The particle nature of cosmic rays
At the time of Cosmic rays discovery the only known forms of penetrating radiation were α, β and γ rays. Consequently CRs were believed to be γ rays up until the 1930s. However, the high penetration power of CRs led to speculations that there could be other forms of radiation. These opposing views created a heated debated about the nature of CRs. The development of Geiger-Muller counters, the coincidence technique and cloud chambers made possible major progress in the field.
The coincidence counting method developed by Walter Bothe  and the Geiger-Müller (GM) counter developed by Hans Geiger and Walther Müller in 1928  were crucial for experimental advances in the field. In 1929 Walther Bothe and Werner Kolhörster designed a major experiment to determine if CRs were γ rays or charged particles . From the results of their experiment, Bothe and Kolhörster concluded that cosmic rays were highly penetrating charged particles. The final blow was given when Arthur Compton demonstrated the geomagnetic latitude dependence of CRs , firmly establishing the particle nature of CRs. This new view on the nature of CRs opened a new panorama regarding their origin and cosmological implications, eﬀectively establishing CR research as another major branch of physics.
Cloud chambers were developed in 1911 by Charles Wilson and allowed him to produce photographs of α− β− and X-rays . The devices consist in a sealed volume containing moist air that reaches a supersaturated state by fast expansion. The passage of a ionizing particles results in a trail of gas ions which act as condensation nuclei. Tiny water droplets condensate forming a cloud track that allows to visualize the passage of the particle. A constraint of the cloud chamber is that the supersaturation condition lasted only a few seconds so a periodic expansion of the air was necessary. This operational constraint resulted in setups that randomly « triggered » the chamber by expanding the air and taking photographs. Cloud chambers were used to detect first subatomic particles in the 1930s: the Positron, Muon and Kaon. All using CRs as the source of ionizing radiation.
Discovery of Extensive Air Showers
Shortly after the publication of the Bothe and Kolhörster results, the coincidence method was further refined by Bruno Rossi . He developed a vacuum-tube device capable of registering the coincidences from any number of counters with a tenfold improvement in time resolution. With his improvement he established three-fold coincidences. This reduced the accidental coincidences and improved the detection of rare cosmic ray events.
In 1932 Blackett and Occhialini placed GM counters above and below a vertical cloud chamber. This way particles passing through the counters would also pass through the cloud chamber and trigger its expansion with the coincidence signal . This marked the birth of « rare event triggering » another essential technique in cosmic ray and high energy physics research ever since. The improvement allowed to enhance the number of CRs photographed.
In 1933 Rossi reported crucial observation with his improved detector. He noticed that the coincidence rate between three adjacent GM counters increased when he placed an absorber plate between the counters and the coincidence rate only decreased until the absorber reached a certain thickness. These plots describing the coincidence rate as a function of the material thickness became known as the Rossi’s transition curves. From this observation he correctly concluded that secondary particles were produced by the cosmic rays entering the material and they were increasingly absorbed as a function of the material thickness . Figure 1.2 show the experimental arrangement Rossi’s transition curves.
An observation similar to Rossi’s was reported in 1935 by Regener and Pfotzer. They studied vertical intensity of cosmic rays up to a height of 28 km by measuring the rate of three-fold coincidences on a stratospheric balloon flight. They observed an unexpected maximum in the coincidence rate at about 14 km above sea level , this eﬀect became known as the « Pfotzer maximum ». Later, Regener correctly interpreted the results were due to the multiplication of electrons in the atmosphere which he called « shower ».
In 1934 Rossi observed that there was a correlation in the arrival time of particles at detec-tors that were widely separated. He named this phenomenon Sciami ». In 1938, Schmeiser and Bothe (unaware of Rossi’s 1934 results) reported that particles in air showers were separated up to 40 cm. Furthermore, they pointed that Rossi’s transition curves implied that « show-ers » were produced in air and named them « air showers ». Independently at the same time, Kolhörster and his group reported similar data by showing the rate at which coincidences between pairs of GM-counters decreased as a function of separation .
Ultimately, despite the work of Rossi, Schmeiser and Bothe, and Kolhörster, the credit for the discovery of Extensive Air Showers (EAS) was given to Pierre Auger and his team. In 1939 they performed an experiment in the swiss alps. They separated their GM counter triggered cloud chambers by 300 m and measured coincident events. The highlight of their discovery was the estimation the primary energy of an event to be around 1015 eV, a five orders of magnitude leap to what was previously know in the 1930s. This formalized the discovery of EAS and for a while the phenomenon was called Auger Showers. Shortly after the discovery many features of EAS were quickly understood from the work of Auger. However, experimental work was halted for almost a decade, once again due to war.
