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Masterthesis Particle & Astroparticle Physics Cosmic Rays and the MUONLAB program Author: Paul Voskuilen*, Bsc. *e-mail:[email protected] Supervisor: Dr. Marcel Vreeswijk* *e-mail: [email protected] Second reviewer: Dr. Dorothea Samtleben April 16, 2012 Abstract The Muonlab setup developed at Nikhef allows for an educational use of secondary cosmic rays, i.e. muons, as a quick test of the theory of special relativity. The program consists of a time of flight measurement as well as a muon lifetime measurement, allowing to quickly determine the muon speed in the atmosphere to be 0.98c and the muon lifetime to be 2.2μs. To improve the accessibility for high school students to the experimental results, a Maximum Log Likelihood fit is added to the software. Muonlab setup costs are expensive, and above the budget of most schools. A feasibility study using ’old’ photo multiplier tubes from the Zeus experiment is performed, allowing to reduce setup costs. The outcomes of this study are positive and the recommendations are currently implemented.

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Page 1: Masterthesis Particle & Astroparticle Physics · Masterthesis Particle & Astroparticle Physics Cosmic Rays and the MUONLAB program Author: Paul Voskuilen*, Bsc. *e-mail:pvoskuil@nikhef.nl

Masterthesis

Particle & Astroparticle Physics

Cosmic Rays and the MUONLAB program

Author:Paul Voskuilen*, Bsc.*e-mail:[email protected]

Supervisor:Dr. Marcel Vreeswijk**e-mail: [email protected]

Second reviewer:Dr. Dorothea Samtleben

April 16, 2012

AbstractThe Muonlab setup developed at Nikhef allows for an educational use of secondary cosmicrays, i.e. muons, as a quick test of the theory of special relativity. The program consists of atime of flight measurement as well as a muon lifetime measurement, allowing to quicklydetermine the muon speed in the atmosphere to be ≈ 0.98c and the muon lifetime to be2.2µs. To improve the accessibility for high school students to the experimental results, aMaximum Log Likelihood fit is added to the software. Muonlab setup costs are expensive,and above the budget of most schools. A feasibility study using ’old’ photo multiplier tubesfrom the Zeus experiment is performed, allowing to reduce setup costs. The outcomes of thisstudy are positive and the recommendations are currently implemented.

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CONTENTS

1 Introduction 3

2 The spectrum of primary cosmic rays 72.1 Composition of cosmic ray flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Cosmic ray spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 The Greisen-Zatsepin-Kuz’min-cutoff . . . . . . . . . . . . . . . . . . . . . . . . 9

3 The origin of cosmic rays 113.1 Restrictions on the cosmic ray origin . . . . . . . . . . . . . . . . . . . . . . . . 11

4 The acceleration of cosmic rays 154.1 Bottom-up acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Acceleration mechanism of Ultra High Energy Cosmic Rays . . . . . . . . . . . 194.3 Top-down acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Extensive Air Showers 235.1 Air shower creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2 Detection of cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.3 Current experiments working on cosmic rays . . . . . . . . . . . . . . . . . . . . 29

6 Muon detection and Muonlab 316.1 Muonlab program at NIKHEF . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.2 Muonlab as an introduction in Special Relativity . . . . . . . . . . . . . . . . . 386.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Bibliography 51

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KORTE NEDERLANDSESAMENVATTING

De ontdekking van kosmische straling in 1912 door Victor Hess heeft gezorgd voor veel nieuweinzichten in zowel de deeltjesfysica als in de astrofysica. In de honderd jaar die volgden zijnniet alleen nieuwe theorieen ontwikkeld en nieuwe elementaire deeltjes ontdekt maar zijn er ookpraktische toepassingen met deze kennis ontwikkeld. Het gebruiken van kosmische straling alseen test voor de speciale relativiteitstheorie (SRT) werd ontwikkeld in de jaren zestig en kantegenwoordig in het onderwijs gebruikt worden om zowel de onderwerpen van de deeltjesfysica,astrofysica als SRT te introduceren. In het Muonlab programma kunnen studenten de snelhedenen levensduur meten van muonen, die geproduceerd zijn op 10 − 15 kilometer hoogte in deatmosfeer. Uit de analyze van deze metingen blijkt dat de theorie van Einstein klopt, i.e. datvoor een bewegend lichaam de tijd relatief langzamer gaat dan voor een lichaam dat niet aanbeweging onderhevig is. Er zijn in de software van het Muonlab programma enkele aanpassingengedaan om zo de experimentele resultaten toegankelijker te maken voor studenten en scholieren.Door middel van een Maximum Log Likelihood berekening kan nu al na enkele metingen delevensduur berekend worden, alsmede de snelheid van de muonen. Ook zijn fotoversterkerbuizengetest, afkomstig van het Zeus experiment te Hamburg, om toegepast te kunnen worden in hetprogramma. Deze ruim voorradige versterkerbuizen worden geimplementeerd in het Muonlabprogramma om scholen de mogelijkheid te geven om in de toekomst het Muonlab experimentzonder budgetaire hindernissen te kunnen aanschaffen. De buizen zijn getest op hun efficientie,door middel van een ’plateau’-meting. Het plateau geeft het gebied in voltage aan, wanneerde buizen met een stabiele versterking werken en niet te veel ruis produceren. Deze buizenkunnen door middel van een spanningsversterker worden gebruikt in het project. Er zijn tweeverschillende spanningsversterkers (A en B) getest en type A blijkt aan alle normen te voldoen.Op het moment worden aanpassingen gemaakt binnen de Muonlab hard- en software om hetgebruik van de goedkope fotoversterkerbuizen mogelijk te maken.

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CHAPTER 1

INTRODUCTION

In 1912 Victor Hess discovered that the ionization of the atmosphere was not coming fromradioactive terrestrial sources but that it increased with altitude. Hess had built three elec-trometers succeeding the work of Theodore Wulf, who tried to show the higher levels of radiationat the top of the Eiffel Tower than at its base. Hess carried the electrometers up to 5300 mhigh with a balloon and found that the ionization rate was four times as much as it was atground level. Doing the ascent during full eclipse, he was able to exclude the Sun as possiblesource for this phenomenon. He conducted that it were particles incident at the top of theterrestrial atmosphere that ionized the air molecules and for this discovery of cosmic radiationHess received the Nobel Prize in 1936.

The discovery of cosmic rays opened an entire field of astrophysics. It turned out that theseparticles reaching us from outside the Earth’s atmosphere have so many unexplainable features,that they are still of interest a hundred years after their discovery. But not only are theyinteresting for new physics, these particles can also be used to show the genuineness of physictheories, such as special relativity. The ”Principle of Relativity” by Albert Einstein states - “thelaws by which the states of physical systems undergo change are not affected, whether thesechanges of state be referred to the one or the other of two systems in uniform translatory motionrelative to each other.”[1] This can be unambiguously proven with cosmic rays. Therefore,doing experiments on cosmic rays can introduce one of the most famous physics principles toyoung students and deserves the attention from experts in the further understanding of thisphenomenon.

In the recent years lots of research has been done on the subject, although still a lot of workneeds to show more on the cosmic ray origin and other properties, such as the supposedinteraction with the Cosmic Microwave Background (CMB) radiation. Also, cosmic rays reachup to ultra high energies, which are not fully understood either. The Pierre Auger Observatory(PAO) is an example of the persisting efforts of particle physicists as well as astrophysiciststo explore the concealed properties of cosmic rays. The ultra high energy particles found inthe experiments provide for energies higher then any terrestrial particles accelerator could have

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with recent technologies. Therefore, the phenomenon of cosmic rays brings the fields of particlephysics and astroparticle physics together.

This research paper first elaborates on the contemporary framework of cosmic rays. By buildingthis framework, the reader can understand the nature of the interest of the scientists workingon the subject. However, cosmic rays can also be used to explain “old”physics. The secondpart of the paper will therefore describe the Muonlab program at the National Institute forSubatomic Physics (NIKHEF). This part will describe how “old”physics can be tested, howmore Muonlab detectors can be constructed and the increase made in functionality. Besidesthe educational use of cosmic rays, the first following paragraphs will give, as a warm-up, shortelaborations on the other uses of cosmic rays in fields such as geology, space weather forecastingand public safety.

Cosmogenic dating

Using radiometric dating, a geologist can date materials such as rocks, by comparing theobserved abundance of a naturally occurring radioactive isotope and its decay products, usingknown decay rates. A source of radioactive isotopes is the interaction of high energy cosmicrays in the atmosphere with nuclei, such as the interaction of cosmic ray neutrons with nitrogenin the upper atmosphere, which is a source of frequently used carbon-14 (n+14

7 N → 146 C+ p).

However, due to the large half-life of carbon-14, this isotope can not be used for all datingpurposes, e.g. to determine mixing processes in the ocean.

A different approach is the use of those cosmogenic isotopes ( e.g. 10Be, 26Al), which arecreated within minerals when high energy cosmic rays hit them, which is dependent on thereaction cross-section of the corresponding mineral [2, 3]. When the quantity of cosmogenicisotopes is known in e.g. a quartz sample found on top of a moraine (glacier deposit), this isrepresentative for the duration of its exposure to cosmic radiation. Therefore, the age of theretreat of the glacier that left the moraine can thus be determined. These exposure ages areused in calculations to estimate the erosion rates of landscapes, and the dating of lunar rocksor the travel times of meteorites after their separation with their larger parent bodies.

Space weather prediction

A network of cosmic ray detectors can also be used for the prediction of space weather con-ditions. Space weather conditions mainly concern solar wind disturbances and consequentincreases of radiation intensity and geomagnetic hazards. Increases of radiation are importantto monitor, since high levels of radiation can cause radiation poisoning to humans and especiallyastronauts. Furthermore, interactions of solar winds with the magnetosphere can create a dragon satellites, which leads to a lower satellite orbit and eventually the satellites will burn upin the Earth’s atmosphere. Also, radiation flares can burn down electrical circuits in satellitesand erase the system memory and thereby disabling the entire satellite. To increase the lifetimes of the satellites and to protect human beings from large increases in space radiation, aspace weather forecasting system was created.

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Introduction

Cosmic ray intensity is related to solar activity (see Chapter 2). When intensive solar flares,solar wind disturbances or coronal mass ejections occur, one can measure these via the cosmicray intensity. As the cosmic rays are propagating through the Inter Planetary Medium with arelativistic velocity, cosmic rays can bring information of these disturbances proceeding theirarrival at the Earth [4, 5]. Making use of the internet, ground-based neutron monitors canregister the real-time variations in (galactic) cosmic ray intensity for more than a 50-years timeperiod.

Muon Radiography

Nobel laureate Luis Alvarez once proposed the use of cosmic rays to search for hidden chambersin the pyramid of Chephren in Giza, Egypt. Although no chambers where found, the applicationof cosmic rays to map inaccessible structures is found to be a useful one [6]. Muon radiographymakes use of secondary cosmic muons. When the particles traverse a variety of materials,their propagation direction slightly alters. Since these muons have high energies, they canpenetrate very dense materials, e.g. lead. The change of direction is measured to determinethe type of material the particles passed through. Besides the detection of cavities in pyramids,muon radiography has other applications. For example, to detect nuclear materials at borderpatrols, muon detector plates are placed above and below passing transport. The detector thendetermines how the path of the muons is changed by the material inside [7]. Another applicationfor muon radiography is to monitor volcanoes. The studying of the magna activity can bedone by placing detectors around the mountain to measure muons that travel horizontally.The measurement of the amount of molten rock within the craters of two active volcanoes inJapan is already ongoing and if this amount rises, a volcano eruption is imminent. One day,an expanded version of the Japanese volcano monitoring system can be used to monitor allpotentially active volcanoes in the world, to better predict eruptions and avoid disasters [8].

