The effects of thermonuclear alpha particles on the stability of global-type shear Alfvén waves in toroidal geometry in an ignition tokamak experiment are described. The presence of finite toroidicity can lead to stabilization of the global shear Alfvén eigenmode. However, toroidicity induces a new global shear Alfvén eigenmode that can be strongly destabilized via transit resonance with alpha particles. In the proposed International Thermonuclear Experimental Reactor (ITER), due to its large size and low density, this latter mode is found to be benign.