Cascade of parametric instabilities in ionospheric heating experiments

Two secondary parametric instabilities providing cascade channels for the Langmuir sidebands of the oscillating two-stream instability (OTSI) and parametric decay instability (PDI), which are excited by O-mode high-frequency (HF) heating waves, are studied. The first one decays a Langmuir pump wave into a Langmuir sideband and an ion acoustic decay mode. Both resonant and nonresonant cascade processes are considered. Nonresonant cascade of Langmuir waves proceeds at the same location and is increasingly hampered by the frequency mismatch effect. Resonant cascade takes place in different resonant locations to minimize the frequency mismatch effect, but it has to overcome the severe propagation loss of the mother Langmuir wave in each cascade step. This process produces a narrow spectrum of frequency-downshifted (from the HP wave frequency) plasma waves. The second employs the lower-hybrid wave as the decay mode. Only the nonresonant cascade is of interest, because the propagation loss of the mother Langmuir wave in each resonant cascade step is far too severe. This is a three-dimensional coupling process, because the wavevectors of coupled three waves have to be matched in three-dimensional space, rather than matched in the conventional way on the plane of the pump wavevector and the geomagnetic field. A broad spectrum of frequency-downshifted plasma waves can be produced by this process in a narrow altitude range preferentially located near the matching heights of Langmuir sidebands of the OTSI and PDI.