Structure in the nonlinear saturation spectrum of parametric instabilities

Abstract

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.

Observations of E region irregularities generated at auroral latitudes by a high‐power radio wave

“…The estimated attenuation based upon riometer measurements made near the heater site at Ramfjordmoen, Norway, is -• 20 dB. [Fejer and Kuo, 1973;Perkins et al, 1974] is found to be 425 mV/m. In most instability theories the more relevant quantity is the peak HF electric field amplitude directed perpendicular to B at the upper hybrid resonance (Eñ).…”

Geometric aspects of HF driven Langmuir turbulence in the ionosphere

“…Early saturation theory was based on weak turbulence formalism (Perkins et al, 1974;Fejer and Kuo, 1973;Rypdal and Craigin, 1979;Das et al, 1985). Recent theoretical efforts have been based on numerical solutions to full wave models of the Zakharov type with damping and parametric drive included (Nicholson et al, 1984;DuBois et al, 1990DuBois et al, , 1991Hanssen et al, 1992;Hanssen, 1992;Sprague and Fejer, 1995;DuBois et al, 1993aDuBois et al, , 2001).…”

Analysis of the backscatter spectrum in an ionospheric modification experiment

“…We now see from (23) and (24) The several peaks in the region near the HF transmitter frequency have been explained previously as the transfer of power from one Langmuir wave to another at a slightly lower frequency via an ion acoustic beat wave Fejer, 1972, Kruer andValeo, 1973;Fejer and Kuo, 1973). The present analysis shows, however, that the standing wave pattern of the pump wave can also result in these pumps.…”

“….... From experimental results obtained at Arecibo (Carlson, Gordon and Showen, 1972;Kantor, 1974), it is believed that the enhanced heating and anomalous absorption occurring in the ionosphere are mainly due to parametric decay instabilities: the HF ordinary (pump) wave supplied by a high power transmitter (-100 kW), and propagating in the F-layer, decays into electron plasma and ion acoustic waves to enhance the plasma fluctuations (DuBois and Goldman, 1965;Nishikawa, 1968). Several analyses have been carried out of the saturation spectra in homogeneous (DuBois and Goldman, 1972a, b;Valeo, Oberman and Perkins, 1972;Kruer and Valeo, 1973;Harker, 1972;Kuo and Fejer, 1972;Fejer and Kuo, 1973;Perkins, Oberman and Valeo, 1974) and inhomogeneous (Arnush, Fried and Kennel 1974) plasmas, with the assumption that the pump field is well above the threshold for parametric amplification. This results in saturation of the electron plasma waves due to nonlinear Landau damping by positive ions, or due to absorption caused by electrons whose orbits are nonlinearly perturbed by the waves (Bezzerides and Weinstock, 1972).…”