Parametric instabilities, excited in the ionosphere by high-power HF transmitters with a frequency below the maximum ionospheric plasma frequency, produce nonlinear energy absorption and enhanced scattering of electromagnetic radiation, which has been detected by the Arecibo Thomson scatter radar. This paper reviews and extends both the linear and nonlinear saturation theory of parametric instabilities within the ionospheric context. The new elements are a modification of the emission term to include the effects of nonlinear plasma waves and a numerical integration of the wave kinetic equation to find the saturation state of parametric instabilities when it is assumed only that the wave intensity has axial symmetry about the pump field in wave number space. Calculations are presented of the magnitude of the nonlinear energy absorption and of the angular dependence, frequency spectrum, and intensity of scattering from instability-created density fluctuations. In the present experiments the nonlinear processes are predicted to absorb roughly 30% of the radio wave energy incident on the ionosphere. As a rule, this energy is deposited in the high-energy tail of the electron velocity distribution and causes enhanced airglow. The scattered radiation has a frequency shift almost equal to the modifier frequency, and its intensity depends strongly on the angle between k and E0, k being the wave vector of the plasma wave responsible for the scattering and E0 the pumping electric field produced by the modification transmitter. Because the instabilities occur only with O mode transmissions, the direction of E0 is close to the geomagnetic field. The angular dependence result rests on a combination of two-dimensional saturation calculations and plasma wave refraction due to propagation in the inhomogeneous magnetoactive ionospheric plasma. For example, the plasma waves responsible for the scattering observed at Arecibo are found to be nonlinearly stabilized and roughly 104 times less intense than plasma waves propagating within 20° of the geomagnetic field. Thus the scattering observed at Arecibo, although it is intense by Thomson scatter standards, is predicted to be ∼40 dB below the scattering observable in the most favorable geometry. Lastly, new aeronomy experiments made possible by parametric instabilities are discussed.

Parametric instabilities and ionospheric modification

The high power radio facility, built jointly by the Max-Planck-Institut fur Aeronomie, Lindau and the University of Tromso, at Tromso in Northern Norway, has been operational since 1980. Since that time an extremely wide range of ionospheric modification phenomena, induced by the powerful radio beam or pump, has been studied by a multitude of diagnostic techniques. This review is concerned, in particular, with the role played by the anomalous absorption of the high power wave. Anomalous absorption arises when the high power electromagnetic waves excite thermal parametric plasma instabilities in the diffusion dominated ionospheric F-region. This leads to the growth of plasma density irregularities, which are highly elongated along the geomagnetic field and which very efficiently couple electromagnetic and electrostatic plasma waves. The conversion of the electromagnetic modifying wave to rapidly damped electrostatic waves constitutes the anomalous absorption process which gives rise to strong plasma heating and the self extinction of the pump. After briefly reviewing some relevant results from earlier experiments carried out in the USA, a number of modification experiments undertaken at Tromso, using both HF diagnostics and the European Incoherent Scatter radar (EISCAT), are described in detail. These experiments were designed to investigate anomalous absorption processes, large scale plasma heating, pump self action and cross-modulation effects. The relevant theories required to interpret these experimental results are also presented. In particular, the relative importance of collisional and anomalous heating at the high latitude site is examined. The importance of the Tromso high power facility to aeronomical studies is also briefly discussed.

The heating of the high lattitude ionosphere by high power radio waves

Results are presented for an extensive study of strong Langmuir turbulence (SLT) in plasmas excited near the critical density by intense coherent radiation beams. The nominal parameters for HF heating experiments imply that the ionospheric plasma is in such a state. A large body of experimental data exists, particularly from incoherent scatter radar (ISR) measurements of HF-enhanced fluctuation levels. Long-time simulations of Zakharov's model of SLT and related theoretical arguments have led to new conclusions and insights: (1) linear parametric instabilities may play a role only during the first few milliseconds after heater turn-on in a quiescent ionosphere, but there is also the possibility of “direct nucleation” of cavitons in preexisting density fluctuations; (2) both possibilities lead to Langmuir collapse; (3) the turbulence is sustained by nucleation of trapped electric fields in burnt-out density cavities from previous collapses; (4) the nucleation-collapse-burnout scenario explains several features of the observed ISR plasma line power spectra in early-time, low-duty cycle experiments and predicts new features; (5) ISR spectra obtained at early times in low-duty cycle heating experiments are consistent with the spectra of uncorrelated caviton events; (6) these spectra contain a “free mode” peak which is due to the radiation of free Langmuir waves by collapsing cavitons; this peak has recently been observed; (7) sharp spectral peaks observed in strong spectra in longer-time, high-duty cycle or CW heating can arise in the SLT model from spatio-temporal caviton correlations, provided overdense domains exist and a Bragg resonance condition is satisfied; (8) correlation models can explain all the sharp features including the decay line, the cascade, the narrow oscillating two-stream instability line, and the anti-Stokes line; these models do not involve parametric instabilities; (9) the characteristic structure of the ISR spectrum is maintained over a much wider range of angles relative to the geomagnetic field than is the case for weak turbulence predictions; (10) the altitude dependence of the plasma line is consistent with observation without postulating large-scale density modifications; and (11) the nonlinear absorption rate of heater energy is much larger than collisional absorption, the absorbed energy going mainly into suprathermal electrons.

Excitation of strong Langmuir turbulence in plasmas near critical density: Application to HF heating of the ionosphere

Resonance instability of small‐scale field‐aligned irregularities

Temporal behaviour of artificial small-scale ionospheric irregularities: Review of experimental results

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.

Structure in the nonlinear saturation spectrum of parametric instabilities

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Structure in the nonlinear saturation spectrum of parametric instabilities