Polarization splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma

Alfvén waves in a dipole magnetosphere with a rotating plasma are studied theoretically. The plasma-motion-related properties of azimuthally small-scale standing Alfvén waves having nearly poloidal or nearly toroidal polarization are analyzed. Equations are obtained that describe the longitudinal (along the magnetic field) structure and spectra of the waves having such polarizations. The equations obtained are then solved both analytically (in the Wentzel-Kramers-Brillouin approximation) and numerically. Attention is focused on the polarization splitting of the spectrum—the difference between the eigenfrequencies of the toroidally and poloidally polarized Alfvén waves. The distribution of this difference in a direction across the magnetic shells is analyzed. It is shown that, unlike in the models in which the plasma is assumed to be at rest, taking into account rotation of the magnetosphere plasma results in an additional splitting of the spectrum of the poloidal Alfvén waves due to the difference in their azimuthal mode numbers.