Interchange modes in the dipole magnetosphere: The finite transverse wavelength influence

This paper is concerned with the interchange (flute) modes in the dipole magnetosphere. The plasma and magnetic field perturbations are described by the system of the wave equations for coupled Alfvén and slow magnetosonic waves. The boundary equations on the ionosphere assume low conductivity ionospheric plasma. In this case, the zeroth harmonic perturbations can appear, when field line moves as a whole. The unstable solutions for this problem correspond to the interchange instability. The finite ratio of the radial λr and azimuthal λa perturbation scales is assumed. The highest growth rate corresponds to λa/λr→0 limit. The conditions for the (interchange) instability are determined depending on the β parameter and the pressure gradient. It is found that large pressure gradients favor the instability. For the larger β values, the threshold is lower. In the β→0 limit, the instability threshold coincides with the well-known Gold–Kadomtsev criterion. The spatial structure of the unstable modes is determined. With the decrease in the λa/λr ratio, the concentration of mode near the equator grows. The spatial structure and the transverse dispersion of the zeroth harmonic of the oscillatory (stable) mode are studied as well.