Abstract
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.
Highlights
This article is dedicated to the analysis of the eigenmode spectrum of transversally small-scale ULF magnetic hydrodynamics (MHD) perturbations in the inner magnetosphere of the Earth
This analysis is an important part of the investigation of waves and instabilities in the magnetospheric plasma
Plasma confined by the geomagnetic field is in a thermodynamical non-equilibrium like any other plasma with pressure
Summary
Parnowski: Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth energetic principle along the field lines, which would lead to a completely different criterion This statement was later supported by Liu (1996), who criticized the confirmation of the Gold criterion by Rogers and Sonnerup (1986), stating that it was only due to an incidental property of the toroidal model used. We tend to agree with Liu (1996), because, as it was shown by Chan et al (1994), the dipole flux surface is pushed outward by the finite pressure and taking this effect into account would lead, in our opinion, to a significant distortion of the stability criterion This statement is proven by this article, as it shows that in the case of curved magnetic field lines, the transversal amplitude of flute perturbations deviates from the constant and is accompanied by significant longitudinal displacements. The model used in this article, unlike others, takes into account magnetic field line curvature, plasma pressure, boundary conductivity and arbitrary polarization of perturbations simultaneously
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