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.

Ionospheric modification and parametric instabilities

Introduction to ionospheric heating at Tromsø—I. Experimental overview

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

Relative or absolute elevation extraction from satellite radar data has been an active research topic for more than 20 years. Various investigations have been made on different methods depending on the predominant “fashion” and data availability, leading each time to new developments to improve the capability and the applicability of each method. The paper presents an update of the state-of-the-art of elevation extraction from satellite SAR data. The performance and limitations of four different methods (clinometry, stereoscopy, interferometry and polarimetry) are reviewed, as well as their applicability to different satellite SAR sensors. Their advantages and disadvantages and how they are addressed during the data processing are also analysed. Finally, concluding remarks look at the complementarity aspects of each method to make the best use of the existing and future radar data for elevation extraction.

State-of-the-art of elevation extraction from satellite SAR data

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

An ionospheric volume in the F layer subjected to high power high frequency illumination is observed to be an effective scattering medium for radio signals. Experimental results are representative of a field-aligned scattering geometry. Scatter of the incident wave into electrostatic waves by these strongly field-aligned density irregularities is considered. This model explains the large decreases in radio wave reflectivity seen during the ionospheric modification.

Anomalous radio wave absorption due to ionospheric heating effects

The excitation of parametric instabilities by radio waves in a magnetoplasma is discussed. A uniform medium is assumed and linear approximations are used. Excitation by a pump wave of ordinary polarization is hardly affected by the magnetic field. Low or zero frequency ion waves and high frequency Langmuir waves are excited simultaneously. For an extraordinary pump wave, the excited high frequency electrostatic waves are in the Bernstein mode. The threshold is slightly higher and excitation can occur only within certain 'allowed' frequency bands. A new type of parametric instability in which the excited waves are electromagnetic in nature and which is more strongly affected by the inhomogeneous nature of the medium is discussed qualitatively.

Excitation of Parametric Instabilities by Radio Waves in the Ionosphere

The threshold of the purely growing mode of stimulated Brillouin scattering is exceeded in ionospheric modification experiments for horizontal wave-lengths longer than about half a km. The “beat wavelength” along the field lines is a few km long and increases with decreasing height. The irregularities are therefore not purely field aligned initially although diffusion across the field lines could, over longer periods of time, produce purely field-aligned irregularities which persist after the heating transmitter is switched off.

Generation of large‐scale field‐aligned irregularities in ionospheric modification experiments

The threshold and growth rate of conventional stimulated Brillouin scattering are first calculated for a uniform magnetoplasma. Approximate calculations of the threshold and growth rate are then carried out for a new instability which could be termed thermally stimulated Brillouin scattering: in this instability the nonlinear Lorentz force (ponderomotive force) is replaced by a pressure force due to differential heating in the interference pattern of the pump wave and the generated electromagnetic wave. The threshold for this new instability in a uniform medium is much lower than for conventional Brillouin scattering if the low-frequency wavelength measured along the magnetic field is much longer than the electron mean free path. The threshold is then calculated for the purely growing version of the new instability numerically, taking both the inhomogeneity of the medium and the effect of the geomagnetic field on wave propagation into account. The growth rate is also calculated and it is concluded that this new instability is probably responsible for the generation of large-scale field-aligned irregularities associated with artificial spread-F produced by ionospheric heating.

Generation of artificial spread-F by a collisionally coupled purely growing parametric instability

Use of a simple method based on energy balance to rederive the well-known threshold condition for the purely growing parametric instability in a homogeneous medium and to estimate the effects of inhomogeneity in a semiquantitative manner. A method different from that of Perkins and Flick (1971) is then used to calculate the threshold in a more quantitative manner for the instance where the effects of inhomogeneity dominate over those of collisions. The result agrees with that of Perkins and Flick for k sub parallel l much greater than 1 in their terminology. For k sub parallel much less than 1, neither theory is directly applicable and the threshold is obtained by numerical methods. The present method of calculation has the advantages that its range of validity is easily checked, that it provides good physical insight, and that it is easily applicable to electromagnetic instabilities.

J. A. Fejer

Papers

Anomalous radio wave absorption due to ionospheric heating effects

Excitation of Parametric Instabilities by Radio Waves in the Ionosphere

Generation of large‐scale field‐aligned irregularities in ionospheric modification experiments

Generation of artificial spread-F by a collisionally coupled purely growing parametric instability

Purely growing parametric instability in an inhomogeneous plasma