Abstract. In this paper, in terms of an axisymmetric model of the magnetosphere, we formulate the criteria for which the Alfvén waves in the magnetosphere can be toroidally and poloidally polarized (the disturbed magnetic field vector oscillates azimuthally and radially, respectively). The obvious condition of equality of the wave frequency ω to the toroidal (poloidal) eigenfrequency Ω_TN (Ω_PN) is a necessary and sufficient one for the toroidal polarization of the mode and only a necessary one for the poloidal mode. In the latter case we must also add to it a significantly stronger condition ∣Ω_TN–Ω_PN∣/Ω_TN ≫ m^–1 where m is the azimuthal wave number, and N is the longitudinal wave number. In cold plasma (the plasma to magnetic pressure ratio β = 0) the left-hand side of this inequality is too small for the routinely recorded (in the magnetosphere) second harmonic of radially polarized waves, therefore these waves must have nonrealistically large values of m. By studying several models of the magnetosphere differing by the level of disturbance, we found that the left-hand part of the poloidality criterion can be satisfied by taking into account finite plasma pressure for the observed values of m ∼ 50 – 100 (and in some cases, for even smaller values of the azimuthal wave numbers). When the poloidality condition is satisfied, the existence of two types of radially polarized Alfvén waves is possible. In magnetospheric regions, where the function Ω_PN is a monotonic one, the mode is poloidally polarized in a part of its region of localization. It propagates slowly across magnetic shells and changes its polarization from poloidal to toroidal. The other type of radially polarized waves can exist in those regions where this function reaches its extreme values (ring current, plasmapause). These waves are standing waves across magnetic shells, having a poloidal polarization throughout the region of its existence. Waves of this type are likely to be exemplified by giant pulsations. If the poloidality condition is not satisfied, then the mode is toroidally polarized throughout the region of its existence. Furthermore, it has a resonance peak near the magnetic shell, the toroidal eigenfrequency of which equals the frequency of the wave.

Key words. Magnetospheric physics (plasmasphere; MHD waves and instabilities) – Space plasma physics (kinetic and MHD theory)