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Effects of energetic particles on zonal flow generation by toroidal Alfvén eigenmode
A. Mikhailovskii, Zh. Eksp. Teor. Fiz 68, 1772 (1975).
Z. Wang, Z. Lin, and I. Holod, “ Generation of zonal fields by toroidal Alfvén eigenmode” (submitted).
F. Zonca, S. Briguglio, L. Chen, G. Fogaccia, and G. Vlad, “ Theoretical aspects of collective mode excitations by energetic ions in Tokamaks,” in Joint Varenna Workshop, Italy (2000).
Note that in Ref. 14, the fine structure of ZF is not considered, such that there is no term.
Note that EP linear contribution to ZFZS may qualitatively change the expression of the neoclassical polarization,27 but detailed analysis of this effect is beyond the scope of this paper.
Note that in deriving Equation (12), we assumed small EP drift orbit in the ideal region. The same equation can be obtained by assuming that EP response is dominated by the l = ±1 transit resonances, while no assumptions on EP drift orbit is needed.
Note that the algebraic growth is obtained from Equation (13). However, as γL → 0, the present analysis is not valid anymore, and both wave-particle nonlinearity and wave-wave nonlinearity due to thermal plasma responses must be taken into account.
Note that phase space wave-particle nonlinearities is not included in the present system yet,1,9 as anticipated in our comments following Equation (8).
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Generation of zonal flow (ZF) by energetic particle (EP) driven toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and micro-scale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.
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