Abstract
The weak non-linear interaction of a discrete set of wave packets which propagate in a warm magneto-plasma is examined within the framework of the two fluid approximation. The equations governing the behaviour of the slowly varying amplitudes of the waves are derived by applying standard perturbation theory to the combined system of Maxwell's equations and the fluid equations for each species of charged particles and by using a multiple scale expansion in both space and time. It is shown that, for arbitrary directions of propagation, the interaction matrix elements possess the familiar symmetry properties with respect to interchanges of the wave vectors of a resonant triplet. It is also verified that the mean energy and momentum of each wave can be written as the product of the wave action with omega and k respectively and that the total wave energy and momentum are conserved during an interaction.
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