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CHAPTER 2

THE SPECTRUM OF PRIMARY COSMICRAYS

2.1 Composition of cosmic ray flux

About 1000 cosmic ray particles m−2s−1 hit the Earths atmosphere. The main component (≈90%) consists of relativistic protons, 9% consists of alpha particles and the rest are heaviernuclei. The cosmic ray composition is however distinguished by the particle’s energy, as recentdevelopments indicate especially those particles at the highest energy end of the spectrum obeya different composition. For example, the Pierre Auger Collaboration [9] states that there is atransition toward increasingly heavier primaries at increasing energies, even though this is notverified by the HiRes experiment [10]. As one indicator for the composition, one can look atthe fact that except for those particles associated with solar flares, the cosmic radiation comesfrom outside the solar system. Therefore, the relative abundances of particles in cosmic rayscan be compared to the abundances of elements in the solar system. The comparison showstwo differences. First, Z > 1-nuclei are much more abundant compared to protons in thecosmic rays than they are in solar system material. The reason for this could originate fromthe fact that hydrogen is relatively hard to ionize for injection into the acceleration process,or that it tells something on the actual difference in composition at the source. Secondly,the overabundance of elements as Li, Be, B and Sc, Ti, V, Cr, Mn in the cosmic radiationtells a great deal about the propagation and confinement of cosmic rays in the galaxy. Theseelements are sometimes called secondary cosmic rays, since they are not end-products of stellarnucleosynthesis, but are a result of interaction of the primary cosmic rays with the interstellargas. Spallation (i.e. the nuclear fission of elements due to the impact of e.g. cosmic rays onobjects) of abundant nuclei as carbon and oxygen (Li, Be, B) and of iron (Sc, Ti,V, Cr, Mn)accounts therefore for the second difference. Knowledge on the spallation cross sections allowsus to learn something about the amount of traversed matter by cosmic rays.

The sample of cosmic rays reaching Earth have average lifetimes in the order of 106 years or

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2.2. COSMIC RAY SPECTRUM

longer. A consequence is that this could be a better representation of the average interstellarmaterial than the material (with lifetimes of 4.6 billion years) of the solar system [11].

2.2 Cosmic ray spectrum

The spectrum of cosmic rays is depleted from the lowest energy galactic cosmic rays, sincethe observed primaries are modulated by interstellar gas and solar wind, which decelerates theparticles. For these particles there exists a clear anti-correlation between solar activity andthe intensity of the cosmic rays with energies below 109 eV. However, the most interestingparts of the spectrum lies above 1015 eV. As seen in Figure 2.1, the spectrum nicely obeys acertain power law E−γ with spectral index γ to be close to 3. However, at ∼ 3 × 1015 eV,the spectral index changes from approximately 2.7 to 3.1 (”The Knee”), which was discoveredby Kulikov and Kristiansen [12] in 1958. From the spectrum we see, that at the Knee only 1particle per m2 per year is detected and this low flux makes it hard to understand the originof the break in the spectrum. However, with improving detectors and understanding of cosmicrays, models are created to explain the Knee as an upper limit of the acceleration process bygalactic supernovae [13]. Another popular explanation is that cosmic rays are not contained tothe Galaxy anymore at high enough energies. This is called the leakage of particles from theGalaxy. Anyhow, it is certain that the Knee is a reflection of the properties of the origin ofcosmic rays.

Figure 2.1: The cosmic ray spectrum, showing intriguing features such as the Knee and theAnkle.

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The spectrum of primary cosmic rays

There is another steeping near ∼ 1018 eV in the spectrum, the ”Ankle”. In this region, wecan only detect one particle per km2 per year. Because of these low statistics again, little isknown about the Ankle, although it is associated with an extragalactic population of cosmicrays which contributes to the spectrum. Because of the extremely low flux, we can not detectthese particles directly, but we can detect the air showers they create. Huge areas are necessaryto measure the initial energy of the primary cosmic ray, as with the Pierre Auger Observatory(see section 5.3). The cosmic rays near the end of the spectrum are called Ultra High EnergyCosmic Rays (UHECRs) and contain many unexplained features and this region will be themain focus of the cosmic ray framework in this paper.

2.3 The Greisen-Zatsepin-Kuz’min-cutoff

The spectrum of cosmic rays shown in Figure 2.1 tells us that we detect UHECRs above 1019 eV.However, the articles of Greisen [14] and Zatsepin and Kuz’min [15] showed after the discoveryin 1965 of the Cosmic Microwave Background (CMB) [16] that the interaction with cosmic rayscreates an upper limit for the cosmic ray spectrum. Despite widely accepted articles for overforty years, the existence of the Greisen-Zatsepin-Kuz’min cutoff (GZK-cutoff) was not verifiedfor a long time. In fact, already in 1962 a particle was found [17] to exceed this limit and sincethen, more and more particles have been found reaching energies above the limit.

The CMB has shown to have different consequences. One of them, considered by Hoyle [18],was the interaction with the cosmic ray protons. But in this interaction, three different pro-cesses have to be taken into account. Hoyle was looking at the proton Compton effect andthus neglected pair creation and photopion production. The results of Hoyle showed that theinteraction through the first process is negligible. This is because the time-scale for energydegradation is greater than the expansion time of the universe for all protons up to 1021 eV.Greisen, Zatsepin and Kuz’min showed that through pair creation and pion production theCMB can interact with cosmic rays. The depletion of the spectrum of UHECR should showin the range of Ep ≥ 1018 eV. In the first two subsequent decades it is mainly a result of pairproduction. In this process, a high energy cosmic ray proton collides with a photon from theCMB to create an electron-positron pair: p+ γ → p+ e+ + e−. The CMB photons energy canbe obtained from the Planck distribution for blackbody radiation with average temperatureTCMB = 2.725 K, Eγ ≈ 1.1 meV with a photon density of n = 411 cm−3. For the collision of acosmic ray photon and a CMB photon, the Lorentz-invariant center-of-mass energy ECMS fora head-on collision is calculated to find the proton threshold energy,

ECMS =√s = {m2

p +m2γ + 4EpEγ}1/2

= {m2p + 4EpEγ}1/2.

(2.1)

The ECMS for the final state consisting of two electrons and one proton equals

ECMS =√s ≥ 2me +mp. (2.2)

From equations 2.1 and 2.2 one can find the proton threshold energy to be

Ep ≥me(me +mp)

Eγ≥ 4.4× 1017eV.

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2.3. THE GREISEN-ZATSEPIN-KUZ’MIN-CUTOFF

At the threshold, the fractional energy loss ∆E/E is 2me/mp ' 10−3. Blumenthal [19] contin-ued steps to calculate the inverse radiation length (L−1 = E−1dE/dx) numerically. It showsthat the process only creates a small depression in the spectrum above 1018 eV with a maximalfactor of about 3, when the radiation length is less than the Hubble radius.

Above Ep ≥ 1020 eV the photopion production (γ+ p→ p+π0,γ+ p→ n+π+) becomes moresignificant. In this part of the spectrum the factor of decreasing is two orders of magnitude.The threshold energy for photopion production can be found in a similar way as for the pairproduction process, using equation 2.1 and with ECMS for the final state consisting of onenucleon N and a pion π to be

ECMS =√s ≥ mπ +mN . (2.3)

The threshold energy for photopion production then equals to

Ep ≥mπ(mπ + 2mN )

4Eγ≥ 6.2× 1019eV.

Above threshold, the cross section σ rises rapidly to a peak (at 400 µb) at the ∆-resonance,for which the threshold energy equals

Ep ≥m2

∆ −m2p

4Eγ≥ 2.3× 1020eV,

while the cross section is descending afterwards ( to 200 µb). Greisen [14] shows that this leadsto a distance scale of the energy loss L = ∆E

E (nσ)−1, with E the initial proton energy and∆E the energy loss per interaction. Now, at threshold energy for single pion production thefractional energy loss = 0.13 while in the case of ∆-resonance and multiple pion productionthis rises to an average of 0.22. The distance scale for the energy loss is calculated to be morethan an order of magnitude less then the distance to the closest quasar. The steepening of thespectrum by this process occurs when the UHECRs originated from out and inside the galaxy.Recent observations from as well the High Resolution Fly’s Eye detector (HiRes) [20] as thePierre Auger Observatory [21] has indeed shown a significant steepening of the cosmic rayspectrum above 4× 1019 eV. As described in the following chapter, the GZK-cutoff limits thesources for UHECR by their distances, but whether or not the GZK-cutoff violating particlesobey this is unknown.

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CHAPTER 3

THE ORIGIN OF COSMIC RAYS

The origin of cosmic rays is at present still unknown. Clear evidence for at least some of thesecosmic rays to be extragalactic was shown by Cocconi [22]. In addition, the entanglement ofcosmic particles in intergalactic and interstellar magnetic fields makes it very hard to pinpointto the origins of cosmic rays. Since the deflection of the original propagation path is dependenton the particles energy, the energy spectrum is very important in the subject. Features as ”theKnee” and ”Ankle” in the spectrum (Figure 2.1) are indicators of probable limitations on theparticles acceleration process. The spectrum can be divided in four regions: (i) the spectrumbelow 1 GeV is flat and the particles are slowed down by the magnetized plasma ejected bythe Sun’s surface, (ii) between 1010 eV and the Knee, it is fitted with the power law, and thisregion is probably where cosmic rays have their origin in supernovae remnants, (iii) betweenthe knee and the ankle, where heavy cosmic rays ( i.e. heavier than protons) are believed tobe accelerated in other environments, such as polar winds, and (iv) the UHECR region, whichprobably shows a dominant extragalactic component in the spectrum [36]. The last region (iv)is the most interesting and will therefore be described more intensively.

3.1 Restrictions on the cosmic ray origin

Protons (the main component of primary cosmic rays) with ultra high energy have a gyroradiusin the galactic magnetic field that is of the order of the size of the Milky Way. This gyroradiusRg is the radius of the circular motion of a charged particle in the presence of a uniformmagnetic field. How could such a particle be accelerated in the galaxy if it can not be confinedin it? Rg is calculated as follows:

Rg = 102 E20/BµGZ kpc, (3.1)

with E20 the particle’s energy in 1020 eV, Z its charge and BµG the intensity of the regularmagnetic field in microgauss, which is the magnitude of the magnetic field of the Milky Way.

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3.1. RESTRICTIONS ON THE COSMIC RAY ORIGIN

The accelerating process of such particles contains many irregular loops in the field. Therefore,there is a limit on the size L of the essential part of the accelerating region in the field. Thescattering centers of the acceleration regions are moving with a characteristic velocity of βc(see Section 4.1), which implies that L has to be larger than 2Rg/β, and thus using formula3.1 [23]:

BµGL100kpc > 2E20/Zβ. (3.2)

The figures in Figure 3.1 are named after A. Hillas, who first described these limitations onthe acceleration regions. These limitations on the acceleration sites are simply based on thegeometry, where the particle should not leave the accelerator before it gains the required energy.For sites lying below the Hillas-diagonal in Figure 3.1, particle acceleration up to UHE isnot possible. This means that supernova remnants (SNR) are not a candidate for protonacceleration up to 1020 eV. However, these sites do remain as key candidate to accelerateparticles up to 1017 eV. Actually, acceleration of cosmic particles within supernovae has beenthe most excepted proposition and its mechanism (see Section 4.1) was first to be described byFermi already in 1949 [24, 25].

Figure 3.1: Left: The original Hillas plot. Constrictions to cosmic ray acceleration sites areonly based on geometry. Also shown the Large Hadron Collider (LHC). Right: The updateversion of the plot with also constraints for radiation losses for 1020 eV protons. The originalHillas criterion is the thick line. The shaded areas are allowed by the radiation-loss constraintsas well: the different colors represent the different acceleration models [30]. The acronyms Sy,RG and BL respectively stand for types of galaxies, i.e. Seyfert, radio galaxies and blazars.

