Self-modulation and filamentation of an electromagnetic wave is considered as a problem of the nonlinear interaction between electromagnetic and ion waves. A new electro-magnetic modulational instability is obtained, whose threshold is the same as that of the oscillating two-stream instability. A simple geometrical model is given of filamentation when the non-linearity is due to the ponderomotive force. The relationship between the filamentation and electromagnetic modulational instabilities and other parametric instabilities is considered. In particular, it is shown that both electromagnetic modulational and filamentation instabilities can occur at the critical density where they have the same threshold as the modulational instability of a Langmuir wave. Finally, a conservation relation (a generalization of the Manley-Rowe relation) for the wave action density is obtained for the filamentation instability. This shows clearly that this instability results from a four wave interaction.
Filamentation instability of an electromagnetic wave in flowing magnetized homogeneous plasma