  We present a detailed mapping of the dominant kinematical domains
contributing to the prompt atmospheric neutrino flux at high neutrino energies
by studying its sensitivity to the cuts on several kinematical variables
crucial for charm production in cosmic ray scattering in the atmosphere. This
includes the maximal center-of-mass energy for proton-proton scattering, the
longitudinal momentum fractions of partons in the projectile (cosmic ray) and
target (nucleus of the atmosphere), the Feynman $x_F$ variable and the
transverse momentum of charm quark/antiquark. We find that the production of
neutrinos with energies larger than $E_{\nu} >$ 10$^7$ GeV is particularly
sensitive to the center-of-mass energies larger than the ones at the LHC and to
the longitudinal momentum fractions in the projectile 10$^{-8}$ $< x <$
10$^{-5}$. Clearly, these are regions where we do not control the parton, in
particular gluon, densities. We also analyse the characteristic theoretical
uncertainties in the charm production cross section coming from its QCD
modelling. The precision data on the prompt atmospheric neutrino flux can
efficiently constrain the mechanism of heavy quark production and underlying
QCD dynamics in kinematical ranges beyond the reach of the current collider
measurements.
