The stability of global Alfve´n eigenmodes is investigated in the presence of super‐Alfve´nic energetic particles, such as fusion‐product alpha particles in an ignited deuterium–tritium tokamak plasma. Alpha particles tend to destabilize these modes when &ohgr;@B|&agr;>&ohgr;A, where &ohgr;Ais the shear‐Alfve´n modal frequency and &ohgr;*&agr;is the alpha particle diamagnetic drift frequency. This destabilization due to alpha particles is found to be significantly enhanced when the alpha particles are modeled with a slowing‐down distribution function rather than with a Maxwellian distribution. However, previously neglected electron damping due to the magnetic curvature drift is found to be comparable in magnitude to the destabilizing alpha particle term. Furthermore, the effects of toroidicity are also found to be stabilizing, since the intrinsic toroidicity induces poloidal mode coupling, which enhances the parallel electron damping from the sideband shear‐Alfve´n Landau resonance. In particular, for typical ignition tokamak parameters, global Alfve´n eigenmodes are found to be completely stabilized by either the electron damping that enters through the magnetic curvature drift or the damping introduced by finite toroidicity.