On the modulational instability of electrostatic ion cyclotron waves

The instability of electrostatic ion cyclotron waves to low frequency density modulations is considered and nonlinear equations are derived which describe its development in terms of a coherent four wave interaction. A dispersion relation for the linear phase of the instability is obtained and threshold conditions for marginal stability determined. It is shown, using data from recent optical observations, that the conditions necessary for the instability to occur in the auroral plasma would probably be satisfied and that modulational frequencies in agreement with the observations are obtained for plausible wave amplitudes. The nonlinear development of the instability is then studied and it is shown that substantial modulation can occur. It is suggested therefore that this instability could lead to the development of a strongly turbulent state.