W. Tkaczyk

The formation of the cosmic ray energy spectrum by a photon field

Abstract The formation of the energy spectrum and mass composition of cosmic rays (CR) has been analyzed taking into consideration the model in which the nuclei (from hydrogen to iron) are accelerated by discrete sources. The spectra of produced nuclei are next modified due to their interactions with soft background UV photons in the source region. The photonuclear reactions (photodisintegration of nuclei) and proton energy losses due to photomeson production are considered. The shape of the energy spectrum and mass composition of cosmic ray particles have been calculated and compared with the experimental data.

Energy spectra of electrons in the extensive air showers of ultra-high energy

We show that the shape of the energy spectrum of electrons in an extensive air shower with an ultra-high energy (E ≥ 10 19 eV) at a given level in the atmosphere depends only on the shower age at this level. It depends practically neither on the primary particle mass nor on its energy. This fact considerably simplifies interpretation of data from the experiments (e.g., Flys Eye, HiRes and Auger) determining cascade curves of single showers by the fluorescence technique. In particular, the contribution of the scattered Cherenkov light to the total flux produced by a shower can be easily taken into account. Our conclusion has been drawn by analysing results of Monte Carlo simulations of showers with the CORSIKA (Heck et al 1998 Report FZKA 6019) program, using the QGSJet interaction model.

Similarity of extensive air showers with respect to the shower age

Using CORSIKA simulations of the highest energy extensive air showers we show that all showers are similar when described by the shower age parameter: the angular and energy spectra of electrons at a given level in the atmosphere depend only on the shower age at this level. Moreover, electrons with a given energy have the same angular distributions at any level (age) of the shower. We have calculated these distributions and found analytical functions describing them quite well. The total number of particles can also be described in a simple way as a function of age by two halves of a Gaussian function with the widths, however, fluctuating from one shower to another. The description of large showers in terms of age (instead of depth in the atmosphere) is very useful in interpreting data from experiments observing fluorescence light, with admixture of Cherenkov, induced by the showers in the air.

On possibilities of the fluorescence detector to measure the shower light curve

A method to determine the primary energy of very rare big extensive air showers is to measure the fluorescence light flashes induced by them in the atmosphere. From a shower fluorescence image (and its time dependence) it is, in principle, possible to reconstruct the shower cascade curve. The Pierre Auger experiment (in construction) has been using this method (together with measuring the shower charged particles as well) to determine the highest energy part of the cosmic ray spectrum (E J 10 19 eV) and particle arrival directions. Here we analyse which shower parameters affect its image, and, if not taken into account in the reconstruction procedure, may lead to systematic errors in determining its light (cascade) curve, and in consequence, the energy and/or mass of the primary particle. In particular, we analyse the lateral distribution of particles, the thickness and curvature of the shower disk, together with the spherical aberration of the collecting mirror. We show that a non-negligible part of the light flux for showers closer than � 15 km to the detector may be hidden in the non-triggered pixels of the camera. For more distant showers this effect is small, but then the atmospheric attenuation has to be known better. We also derive an analytical solution for a spherical mirror focal plane position and the minimal size of the image (spot size) of a parallel light beam. � 2002 Elsevier Science B.V. All rights reserved.