Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth

Abstract. We analyze coupled Alfvén and slow magnetosonic eigenmodes in a dipole geomagnetic field with different ionospheric conductivities in the framework of ideal magnetic hydrodynamics (MHD) with finite pressure. We use numerical and, if possible, analytical methods to describe eigenmode frequencies, growth rates and eigenfunctions. The spectrum of Alfvén and slow magnetosonic modes is discrete and equidistant. The frequencies of the first Alfvén and slow magnetosonic eigenmodes are estimated as ~1 Hz and ~1 mHz, respectively. In the case of finite conductivity, periodic and aperiodic modes are separated and their interaction analyzed. It was shown that periodic and aperiodic perturbations can mutually transform into each other. A new flute stability criterion is derived (α~4.25), which is stricter than the Gold criterion (α=20/3). Here, as usual, α=−L/p dp/dL. For flute perturbations, the deviations of transversal displacement from a constant are calculated. An approximation for longitudinal displacement is derived. We determined the position of the main longitudinal peak, which can be responsible for nonlinear structures observed by Freja. An influence of nonlinear terms in pressure is estimated as well.