Second Harmonics of Reversed Shear TAE in Alcator C-Mod Geometry

Experiments on Alcator C-Mod, operating with reversed magnetic shear, reveal Toroidal Alfven Eigenmodes (TAE) together with signals at twice the mode frequency. The double frequency signals can be viewed as second harmonic sidebands driven by quadratic non-linear terms in the MHD equations, in analogy with a corresponding theory for Alfven Cascades [1]. However, these nonlinear sidebands have not yet been quantified by any of \newline the existing codes. In this work, we extend AEGIS code [2] to capture nonlinear effects iteratively by treating the nonlinear terms as a driving source in the linear MHD solver.~ We first compute the TAE mode structure for realistic geometry and q-profile and then use it to find the spatial structure of the second harmonic density perturbation, which can be directly compared with PCI measurements at Alcator C-Mod. [1] H. Smith, B. N. Breizman, M. Lisak and D. Anderson, Physics of Plasmas 13 042504 (2006) [2] L. J. Zheng and M. Kotschenreuther, Journal of Computational Physics 211 (2006) 748-766