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The properties of cosmic rays with energies above 10**6 GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air…
The predictions of hadronic interaction models for cosmic-ray induced air showers contain inherent uncertainties due to limitations of available accelerator data and theoretical understanding in the required energy and rapidity regime.…
The properties of cosmic rays with energies above 1PeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review, a summary of the phenomenology of these giant air showers is…
The increasing cosmic ray statistics collected by present experiments and the future prospects with new large arrays demand accurate calculations of the extensive air shower parameters. The energy of the primary particle is estimated by…
At ultra-high energies, the flux of cosmic rays is too low for direct measurements to be meaningful. When a cosmic ray enters the atmosphere, it initiates an extensive air shower, producing a cascade of secondary particles that propagate…
Measurements of cosmic ray particles at energies above E = 5 x 10^{14} eV are performed by large area ground based air shower experiments. Only they provide the collection power required for obtaining sufficient statistics at the low flux…
The collection of a statistically significant number detected of cosmic rays with energy above $10^{17}$ to $10^{18}$ eV requires widely-spaced particle detectors at the ground level to detect the extensive air showers induced in the…
We study basic characteristics of distributions of the depths of shower maximum in air showers caused by cosmic rays with the highest energies. The consistency between their average values and widths, and their energy dependences are…
The Cherenkov light produced in air showers largely contributes to the signal observed in ground-based gamma-ray and cosmic-ray observatories. Yet, no description of this phenomenon is available covering both regions of small and large…
The mass composition of ultra-high energy cosmic rays can be studied from the distributions of the depth of shower maximum and/or the muon shower size. Here, we study the dependence of the mean muon shower size on the depth of shower…
Extensive air showers are generated through interactions of high-energy cosmic rays impinging the Earth's atmosphere. A new method is described to infer the attenuation of hadrons in air showers. The numbers of electrons and muons,…
The profile of the longitudinal development of showers produced by ultra-high energy cosmic rays carries information related to the interaction properties of the primary particles with atmospheric nuclei. In this work, we present the first…
The detection of inclined air showers (zenith angles $\theta \gtrsim 65^\circ$) with kilometer-spaced radio-antenna arrays allows measuring cosmic rays at ultra-high energies ($E \lesssim 10^{20}\,\mathrm{eV}$). Radio and particle detector…
The latest observations of extensive air showers (EAS) induced by ultra-high-energy cosmic rays (UHECR) appear to indicate, prima facie, a transition to heavy primaries at the highest energies. However, this interpretation, which is based…
In this paper we review air shower data related to the mass composition of cosmic rays above 10$^{15}$ eV. After explaining the basic relations between air shower observables and the primary mass and energy of cosmic rays, we present…
In the sub-TeV regime, the most widely used hadronic interaction models disagree significant lying their predictions for post-first interaction and ground-level particle spectra from cosmic ray induced air showers. These differences…
Extensive air showers, induced by high energy cosmic rays impinging on the Earth's atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the…
We developed a radio interferometric technique for the observation of extensive air showers initiated by cosmic particles. In this proof-of-principle study we show that properties of extensive air showers can be derived with high accuracy…
Atmospheric conditions, such as the pressure (P), temperature (T) or air density ($\rho \propto P/T$), affect the development of extended air showers initiated by energetic cosmic rays. We study the impact of the atmospheric variations on…
Collisions of cosmic rays in the atmosphere may produce heavy hadrons of very high energy. The decay length of a $B$ meson of energy above $10^7$ GeV is larger than 1 km, implying that such a particle tends to interact in the air before it…