ANISOTROPIC ALFVEN-BALLOONING MODES IN EARTHS MAGNETOSPHERE

We have carried out a theoretical analysis of the stability and parall el structure of coupled shear Alfven and slow magnetosonic waves in Ea rth's inner magnetosphere (i.e., at equatorial distances between about five and ten Earth radii) including effects of finite anisotropic pla sma pressure. Multiscale perturbation analysis of the anisotropic Grad -Shafranov equation yields an approximate self-consistent magnetohydro dynamic (MHD) equilibrium. This MHD equilibrium is used in the numeric al solution of a set of eigenmode equations which describe the field l ine eigenfrequency, linear stability, and parallel eigenmode structure . We call these modes anisotropic Alfven-ballooning modes. The main re sults are: (1) The field line eigenfrequency can be significantly lowe red by finite pressure effects. (2) The parallel mode structure of the transverse wave components is fairly insensitive to changes in the pl asma pressure, but the compressional magnetic component can become hig hly peaked near the magnetic equator as a result of increased pressure , especially when P-perpendicular to > P-parallel to (here P-perpendic ular to and P-parallel to are the perpendicular and parallel plasma pr essure). (3) For the isotropic (P-parallel to = P-perpendicular to = P ) case ballooning instability can occur when the ratio of the plasma p ressure to the magnetic pressure, beta = P/(B-2/8 pi), exceeds a criti cal value beta(0)(B) approximate to 3.5 at the equator. (4) Compared t o the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field line bending stabilization when P-paral lel to > P-perpendicular to or due to increased ballooning-mirror dest abilization when P-perpendicular to > P-parallel to. (5) We use a beta -delta stability diagram to display the regions of instability with re spect to the equatorial values of the parameters ($) over bar beta and S, where ($) over bar beta = (1/3)(beta(parallel to) + 2 beta(perpend icular to)) is an average beta value and delta = 1 - P-parallel to/P-p erpendicular to is a measure of the plasma anisotropy. The diagram is divided into regions corresponding to the firehose, mirror and balloon ing instabilities. It appears that observed values of the plasma press ure are below the critical value for the isotropic ballooning instabil ity but it may be possible to approach a ballooning-mirror instability when P-perpendicular to /P-parallel to greater than or similar to 2.