Nonlinear analysis of q ≳ 1 non-resonant fishbone modes in tokamak plasmas with weakly reversed magnetic shear

The nonlinear properties of q greater than or similar to 1 non-resonant fishbone (NRF) instabilities excited by energetic ions are analyzed theoretically for weakly reversed shear in this work. Nonlinear radial displacement of the NRF mode xi(0) is derived by the method of matched asymptotic expansions. It is found that xi(0) depends on the energetic ion beta in a power law of similar to beta(alpha)(h) with alpha = 1/3, alpha = 1/7, and alpha << 1, corresponding to a finite q(s)'', q(s)'' = 0, and an extremely flattened q-profile, respectively. The scaling dependence of xi(0) on the linear growth rate similar to gamma(1/4) is also different from that of similar to gamma in a conventional positive shear configuration. The scaling suggests that xi(0) weakly depends on beta(h) and gamma when the q-profile is flattened. Nonlinear saturation amplitude of the mode for an ITER-like plasma is also estimated by numerical analysis. (C) 2015 AIP Publishing LLC.