Relying on the good agreement observed between the gyrokinetic PENN model and the low toroidal mode number n damping measurements from JET, the stability of Alfven eigenmodes (AEs) is predicted for reactor relevant conditions. Full non-local wave-particle power transfers are computed between global wavefields and alpha particles in an ITER reference equilibrium, showing that low-n eigenmodes (n similar or equal to 2) are strongly damped and intermediate-n eigenmodes (n similar or equal to 12) with a global radial extension are stable with a damping rate gamma/omega similar or equal to 0.02. Even though an excitation of alpha particle driven instabilities remains in principle possible in reactors, this study suggests that realistic operation scenarios exist where all the AEs of global character are stable.