The growth rate of toroidal Alfven eigenmodes (TAEs) driven unstable by resonant coupling of energetic charged particles is evaluated in the `ballooning` limit over a wide range of parameters. All damping effects are ignored. Variations in orbit width, aspect ratio and the ratio of Alfven velocity to energetic particle `birth` velocity are explored. The relative contribution of passing and trapped particles, and finite Larmor radius effects, are also examined. The phase space location of resonant particles that interact strongly with the modes is described. The accuracy of the analytic results with respect to growth rate magnitude and parametric dependence is investigated by comparison with numerical results