$D$ - meson production at very forward rapidities: estimating the intrinsic charm contribution

We study $D$ - meson production at forward rapidities taking into account the non - linear effects in the QCD dynamics and the intrinsic charm component of the proton wave function. The total cross section, the rapidity distributions and the Feynman - $x$ distributions are calculated for $pp$ collisions at different center of mass energies. Our results show that, at the LHC, the intrinsic charm component changes the $D$ rapidity distributions in a region which is beyond the coverage of the LHCb detectors. At higher energies the IC component dominates the $y$ and $x_F$ distributions exactly in the range where the produced $D$ mesons decay and contribute the most to the prompt atmospheric neutrino flux measured by the ICECUBE Collaboration. We compute the $x_F$ - distributions and demonstrate that they are enhanced at LHC energies by approximately one order of magnitude in the $0.2\le x_F\le 0.8$ range.