The field of astrophysics experienced enormous progress since the article of Hillas, and therefore3.1 also shows a modified version of the original plot. Potential astrophysical accelerators areshown based on measurements or estimates of these, including some unlikely UHE sources (seesection 4.1) as Gamma-ray Bursts (GRBs), Anomomolous X-ray Pulsars (AXPs) and neutronstars (NS). Also, a distinction is shown between several active galaxies which differ in magnetic

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The origin of cosmic rays

field strength by many orders of magnitude [30]. Finally, the acceleration sites are posed witha restriction due to radiation losses. These radiation losses are inevitable in the acceleratingprocess and the constraints to accelerators by these losses were found by Medvedev [26].

The GZK-cutoff limits the sites of UHECR to be closer to us when the particle’s energy in-creases. From the results of HiRes [20] and PAO [21], this should tell us that those sources ofcosmic rays should not be to distant. Extrapolation of Figure 3.2 shows that with 90% proba-bility, protons with energy above 5×1019 eV come from no further than 250 Mpc, and when theenergy increases above 1020 eV no further than 75 Mpc. This being a criteria for the determin-ing of the origin of the UHECR, active galactic nuclei (AGN) seem an appropriate candidateas a source [27, 28, 29]. Among the remaining acceleration sites according to Figure 3.1 are themost powerful AGN (AD) and their jets, lobes (L), knots (K) and hot spots (HS) [30]. AGNconsist of a compact region in the center of a galaxy, which has a much higher luminosity thannormal. The AGN are powered by the accretion of matter onto a super-massive black hole(BH). When the cosmic ray particles have high enough energies, they can point back to theirsource. The Pierre Auger Collaboration explored the correlation between the arrival directionsand the positions of known AGN [31]. They indicated a cutoff for the maximum distance ofan AGN, a cutoff for the minimum energy of the cosmic rays and the angular separation ofan event from some AGN. Initially, a 98% correlation was found of events with high enoughenergies (above 6× 1019 eV) with AGNs at a distance less than ∼ 75 Mpc, which agrees withthe GZK-cutoff. However, later results weakened the correlation [32]. In Figure 3.3, 69 cosmicray arrival directions detected by the PAO are shown as well as the known locations of AGNs.The 38% correlation found by the PAO is not very convincing, while the observation that theheavier composition of cosmic rays at higher energy [9] makes it harder to pinpoint back to thesource of these UHECR. However, the correlation can still function as a hint in the search forthe UHECR origin.

Figure 3.2: The GZK-effect limits particles with higher energies to originate from greaterdistances. [33]

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3.1. RESTRICTIONS ON THE COSMIC RAY ORIGIN

?

Figure 3.3: The circles of 3.1◦ are centred at the positions of 318 AGNs that lie within 75 Mpcand are within the field of view of the Pierre Auger Observatory. The arrival directions of 69cosmic rays with E> 55 EeV detected by the PAO up to 31 December 2009 are plotted as theblack dots in this Aitoff-Hammer projection of the sky in galactical coordinates. The solid linerepresents the border of the field of the view for zenith angles smaller than 60◦. Darker blueindicates larger relative exposure.

The results of the Pierre Auger Observatory can rule out other models which place the originof cosmic rays within our Galaxy, our in its halo. The measurements also limit models whichsay that cosmic rays could find their origin in exotic objects, such as topological defects, orby the decay of super-heavy dark matter particles [34]. This class of theoretical models of theacceleration process is called the ’top-down’ scenario (see Section 4.3). In these models, thesuper-heavy dark matter particles should be relatively local since they should not be interactingwith the CMB. Therefore, the spatial distribution of the UHECR should be consistent withthe local (e.g. the galactic halo) matter distribution to avoid being discarded as cosmic raysource. These models also suffer from the low fraction of high energy photons measured in theCR distribution [35].

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CHAPTER 4

THE ACCELERATION OF COSMICRAYS

The theory of cosmic ray acceleration is divided in two scenarios, i.e. the ’bottom-up’-scenarioand ’top-down’-scenario. Where as the former consist of using individual components to explainfor the general observations, the latter is based upon explanation of the general observationsdown to individual components. The first actual acceleration mechanism for cosmic rays wasproposed by Enrico Fermi in 1949. In this model, stochastic collisions of particles with magneticclouds in the interstellar medium provide for the acceleration. Since then the understanding ofthese ’bottom-up’ acceleration scenarios has developed enormously. However, for a huge partof the spectrum (part (ii) in chapter 3) a modern version of this mechanism is still believed tobe accurate.

4.1 Bottom-up acceleration

Because supernovae (SNe) have sufficient energy to power the Galactic Cosmic Ray (GCR)population, they are still the most probable sites where cosmic rays can be accelerated to highenergies. The GCR suffers from ionization energy loss, nuclear reactions and loss by escapebut SNe energies exceed the critical luminosity to power the GCR [13]. This energy could beprovided by a small fraction (±10%) of the kinetic energy released in supernovae, if a typicalGalaxy has a rate of about three supernovae per century. The process which describes theactual acceleration of these particles is called diffusive shock mechanism, or first order Fermi-mechanism. However, this mechanism has its limitations, which probably show as the Knee ofthe spectrum. Described is how the second order mechanism proposed by Fermi in 1949 works,succeeded by the more efficient first order mechanism, and why they fail for high energy cosmicrays.

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4.1. BOTTOM-UP ACCELERATION

Fermi second order mechanism

Stochastic collisions of particles with the irregularities of the interstellar magnetic field canaccelerate particles. Since a stationary, constant magnetic field does not do any work on theparticles, only time variation of the magnetic fields is allowed to accelerate particles throughthe inducted electrical fields. The process is shown in the simple drawing of Figure 4.1, wherea particle with energy E1 goes into the high density matter cloud and scatters (there are nocollisions in fact) on the irregularities of the magnetic field inside the (magnetic) cloud. Thepositive balance between the gains in the head-on collisions with these clouds of matter andthe losses in overtaking collisions provides for the acceleration. Now, the average motion of theparticle coincides with that of the magnetic cloud after a few of these scatterings. Consideringthe rest frame of the moving gas, the cosmic particle has a total energy of

E′1 = γE1(1− β cosθ1), (4.1)

where β is the mean velocity of the magnetic cloud in units of the speed of light in vacuumc,γ is the Lorentz factor and the primes denote quantities measured in a frame moving withthe cloud. Since all n scatterings are due to motion inside the magnetic field, they are elasticand therefore is the energy of the particle in the moving frame just before it escapes E′2 = E′1.Now if the energy is transformed back to the frame of the interstellar medium, our lab frame,we have the energy of the particle after its encounter with the cloud

E2 = γE′2(1 + β cosθ′2). (4.2)

Both equations are written for a particle which is already sufficient relativistic so that E ≈ pc.Substituting the formula of E′1 in that of E2, and finding the averages for cos θ′2 and cos θ1

one finds that the energy gain is given by 〈∆EE 〉 ∼ 4/3 × β2. The relative energy gain showsnot to be dependent on the charge of the particle nor the magnetic field strength, but onlyon the square of the velocity of the clouds. Because the second-order Fermi mechanism leadsto a power-law spectral distribution N(E) it fits the observed spectrum for the power lawN(E) ∼ E−α. However, propagation properties of the particles make it hard to predict thevalue of α by theory. The model also allows particles to gain only a little amount of energy,since the velocity of the clouds is about 10−4c and so 〈∆EE 〉 ∼ 10−8 . Also, considering theaverage distance between the magnetic clouds ( 1 pc), the lifetime of the cosmic particles (orderof Myr) and the collision rate of 1 per year, these particles will not be accelerated quick enough.

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The acceleration of cosmic rays

Figure 4.1: A particlewith energy E1 goesinto a cloud of mat-ter, where it acceler-ates due to its scat-terings on the irregu-larities of the magneticfield.

By considering the medium to be less inhomogeneous, the clouds of turbulent magnetic fieldare represented in idealization as clumps of matter transversing the galactic space at Alfvenvelocity vA in the plasma. This is a modern version of Fermi’s mechanism. The Alfven velocityvA is given by vA = B0√

4πρ, where B0 represents the background magnetic field, and ρ depicts

the matter density in the plasma. In this model, the scatterings are much more frequent thanin the original model and the acceleration is much more efficient [23, 36].

Fermi first order mechanism

The acceleration process of cosmic rays was found by several researchers [37, 38] to consist ofa strong shock wave. This process is more efficient than the second order mechanism whenthe velocity of the shock vs is larger than the Alfven velocity vA representing the interstellarmedium. In the downstream region of the shock frame the shocked plasma moves with velocityvp away from the shock (see Fig. 4.2). This means that in the laboratory frame the plasmawill have a velocity of vs− vp. Now when a particle from the upstream region collides with theshock front and is reflected afterwards, it will have an energy gain as 〈∆EE 〉 ∼ 4/3×β [39], where

β =vs−vpc , the relative velocity of the plasma flow and the difference with the second order

mechanism originates from the different average angles. This mechanism allows the particlesenergy gain to be first-order in β and thus the following acceleration will be more rapid. Thereis a probability each cycle that the particle is lost in the downstream and does not return fromthe shock. With a longer period in the vicinity of the shock, particles then have time to achievehigher energy. The maximum particle energy obtained in the acceleration region, following thesteps in section 3.1, can be Emax ≈ 1018 eVZβsRkpcBµG, with βs being the shock velocity inunits of c and BµG the magnetic field strength in microgauss.

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4.1. BOTTOM-UP ACCELERATION

Figure 4.2: The schematics of a shock-wave acceleration is the lab frame of the interstellargas, where the plasma behind the shock has a velocity of vs − vp.

These non-relativistic shocks precede the expansion of matter flowing at speeds larger than thespeed of sound in that medium, e.g. a supernova remnant (SNR). An advantage in acceleratingthe particles opposed to the second-order mechanism is that the collisions are always head on.In the case of collisions with clumps of matter (second-order) the energy gain is a result of thedifference between head-on collisions and the energy losses in the overtaking collisions.

Supernova acceleration

The acceleration process for the first part of the cosmic ray spectrum, which is expected toconsist of GCR particles, can be understood with the first-order Fermi mechanism. The signif-icant parameters in the process to make it efficient enough are the time ta the particle staysin the acceleration region and the time te it takes to escape it. Such mechanisms have in favorthat they predict a power law spectrum, of which the index α = 1 + ta/te. Therefore, to fit theslope of the spectrum we can say ta ∼ te. For as te decreases and ta increases with increasingenergy, the energy gain will stop to come to equilibrium with energy loss. When observingpossible acceleration sites, typical values for supernovae exploding in the interstellar medium(ISM) allow Emax = 1014 eV [40]. In a SNR, the high velocity ejecta from the explosion createsa strong blast wave when passing through the ambient medium. The research by Lagage andCesarsky showed however that the maximum energy of cosmic rays at such locations was re-stricted to 1014 eV. The shocks are mainly limited by two effects: the finite lifetime of the shockand its curvature. Since the diffusive forth and back motion of particles is naturally slow, theacceleration process is as well. When these particles were injected at the beginning of the SNRexpansion, and luckily remained trapped in the vicinity of the shock, then they can only havea limited amount of energy gained. Also, when the length of diffusion of the particles becomescomparable to the shock radius, considering the shock as a plane is invalid. The particles wouldnot gain the same amount of energy, since they lose some energy when travelling away from theshock and have a greater possibility of escaping the shock upstream. Using a minimum valuefor the diffusion coefficient Dmin, as the relation of Dmin to the turbulence spectrum mightdecrease the acceleration time for the particle, Lagage and Cesarsky found that the maximumenergy attained in a SNR expansion was Emax ∼ 1014Z/A eV/n, where A is the mass numberof the particle. Despite this limit, it was found that some types of supernovae yield a maximum

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The acceleration of cosmic rays

particle energy of a magnitude higher by using more recent estimates [41]. Also, the cosmic raysmay interact with the magnetic fields in the acceleration region, amplifying the fields, to reacheven higher particle energies [42]. Therefore, SNR are widely accepted as the most probableacceleration site of cosmic rays for part (ii) of the spectrum and the origin of the Knee.

