Theory of a high-n toroidicity-induced shear Alfvén eigenmode in tokamaks

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Abstract
A high‐n WKB‐ballooning mode equation is employed to study toroidicity‐induced shear Alfvén eigenmodes (TAE) in s‐α space, where s=(r/q)(dq/dr) is the magnetic shear and α=−(2Rq2/B2)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value αc. It is found that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by the Wentzel–Kramers–Brillouin (WKB) method and are found to be bounded radially if the local mode frequency has a maximum in radius.