_A= 0.17 for about 70% of the total events. right : (b) Distribution of ∆t21 = t2 − t1 analized with method B. The distribution is rather poor compared with the one obtained with method A left.

Bbecause of the relatively poor chi-square probability of P_B = 0.05 (method B) instead of PA = 0.17 (method A) time measurements with method B will be ignored. A bigger fit window resulted in an even lower χ²/ndf value for both cases.

5.4.2 Time offset values

5.4.3 Time offset values with fitted maximum

For each trace q we have made a fit through the points (y_q[i_m− 1], x_q[i_m− 1]), (y_q[i_m], x_q[i_m]) and (y_q[i_m+ 1], x_q[i_m+ 1]) where i_m the binnumber given by y[i_m] = V^max^q and V^max^q the maximum voltage defined earlier. In this case the maximum of the fit V_{f it}^max^q of trace q is given by V_{f it}^max^q = P (x^max_{f it} ^q) where

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Entries 24517

Mean 20.43

RMS 0.3165

/ ndf

χ2 71.61 / 44

Prob 0.005323 Constant 403.3 ± 4.6 Mean 20.31 ± 0.00 Sigma 0.2103 ± 0.0049

(ns) t43

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 50 100 150 200 250 300 350 400

450 Entries 24517

Mean 20.43

RMS 0.3165

/ ndf

χ2 71.61 / 44

Prob 0.005323 Constant 403.3 ± 4.6 Mean 20.31 ± 0.00 Sigma 0.2103 ± 0.0049 (2points 30%)

-t3

t4

Entries 24517 Mean 20.44 RMS 0.3048

/ ndf

χ2 56.69 / 40 Prob 0.04202 Constant 416.6 ± 4.9 Mean 20.29 ± 0.00 Sigma 0.1759 ± 0.0036

(ns) t43

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 50 100 150 200 250 300 350 400 450

/ ndf

χ2 56.69 / 40 Prob 0.04202 Constant 416.6 ± 4.9 Mean 20.29 ± 0.00 Sigma 0.1759 ± 0.0036 (3points 30%)

-t3

t4

Figure 5.4: left : (a) Distribution of ∆t43= t4 − t3 analized with method A. Results of the fit show a resolution of σ₂₁= 0.21ns and an average ofset of δ₂₁= 20.35ns with a chi-square probablility of P_A = 0.02 for about 70% of the total events. right : (b) Distribution of

∆21 = t2 − t1 analized with method B. Also here we find the distribution poor compared with the one obtained with method A (picture plaatje delta21 2points). The results can be ignored because of the relatively poor chi-square probability of P_B = 0.004 (method B) instead of PA= 0.15 (method A).

P (x^max_{f it} ^q) = (x^max_{f it} ^q− x_q[im])(x^max_{f it} ^q− x_q[im+ 1])

(xq[im] − xq[im])(xq[im] − xq[i + 1]) yq[im− 1] + + (x^max_{f it} ^q − x_q[im− 1])(x^max_{f it} ^q − x_q[im+ 1])

(xq[im] − xq[im− 1])(x_q[im] − xq[im+ 1])yq[im] + + (x^max_{f it} ^q − x_q[im− 1])(x^max_{f it} ^q− x_q[im])

(xq[im+ 1] − xq[im− 1])(x_q[im+ 1] − xq[im])yq[im+ 1] (5.5)

with x^max_{f it} ^q the solution of ^{dP (x}

maxq f it )

dy = 0 explicitly

x^max_{f it} ^q = a_q 2bq

(5.6)

where

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40% threshold t21

∆

t (ns)

18 19 20 21 22 ∆ 23

eventsN

0 100 200 300 400 500

40% threshold t21

∆

Entries 26339 Mean 20.43 RMS 0.2878 5% threshold t21

∆

Entries 26339 Mean 20.48 RMS 4.506 -t1

t2

5% threshold t21

∆ 40% threshold t21

∆

40% threshold t43

∆

t (ns)