Part (iii) of the spectrum, in the particle energy range from 1015 -1018 eV, is believed to be thetransition region from galactic to extragalactic origin. Pulsar winds, i.e. winds of relativisticparticles emitting by a rapidly pulsating and rotating star, are the accepted location werethese particles have been boosted. However, it could also be that this part is still governedby the acceleration process as described above. If this region represents the upper limit of anacceleration process, this would show in the relative abundance of heavy nuclei such as heliumor iron [43]. However, although the extends of at SNR accelerated particles contribute to thispart of the spectrum, according to Hillas [44] there also is another component, component ’B’.This extra, high energy component is actually obtained by subtracting two known componentsfrom the spectrum (see Figure 4.3). One component consists of the low energy galactic partof the spectrum, the other known component is the extragalactic part which is normalizedto observations above E = 1019 eV. The ’B’ components accounts for the gap between thesecomponents. Gaisser [43] states that the power needed to supply the component is to be lessthan 10% of the total power requirement for all GCR, and not much bigger than power observedin individual galactic objects. It is also possible that the gap is filled with ultra-heavy nuclei.

Figure 4.3: Cosmic ray intensity as a function of its energy. The two ’known’ componentsof the spectrum. The dashed line represents the galactic component, and the dot-dashed linerepresents to extragalactic component [45].

4.2 Acceleration mechanism of Ultra High Energy Cosmic Rays

The energies of cosmic rays in the end of the spectrum are extremely high and this is whatmakes them very interesting to study. The energies reach significantly higher than the mostsophisticated terrestrial accelerator at CERN (Geneva), which can reach a maximum of 7 TeVper beam in 2013. The detection of these high energy cosmic particles (see chapter 5) is

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4.2. ACCELERATION MECHANISM OF ULTRA HIGH ENERGY COSMIC RAYS

done through secondary particles, created by a large shower when the primary cosmic raysenter the atmosphere. To improve our understanding of this particles, extrapolation of particleaccelerator results is needed. However, acceleration models of these UHE are present, andupcoming observations are necessary to discriminate between them.

The source of UHECR must hold certain conditions [45]. First, the site must be able topower the acceleration and therefore the luminosity of the source may not be less than Lp ∼2 × 1045 − 3.5 × 1046 erg Mpc−3 yr−1 depending on the produced spectrum. Extragalacticsources fulfilling this criteria are active galactive nuclei (AGN) and gamma-ray bursts (GRBs).However, to be considered as the main source of UHECR, GRB do not have sufficient power.

The second requirement for extragalactic sources contains the power-law cosmic ray spectrum.To produce a power-law spectrum up to the highest energies, the source must accommodatethe GZK suppression. AGN relativistic shocks, GRBs and frictional acceleration at the sidesof AGN jets are discussed to accelerate the particles. For Emax ∼ ZBRβs, GRBs show notto have sufficient power to account for the high energy end of the spectrum. Again, AGN doshow to fulfill the condition.

AGN acceleration

AGN are powered by matter accretion onto a super-massive 106 − 108M� black hole at thecenter of a galaxy. The recent analysis which considers the AGN spatial distribution by theirhard X-ray flux supports AGNs to be a candidate for the origin of UHECR [46]. Also, AGNwithin 100 Mpc are correlated at a significant level of 98 percent. Beyond ∼ 100 Mpc thecorrelation sharply decreases, suggestion the GZK suppression. Now, the big question is: canAGN accelerate up to the ultra high energies?

Active galaxies can be roughly placed in the following categories: Seyfert galaxies, radio galaxiesand blazars. Seyfert galaxies are spiral galaxies, are radio weak and do not possess large scalerelativistic jets. Radio galaxies and blazars are radio loud elliptical galaxies where relativisticjets are present. The extensions of AGN are supposed to be the regions where UHECR can beaccelerated [20, 21] and are shown in Fig. 3.1. In contrast to Seyfert galaxies, where no jetsoccur, radio galaxies and blazars do allow jets. They are strongly collimated relativistic flowsof kinetic energy powered by the central black hole. When a relativistic jet is present, it canbe accompanied by the internal shock regions (knots), thermal shock regions (hot spots) andthe extended regions in the intergalactic space that are powered by the jet after its termination(radio lobes) [30]. Since Seyfert galaxies, low power radio galaxies and low power blazars donot have these regions, they are not considered to be able to accelerate up to UHE.

In powerful radio loud AGNs (i.e. the subclass FR II radio galaxies) the jet is slowed downvia strong terminal shocks, which are considered to be the hot spots. When the shockedplasma then expands sideways and envelopes the whole jet system it is called the cocoon.This cocoon can be considered as a by-product of the interaction between the AGN jets andthe surrounding intracluster medium. The internal energy of the shocked plasma continuouslyinflates this cocoon. The expansion speed Vc of the hot cocoon surrounding a relativistic jetin AGN, is dependent on the luminosity of the jet Lj and the velocity of the hot spot speedVh as Vc ≈ [Lj/(ρVh)]1/4t−1/2, with ρ the external gas density. Using this together with theexpression for the maximum cosmic ray energy earlier mentioned in the section, we can see

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The acceleration of cosmic rays

that the proton maximum energy is decreasing with increasing jet length from 1 kpc to 10 Mpcfrom Emax = 1020 eV to Emax = 1018 eV [45].

Radio lobes

The AGN radio lobes are also considered to be a good candidate to host the stochastic acceler-ation for UHECR. However, AGN with prominent radio lobes are rare and follow the observedcorrelation between UHECR directions and AGN. Only one exception, Cen A at 3.4 Mpc rel-atively close, is proposed to be an acceleration site [47]. Cen A is a complex and extremelypowerful radio source, which displays jets, radio lobes and a variable compact nucleus. Thefurther characteristics of the object strongly supports the object to be an active radio galaxywith a jet forming a relatively small angle with the line of sight. The acceleration process insuch systems was previously believed to consist of a first order Fermi mechanism with shockscreated like those in SNRs. However, because of kinematic restrictions the particles are unableto reach ultra-high energies in this process. When the shock velocity exceeds the Alfven speed,the first order is dominant but the acceleration region can not contain the particles. Therefore,in such a process, where the shock velocity is relativistic, the second order Fermi mechanismtakes over to attain ultra high energies. The feasibility of second order acceleration in radiogalaxy is found through the steady re-acceleration in certain hot spots [29].

4.3 Top-down acceleration

Recent observations concerning UHECR have definitely shown indications that favor the bottom-up scenario. However, the difficulties in the understanding of the acceleration mechanism, theGZK-cutoff and origin of cosmic rays lead to a different scenario as well. In the so-called ’Top-down’-scenario, the decay products of a supermassive X particles with mass mX >> 1020 eVaccount for UHECRs. In this scenario, there is no acceleration mechanism necessary. Thereare different ways the X particles can be produced, which determines their distribution. Ashort lifetime implies a continuous production of the particles. Therefore, if the particle orig-inated from a topological defect such as cosmic strings or magnetic monopoles left over froma cosmological phase transition that occurred in the early Universe, they would be evenly dis-tributed in the Universe. When produced only in the early Universe, these particles show adistribution identical of that of the local dark matter in the halo of our Galaxy. An advantageof non-astrophysical solutions is that they connect with new ideas beyond the standard model,such as the Grand Unified Theory (GUT) and supersymmetry (SUSY) and probe the condi-tions in the very early Universe. The observations of PAO and HiRes excluded the Top-downmodel, since the primary particles do not consist of the photons expected in such models [48].Obtained were 95% c.l. upper limits on this photon flux above the first direct bounds on theflux of UHE photons. These limits have put strong constraints on the model of the origin ofcosmic rays. The superheavy dark matter scenario does not hold as an adequate explanationof UHECRs. The results do show to be in agreement with the bottom-up scenario, since theexpected photon fluxes are well below the current bounds.

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CHAPTER 5

EXTENSIVE AIR SHOWERS

5.1 Air shower creation

Primary cosmic rays interact with the terrestrial atmosphere to create extensive air showers(EAS). The coincidence of these air showers with a single cosmic ray particle was found byPierre Auger [49]. His estimation showed that the primary particle energy needed to extendover 1015 eV to reach sea level and therefore relates the showers with the high energy end ofthe cosmic ray spectrum. Due to the low particle flux in this energy region, the correlationwith the EAS was critical for the detection of high energy cosmic rays.

EAS consist of three main components, i.e. an electromagnetic (EM), a muonic and hadroniccomponent (see Figure 5.1). Of these, the hadrons hardly reach the ground. The initial protonsand alpha particles cascade in the atmosphere. Most of the energy is converted to gamma raysvia π0 → γγ and ionization in electromagnetic showers. These high energy photons generatesubsequent EM showers of alternate pair production and bremsstrahlung starting at its pointof injection. At each hadronic interaction about one third of the energy will go to the EMcomponent. High probability of the re-interaction of these hadrons shows that most of theprimary energy will be dispersed in the EM part. The rapid multiplication of EM cascadescauses a large number of electrons and positrons in the air shower. Since these are the mostnumerous particles, the shower energy will eventually be dissipated by ionization losses.

Figure 5.2 displays the estimated vertical flux of the most abundant cosmic rays when propa-gating through the atmosphere, in those regions where the particles are most numerous, withthe exception of electrons. These particles originate from the interaction of primary cosmicrays with the air molecules, although some part of the protons and electrons are already abun-dant in the top of the atmosphere. Figure 5.2 shows clearly that neutrinos and muons are themost abundant particles reaching sea level. They are produced in the decay of charged pions,following π± → µ±+νµ(νµ). Also charged kaon decay can contribute to the muonic part, eitherdirect via K± → µ± + νµ(νµ), or via the decay of the intermediate produced charged pions.

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5.1. AIR SHOWER CREATION

Figure 5.1: An incident cosmic ray particle triggers an air shower.

Figure 5.2: From the intensity of primary nucleons with E > 1 GeV an estimation on thevertical fluxes of cosmic rays [50] from Equation 5.1. Negative muons with energy above 1 GeVare shown with the points.

The primary nucleon intensity is important to describe the particle flux in the EAS. For pri-maries with energies between a few GeV to a several hundreds TeV the differential flux is

IN (E, 0) ≈ 1.8 E−2.7 nucleons

cm2 sr s GeV. (5.1)

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Extensive Air Showers

Using equation 5.1, the flux of the primary cosmic rays can be described by a set of coupledcascade equations [50]. However, numerical or Monte Carlo calculations are needed to accu-rately describe all the decay and energy-loss processes. In limited regions however, analyticalsolutions show the vertical intensity of the nucleons at depth X (g cm−2) in the atmosphere tobe

IN (E,X) ≈ IN (E, 0) e−X/Λ, (5.2)

with Λ the attenuation length of nucleons in air. From this, a subsequent expression forthe vertical intensity of pions can be generated. The cascade equations are mainly based oninteractions and decays. In the case of pion flux Π, the loss due to decay and thus the decaylength dπ are dependent on X and on ρ, the local atmospheric density:

∆Π = −Π∆X

ργcτπ≡ − Π

dπ∆X. (5.3)

By analyzing the atmosphere, following [51], the relation between ρ and X can be defined by in-troducing a constant scale height, h0. This comes from the assumption that in an isothermal at-mosphere the ratio between pressure at vertical depth Xν (p = Xν) and density (ρ = −dXν/dh)remains constant. Then using the relation between ρ and X in the approximation that thezenith angle θ ≤ 60°, ρ ≡ Xcos θ

h0. The pion decay length can then be expressed as

1

dπ=

mπc2h0

EcτπXcos θ≡ επEXcos θ

, (5.4)

and can be the dominating term in the cascade equation when 1/dπ grows large. Thus, forwhen Eπ << επ = 115 GeV, the loss of pion flux by decay can not be neglected and

Iπ(Eπ, X) ≈ ZNπλN

IN (Eπ, 0) e−X/ΛX Eπεπ

. (5.5)

The quantity ZNπ is the spectrum weighted moment of the inclusive distribution of chargedpions from the interaction of incident nucleons with the nuclei in the air, and λN is the nucleoninteraction length. The value for ZNπ is so small that the intensity of low energy pions is muchless than that of nucleons. The maximum of this expression shows op at Λ ≈ 121± 4 g cm−2

[50], which equals an altitude of 15 kilometers, as seen in Figure 5.2 as well.

