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Abstract-A set of models for Monte Carlo simulation of production and interaction of high energy muons is developed in the framework of the Geant4 toolkit. It describes the following physics processes: ionization of high energy muons with radiative corrections, bremsstrahlung, electron-positron pair production, muon induced nuclear reactions, gamma annihilation into muon pair, positron annihilation into muon pair, and into pion pair. These processes are essential for the LHC experiments, for the understanding of the background in underground detectors, for the simulation of effects related with high-energy muons in cosmic ray experiments and for the estimation of backgrounds in future colliders. The applicability area of the models extends to 1 PeV. The major use-cases are discussed.Index Terms-Bremsstrahlung, mesons, modeling, Monte Carlo method, positron beam.

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TAIGA stands for ``Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy'' and is a project to built a complex, hybrid detector system for ground-based gamma-ray astronomy from a few TeV to several PeV, and for cosmic ray studies from 100 TeV to 1 EeV. TAIGA will search for ``PeVatrons'' (ultra-high energy gamma-ray sources) and measure the composition and spectrum of cosmic rays in the knee region (100 TeV–10 PeV) with good energy resolution and high statistics. TAIGA will include Tunka-HiSCORE — an array of wide-angle air Cherenkov stations, an array of Imaging Atmospheric Cherenkov Telescopes, an array of particle detectors, both on the surface and underground and the TUNKA-133 air Cherenkov array.