  We investigate the linear dynamics of an electromagnetic field propagating in
curved spacetime in the presence of plasma. The dynamical equations are
generically more involved and richer than the effective Proca equation adopted
as a model in previous work. We discuss the general equations and focus on the
case of a cold plasma in the background of a spherically-symmetric black hole,
showing that the system admits plasma-driven, quasibound electromagnetic states
that are prone to become superradiantly unstable when the black hole rotates.
The quasibound states are different from those of the Proca equation and have
some similarities with the case of a massive scalar field, suggesting that the
linear instability can be strongly suppressed compared to previous estimates.
Our framework provides the first step towards a full understanding of the
plasma-photon interactions around astrophysical black holes.
