A kinetic‐magnetohydrodynamic model for low‐frequency phenomena

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Abstract
A hybrid kinetic‐magnetohydrodynamic (MHD) model is presented for describing low‐frequency phenomena in high‐beta (β ∼ O(1)) anisotropic plasmas that consist of two components: a low‐energy core component and an energetic component with low density. The kinetic‐MHD model treats the low‐energy core component by magnetohydrodynamic description, the energetic component by a kinetic approach such as the gyrokinetic equation, and the coupling between the dynamics of these two components through plasma pressure in the momentum equation. The kinetic‐MHD model optimizes both the physics contents and the theoretical efforts in studying low‐frequency MHD waves and transport phenomena in general magnetic field geometries and can be easily modified to include the core plasma kinetic effects if necessary. It is applicable to any magnetized collisionless plasma system where the parallel electric field effects are negligibly small. In the linearized limit, two coupled eigenmode equations for describing the coupling between the transverse Alfvén type and the compressional Alfvén type waves are derived. The eigenmode equations are identical to those derived from the full gyrokinetic equation in the low‐frequency limit and were previously analyzed both analytically and numerically to obtain the eigenmode structure of the drift mirror instability (Cheng and Lin, 1987) which explains successfully the multisatellite observation of the antisymmetric field‐aligned structure of the compressional magnetic field of Pc 5 waves (Takahashi et al., 1987) in the magnetospheric ring current plasma. Finally, a quadratic form is derived to demonstrate the stability of the low‐frequency transverse and compressional Alfvén type instabilities in terms of the pressure anisotropy parameter τ the magnetic field curvature‐pressure gradient parameter αp as defined in equations (31) and (69), respectively. A procedure for determining the stability of a marginally stable MHD wave due to wave‐particle resonances is also presented.