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.