  We consider a neutral holographic plasma with dynamical electromagnetic
interactions in a finite external magnetic field. The Coulomb interactions are
introduced via mixed boundary conditions for the Maxwell gauge field. The
collective modes at finite wave-vector are analyzed in detail and compared to
the magneto-hydrodynamics results valid only at small magnetic fields.
Surprisingly, at large magnetic field, we observe the appearance of two
plasmon-like modes whose corresponding effective plasma frequency grows with
the magnetic field and is not supported by any background charge density.
Finally, we identify a mode collision which allows us to study the radius of
convergence of the linearized hydrodynamics expansion as a function of the
external magnetic field. We find that the radius of convergence in momentum
space, related to the diffusive transverse electromagnetic mode, increases
quadratically with the strength of the magnetic field.