The first event above 1020 eV
New advances in the field became possible due to the increasing availability of photomultiplier tubes (PMTs) and the use of liquid scintillators. Despite PMTs being available since the 1930s, their use on cosmic rays studies started until the 50s mainly focused on the study of Cherenkov light produced by EAS. PMTs are capable of detecting very faint light, even single photons, and yet produce detectable signals. Coupled with scintillators, PMTs started to replace GM counters as the detectors for cosmic ray studies.
Rossi realized that the inexpensiveness and fast decay time of scintillators would allow him to build a large area detector using PMTs to detect the scintillation light. To test this, his team build an array of three detectors consisting of 20 liter drums of 600 cm2 arranged in various configurations. Bassi, Clark and Rossi  showed that the direction of air showers could be determined without the use of cloud chambers by measuring electronically the arrival time of the shower particles. This is because the secondary particles are highly relativistic and form a think disk region around the shower core.
This pioneering experiment led to the development of a larger array at the Agassiz site in Harvard university which started operations in 1954. The Agassiz array consisted in 15 0.9 m2 scintillators. In 1955 a lightning set on fire the inflammable liquid scintillators briefly stopping the work. This prompted the team to develop plastic scintillators and then the work was resumed and continued until 1957. The major achievements of the Agassiz array included being the first experiment capable of measuring the energy and direction of cosmic rays greater than 1015 eV. It measured the spectrum from 1016 up to about 1018 eV . The group also developed analysis methods that were useful in the analysis of data from future arrays.
The Agassiz array proved that the method was so economical that other arrays were soon developed using Agassiz’ technology. In 1957, Rossi put John Linsley in charge of designing a larger array to study higher energy events. The new array was located at Volcano Ranch, New Mexico. It was built by Linsley and his colleague Livio Scarsi and became operational in 1957. The array consisted in nineteen 3.3 m2 detectors arranged in a hexagonal pattern with an initial spacing between detectors of 442 m. Later the distance was expanded to 884 m becoming the first array to cover more than 1 km2 . Observations from Volcano ranch extended the known cosmic ray spectrum, improved the understanding of the structure of EAS, provided the first experimental results on UHECR composition and the first evidence of anisotropy from the arrival direction of CRs . Most notably the Volcano Ranch array was the first experiment to detect an UHECR with an energy higher than 1020 eV , still one of the most energetic events detected to date.
For the next decades and up to this day, array experiments continue dominate the cos-mic ray field. A particular trend is that these experiments have become larger in order to increase their observational exposure and detect more events. These experiments have proven important in understanding particular features of the CR energy spectrum (see sec. 1.2), in the development of models of EAS development and computational methods. Also other techniques were developed almost in parallel to arrays. These techniques rely on op-tical observations to detect the fluorescence (see sec. 1.4.2) and Cherenkov light (see sec. 1.4.3) produced by EAS. Newer arrays have incorporated a hybrid observation approach to complement both type of measurements to improve their performance.
Cosmic ray energy spectrum
As we have seen, the study of the cosmic ray spectrum has taken many decades. It spans over 8 and 24 orders of magnitude in energy and flux respectively. A feature of the CR spectrum is that it can be described over large energy regions by an broken power law Es with an spectral index s which varies according to the region. The spectrum is divided mainly in four regions: from 109 to 1015 eV the spectral index is s ≈ −2 7, at ≈ 3 × 1015 eV the spectrum steepens to s ≈ −3 1, at ≈ 4 × 1017 eV there is a second steepening to s ≈ −3 3, at ≈ 4 × 1019 eV the spectrum flattens to s ≈ −2 6 and around 1020 eV there is an apparent cutoﬀ in the spectrum. The spectral index transition regions are respectively called the « knee », the « second knee » and the « ankle » of the CR spectrum. Figure 1.3 shows the all particle cosmic ray spectrum as measured by various experiments developed through several decades, one can clearly see the spectral index transitions which give the knee and ankle their respective names.
