  In a constant and homogeneous magnetic background, quantum vacuum
fluctuations due to axion-like fields can dominate over those associated with
the electron-positron fields. Considering the framework of
axion-electrodynamics, the self-energy operator for the electromagnetic field
is determined with an accuracy to second-order in the axion-diphoton coupling.
This outcome is utilized for establishing modifications to the propagation
characteristics of photons and to the Coulomb potential of a static pointlike
charge. Notably, in the magnetosphere of a neutron star, the effect of photon
capture by the magnetic field, known in QED as relating to gamma-quanta, is
extended in axion electrodynamics to include X-ray photons with the result that
a specially polarized part of the heat radiation from the surface is canalized
along the magnetic field. Besides, for field strengths larger than the critical
scale associated with this theory, the modified Coulomb potential is of
Yukawa-type in the direction perpendicular to the magnetic field at distances
much smaller than the Compton wavelength of an axion, while along the field it
follows approximately the Coulomb law at any length scale. We find that at
unlimitedly large magnetic fields the longstanding problem -- overcome in QED
-- that the ground-state energy of a hydrogen atom is unbounded from below, is
reinstated. However, in axion-electrodynamics this unboundedness is cut off
because the largest magnetic field treatable within this theory is limited by
the unitarity of the associated scattering matrix.
