Influence of dispersion on the modulational instability of a whistler wave

The modulational instability of a whistler wave propagating along an external magnetic field is investigated, taking into account the dispersion of the low-frequency modulations. The dispersive effects are significant if the modulation frequencies Ω are comparable to or greater than the ion cyclotron frequency ω_ci. It is shown that in this case there are four unstable branches: the long-wave modulational instability and three others with much larger growth rates. At Ωω_ci the latter correspond to fast magnetic sound, Alfvén and slow magnetic sound branches.