Fixed target project AFTER at the LHC beams for heavy ion and hadron physics

High intensity proton and lead ion beams at the LHC collider allow one to use the beam halo by placing a fixed target or a bent crystal for beam extraction. The particle energy in this case is just half that at the RHIC collider, but the luminosity exceeds the collider luminosity many times. It is also possible to install a polarized target in the extracted beam. The project AFTER is aimed at investigation of rare processes, polarization phenomena, determination of the parameters required for analysis of cosmic rays and neutrino astrophysics, detailed investigation of quarkonia production and suppression depending on the phase transition of matter to the quark-gluon phase.