Self-modulation and stability of finite-amplitude ordinary and extraordinary waves in a cold magnetoplasma

The self-modulation parameter of the ordinary and the extraordinary waves propagating in a cold magnetoplasma is given explicitly, by the familiar reductive perturbation method, in the framework of the hydrodynamic approach. Both quantitative and qualitative order-of-magnitude analysis of this parameter are carried out for the lower-hybrid and the upper-hybrid branches of the extraordinary wave. The usefulness of the stability criterion, which is linear with respect to an envelope of these linear waves, is also discussed.