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

Abstract

The paper examines the ballooning instability in gyrokinetic approximation taking into account the effects of finite-β, magnetic field line curvature, and diamagnetic drift. We used a simple model with a constant curvature of magnetic field lines which enabled us to obtain analytical results. The possible plasma oscillatory modes comprise the poloidal Alfvén and drift compressional modes, coupled due to the magnetic field line curvature and plasma inhomogeneity. The frequencies of these modes depend on the westward current value. As this value grows, the frequencies of these two branches approach to each other, and the branches are merged at some critical value of the current. Then an instability develops which is called the drift ballooning coupling instability. There are three major differences of the drift ballooning coupling instability from the ordinary MHD ballooning instability: (1) the drift ballooning coupling instability is not aperiodic, there is a real part of the oscillation frequency of the order of the drift frequency, (2) only the mode with the same direction of the azimuthal phase speed as the velocity of the ion diamagnetic drift can be unstable, (3) the instability threshold depends on the diamagnetic drift frequency.

Drift‐compressional modes generated by inverted plasma distributions in the magnetosphere

“…As was showed by Higuchi and Kokubun [], in many cases, these pulsations had also large azimuthal (toroidal) component of the transverse magnetic field, which allows one to identify them with the drift‐compressional resonant modes considered in this paper. In the cases where the observed waves have large radial (poloidal) component, more sophisticated theory is needed, which implies the coupling between the drift compressional and Alfvén modes [ Klimushkin and Mager , ; Klimushkin et al , ].…”

“…Previous studies showed that the drift‐compressional modes are narrowly localized near the magnetic equator, have frequencies of the same order as the diamagnetic plasma frequency ω ∗ , and can be related to plasma instability due to energy exchange with energetic protons [ Ng et al , ; Crabtree et al , ; Crabtree and Chen , ]. The coupling of these modes with the transverse Alfvén modes due to field line curvature may significantly complicate the conditions for the instability [ Klimushkin and Mager , ; Klimushkin et al , ]. In a simplified model with circular field lines, Klimushkin and Mager [] showed that the drift‐compressional modes must experience a resonance when the oscillation frequency coincides with the wave eigenfrequency.…”

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

“…It can substantially modify the ballooning instability (Andrushchenko et al, 1990;Cheng, 1982;Cheng & Lui, 1998;Horton et al, 1983;Klimushkin et al, 2012;Xia et al, 2017). In kinetics, the modes of the ULF oscillations are different from those in MHD theory.…”

Corrugation Instability of a Coronal Arcade

“…Ma, Hirose, and Liu (2014) studied the instability in the Hall-MHD framework. Klimushkin, Mager, and Pilipenko (2012) and Mager and Klimushkin (2017) generalised the theory of ballooning perturbations accounting for kinetic effects. The exploitation of the coronal-magnetospheric analogy opens up interesting opportunities for knowledge transfer (Nakariakov et al, 2016).…”