Muons in the atmosphere

The pion flux tells us a great deal about the high amount of muons detected at sea level. Thesemuons are nearly stable and have small cross sections for interactions, which allows them topenetrate the atmosphere. In this section, the production spectrum of the muons and therecovery of the primary particle energy is discussed.

Charged pions decay mainly into muons and their neutrinos (∼ 100% branching ratio). Theneutral pions mainly decay very quickly (τπ0 = 8.4 × 10−17s) into two photons, but thereis another component responsible for the muons. Charged kaons decay into muons with abranching ratio of ∼ 63, 5%. These are the main processes needed to describe the productionspectrum of muons.

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5.1. AIR SHOWER CREATION

An equation for the muon energy spectrum is dependent on the values of the interaction crosssections. Using values from terrestrial particle accelerator experiments, it is given by:

dNµ

dEµ≈ 0.14 E−2.7

cm2 s sr GeV× { 1

1 +1.1 Eµ cos θ

115 GeV

+0.054

1 +1.1 Eµ cos θ

850GeV

}. (5.6)

In this equation, the contribution of the pion (επ = 115 GeV) and kaon (εK = 850 GeV)decays are taken into account. This equation neglects however the contribution from charmand heavier flavors, as these will only contribute at high energy. Also, muon decay (Eµ > 100GeV/cos θ, εµ = 1 GeV) and the curvature of the Earth (θ < 70◦) are neglected. Comparingthe calculated muon flux with the observed flux, the equation 5.6 overestimates the flux sinceenergy loss and muon decay do become important below 10 GeV. After the production high inthe atmosphere, the muons lose about 2 GeV to ionization before reaching the ground. Thisenergy loss reduces the decay length of the muons significantly.

The relative contribution of kaons increases with energy. Where at low energy only 5% ofthe muons originate from kaons, at 1000 GeV this is 19%, and it increases asymptotically athigher energies. But at higher energies, the muon component of EAS will also be joined bythe so-called prompt muons. Charmed particles have very short lifetimes. Therefore, theseparticles almost always decay before they interact. For Eµ < εcharm ≈ 4 × 107 GeV the fluxof prompt muons can be calculated by looking at the branching ratio for charm decay and thespectrum weighted momentum of the distribution of a muon from charm decay. The ratio ofprompt muons to ordinary muons is dependent on these quantities as well. When Eµ exceeds1000 TeV this ratio will show the prompt muon component to dominate over ordinary muons.

The muonic component in EAS is subject to energy loss by ionization when traversing theatmosphere. Therefore, the muons in a shower show to build up to a maximum and thenslowly attenuates, which is quite different from the other components in EAS. The electroncontent of the shower attenuates relatively rapidly after the maximum. The flatter energyprofile makes the muonic component a better measure of the primary energy of cosmic rays,since fluctuations are reduced. This is one of the reasons why the muons are interesting tomeasure. To investigate the muon component and relate it to the primary particle energynumerical calculations are needed to be done. Experiments at sea level let Greisen [52] toparametrize the lateral distribution of > 1 GeV muons. The density of muons was expressedas

ρµ(m−2) = 18 (Ne

106)3/4 r−0.75 (1 +

r

320 m)−2.5, (5.7)

where Ne stands for the total number of charged particles in the shower front and r is thelateral distance in meters from the center of the shower. The equation expresses experimentalobservations and allows us to calculate the total number of muons Nµ with energy > 1 GeV inan air shower:

Nµ(> 1 GeV) ≈ 0.95× 105 (Ne

106)3/4. (5.8)

Also, the equation shows that the number of muons per square meter, as a function of r, is

ρµ(m−2) =1.25 Nµ

2πΓ(1.25)(

1

320)1.25 r−0.75 (1 +

r

320)−2.5, (5.9)

where Γ is the Gamma function. The formula relates Nµ to Ne more than to the primaryparticle energy, because its experimental basis. These quantities can be directly determined

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Extensive Air Showers

from measurements whereas E0 can not. To determine the primary particles energy E0 severalproblems need to be dealt with. A relationship between E0 and Ne is troubled since there arelarge fluctuations for Ne for a fixed E0 and vice versa. Therefore, the relation can only beinterpreted in an average sense, still dependent on the depth in the atmosphere. For verticalshowers with 1014 < E < 1017 eV at 920 g cm−2 (965 m above sea level) an estimate for thisrelation is given by Nagano [53],

E0 ∼ 3.9× 1015 eV(Ne/106)0.9. (5.10)

The shower maximum (on average) will be lowered in the atmosphere when E0 increases andso changes the relation between Ne and E0. Also, obtaining results for Ne by inverting therelation 5.10 is invalid because of fluctuations. Even tough all these complications, the spectrumof cosmic rays is determined in surface experiments for many years.

5.2 Detection of cosmic rays

The flux of cosmic ray particles with energy below 1014 eV is high enough to detect the cos-mic rays directly. For such particles, quite familiar detection techniques are used, such ascalorimeters carried in balloons to high altitudes or placed in satellites and space shuttles.These experiments tell us directly about the cosmic ray flux and composition up to this en-ergy. However, indirect measurement of higher energy cosmic rays is necessary, and EAS haveproven to be the useful tool. A short description of the three detection techniques is given here,and slightly more details are given for two of the most important cosmic ray observatories inthe next sections. Also, the recovery of primary cosmic ray characteristics for each detectionmethod is sketched.

Surface arrays

A typical EAS can range over billions of energetic particles which are spread out over an areaof 15 square kilometers. By detecting several particles at different locations, the verification ofthese particles originating in the same shower is easily made. To create an observatory whichcan detect the largest part of an EAS, a spread array of surface detectors (SDs) is necessary.This is the oldest method to (indirectly) measure cosmic rays.

To create a shower of such proportions, the incoming particle must at least have an energy above1014 eV, but this depends also on the altitude of the detector. The idea of the detector is that itsamples the charged particle component of the EAS at the earth’s surface and to determine thelateral distribution function. In the energy range mentioned, the lateral distribution functionis fairly broad, so counters are widely spaced to cover a large area. For the detection of theparticles, an array SDs can consist of scintillation counters or Cherenkov light detectors.

Scintillation counters are used in most experiments as the basic detector. They consist primarilyout of plastic scintillators which release a photon when a charged particle passed through thematerial. This photon carries information from the traversed particle, and are collected in PhotoMultiplier Tubes (PMTs). Via good timing resolution, the EAS angle can be measured. Thistechnique is also used in by NIKHEF coordinated HiSPARC experiment, where participating

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5.2. DETECTION OF COSMIC RAYS

high schools in the Netherlands have constructed a large array of detectors to measure highenergy cosmic rays (HiSPARC web).

Cherenkov detectors

Another technique to detect the charged particles in an EAS is the use of Cherenkov detectors.In a similar array as in the scintillator detectors, water Cherenkov basins are placed at largedistances. When a high energy charged particle passes through such a water tank with a speedhigher than c of that medium it emits Cherenkov light. An advantage of Cherenkov detectorsis that the EM component of the shower will be completely absorbed. The Cherenkov lightwill be converted in an electrical signal by PMTs. The pattern of counter hits and the pulseheights will allow a first determination of the core location of the EAS. The trajectory of theincoming particle is reconstructed via times of arrival in different stations, as the pulse heightshelp to determine the lateral distribution. The primary particles energy is hard to determine,since the lateral distribution function is not measured at the same depth of development foreach shower [54]. With the help of simulations and several assumptions the primary particleenergy can be calculated.

In the framework of Cherenkov light detection, a different technique to detect EAS is devel-oped as well. The charged particles produce Cherenkov light also when passing through theatmosphere, since the atmosphere is of higher density than the ISM. Therefore, as the atmo-sphere consists of several densities at different altitude, already by entering the atmosphereand traversing it the EAS exposes it self. Using PMTs to detect the Cherenkov light, thelateral distribution of the shower can be measured, as the total light flux in the shower. Usingsimulations, this technique can also be used to measure the primary particle energy.

Air fluorescence detection

Using air fluorescence as a technique to study and measure EAS was an idea developed in the1960s, where Greisen and his group successfully detected such signals. A complete detectorwas constructed later and will be discussed in the HiRes section.

By detecting fluorescence photons, the shower can be observed from a distance since the light isemitted isotropically and therefore is the one technique where not only the lateral distributionof the EAS can be measured, but also the longitudinal distribution. Therefore, this techniquehas many advantages over others. These fluorescence photons are emitted when an ionizingparticle excites nitrogen molecules in the atmosphere. Particles with primary energy greaterthan 1017 eV will have more than 108 electrons at shower maximum, so even with the smallfluorescence yield this allows a substantial number of photons. The fluorescence yield is onlymildly dependent on altitude as of atmospheric temperature.

Together with the relative time of arrival, the total integrated light is sampled by each PMTwhich pinpoints in a different direction. One problem in recovering the appropriate charac-teristics in this technique is the existence of sky noise. Scattered starlight, photochemicalatmosphere light and light pollution by man self are examples of background light contribu-tions. Therefore, the fluorescence detection method works mainly on clear moonless lights,whereas surface detectors can work regardless of atmospheric conditions.

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Extensive Air Showers

5.3 Current experiments working on cosmic rays

As the subject of cosmic rays still has still plenty debatable features, the interest of research iscontinuously high. Therefore, still new and improved observatories are constructed and usedto gather data of especially the low flux cosmic particles, the UHECR. So far, these improvingways of detecting cosmic particles has led to numerous results, but still have not solved at leastas much issues in the subject. The focus is on two observatories, since the detection methodsused are effective but differ in their aspects.

HiRes

The original Fly’s Eye detector operated from 1981 to 1993 and was joined by a second detectorin 1983. These two ”eyes” observing the sky were using the passage of the EAS throughto atmosphere and the subsequent produced nitrogen fluorescence light, which is given offafter excitation by the relativistic charged particles in the shower. This method circumventedproblems other detection techniques suffered, including Cherenkov light detection and surfacebased detector arrays. In these methods, the observations showed to be limited to smallareas and low event rates for high-energy showers, and suffered from a poor resolution of thelongitudinal shower development [56].

The Fly’s Eye detector, based in Utah, was constructed to gather data via this method. Thisdetector, had the specific ability not only to detect the highest energy cosmic rays at distancesof roughly 20 kilometer from the detector, but also to ascribe each event with enough certaintyto the energy of the primary cosmic ray and the longitudinal structure of the resultant EAS.

To increase resolutions and focus on the UHECRs, the Fly’s Eye was superseded by the HighResolution Fly’s Eye Observatory (HiRes), which operated from May 1997 until April 2006.Using the same technique as the originals Fly’s Eye detector, the new detector consisted out67 mirrors. The signal to noise ratio was improved intensively in this new detector.

Among many results, the final result of the HiRes experiment consist of the proof for theexistence of the suppression at ultra high energies, i.e. the GZK-cutoff.

