Nonlinear interaction of resonant plasma oscillations

Using the water-bag model of an electron plasma the nonlinear interaction of two plasma wave pulses (each of sufficiently narrow wave-number spectrum) is discussed. It is shown that, for the special case of a resonant (zero group velocity) pulse interacting with a non-resonant pulse, the interaction produces an effective slowing down of the group velocity of the non-resonant pulse. An application of this theory to the explanation of the apparent resonances at fractions of the plasma frequency observed in the ionosphere is discussed.