A numerical study of the high-<i>n</i> shear Alfvén spectrum gap and the high-<i>n</i> gap mode

The toroidicity-induced gaps of the shear Alfvén wave spectrum in tokamaks are shown to satisfy an envelope equation. The structure of these gaps, and the location of the high-n gap modes, which are localized modes with frequency in the gap, are studied for general numerically generated equilibria. The dependence of the frequencies of the gaps and the gap modes on the equilibrium properties, such as elongation, triangularity, and β of the plasma are explored.