18 19 20 21 22 ∆ 23

eventsN

0 50 100 150 200 250 300 350 400

40% threshold t43

∆

Entries 24517 Mean 20.3 RMS 0.8268 -t3

t4

5% threshold t43

∆ 40% threshold t43

∆

Figure 5.5: left : (a) Distribution of ∆t21= t2 − t1 for two different threshold levels of 5%

and 40%. It is clear that the 5% distribution is much more broader than the 40% distribution with a sigma value of respectively σ_5% = 4.51ns and σ_40%= 0.29ns. A possible answer can be given by doing a slope analysis. right : (b) Distribution of ∆t43= t4−t3 also at threshold level 5% and 40%. It is clear that the 5% distribution still looks broader than the 40% but with a smaller sigma value (σ_5% = 0.83ns) than in (a).

a_q = y_q[i − 1](x_q[i] + x_q[i + 1])(x_q[i] − x_q[i + 1]) −

− y_q[i](x_q[i − 1] + x_q[i + 1])(x_q[i − 1] − x_q[i + 1]) +

+y_q[i + 1](x_q[i − 1] + x_q[i])(x_q[i − 1] − x_q[i]) (5.7) bq = yq[i − 1](xq[i] − xq[i + 1]) − yq[i](xq[i − 1] − xq[i + 1]) +

+yq[i + 1](xq[i − 1] − xq[i]) (5.8)

A possible anwer can be given if we do a slope analysis of de calibration puls of both detector 1 and 2. When we look at the slope difference |^dV_dt²¹| between detector 1 and 2 in figure5.5b it is clear that almost all 5% threshold events are below zero. The 40% distribution on the other hand has a significant number of events with |^dV_dt²¹| > 0. An understanding of the larger time differences and thus the broad distribution of ∆t21 at 5% can be given as follows.

Within the s2− s₁> 0 range we are left with two possibilities in which only the slope of the two calibration pulses of detector 1 and 2 can differ in magnitude. These options are drawn in figure 5.9.

The time difference ∆ta with |s1| > |s₂| is relatively larger than the time difference ∆t_b with

|s₁| < |s₂|. In both cases (5% and 40%) there are more events with s₂− s₁> 0. Because the 5% distribution is more asymetric around zero than the 40% distribution there are relatively more events with the larger time difference ∆taat 5% threshold level than at 40% threshold level which explains the larger RMS value at 5% threshold level.

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Entries 24525

Mean 19.9

RMS 0.1767

/ ndf

χ2 34.48 / 57

Prob 0.9921

(ns) t21

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 100 200 300 400 500

600 Entries 24525

Mean 19.9

RMS 0.1767

/ ndf

χ2 34.48 / 57

Prob 0.9921

Constant 568.8 ± 5.1 Mean 19.88 ± 0.00 Sigma 0.1694 ± 0.0015 (2points 30%) with threshold bias

-t1

t2

Entries 24517

Mean 20.09

RMS 0.1966

/ ndf

χ2 57.02 / 46

Prob 0.128

(ns) t21

19 19.5 20 20.5 21 21.5∆ 22

eventsN

0 100 200 300 400 500 600

Entries 24517

Mean 20.09

RMS 0.1966

/ ndf

χ2 57.02 / 46

Prob 0.128

Constant 604.7 ± 5.8 Mean 20.05 ± 0.00 Sigma 0.1486 ± 0.0016 (3points 30%) with threshold bias

-t1

t2

Figure 5.6: left : (a) (binsize=0.01) Distribution of ∆21 = t2 − t1 analized with method A this time with an offset of -10 mV on the maximum voltage of detector 2. Results of the guassian fit do not deviate much from 5.3a. The χ²/ndf value is lower with a better probability, PABIAS = 0.99 v.s. PA = 0.54 even while the fit includes more events. The resolution is σ₂₁_BIAS = 0.17ns and the average ofset δ₂₁= 19.88ns. right : (b) Distribution of ∆₂₁ = t2 − t1 analized with method B. A bigger fit window resulted in an even lower χ²/ndf value for both cases.