Pierre Auger Observatory

The Pierre Auger Observatory (PAO) (Argentina) is one of the most important cosmic rayobservatories in the world. It is a collaboration of over 50 institutions and more than 250physicists [55] and was named after Pierre Auger. The observatory makes use of two differenttechniques to detect these EAS. At ground level, there is a surface detector array (SD) as wellas a fluorescence detector (FD). This FD is quite similar to HiRes [33]. The PAO combinesthis successful technique with that of the detection of the EAS particles, by using a huge arrayof water tanks, causing these secondary particle to produce Cherenkov light that is detectedby PMTs. This array is 3,000 km2 wide and has 1600 of these tanks, as the PAO is mainlyinterested in UHECR. The 24 optical telescopes are in addition to the SD to have complementinformation on these big events when occurring. They can detect the total energy of an EAS,which is necessary to determine the primary particles energy, which differs from SDs that onlydetect a part of the shower.

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5.3. CURRENT EXPERIMENTS WORKING ON COSMIC RAYS

Since the final stages of construction data has been gathered in the PAO, which led to bothconvincing and promising results. As well as the HiRes results have shown, the Pierre AugerCollaboration has shown the existence of the GZK-cut-off. This has several consequences forthe theories for the acceleration of cosmic rays, as mentioned before. To improve the coverageof the observatory, a northern hemisphere observatory is yet to be build, although it is yet tobe determined if this will carry through.

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CHAPTER 6

MUON DETECTION AND MUONLAB

From an educational point of view, the field of cosmic rays is an important one. Not only, is it afield of high current interest, but also it allows us to demonstrate the existence of extraordinaryphenomenons such as the theory of special relativity. In the Muonlab program, students getin touch with particle and astroparticle physics. Through the detection of secondary muons,originating from cosmic rays, it is possible to measure the velocity of these muons as well asthe muon lifetime. The research done concerned the detection of muons as an indicator of theprinciple of special relativity (SR), as well as the comfortable way of introducing the subject ofparticle physics to undergraduates and high school students. Therefore, after a description ofthe detector materials, a short introduction on the elementaries of SR and the experiments isgiven, followed by the adjustments of the Muonlab’s program software. The research allows amore comfortable use of existing and yet to be made muons detectors in the Muonlab program.

6.1 Muonlab program at NIKHEF

The Muonlab program at the National Institute for Subatomic Physics (NIKHEF) allows stu-dents to measure the lifetime and speed of muons at sea level. Using a classical time of flight(TOF) experiment, students can obtain an image of cosmic muons passing through the atmo-sphere. A TOF experiment measures the time of flight of particles to calculate the velocityof these particles. It typically consists of multiple layers (see Fig. 6.1) of scintillator platesattached to PMTs to create a high time resolution measurement.

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6.1. MUONLAB PROGRAM AT NIKHEF

Figure 6.1: Setup of TOF measurement in the Muonlab program, with the Muon Interface Boxattached two scintillator paddles.

Scintillator material is essential to convert the propagation of the muon in a measurable signal.As the muon is a charged particle, it releases photons when propagating through a piece ofscintillation material. The scintillation material in the Muonlab program is a plastic solid con-sisting of organic scintillating molecules in a polymerized solvent. These are typically detectorswith average dimensions of 1300x100x50mm. So with the average muon flux at sea level forhorizontal detectors to be 1 muon per cm2 per minute [50] we will detect 1300 particles perminute.

Preventions are made to avoid photons leaving the scintillator detector. The common wayto redirect escaping light is by external and/or internal reflection. A good choice to reflectthe photon is basic aluminum foil. Also, with a thin layer of air between the scintillator andthe aluminum, the internal reflection is maximized as air has an index of reflection (nair=1)which is less then the refraction index of the scintillator nscint (i.e. typically nscint = 1.5). FromSnell’s law, we can find the critical angle for which the incident light is totally internal reflected.Snell’s law states that the ratio of the angles of incidence θi and refraction θr are equal to the

opposite ratio of the indices of refraction of the respective medium:sin(θi)

sin(θr)=

noutnscint

. For total

internal reflection we can derive the critical incident angle θc for when θr equals 90°. At thisangle, sin(θr) = 1 and therefore

θc = arcsin

(noutnscint

).

When the incidental angle is larger then θc, total internal reflection occurs, while if the incidentangle is less then θc there is partial reflection and the remainder is transmitted. With the useof air, θc ' 41°. The scintillator material is subsequently covered in black tape to preventany photons getting into the detector, besides those released by the charged particles. As thegeometry of the scintillator does not perfectly fit the window of the PMTs, a light guide ofPerspex (PMMA) is used, which reflects the light internally back and forth between the interiorwalls to reach the PMT. The scintillator and the light guide are attached to a PMT such thatphotons can only leave the scintillator at the window of the PMT.

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Muon detection and Muonlab

Figure 6.2: The principle of a photomultiplier tube. The PMTs used in the Muonlab programhave a slightly different configuration, as the windows of the PMTs used are focused head-on.

A PMT is an electron tube device, which converts light into a measurable electric current.The typical process in a PMT is pictured in Figure 6.2. After the released photons enter thewindow of the PMT, they reach a photosensitive cathode, followed by an electron collectionsystem, a dynode string and eventually an anode from where the final signal is taken. Whenthe photon reaches the photocathode, it will release an electron due to the photo-electric effect.The response of a PMT to an incident photon is unfortunately not always the release of anelectron, as this process depends on the frequency of the incident photon and the structureof the material. The actual spectral response of a PMT is therefore defined by its quantumefficiency η(λ),

η(λ) =number of photoelectrons released

number of incident photons on photocathode,

with λ the wavelength of the incident light. As the spectral response of photosensitive materialsis well known, one can select the proper PMT to the light coming from the scintillation materialto fit the maximum quantum efficiency.

During operation, the cathode, dynodes and anode are applied with a high voltage (HV), tocreate a potential ladder along the length of the PMT. The applied voltage will direct andaccelerate the electron towards the first dynode, where it transfers some of its energy to theelectrons in the dynode. Secondary electrons will be emitted and these are accelerated towardsthe next dynode where the process is repeated and finally collected in the anode. The gain ineach dynode δ is clearly a function of the potential difference Vd between the dynodes and aconstant K of the material used, so the gain in the complete dynode string G is dependent onthe amount of dynodes n,

G = δn = (KVd)n

A typical gain in a PM is 106−108. The gain stability is one of the crucial characteristics of thePMT and can be influenced by different factors, and should therefore be monitored extensively.

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6.1. MUONLAB PROGRAM AT NIKHEF

Assembling more muon detectors

The current scintillation counters in the Muonlab program are using Philips PMTs, which arecostly, typically e500,- per piece. However, as NIKHEF was granted with the former ZEUScalorimeter R580-12 type PMTs from HERA in Hamburg the number of Muonlab detectors canbe enlarged to serve a larger public. These PMTs have a photocathode made from Bi-alkali,which has a spectral response of 300 to 650 nm, and therefore is perfectly suited to the lightcreated in the scintillation material. The 10 nodes to produce the potential ladder create atypical gain at 25 � of 1.1× 106.

Table 6.1 General specifications of R580-12 PMTs. From hamamatsu.com.

Parameter Description Unit

Spectral Response 300 to 650 nm

Wavelength of Maximum Response 420 nm

PhotocathodeMaterial Bi-alkali -Minimum Effective Area �34 mm

Window Material Borosilicate glass -

DynodeStructure Linear focused -Number of Stages 10 -

For the calorimeter in Hamburg, extensive PMT testing was inevitable, to achieve a satisfac-tionary data set. Automatic testing was involved, testing the PMTs on their dark current, gain,linearity, long-term stability and gain stability under different intensities of dc background light[57]. The test for dark current is a test to measure the background current when no photons areentering the PMT window and is together with the tests for gain, linearity of the PM, long termstability and gain stability under different intensities of high significance. However, regardingthe PMTs used in the Muonlab program, the necessity for those tests is lower, as not the pulsesignal it self is essential for the measurement but only the timing of the signal. Therefore, PMTsignals are analyzed on an oscilloscope in the program, to exclude noise from being interpretedas muons releasing photons in the scintillator material. The analysis of the PMT signal on anoscilloscope allows users to determine the threshold of those signals included in the TOF andlifetime measurements. A PMT signal coming from a muon passing through the scintillatorin the Muonlab program is typically of the order of hundreds of mV. Therefore a thresholdset at roughly 20-30 mV discriminates well between true particles passing through and thebackground noise. A quantitative research of further PMT characteristics is not performed.

The most essential characteristic for the PMTs to work properly and efficient has been inves-tigated. The applied voltage on the PMT to generate secondary electrons is related to theefficiency of the PMT as a proper output signal was needed to test for decent sensitivity. Thehigh voltage (HV) applied to the PMTs currently operating in the Muonlab program is differ-ent from that of the R580-12 PMTs. The operating HV can be determined using a coincidentcounter test, from where a stable efficiency is determined using count rates.

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Muon detection and Muonlab

Table 6.2 Maximum ratings for Hamamatsu R580-12 PMTs. From hamamatsu.com.

Parameter Value Unit

Supply VoltageBetween Anode and Cathode 1750 VBetween Anode and Last Dynode 350 V

Average Anode Current 0.1 mA

The specifications given by the manufacturer are shown in Table 6.2. The nominal voltageapplied to a R580-12 PMT is in the range of 1200-1600 V. However, wear and tear may havecaused that the PMTs have a lower efficiency in both the photocathode and the dynode chain.This can be compensated by applying a higher HV, but also leads to an increase of the noise,for example from electrons sparking through the PMT when the HV is high enough to extractelectrons from the dynodes even without an incidental photon.

Figure 6.3: Drawing of the setup of the count rate measurement. Two scintillator paddles (Aand B) are placed above each other, while the tested PMT is attached to a scintillator paddle(C) which is placed perpendicular between paddles A and B.

The appropriate HV for the PMTs from Zeus were tested in a scintillation counter operation,using real cosmic particles and three rectangular scintillator counters. In this setup, whichis shown in Figure 6.3, two counters were mounted perfectly above each other, while theattached PMTs were applied with default HV of 1600 V. Tested PMTs were attached toa third scintillation paddle which was placed perpendicular in between, with roughly 10-15cm2 of scintillator material overlapping with the other scintillation paddles. All three outputsignals were analyzed using a discriminator (set at 30 mV), a coincidence unit and a counter.By starting at the low voltage end for the tested PMT, very few counts were made by thecoincidence counter. By integrating over time, the total amount of counts rises when theapplied HV is rising. The measurement is a so-called plateau measurement (see Figure 6.4).It rises steep in the beginning and then flattens, so it can be interpreted as a plateau. It isknown from previous PMT testing that the curve rises sharply again after the plateau. Thelatter rise is due to the regeneration effects in the PMT, e.g. the sparking and discharges inthe dynode chain. This rise has not been detected, as the maximum input voltage was notsufficient. Nevertheless, the flattening in the curve indicates a region of HVs at which the

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6.1. MUONLAB PROGRAM AT NIKHEF

PMT is stable and as efficient as possible. The PMTs should be applied to the voltage in themiddle of the plateau, to make sure that occasional changes in the applied voltage or drifts inthe PMT gain do not bear severe counting variations. The absence of the second rise in thecurve makes it hard to determine the exact middle of the plateau. However, the HV can be setsafely 50V higher than the turning point, which is determined at the first of two subsequentmeasurements were the count rate increases with less than 10 %.

Figure 6.4:Scatter plot ofPMT high volt-age vs. countrate s−1 forthree R580-12PMTs usingthe triple coin-cidence setupof Figure 6.3 .The plateaus arereached at 1600V for all threePMTs.

