1063-780X/97/2310- $10.00 © 1997 åÄàä ç‡Û͇ /Interperiodica Publishing 0858 Plasma Physics Reports, Vol. 23, No. 10, 1997, pp. 858–871. Translated from Fizika Plazmy, Vol. 23, No. 10, 1997, pp. 931–944. Original Russian Text Copyright © 1997 by Klimushkin. INTRODUCTION This paper is aimed at studying the structure of hydromagnetic waves in a finite-pressure plasma in the presence of a curvilinear magnetic field. As an example of such a plasma, we can mention the plasma of the earth’s magnetosphere, in which various MHD oscilla- tions (geomagnetic pulsations) are observed; many of these oscillations are small-scale in the azimuthal direction; i.e., their azimuthal wavenumbers satisfy the condition m  1 [1]. It is well known that, in a high-temperature plasma, three types of hydromagnetic oscillations can arise, spe- cifically, Alfvén, fast magnetosonic (FMS), and slow magnetosonic (SMS) waves. In an inhomogeneous plasma, the frequency ϖ of Alfvén waves is independent of the transverse component of the wave vector , where A is the Alfvén velocity, and k || is the longitudinal component of the wave vector. In order to consider the dispersion of waves related to the transverse compo- nent of the wavenumber, we need to take into account kinetic effects, e.g., finite ion Larmor radius and elec- tron inertia. Here, we will study the effect of plasma inhomogeneity on the dispersion relation for Alfvén waves. In the presence of a curvilinear magnetic field, the spectrum of Alfvén waves is modified, and the so- called polarization splitting of the spectrum occurs (see, e.g., [2]); i.e., the frequencies of the radial (poloi- dal) Ω PN and azimuthal (toroidal) Ω TN oscillations of the field lines are different, Ω PN (x 1 ) < Ω TN (x 1 ). (Here, x 1 is the radial coordinate that marks the magnetic sur- ϖ 2 k || 2 A 2 = faces. In an axisymmetric plasma, the frequencies Ω PN and Ω TN depend only on this coordinate.) Leonovich and Mazur [3] showed that the polarization splitting of the spectrum gives rise to an additional transverse dis- persion of Alfvén waves, i.e., the dispersion due to the curvature of the magnetic field lines. In [4], the struc- ture of Alfvén waves with m  1 in a cold (β = 0) axi- symmetric magnetospheric plasma was studied, and it was shown that poloidal and toroidal magnetic surfaces exist at which the conditions ϖ = Ω PN and ϖ = Ω TN are, respectively, satisfied. In the earth’s magnetosphere, a poloidal magnetic surface with a fixed longitudinal wavenumber m is closer to the earth than the toroidal magnetic surface with the same wavenumber. In the case of a dispersion due to the curvature of the mag- netic field lines, an Alfvén wave is excited near the poloidal surface and then propagates at a slow velocity toward the toroidal surface, at which it is either com- pletely absorbed due to dissipation in the ionospheric plasma or converted into an ultrashort kinetic Alfvén wave [5]. The theory of Alfvén waves with m  1 in a cold magnetospheric plasma was developed in [5–7]. In contrast to the case of Alfvén waves, there is a dispersion of magnetosonic waves even in an inhomo- geneous plasma. The dispersion relation for magneto- sonic waves can be written in the form where k x and k y are the transverse components of the wave vector, s is the speed of sound, and ≡ s 2 A 2 /(s 2 + A 2 ). In a one-dimensional inhomogeneous plasma with k x 2 ϖ 4 ϖ 2 s 2 A 2 + ( 29 k y 2 k || 2 + ( 29 – s 2 A 2 k || 2 k y 2 k || 2 + ( 29 + s 2 A 2 + ( 29 ϖ 2 v S 2 k || 2 – ( 29 ---------------------------------------------------------------------------------------------------------- , = v S 2 PLASMA OSCILLATIONS AND WAVES Spatial Structure of Small-Scale Azimuthal Hydrodynamic Waves in an Axisymmetric Magnetospheric Plasma with Finite Pressure D. Yu. Klimushkin Institute of Solar and Terrestrial Physics, Siberian Division, Russian Academy of Sciences, Irkutsk, 664033 Russia Received October 3, 1996 Abstract—A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in the magnetosphere. The finite plasma pressure, the transverse equilibrium current, and the curvature of the mag- netic field lines are taken into account. It is shown that these effects lead to a transverse dispersion of Alfvén waves and change the dispersion relation for slow magnetosonic waves. There are two transparency regions for MHD waves, one located near the Alfvén resonance and the other near the magnetosonic resonance. In the radial direction, each of these regions is bounded by a surface formed by conventional turning points (a poloidal surface) and a surface formed by singular turning points (a resonant surface). In each transparency region, the mode is a standing wave in the longitudinal direction and propagates in the transverse direction from the poloi- dal surface toward the resonant one, at which it is completely absorbed.