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

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.

Ballooning Instability in the Magnetospheric Plasma: Two‐Dimensional Eigenmode Analysis

“…It agrees with the earlier results (Agapitov et al, 2008;Mazur et al, 2012;Parnowski, 2007;Zhu et al, 2004): Increase of the wave vector's radial component leads to the deterioration of the instability's conditions. It agrees with the earlier results (Agapitov et al, 2008;Mazur et al, 2012;Parnowski, 2007;Zhu et al, 2004): Increase of the wave vector's radial component leads to the deterioration of the instability's conditions.…”

“…Let us illustrate these results by the dipole magnetosphere model earlier considered in Parnowski () and Agapitov et al (). The approximate validity of the dipole model for reasonable pressure and current profiles up to L ≃10 is confirmed by numerical studies (Cheng, ; Xia et al, ).…”

“…As was demonstrated in Zhu et al (2004), Parnowski (2007, Agapitov et al (2008), Mazur et al (2012), and Leonovich and Kozlov (2013), the increase of the k r value deteriorates conditions for the development of the ballooning instability. As was demonstrated in Zhu et al (2004), Parnowski (2007, Agapitov et al (2008), Mazur et al (2012), and Leonovich and Kozlov (2013), the increase of the k r value deteriorates conditions for the development of the ballooning instability.…”

“…Earlier, eigenmode analysis of ballooning perturbations in the Earth's magnetosphere was performed in Chan et al (), Cheremnykh and Parnowski (), Parnowski (), Agapitov et al (), Xia et al (), and Rubtsov, Mager, et al (). These works allowed to determine the threshold of the ballooning instability under different assumptions on the magnetospheric plasma and boundary conditions on the ionosphere.…”

On the ballooning instability of the coupled Alfvén and drift compressional modes

“…However, coupling to the compressional mode was neglected. The instability threshold, under different assumptions, was also calculated in a number of other recent papers, mainly dealing with single-fluid MHD theory; to mention a few: Liu (1997), Miura (2000Miura ( , 2004, Cheremnykh and Parnowski (2004), Golovchanskaya et al (2006), Parnowski (2007), Agapitov et al (2008).…”