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The evolution of the muon content of very high energy air showers (EAS) in the atmosphere is investigated with data of the KASCADE-Grande observatory. For this purpose, the muon attenuation length in the atmosphere is obtained to $\Lambda_\mu = 1256 \, \pm 85 \, ^{+229}_{-232}(\mbox{syst})\, \mbox{g/cm}^2$ from the experimental data for shower energies between $10^{16.3}$ and $10^{17.0} \, \mbox{eV}$. Comparison of this quantity with predictions of the high-energy hadronic interaction models QGSJET-II-02, SIBYLL 2.1, QGSJET-II-04 and EPOS-LHC reveals that the attenuation of the muon content of measured EAS in the atmosphere is lower than predicted. Deviations are, however, less significant with the post-LHC models. The presence of such deviations seems to be related to a difference between the simulated and the measured zenith angle evolutions of the lateral muon density distributions of EAS, which also causes a discrepancy between the measured absorption lengths of the density of shower muons and the predicted ones at large distances from the EAS core. The studied deficiencies show that all four considered hadronic interaction models fail to describe consistently the zenith angle evolution of the muon content of EAS in the aforesaid energy regime., Comment: Published in Astroparticle Physics 95 (2017) 25-43

The KASCADE-Grande large area (128 m2) Muon Tracking Detector has been built with the aim to identify muons ( E μ thr = 800 MeV) in Extensive Air Showers by track measurements under 18 r.l. shielding. This detector provides high-accuracy angular information (approx. 0.3 ° ) for muons up to 700 m distance from the shower core. In this work we present the lateral density distributions of muons in EAS measured with the Muon Tracking Detector of the KASCADE-Grande experiment. The density is calculated by counting muon tracks in a muon-to-shower-axis distance range from 100 m to 610 m from showers with reconstructed energy of 10 16 – 10 17 eV and zenith angle θ 18 ° . In the distance range covered by the experiment, these distributions are well described by functions phenomenologically determined already in the fifties (of the last century) by Greisen. They are compared also with the distributions obtained with the KASCADE scintillator array ( E μ thr = 230 MeV) and with distributions obtained using simulated showers.