Effect of the Toroidal Asymmetry on the Structure of TAE Modes in Stellarators

It was found recently with the use of the ballooning formalism that the toroidal asymmetry of the stellarator magnetic configuration can significantly change the structure of Torodicity-induced Alfvén Eigenmodes (TAE) with high toroidal mode numbers (n), producing singular (stepwise) wave functions [Yakovenko, Yu.V., et al., Energetic Particles in Magnetic Confinement Systems (Proc. 10th IAEA Tech. Mtg, Kloster Seeon, 2007), IAEA, Vienna (2008), CD-ROM file Iv.03]. In this work, the effect of the toroidal asymmetry on TAE-modes with finite n in stellarators is studied with the code BOA-en. A sequence of TAE-modes with almost the same frequency and localization but with different n is considered. The asymmetry consecutively couples the modes in the sequence. When the magnitude of the asymmetry is sufficiently large, the modes are strongly mixed (that is, the contributions of separate TAE-modes to the resulting wave functions are comparable). The mixed wave functions are strongly anharmonic in the toroidal direction, having a tendency to localization of the wave energy along certain field lines. They cannot be characterized by a certain number n; their periodicity in the toroidal direction is determined by the periodicity of the magnetic configuration harmonic that couples the individual TAEmodes. Strongly anharmonic TAE-modes can appear most easily in stellarators with an even number of the field periods (N). In particular, one can expect that the TAE-modes that will appear near several rational flux surfaces in the 2-period stellarator QPS may turn out to be strongly anharmonic. In the devices with odd N , coupling between TAE-modes with different n is weaker, and Ellipticity-induced Alfvén Eigenmodes (EAE) may become strongly anharmonic more easily than the TAE-modes.