Eigenmodes of the Boundary of a Magnetic Barrier Flowed Around by Plasma: the Boundary Membrane Model, Linear and Nonlinear Resonances, and Couplings with Internal Modes

Abstract

The linear and nonlinear resonances and cascades affecting significantly the interaction of a collisionless plasma flow with a magnetic barrier and the plasma penetration into the barrier are studied using the near-Earth magnetopause as an example. Our linear theory of the membrane instability of the boundary of a magnetic barrier, the magnetopause, explains the structure of the spectra and bi-spectra of fluctuations on different segments of the boundary layers near the magnetopause and the resonances at frequencies 0.05–0.5 mHz. The recorded compressibility of waves under the magnetopause implies that their excitation by Alfv’en resonances alone is impossible. We assume, as a general principle, an approximate coincidence of the frequencies of different harmonics of different resonances as a condition for the amplification of resonances to nonlinear amplitudes and their propagation into the ionosphere. We confirm the presence of resonant waves near the magnetopause and demonstrate a nonlinear three-wave cascade interaction of compressible (0.05–5 mHz) and incompressible waves under the magnetopause that provides the excitation of resonances of magnetic field lines and waveguide resonances at frequencies 1–25 mHz without a close coincidence of the frequencies with linear resonances at the magnetopause and the bow shock. This can also provide a nonlinear coupling of linear and nonlinear resonances in other multilayered media (for example, in the plasma and neutral sheets of the geomagnetic tail and between it and the magnetopause). An example of the excitation of a waveguide mode inside the magnetopause by nonlinear membrane waves is given. We have detected a nonlinear excitation and interaction of most “magic” harmonics under the magnetopause.