We present an analytic study of the dispersion relation for an isotropic,
non-degenerate plasma interacting with an axion-like particle through the
axion-photon coupling. We aim to provide a general qualitative picture of the
electromagnetic oscillations for both the ultra-relativistic and
non-relativistic plasmas, taking into account separate parts of the dispersion
curves depending on the plasma temperature and the ratio of the phase velocity
to the characteristic velocity of the particles. We include the treatment of
the Landau damping, which could be responsible for a sympathetic damping of
axions in the plasma waves. We show that there are two kinds of electromagnetic
oscillations, i.e. normal super-luminous, undamped and sub-luminous,
aperiodically damped oscillations.Comment: ten pages, two figure