  Recent work has shown that axions can be efficiently produced via
non-stationary pair plasma discharges in the polar cap region of pulsars. Here,
we point out that for axion masses $10^{-9} \, {\rm eV} \lesssim m_a \lesssim
10^{-4} \, \rm eV$, a sizable fraction of the sourced axion population will be
gravitationally confined to the neutron star. These axions accumulate over
astrophysical timescales, thereby forming a dense `axion cloud' around the
star. We argue that the existence of such a cloud, with densities reaching and
potentially exceeding $\mathcal{O}(10^{22}) \, {\rm GeV \, cm^{-3}}$, is a
generic expectation across a wide range of parameter space. For axion masses
$m_a \gtrsim 10^{-7} \, \rm eV$, energy is primarily radiated from the axion
cloud via resonant axion-photon mixing, generating a number of distinctive
signatures that include: a sharp line in the radio spectrum of each pulsar
(located at the axion mass, and with a percent-level width), and transient
events arising from the reconfiguration of charge densities in the
magnetosphere. While a deeper understanding of the systematic uncertainties in
these systems is required, our current estimates suggest that existing radio
telescopes could improve sensitivity to the axion-photon coupling by more than
an order of magnitude.
