On the propagation of transversally small‐scale standing Alfven waves in a three‐dimensionally inhomogeneous magnetosphere

Abstract

In terms of a three‐dimensionally inhomogeneous model of the magnetosphere, we have investigated theoretically the process of propagation across the geomagnetic field of monochromatic standing Alfven waves that are transversally small‐scale ones. For this purpose we introduced an orthogonal coordinate system tied in a natural manner to the geomagnetic field. It is shown that a three‐dimensionally inhomogeneous magnetosphere is composed of sectors that differ from each other by the propagation character of the waves with a different sign of azimuthal wave number. The study revealed the existence of transversally small‐scale waves produced near the toroidal surface in one sector and absorbed near this same surface in another sector of the magnetosphere. These phenomena have no analog in the theory of the axisymmetric magnetosphere where oscillations come into being near the poloidal surface and propagate toward the toroidal surface.

Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure

“…In the course of the propagation the polarization of the Alfve n wave changes from radial (poloidal) to azimuthal (toroidal). An extension of this theory is reported by Leonovich and Mazur (1995a,b) and Klimushkin et al (1995). This theory is, we believe, a realistic theory for small-scale hydromagnetic waves in cold regions of the magnetosphere; however, the main merit of Paper I is a mathematical theory of WKB-approximation for a two-dimensionally inhomogeneous plasma.…”

“…We did not make any assumptions about FMS, but we found that the condition m ) 1 automatically entails its absence. For fast magnetosound with m ) 1 the magnetosphere is opaque; see also Walker (1987), Leonovich and Mazur (1990).…”

“…A speci®c feature of the Alfve n waves in a curved magnetic ®eld is the discrepancy between poloidal and toroidal frequencies of ®eld line oscillations which is the reason for a transversal dispersion of Alfve n waves (Leonovich and Mazur, 1990). It leads to the following picture of their structure according to Paper I.…”

“…Among three hydromagnetic modes in the m ) 1 case, only Alfve n and slow magnetosound (SMS) modes are important in the magnetosphere since fast magnetic sound (FMS) is concentrated near the magnetopause and can not penetrate deep into the magnetosphere (Walker, 1987;Leonovich and Mazur, 1990). Recall that there is no SMS in a cold plasma.…”

Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth's magnetosphere

“…When studying the structure of the toroidal and poloidal modes, it is appropriate to take into account the plasma inhomogeneity not only across magnetic shells, but also in the direction along the external magnetic field, and, in addition, the field line curvature and finite plasma pressure, because all of these factors affect the difference between the frequencies of poloidal and toroidal oscillations (Krylov et al, 1981;Walker, 1987). A study of the global structure of the wave was carried out by Leonovich and Mazur (1993), Klimushkin et al (1995), Kouznetsov and Lotko (1995), Vetoulis and Chen (1996), and Klimushkin (1998a, b). However, the question still is: What are the conditions and magnetospheric regions where Alfvén waves can have particular polarization properties?…”