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 even weak toroidal asymmetry can significantly change the structure of Torodicity-induced Alfven Eigenmodes (TAE) with high toroidal mode number n, producing wave functions strongly anharmonic in the toroidal coordinate. In this work, the effect of the toroidal asymmetry on TAE modes with finite n in stellarators is studied with the code BOA-fe. 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. As the asymmetry is gradually increased to realistic values, the modes become strongly mixed (that is, mixed wave functions arise in which the contributions of separate TAE-modes are comparable). The mixed wave functions are strongly anharmonic, having a tendency to localization along field lines. The strong mixing is achieved most easily for modes with large n; then it spreads to lower n as the asymmetry increases. An analytical estimate for the level of asymmetry required to mix the modes is derived, which results from a relationship between the difference of the mode frequencies and the matrix element of their interaction due to asymmetry. The estimate is in agreement with the numerical results. The critical value of n for the mode mixing is evaluated analytically, depending on the profile of the rotational transform and parameters of the magnetic configuration. Possible influence of non-ideal factors on the obtained solutions is discussed. The circumstances under which strongly anharmonic TAE-modes can be observed experimentally in stellarators are outlined. (author)