High-energy particles enter the solar atmosphere from Galactic or solar coronal sources, and produce ‘albedo’ emission from the quiet Sun that is now observable across a wide range of photon energies. The interaction of high-energy particles in a stellar atmosphere depends essentially upon the joint variation of the magnetic field and plasma density, which heretofore has been characterized parametrically as P ∝ Bα with P the gas pressure and B the magnitude of the magnetic field. We re-examine that parametrization by using a self-consistent 3D MHD model (Bifrost) and show that this relationship tends to P ∝ B3.5 ± 0.1 based on the visible portions of the sample of open-field flux tubes in such a model, but with large variations from point to point. This scatter corresponds to the strong meandering of the open-field flux tubes in the lower atmosphere, which will have a strong effect on the prediction of the emission anisotropy (limb brightening). The simulations show that much of the open flux in coronal holes originates in weak-field regions within the granular pattern of the convective motions seen in the simulations.