Thresholds and linear growth rates for stimulated Brillouin and Raman scattering and for the parametric decay instability are derived by using arguments of energy transfer. For this purpose an expression for the ponderomotive force is derived. Conditions under which the partial pressure force due to differential dissipation exceeds the ponderomotive force are also discussed. Stimulated Brillouin and Raman scattering are weakly excited by existing incoherent backscatter radars. The parametric decay instability is strongly excited in ionospheric heating experiments. Saturation theories of the parametric decay instability are therefore described. After a brief discussion of the purely growing instability the effect of using several pumps is discussed as well as the effects of inhomogeneity. Turning to detailed theories of ionospheric heating, artificial spread F is discussed in terms of a purely growing instability where the nonlinearity is due to dissipation. Field‐aligned short‐scale striations are explained in terms of dissipation of the parametrically excited Langmuir waves (plasma oscillations); they might be further amplified by an explosive instability (except at the magnetic equator). Broadband absorption is probably due to scattering of the electromagnetic pump wave into Langmuir waves. This absorption is probably responsible for the ‘Overshoot’ effect: the initially observed level of parametrically excited Langmuir waves is much higher than the steady state level.

The generation of small‐scale field‐aligned irregularities in ionospheric heating experiments is explained in terms of a purely growing parametric instability with thermal coupling based on the scattering of the pump field by the irregularities into plasma oscillations. The standing wave nature of the pump field is a necessary aspect of the present instability which does not require the previous presence of nonthermal irregularities.

The nonlinear saturation spectrum of the decay instability is obtained in the limit of small spontaneous emission, for comparable ion and electron temperatures, from numerical solutions of a kinetic equation based on an accurate expression for the nonlinearity. The spectral energy occupies several pairs of isolated saucer-shaped regions in wave-vector space. The regions increase in thickness, angular diameter, and number as the pump power is increased. The theory thus predicts the generation of waves propagating in directions which can differ substantially from the direction of the pump field. Ionospheric observations confirm this prediction; they were difficult to reconcile with the predictions of previous theories based on an approximate expression for the nonlinearity. The present work also corrects the results of previous one-dimensional theories that used an accurate expression for the nonlinearity and predicted “spectral lines” in the limit of vanishing spontaneous emission. Excitation of the purely growing instability is predicted for pump powers greater than about 2.5 times the threshold of the decay instability.

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