  Cosmic ray protons propagating in a spatially-homogeneous but time-dependent
field of axions or axion-like particles (ALPs) emit photons in a way that is
reminiscent of Cherenkov radiation by charged particles in a preferred
background. We compute the emission rate and energy spectrum of the photons,
and discuss the possibility of their detection using the Square Kilometre Array
which is currently under construction. In the case of a non-detection,
constraints can be placed on the parameter space of ALPs whose mass lie between
$10^{-7}$eV and $10^{-5}$ eV under the assumption that they are the primary
constituent of dark matter.
