Anisotropic Alfvén‐ballooning modes in Earth's magnetosphere

Abstract

We have carried out a theoretical analysis of the stability and parallel structure of coupled shear Alfvén and slow magnetosonic waves in Earth's inner magnetosphere (i.e., at equatorial distances between about five and ten Earth radii) including effects of finite anisotropic plasma pressure. Multiscale perturbation analysis of the anisotropic Grad‐Shafranov equation yields an approximate self‐consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfvén‐ballooning modes. The main results are: (1) The field line eigenfrequency can be significantly lowered by finite pressure effects. (2) The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure, but the compressional magnetic component can become highly peaked near the magnetic equator as a result of increased pressure, especially when P⊥ > P∥ (here P⊥ and P∥ are the perpendicular and parallel plasma pressure). (3) For the isotropic (P∥ = P⊥ = P) case ballooning instability can occur when the ratio of the plasma pressure to the magnetic pressure, β = P/(B²/8π), exceeds a critical value β0B ≈ 3.5 at the equator. (4) Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field line bending stabilization when P∥ > P⊥ or due to increased ballooning‐mirror destabilization when P⊥ > P∥ (5) We use a β‐δ stability diagram to display the regions of instability with respect to the equatorial values of the parameters β and δ, where β¯=(1/3)(β∥+2β⊥) is an average beta value and δ = 1 − P∥/P⊥ is a measure of the plasma anisotropy. The diagram is divided into regions corresponding to the firehose, mirror and ballooning instabilities. It appears that observed values of the plasma pressure are below the critical value for the isotropic ballooning instability but it may be possible to approach a ballooning‐mirror instability when P⊥/P∥ ≳ 2.