  We calculate the Thomson scattering cross section in a non-relativistic,
magnetized, high density plasma -- in a regime where collective excitations can
be described by magnetohydrodynamics. We show that, in addition to cyclotron
resonances and an elastic peak, the cross section exhibits two pairs of peaks
associated with slow and fast magnetosonic waves; by contrast, the cross
section arising in pure hydrodynamics possesses just a single pair of Brillouin
peaks. Both the position and the width of these magnetosonic-wave peaks depend
on the ambient magnetic field and temperature, as well as transport and
thermodynamic coefficients, and so can therefore serve as a diagnostic tool for
plasma properties that are otherwise challenging to measure.
