Strong turbulence theory of ionospheric cross-field instability

Abstract

In the presence of external dc electric and magnetic fields that are perpendicular to each other, a weakly ionized plasma is subject to the so-called cross-field instability if there is an appreciable gradient of plasma density. The strong plasma turbulence theory of Dupree and Weinstock is used to develop the nonlinear theory of this cross-field instability, and the theory is applied to F-region irregularities in the ionosphere. As the waves grow, the nonlinearity is manifest in a growing enhanced ion diffusion coefficient proportional to an integral of the wave spectrum. As the wave spectrum grows, the ordered motion of the ions, necessary to sustain the waves, is offset by the turbulent diffusion, so that eventually the wave growth stops and a stationary turbulent state is reached. The nonlinear dispersion relation, the stabilization time, and the asymptotic spectrum are calculated.