  The relativistic Vlasov-Maxwell system describes the evolution of a
collisionless plasma. The problem of linear instability of this system is
considered in two physical settings: the so-called "one and one-half"
dimensional case, and the three dimensional case with cylindrical symmetry.
Sufficient conditions for instability are obtained in terms of the spectral
properties of certain Schr\"odinger operators that act on the spatial variable
alone (and not in full phase space). An important aspect of these conditions is
that they do not require any boundedness assumptions on the domains, nor do
they require monotonicity of the equilibrium.