This can been also be shown mathematically. Given two polinominal functions f₁(t) and f₂(t) of order 1 with slope s₁ and s₂ respectively:

f₁(t) = s₁t f₂(t) = s₂t − t₀

where f₂ is shifted t₀ to the right of f₁ so that ∀t 0∈ <

Next thing to investigate is the asymmetry difference in the distributions of ∆t21in figure 5.5a between 5 and 40% threshold level. The asymmetry itself could be related to a bug in the code or a real time difference.

When we look at the RMS values in table5.3and5.4 we see that in both cases (2points and 3points) the RMS values are

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Puls 2

Vmax Entries 24525 Mean -247.8 RMS 1.595

(mV) Vmax

-260 -255 -250 -245 -240

eventsN

0 100 200 300 400 500 600

Puls 2

Puls 1

Vmax Entries 24525 Mean -249 RMS 2.824

Puls 1

Vmax Entries 24525 Mean -249 RMS 2.824 Calibration puls 1&2

Vmax

Puls 1

Vmax

Puls 2

Vmax

Puls 2

(mV) Vmax

-260 -255 -250 -245 -240

eventsN

0 100 200 300 400 500 600

Puls 2

Puls 1

Vmax Entries 24517 Mean -249 RMS 2.825 Calibration puls 1&2 after correction

Vmax

Puls 1

Vmax

Puls 2

Vmax

Figure 5.7: left : (a) Voltage distribution of the maximum voltage V^max¹ and V^max² of the calibration puls of det 1 and 2 before voltage correction. right : (b) Voltage distribution after correction. Here V¹ and V² are multiplied with a factor of 1 and _247.8²⁴⁹ respectively.

Puls 3

(mV) Vmax -300 -280 -260 -240 -220 -200 -180

eventsN

0 100 200 300 400 500 600

Puls 3

Puls 4

Vmax Entries 24533 Mean -281.3 RMS 3.26 Calibration puls 3&4

Vmax

Puls 3

Vmax

Puls 4

Vmax

Puls 3

(mV) Vmax

-260 -255 -250 -245 -240

eventsN

0 100 200 300 400 500 600

Puls 3

Puls 4

Vmax Entries 24517 Mean -249 RMS 2.411 Calibration puls 3&4 after correction

Vmax

Puls 3

Vmax

Puls 4

Vmax

Figure 5.8: left : (a) Voltage distribution of the maximum voltage V max3 and V max4 of the calibration puls of det 3 and 4 before voltage correction. right : (b) Voltage distribution after correction. Here V₃ and V₄ are multiplied with a factor of _215.8²⁴⁹ and _281.3²⁴⁹ respectively.

the HiSPARC-NIKHEF ground array

Angular Reconstruction and Showerfront Thickness of low energy Air Showers detected at

the HiSPARC-NIKHEF ground array

Versie 1.4

Contents

Chapter 1

Introduction

1.1 High Energy Cosmic Rays

1.2 GZK cutoff

1.3 Outline of this thesis

Chapter 2

Air-Shower experiments

2.1 Introduction

2.2 The AGASA experiment

2.3 The Fly’s Eye experiment

2.4 The HiSPARC project

NIKHEF 1

NIKHEF 1

NIKHEF 19

NIKHEF 19

Chapter 3

The HiSPARC-NIKHEF ground array

3.1 Detector architecture

3.2 Data acquisition

Chapter 4

Theoretical overview of Cosmic Ray Air Showers

4.1 Time structure of the front of an air shower

4.2 Simulation

4.3 Shower development

4.4 Summary

Chapter 5

Data analysis

5.1 Background 5.2 Pulshight

5.3 Time Reconstruction

5.4 Calibration data