To test more PMTs, a different method was involved. Using an optic fiber, illuminating with apulse frequency of 1000 Hz, the output signals were analyzed for over 20 PMTs ( 10 are shown inFigure 6.5). This was done to understand the response of the PMTs to an incoming light source,as such PMTs are normally used to gain information of the energy of an incident particle in thescintillator, which is represented in the pulse height. However, within the Muonlab program,the pulse heights can only indicate that the Zeus PMTs are still very sensitive despite the wearand tear of the past two decades and that the applied HV for different PMTs can range roughly250 V to produce similar pulse heights. However, a higher sensitivity is no indication for thelocation of the plateau, while a clear relation to the count-rate was not found.

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Muon detection and Muonlab

Figure 6.5:Output pulseheights ofPMTs (10showed) vshigh voltagewith con-stant pulseillumination.

To supply sufficient voltage for the PMT, the output voltages which can be set by the MuonlabInterface Box (MIB) needed to be converted. Standard settings in the program allow for anoutput USB voltage between 0,3 and 1,5 V. Initially, assumptions were made that an existingpower converter ( converter A), rising the voltage to 24 Volt, could not provide for sufficientHV to reach the PMTs plateau and the second rise in the count-rate due to noise and sparkingelectrons. Therefore, a new converter (converter B) was constructed which could subsequentlyallow voltages of roughly 5,5 V to 27,5 V. Converter B was investigated for implementation inthe Muonlab program. It was found that the discrepancy between the voltages measured afterthe voltage converter was very minimal, so we could assume that the voltage converter didnot create any variations in the voltages applied. In Figure 6.6 one can see the stability of B,which also shows the HV in the PMT as a function of the applied voltage from B. However, fornot completely understood reasons, B initiated severe complications. While the hardware wasworking proper independently, setting up the MIB with converter B and the computer createdconnection errors (see Discussion). It was therefore decided to continue with converter A. Ascan be seen, applied voltages up to 24 Volt can result in a HV of about 1800 Volt. Figure6.4 shows that the PMTs have reached their counting efficiency at that voltage. However, aconsequence of this is that the second rises in the counting rate due to noise can not be found.Also important for the MIB is that currents remain low, well below the specifications of the

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

MIB, which has a maximum of 200 mA.

Figure 6.6: Averages of input voltages and output voltages, for 14 R580-12 PMTs.

Figure 6.7: Theaverage currentthe PMTs pullwith increasingHV. It showsthese PMTs arecompatible withthe MIB.

6.2 Muonlab as an introduction in Special Relativity

One of the fundamental theories in the early years of particle physics was the theory of Yukawain 1934. The theory would explain why the neutron and proton were attracted to one anotherby some sort of field. This field was quantized and Yukawa was searching for a particle whoseexchange would account for the known features of this strong force and would have a mass of300 times that of the electron. In the search for support for the strong force theory, particlephysicists searched in cosmic rays for new particles as no particle accelerators were available.However, the new found particle by Anderson and Neddermeyer in 1936 in cosmic rays was ofa different mass. While the true particle to describe the strong force was found to be the pion,the particle discovered by Anderson and Neddermeyer was the muon.

In contrast to pions, muons do not disintegrate long before reaching the Earth’s surface. There-fore, the muon was an excellent candidate to verify the theory of special relativity. In the theory

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Muon detection and Muonlab

of SR, the relative motion of bodies causes time dilation for the moving object, i.e. the bodieshave a reference frame in which time is moving slower. As in SR relativistic particles, i.e.particles which move with or near c, undergo this time dilation, this would account for thelarge observed number of muons at sea-level, which was sixteen times of that expected withoutdilation. Rossi and Hall were the first to verify this in 1941 [58]. As described in section5.1, these muons are created when cosmic ray protons collide with nitrogen or oxygen in theatmosphere at an altitude of about 10-15 km. In classical mechanics, these muons which havean average lifetime of τ = 2.2µs in the rest frame, could reach only an average distance ofcτ = 659 m when they are travelling with the speed of light.

Software and Muonlab program

A quick verification of the muon lifetime and speed, to introduce the extraordinary phenomenonof SR, can be done with the MuonlabII.2 program. The Muonlab program is used to setup, measure, understand and analyze the TOF experiment, the propagation speed of light inthe scintillator material, and the lifetime measurement. The initial MuonlabII graphic userinterface (GUI) was constructed with NI LabWindows�/CVI 8. LabWindows allows usersto easy construct and design user interfaces. Therefore, the MuonlabII GUI was designed insuch a way that users could set their desired PMT voltage, signal thresholds, USB-connectionport, measurement method and histogram settings, to easily start their TOF and lifetimemeasurements. These measurements are gathered in 8-bit data set, where the first two bits areused to determine from which PMT the first signal arrived. The other bits are used to expressthe measurement value waarde. This value is converted according to the appropriate factor permeasurement method: waarde ∗ 12, 5/24 ns for the TOF measurement and waarde ∗ 6, 25 nsfor the lifetime measurement. These converting factors simply originate from the experimentalresolutions. Both values can provide the proper measurement values with sufficient accuracy.Together with a hit counter, the measurements are displayed in a histogram in the program.From here, the student can interpret the data further and see whether or not the data that iscollected is a proper representation of the experiment done.

In continuation and enhancement of the program, MuonlabII.2 was constructed. Although someanalyzing functions were available in newer NI LabWindows�/CVI 9, these functions could notbe used to analyze the data to full satisfaction. For example for the lifetime measurement, theExpFitEx curve fit of LabWindows which was used in MuonlabII, fits an exponential curve usingeither the method of Least Squares, Bisquare or Least Absolute Residual. These methods aremainly used to find the amplitude and damping of the exponential function. Although thesemethods are definitely useful and can provide one with the proper solutions, they are onlyefficient when a significant amount of data is gathered and bins will be filled with more thanone hit. This comes from the fact that one can not say much about the exponential functionas ln(y) = 0 when y = 1.

Therefore, in MuonlabII.2, the function ’Curve Fit’ is constructed which allows the user to fitthe histogram with respect to the exerted measurement. In the case of the TOF measurement,a Gaussian function is fitted to the delta times, which are the time differences between theparticles arriving in the first scintillator paddle and the second paddle. The measured valuesare represented with the fitted graph, while the calculated values are displayed in text boxes. Inthe case of the lifetime measurement, the ”curve fit” uses a Maximum Log Likelihood function.

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

Delta time

The TOF measurements use coincidence to measure the speed of a particle passing through thescintillators, with the set up as in Figure 6.1. The ’Delta Time’ mode in the Muonlab II.2 userinterface registrates the delta times. By varying the distance between the scintillator platesone can find a good estimate for the speed of the muon. However, there are several things oneneeds to take into account.

� The resulting distribution of delta times will consequently follow a normal or Gaussiandistribution. The Central Limit theorem states that if independent random variablesx1, ..., xn are distributed according to any probability distribution functions (pdf’s) withfinite mean and variance, the sum of these variables y = Σn

i=1xi will have for large n apdf that approaches a Gaussian distribution. This pdf P (x) is given for a mean value< x > and a standard deviation σ:

P (x;< x >, σ) =1

σ√

2πexp (−(x− < x >)2

2σ2). (6.1)

The distribution of the delta times follows the Gaussian distribution with mean value< x > and standard deviation σ. The mean value x can be determined with the estimator

Sx = x =1

n

n∑i=1

xi (6.2)

with x is the sample mean. This estimator is a good estimator as it is unbiased (E{x} =<x >) and consistent ( lim

n→∞σ2(x) = 0).

A good estimator for the variance can be found using

Sσ2(x) = σ2 = σ2(x) =1

n

n∑i=1

(xi − x)2 (6.3)

where σ2 is the sample variance and x is the sample mean. Also, this estimator isunbiased and consistent for large values of n. Now, as the values < x > and σ are found,the function of formula 6.1 is shown in the histogram using n√

2πσ2for the amplitude

after normalization. Assumed is a flat background which is gathered from one side ofthe distribution, since the distribution is assumed symmetric. Typical distances for theexperiment are in the magnitude of meters, so measurements far away from the mean canbe considered as background and the probability function goes to zero for large values ofx. This background is subtracted from all measurements. The separation distance andits error can be inserted in the GUI and allows MuonlabII.2 to calculate the speed of themuons and the error in units of cm/ns and c, after subtraction of the measured offset.

� When separating the scintillators with the smallest distance, i.e. completely overlappingwith no separating distance, there will still be an offset delta time measured. This comesfrom occasional sparking PMTs and incidental interfering particles, which happens whenone particle goes through one scintillator and another passes through the other scintillator.

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Muon detection and Muonlab

Although the chance for this is relatively small, both effects lead to an offset measurementof the delta time. Therefore, before performing a TOF measurement, first the offsetmeasurement is necessary to be determined.

Figure 6.8: The setup for the offset measurement. Two scintillator paddles placed on topof each other, attached to the MIB. It is recommended to use one longer cable to delay themeasurement to exclude measurements with very small delta times ( ∆t < 2 ns).

Since in the offset measurement delta times are really small, the Muonlab Interface Boxcan not decide for all measurements which signal arrived first (see Discussion). Therefore,it is recommended that in order to avoid this complication in the offset measurement,one uses a delay cable of 2 or 3 meters.

� The total muon intensity at sea level is obtained to be

Iµ = Iµ(θ = 0) cos2θ, (6.4)

for not too large zenith angles θ. Therefore, most particles are assumed to pass straightthrough both scintillator paddles, indicating one certain delta time, ignoring minor speedvariations. However, the particles arriving with a certain θ will dilute the measurementsas some are less abundant but also have to cross a different distance in comparison to theparticles which follow Iµ(θ = 0). In the case of the standard Muonlab scintillator platesthis smears delta times up to 20% for separation distance > 200 cm.

When the offset measurement is done, one can separate the scintillators to perform the defaultTOF experiment. When the offset delta time and the separation distance and their standarddeviations are filled in, the Muonlab II.2 program automatically calculates the center if thedelta times, subtracts the offset from it and calculates the velocity of the propagating muonsand standard deviation of it. Figure 6.9 shows such a measurement in the Muonlab program,using the existing scintillation paddles, set at their appropriate HV, and the calculated muonspeed of 0.99± 0.017 c, in accordance with the theoretical value of 0.98c.

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

Figure 6.9: Part of the graphic interface of the MuonlabII.2 program, for 1550 speed measure-ments.

Propagation speed

The various incident angles of the muons make the propagation speed of the released photons inthe scintillator an important subject in the analysis, as the delta times are also dependent on thetime spent by the photon in the scintillator plate. In the case that the particles will pass throughboth scintillator plates with the biggest possible angle θ, the difference in arrival time of thesignals due to the propagation time inside the scintillator can go up to 1300 mm/0.6c = ±7, 4ns. The ± symbol reflects the sign of the angle. The propagation speed through the scintillationmaterial is also part of the experiment. In this part, one scintillator paddle is fixed while anotherscintillator paddle is placed perpendicular to the former, such that there is a relatively smalloverlapping area. From a delta time measurement one can find the speed of propagation of thephotons through the material to be ∼ 0.60c, which agrees roughly with the refractive index ofthe scintillator material ≈ 1, 4− 1, 6.

In an extensive version of the propagation time measurement, using configurations as shown inFigure 6.10, not only the propagation speed inside the scintillators can be calculated. The marks(on scintillator 1 marks A,B,C, on scintillator 2 marks D,E,F) on the two scintillators have anintermediate distance of 50 cm. The use of a delay cable attached to one of the PMTs avoids

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Muon detection and Muonlab

any measurements with really small delta times and the accompanying complications. Figure6.11 shows 9 plots of delta time measurement for all 9 possible configurations. These deltatimes follow the Gaussian distribution described in formula 6.1. However, in configurationsDC, EC and FA, we also see measurements being spread out - to the left (DC,EC) and to theright (FA). This spread comes from the different lengths of the paths of the photons insidethe scintillator. In the configurations where the relative path is small (e.g. from the center ofD inside the scintillator paddle straight to the PMT) the difference in length with the pathsof those photons which move in the direction of the PMT with an angle θ and get reflectedinside the scintillator is relatively large. This difference in path length is only important incases where one measures delta times close to the PMTs, as the relative difference in pathsin configurations (FC) far away from the PMTs is small. The count rates measured in thisexperiment reflect that some created photons which traverse away from the PMT can attenuatewhen propagating through the relative large path in the scintillator and therefore cause for alower count rate. Another effect of the material on the delta times is that the outcoming pulseof the PMT is spread out since not all the light hits the PMT simultaneously and thereforebiases the timing. This effect has not been further investigated.

