Motivated by recent satellite observations, we have carried out a comprehensive theoretical analysis on the generation of hydromagnetic Alfv¿n waves in a realistic magnetospheric plasma environment consisting of a core (~100 eV) component and energetic (~10 keV) component. Our theoretical formulation employs the gyrokinetic equations and, thus, retains anisotropy, finite Larmor radii, magnetic trapping, and wave-particle interactions in addition to nonuniform plasma equilibria. A set of coupled equations for transverse and compressional magnetic perturbations is derived and analyzed for its stabilities assuming equilibrium distribution function which are interchange stable. Our findings are as follows: (1) compressional and transverse shear Alfv¿n oscillations are generally coupled in realistic plasmas; (2) in the decoupled limit, for the compressional wave branch, one recovers the drift mirror instability due to the Landau resonances and &tgr;≡1+4&pgr;(∂P⊥/B∂B)0; (4) for both branches, the most unstable modes have antisymmetric structures and propagate in the diamagnetic drift direction of the energetic ions; and (5) finite coupling can be shown to further enhance the drift Alfv¿n ballooning instabilities. Thus we conclude that for &tgr;≥0, the coupled drift Alfv¿n ballooning mirror instability constitutes an important internal generating mechanism of geomagnetic pulsations. The various predicted features of this instability are consistent with satellite observations. ¿1991 American Geophysical Union