The excitation of Toroidal Alfven Eigenmodes by high energy alpha part
icles is examined. Specifically, the kinetic alpha-particle response i
s retained directly in the linear mode coupling-equations, and represe
nts a driving source proportional to the spatial gradient of the alpha
distribution. The model is an extension of the recently studied high-
m, large-aspect-ratio, asymptotic boundary layer theory of the nonidea
l TAE [1], and provides a self-consistent method for the determination
of the instability threshold and growth rate of the excited TAE. Anal
ytical and numerical stability thresholds are presented for the simple
case of slowly varying density and shear.