Figure 6.10: By positioning two scintillator paddles in several perpendicular configurations, thepropagation time of photons inside the scintillator material can be found. The configurationof the scintillation paddles themselves are identical and the separation distance between marksis 50 cm. In the configuration the R580-12 PMTs are shown.

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

Figure 6.11: Grid of 9 delta time plots following the configurations shown in Figure 6.10. Fromthese plots one can derive the propagation speed of light in the scintillator to be near 0.60 c,and also understand that the relative path of the created photon in the scintillator can spreadout the delta times (DC,EC,FA). A delay cable of 3 meters is used to avoid complications nearvery small delta times.

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Muon detection and Muonlab

Lifetime

In the lifetime measurement, only one scintillator paddle is used. Although higher energymuons simply pass through the plate, there is a chance that the lower energy muons will decaywithin the material of the scintillator plate. When this occurs, primarily a photon is releasedby the muon when entering the paddle and a pulse is measured in the PMT, opening the timinggate, just as with the delta time measurement. However, when the muon then decays in thescintillator it releases another photon when µ± → e± + νµ(νµ) + νe(νe). This will close thetiming gate, and the time elapsed is representative for the lifetime of the particle stopped inthe paddle.

In the experiment we have a sample of decaying particles. This decay is a random process,and therefore we need to describe the probability distribution P (t)dt to observe a particle notdecaying from 0 to t and decaying in the time interval t+dt. The distribution describing this isthe Poisson distribution. If n is a very large discrete number and λ is the expected value for thechange in n per time interval, the probability that a muon will decay in one subinterval is λt/n.Therefore, the probability that the muon will not decay in this time interval is (1− λt/n) andthe probability that it will not decay in n intervals will be (1− λt/n)n. Thus, the probabilityfor the particle to not decay from 0 to t is equal to (1− λt/n)n, while the probability to decayin the interval from t+ dt equals λdt:

P (t)dt = λ(1− λt/n)ndt. (6.5)

Now, as the particle can decay continuously instead of within discrete intervals, we should takethe limit n→∞ and use limn→∞(1− λ

n)n = e−λ to get:

limn→∞λ(1− λt/n)ndt = λe−λtdt, (6.6)

which is normalized (∫∞

0 P (t)dt = 1). For the lifetime of the particle we have the expectationvalue for λ = 1

τ0and therefore the probability for an individual muon to decay in the scintillator

to be

P (t; τ0) =1

τ0e− tτ0 . (6.7)

To get a quicker perspective on the measured lifetimes of the muon than those provided byLabWindows, the Maximum Likelihood (ML) method can be used to determine the values ofτ0, σ and the amplitude. The concept of likelihood depends on the combined probabilities tofind, in n measurements, the decay times t1, t2, ...tn and is determined by:

L(t1, t2, ...tn;κ) =n∏i=1

P (ti;κ) =n∏i=1

1

κe(− ti

κ) (6.8)

where here κ is used for the unknown quantity representing the lifetime of the particle. Withthis concept of likelihood determined we can search for the maximum likelihood. The MLmethod states that the best estimate for κ is the value which maximizes L(κ) and thereforealso maximizes lnL(κ). The value of κ can be found by solving the equation

dlnL(κ)

dκ=

n∑i=1

dlnP (ti;κ)

dκ= 0. (6.9)

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

Using equation 6.7, we find

dlnL(τ0)

dτ0=

n∑i=1

(− 1

τ0+tiτ2

0

) = 0→ τ0 =1

n

n∑i=1

ti. (6.10)

So by taking the average of the measured decay times, we can find the actual lifetime of theparticle. However, we can not use all the measurements as the measured values in the firsthundred of nanoseconds are not reliable. The selection of the zoom of the x-axis (indicatingtime) in the histogram can be done in the GUI of MuonlabII.2 and therefore allowing users todetermine themselves which values are included in the analysis. To cope with this, we need touse a weight function to re-normalize the probability function:

g(τ0) =

∫ ∞tmin

1

τ0e

(− tτ0

)dt = e

(− tminτ0

)

→ P (t; τ0) =1

τ0

1

g(τ0)e− tτ0 =

1

τ0e

(tminτ0

)e

(− tτ0

).

This will show in lnL(τ0) as

lnL(τ0) =n∑i=1

(−ln(τ0) +tminτ0− tiτ0

).

Numerically the maximum value of for lnL(τ0) is found, which will give the best estimate forτ0. The statistical error of this value can be found after a closer look at the shape of lnL(τ0) .Expansion of lnL(τ0) with a Taylor-series around λ = λ gives

dlnL

dλ(λ) =

dlnL

dλ(λ) + (λ− λ)

d2lnL

dλ2+ ... = (λ− λ)

d2lnL

dλ2(λ) + ....,

where the first derivative vanishes in the maximum of dlnL. Now, for a large value of n, wecan use the information of λ I(λ), which is defined to be I(λ) = −d2lnL

dλ2(λ), to show that the

lnL(λ) functions behaves like:

lnL(λ) = −I(λ)

2(λ− λ)2 + const. (6.11)

Apparently, in the proximity of the maximum, lnL(λ) behaves like a parabola. L(λ) will then

follow the Gaussian distribution L(λ) = k · e{−I(λ)2

(λ−λ)2}. For an efficient estimator we have acondition for the variance of the distribution and the estimator, which is

V (Sλ) = V (λ) = I−1(λ) (6.12)

and the standard deviation of the distribution and the estimator is

σ(Sλ) = σ(λ) =

√I−1(λ). (6.13)

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Muon detection and Muonlab

Now combining equations 6.11 and 6.13 we can find the following formula, which describes thatthe change in λ by one standard deviation σ from its maximum likelihood estimate leads to adecrease in lnL(λ) from its maximum by 1

2 :

lnL(λ± σ(λ)) = lnL(λ)− 1

2. (6.14)

Since finding the exact values of lnL(λ) − 12 is very unlikely, MuonlabII.2 is looking at those

subsequent values of ti which satisfy the following condition:

[lnL(τi−1)− lnL(τ0) + 0.5] · [lnL(τi)− lnL(τ0) + 0.5] < 0 (6.15)

The corresponding points are averaged and the corresponding values are subtracted from thecalculated proper decay time, following λ± σ(λ)− λ = ±σ. These values of τ0 and σ are usedto fitted the data using formula 6.7 and shown in the GUI.

This exponential function will be fit to data in the user interface of Muonlab II.2 after enoughdata is acquired and can be seen in Figures 6.12 and 6.13. When calculating the lifetime, oneshould take into account accidental interfering muons within the time interval and noise causedby the detector. Therefore, as this background is assumed flat through out the measuredtime interval, a sample of the data in the last 10 microseconds is gathered and the averageis subtracted from the data. In these last microseconds, i.e. the time interval is 25600 ns soafter t = 15600 ns, the probability of a muon not to have decayed is 8,3×10−2%. For the 37022measurements shown in the figures, this accumulated in 37022 * 8,3 ×10−2 ∼ 31 hits. A sampleof background noise is shown in Figure 6.14.

Figure 6.12:The full his-togram in aMuonlab lifetimemeasurement.The appliedvoltage on thePMT is 740 Vand operateswith a 20 mVthreshold. 37022measurementswere recorded.The slope fitsthe data witha measuredτµ ≈ 2.00µs.

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6.2. MUONLAB AS AN INTRODUCTION IN SPECIAL RELATIVITY

Figure 6.13:Zoom of Figure6.12, where thehistogram is cutafter t = 10µs.

Figure 6.14: Sample ofthe measurements in fi-nal 10 µs of histogramof Figures 6.12 and6.13, indicating a flatbackground.

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Muon detection and Muonlab

6.3 Discussion

The implementation of new PMTs was not dependent of many specifications. The tests ofthe PMT sensitivity and efficiency indicated that the efficiency plateau could be reached insubsequent measurements in the Muonlab program, as will the PMTs give useful and powerfuloutput signals. However, to reach the plateau and the secondary rise, a new voltage converterwas tested. This voltage converter converted the input voltage ranging from 0,3- 1,5 Volt to5,5-27,5 Volt, instead of the existing converter which could convert up to 24V. It can be seenin Figure 6.6 how this is related to the high voltage in the PMTs. In the consecutive extensiveresearch considering the functionality of the PMTs, malfunctioning in the application of thenew voltage converter has been detected. Even though all components separately did notsuffer difficulties, connecting R580-12 PMTs to the MIB and the computer did show significantmalfunctioning. In an apparent stochastic process, the connection between USB-ports and theinterface box was lost whenever the voltage reached its highest value (roughly between 24-27,5V). Therefore, the use of such a converter became unwanted, as the existing voltage converterdid not cause such problems. It is also shown, that with a voltage conversion up to 24 V,the plateau can be reached, as it corresponds to high voltage values of 1700-1800 V. In Figure6.15 the low voltage applied to the PMT and its resulting high voltage is shown. Since theexisting voltage converter allows the R580-12 PMTs to reach the plateau and does not causefor additional connection problems, it is now being implemented in the Muonlab program.

Figure 6.15: The region of volt-ages used in implemented con-verter

In the development of the software an important complication of the hardware compositionwas found to have severe consequences. The TOF measurements involve coincidence and thetiming of several measurements in the primary nanoseconds could not be distinguished fromeach other for reasons that are not yet completely understood. It is to say, that when the valueof waarde is calculated, it is dependent on the information provided in the first two bits bythe MIB, to determine whether the first or the second gate opened the timer in the Muonlabinterface. Those measurements where the interface box can not distinguish between first timeof arrival are counted but not represented in the histogram. It is chosen not to discard thesemeasurements since any flux or plateau measurements are otherwise misrepresentative.

Furthermore, with the use of the Maximum Log Likelihood method regarding the lifetimemeasurements, the selection of the analyzed data can be done by selecting a proper zoom on

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6.4. CONCLUSION

the histogram. The consequence of this is that students should well argue their cuts madein the histogram, and understand why these cuts should be made. When not performed, theanalysis also include those values which can be considered as noise.

6.4 Conclusion

The thesis provides a clear view of the present theory of cosmic rays, their origin, accelerationand several techniques of detection. Although the subject of cosmic rays is still a mystery inseveral parts of particle and astroparticle theory, the described cosmic ray properties providefor an insight in the contemporary cosmic ray knowledge. Still, disregarding the concealedproperties of cosmic rays, the subject can serve several causes, even commercial ones. However,the educative use intrigues undergraduate students and allows them to study all sorts of subjectsin both particle as astroparticle physics. The improvements made to the Muonlab programin both hardware and software, furnishes a comfortable use to a larger public at NIKHEF.Measuring the speed of muons in the atmosphere (0.98 c) and the muon lifetime (2, 2µs) canbe determined with relative small error. The measured characteristics of the R580-12 PMTs,have shown that these PMTs can be used in the program with the use of voltage converter A.The analysis improvements to the software have made MuonlabII.2 to an easy to use educativeprogram, which is well suited for the implementations of the Zeus PMTs.

Acknowledgments I wish to acknowledge with gratitude Jan Oldenziel for extensive dis-cussions regarding the testing of the PMTs. Also I wish to thank my supervisor dr. MarcelVreeswijk, for his persistent support and guidance in the research done. The last words of thisthesis are to express my gratitude to Maxim Willemse MSc. and my parents, who supportedme greatly not only during the work on this thesis but also in my entire study of physics.

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