Energetic ion beta scaling of q ≳ 1 non-resonant modes in tokamak plasmas with a weak magnetic shear configuration

Fast ion beta scaling of non-resonant modes (NRMs) with a safety factor profile close to but above unity (q(min) greater than or similar to 1) in tokamak plasmas with a reversed magnetic shear configuration, particularly those with a weak shear (q(s)'' similar to 0) of around q(min), are analysed in this study. It is found that, in three different regimes of magnetic shear configuration, the fast ion beta scaling of the NRM growth rate are: (1) similar to beta(2/3)(h) in the small but finite q(s)'' regime, (2) similar to beta(4/7)(h), in the q(s)'' = 0 regime, and (3) similar to beta(1/2)(h) in an almost flat q-profile regime. The scalings suggest that the growth rate of the mode is related to the fast ion beta and weakens as the q-profile is flattened. The dispersion relation of NRM in the q(s)'' = 0 regime is then derived and analysed.