Motivated by recent satellite observations, we have carried out a comprehensive theoretical analysis on the generation of hydromagnetic Alfvén waves in a realistic magnetospheric plasma environment consisting of a core (∼100 eV) component and an 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 functions which are interchange stable. Our findings are as follows: (1) compressional and transverse shear Alfvén 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 τ ≡ 1 + 4π(∂P/BB) < 0; here, P = P(ψ, B) is the perpendicular pressure and ψ is the magnetic flux function; (3) for the decoupled transverse shear Alfvén branch, one obtains the drift Alfvén ballooning instability due to the Landau resonances and free energy of the pressure gradient for τ > 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 Alfvén ballooning instabilities. Thus we conclude that for τ ≥ 0, the coupled drift Alfvén ballooning mirror instability constitutes an important internal generating mechanism of geomagnetic pulsations. The various predicted features of this instability are consistent with satellite observations.