Nonlinear interaction between three ordinary electromagnetic modes

In this paper we consider the resonant interaction between three modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field. We show that for the modified mode to be a normal mode we must have the unperturbed current equal to zero. Using the averaged Lagrangian method, we calculate the coupling coefficient for the resonant interaction between three of these modes. It is proportional only to the cube of the drift velocity, as expected from the vanishing of the unperturbed current.