  In the second magnetohydrodynamic (MHD) ballooning stable domain of a
high-beta tokamak plasma, the Schroedinger equation for ideal MHD shear Alfven
waves has discrete solutions corresponding to standing waves trapped between
pressure-gradient-induced potential wells. Our goal is to understand how these
so-called alpha-induced toroidal Alfven eigenmodes alpha-TAE are modified by
the effects of finite Larmor radii (FLR) and kinetic compression of thermal
ions in the limit of massless electrons. In the present paper, we neglect
kinetic compression in order to isolate and examine in detail the effect of FLR
terms. After a review of the physics of ideal MHD alpha-TAE, the effect of FLR
on the Schroedinger potential, eigenfunctions and eigenvalues are described
with the use of parameter scans. The results are used in a companion paper to
identify instabilities driven by wave-particle resonances in the second stable
domain.
