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Abstract

The technique of adjoint cascade equations has been applied to calculate the properties of air showers produced by extremely high energy (EHE) gamma-rays in the energy range 10(18)-10(22) eV. The high intrinsic accuracy, combined with very modest (compared with the traditional Monte Carlo codes) computational time requirements, make this method as an effective tool for the detailed study of development of EHE showers in the Earth's atmosphere. In this paper a wide range of parameters of gamma- ray-induced showers are analysed taking into account two independent effects which become crucial for the cascade development in the EHE reaime-the Landau-Pomeranchuk-Migdal (LPM) effect and the interaction of primary gamma-rays with the geomagnetic field (GMF). Although the LPM effect leads to dramatic modifications of shower characteristics, especially at primary energies exceeding 10(19) eV, the GMF effect, which starts to 'work' at approximately the same energies, prevents, to a large extent, the LPM effect by converting the primary gamma-ray into a bunch of synchrotron gamma-ray photons with energies effectively below the threshold of the LPM effect. This bunch of secondary photons hits the atmosphere and creates a large number of simultaneous showers. The superposition of these independent showers mimics a single shower with energy E = Sigma E-i similar or equal to E-0, but without the signatures of the LPM effect. This makes the longitudinal profile of such a composite electromagnetic shower quite similar to the longitudinal profile of hadronic showers. At the same time, the number of muons as well as their lateral distribution differ significantly from the corresponding parameters of proton- induced showers. In the 'gamma-ray bunch' regime, the total number of muons is less, by a factor of 5-10, than the number of mucus in hadronic showers. Also, compared with the hadronic showers, the electromagnetic showers are characterized by a significantly narrower lateral distribution of muons. Even so, for inclined EHE gamma-ray showers the density of muon flux at large distances from the shower core (greater than or equal to 1000 m) can exceed the electron density.