  We consider the interactions of a strong gravitational wave with
electromagnetic fields using the 1+3 orthonormal tetrad formalism. A general
system of equations are derived, describing the influence of a plane fronted
parallel (pp) gravitational wave on a cold relativistic multi-component plasma.
We focus our attention on phenomena that are induced by terms that are higher
order in the gravitational wave amplitude. In particular, it is shown that
parametric excitations of plasma oscillations takes place, due to higher order
gravitational non-linearities. The implications of the results are discussed.
