  One of the promising new proposals to search for axions in astrophysical
environments is to look for narrow radio lines produced from the resonant
conversion of axion dark matter falling through the magnetospheres of neutron
stars. For sufficiently strong magnetic fields, axion masses in the
$\mathcal{O}(10\mu{\rm eV)}$ range, and axion-photon couplings $g_{a\gamma}
\gtrsim 10^{-12} \, {\rm GeV^{-1}}$, the conversion can become hyper-efficient,
allowing axion-photon and photon-axion transitions to occur with
$\mathcal{O}(1)$ probabilities. Despite the strong mixing between these
particles, the observable radio flux emanating from the magnetosphere is
expected to be heavily suppressed -- this is a consequence of the fact that
photons sourced by infalling axions have a high probability of converting back
into axions before escaping the magnetosphere. In this work, we study the
evolution of the axion and photon phase space near the surface of highly
magnetized neutron stars in the adiabatic regime, quantifying for the first
time the properties of the radio flux that arise at high axion-photon
couplings. We show that previous attempts to mimic the scaling in this regime
have been overly conservative in their treatment, and that the suppression can
be largely circumvented for radio observations targeting neutron star
populations.