The knee region is typically assumed to represent the end of the galactic cosmic accelera-tors spectrum whereas the ankle is assumed to represent the emergence of extragalactic ones
. This is assumed because the Larmor radius of a particle with an energy of about 1020 eV will be larger than the size of the galactic disc. Therefore, the conditions to confine UHECRs make it reasonable to assume that they are of extragalactic origin and motivates the search for sources outside of the Milky Way.
Candidate acceleration sources must meet certain size and magnetic field strength condi-tions to accelerate particles to extreme energies. These conditions were summarized by Hillas  and represented graphically in the so called Hillas plot shown in figure 1.4. The plot marks the magnetic field strength and radius necessary to accelerate and confine UHECR proton and iron nuclei with an energy of 1020 eV, denoted by the diagonal lines. Anything below the line is not a viable source.
In the next section we will review two significant eﬀects that aﬀect the propagation of CR in the galactic and extragalactic medium and review potential acceleration mechanisms and sources proposed in the literature.
The question of the origin of CR is tightly connected with the propagation of cosmic rays in the galactic and intergalactic medium. Upon their arrival on earth, CRs have already traveled vast distances, suﬀering energy losses and deviations due to the interaction with the interstellar/intergalactic medium. This aﬀects the observations and limit the ability to trace back the CR to a particular source.
The GZK cutoﬀ
In 1966 K. Greisen , G. Zatsepin V and Kuz’min  independently realized that the photons of the cosmic microwave background (CMB) made the universe opaque to protons and nuclei of ultra high energies and predicted an upper limit on the energy of cosmic rays due to the interaction of UHECR with the primordial photons. This eﬀect is named the « GZK cutoﬀ » after the authors and occurs for protons with energies above the photo-pion production threshold, at about 3 × 1019 The GZK cut-oﬀ implies that UHECR are cosmologically young and should come from relatively close sources.
Eﬀect of magnetic fields
Being charged particles, the rigidity2 of a CR plays an important role in it’s propagation through the galactic and extragalactic medium magnetic fields. Depending on the strength of the magnetic fields and energy of the CR, its trajectory can be significantly deviated, aﬀecting the accurate determination of the source location. For instance, by means of simulations shown in figure 1.5, we can see that a turbulent magnetic field of about 10 nG significantly aﬀects the propagation of CRs with E < 1020 eV and the source direction is totally lost. Only a CR above this energy can maintain an almost ballistic trajectory .
Extensive Air Showers
hen a cosmic ray or high energy photon arrives to earth, it interacts with the nuclei of air molecules, producing a flux of secondary, tertiary and ensuing generations of particles. This event forms a particle cascade called Extensive Air Shower (EAS) which develops lon-gitudinally along the arrival direction of the primary particle. As the shower develops, the newly produced secondaries become less energetic since the energy of the primary particle is distributed among newly generated particles.
Table of contents :
1 The Search for Ultra High Energy Cosmic Rays
1.1 A brief history of Cosmic Ray research
1.2 Cosmic ray energy spectrum
1.3 Extensive Air Showers
1.4 UHECR detection Methods
2 Towards Space Detectors of UHECR: The JEM-EUSO Framework
2.1 The JEM-EUSO Mission
2.2 JEM-EUSO Pathfinders
2.3 Future projects in the JEM-EUSO framework
2.4 Projects integrated in the JEM-EUSO Framework
3 The Optics performance of the JEM-EUSO balloon pathfinders
3.2 History and principle of Fresnel Lenses
3.3 Description of the EUSO-Balloon and EUSO-SPB1 optics
3.4 EUSO-Balloon optics characterization
3.5 EUSO-SPB1 Optics characterization
3.6 Post Characterization conclusions
3.7 Observation of diffraction effects by the Fresnel lenses
3.8 Scattering of light by small-scale structure of the lens surface
3.9 Fresnel lens diffusion experiment
3.10 Model of the EUSO-Balloon optics
3.11 Improvement of the Fresnel optics
4 The EUSO-SPB1 campaign
4.2 EUSO-SPB1 optics characterization and end to end tests
4.3 Wanaka balloon launch campaign
5 Data analysis of EUSO-SPB1
5.2 Instrument flight performance
5.3 Data Structure
5.4 Analysis method of the EUSO-SPB1 data
5.5 Analysis results of the event database
6 Conclusion (English)
6.1 The optics performance of the balloon pathfinders
6.2 Classification of the triggered events in EUSO-SPB1
7 Conclusion (Français)
7.1 La performance optique des démonstrateurs ballon
7.2 Classification des événements enregistrés dans EUSO-SPB1