A new nonlinear approach to the theory of E region irregularities

Abstract

Abstract. In the study of E region irregularities the standard procedure is to Fourier analyze the irregularities in both time and space, that is, to describe them as a superposition of plane waves. This introduces di•culties when the amplitude of the plane waves becomes large, thereby adding nonlinear terms to the original equations and forcing all the plane waves to become coupled to one another. In the present work we stay away from Fourier analysis and use the standard fluid description of the instabilities in the limit of perturbed electric fields that are strictly perpendicular to the geomagnetic field. We obtain a nonlinear generalization of the standard results whereby the diffusion-like operator found in linear theory is now a function of the density itself. Therefore, as the structures grow, the net electric field seen by the ambient plasma inside the structures changes in time: it rotates and its amplitude decreases. Consequently, one possible saturation mechanism for the instabilities is a. reduction in the net electric field inside the structures, which brings them to threshold velocity conditions. This being stated, other nonlinear saturation mechanisms remain possible if they require smaller saturation amplitudes than the present work. Either way, our work is consistent with intermittency and implies that the largest amplitude structures in the medium should be rotated away from zero flow angle conditions by a measurable amount. Finally, we show that when compared to an irregularity-free situation, there should be a measurable reduction in the average Hall current carried by the plasma, while the average Pedersen current should not be affected.

Structure functions and intermittency in ionospheric plasma turbulence

“…The zero aspect angle is likely to be a part of the earlier evolution of the amplitude. The full evolution of the structures may be three dimensional and such that once the amplitude has increased enough for the growth rate to slow down through the nonlinear effects (St.-Maurice and Hamza, 2001), then shears and rotations can introduce a fast evolving aspect angle that destroys the structures while heating the electrons (J.-P. St.-Maurice, private communications, 2008). The largest amplitudes may be met when the phase speed has slowed down to be the threshold speed, i.e.…”

The equatorial E-region and its plasma instabilities: a tutorial

“…In fact, we do not yet know if the dominant nonlinear limiting mechanism is two-dimensional (aspect angle effects are unimportant) or three-dimensional (coupling to damped waves propagating at off-perpendicular angles is the primary loss mechanism). There is a considerable literature covering analytical and numerical studies of 2-D mode coupling; see for example St.-Maurice and Hamza (2001), Otani and Oppenheim (2006), Oppenheim et al (2008a), and earlier references therein. Unfortunately numerical simulations are still Fig.…”

New insights from a nonlocal generalization of the Farley-Buneman instability problem at high latitudes

“…He concluded that under anisotropic turbulent conditions, the suggested mechanism could work, but at the expense of having broad-band density levels of the order of 20%, which seemed contrary to observations. However, for weakly growing conditions with isotropic two-dimensional turbulence, St.- Maurice (1990) found that an equivalent (or "anomalous") collision frequency of the order of four times the electron-neutral collision frequency was possible. This result seemed to be most useful in the equatorial regions near the 100 km altitude region, by providing an explanation for observed current densities that are systematically smaller than inferred from model calculations based on classical conductivity profiles (Gagnepain et al, 1977).…”

“…St.-Maurice (1987) countered that there was a problem with the physics used in the anomalous diffusion theories, in that the diffusion produced by unstable waves is perpendicular to their propagation direction when in fact, one needs to introduce diffusion at right angles to that direction if the waves are to saturate in response to increased diffusion. As a result, St.-Maurice (1990) tried to generalize the anomalous diffusion idea by including a bath of background waves pointing in all directions in the plane perpendicular to the magnetic field. He concluded that under anisotropic turbulent conditions, the suggested mechanism could work, but at the expense of having broad-band density levels of the order of 20%, which seemed contrary to observations.…”