Breaking Quasi-translational Invariance of Toroidal Eigenmodes

Toroidal eigenmode structure in the presence of strong ${\bf E \times B}$ shear is examined to explore a possible spontaneous symmetry breaking in the parallel wave vector of turbulence which can contribute to radial flux of toroidal angular momentum. Even in the weak shear limit, FULL code [1]results have shown a significant departure of mode structure from the usual ballooning-type eigenmode towards the CZC-like [2] mode structure with the amplitude peaking between rational surfaces. In the strong shear limit, Ballooning Mode Formalism is confusing and invalid. At the low B field side, the radial eigenmode equation can be reduced to the Whittaker's form which should obey the Berk outgoing wave condition [3]. However, the magnetic shear induced damping is negligible and the most effective damping is from the perpendicular ${\bf E \times B}$ flow shear. \newline [1] G. Rewoldt et al., Nucl. Fusion, 42, 403 (2002). \newline [2] C.Z. Cheng, L. Chen, and M. Chance, Ann. Phys. 161, 21 (1985). \newline [3] L.D. Pearlstein and H. Berk, Phys. Rev. Lett. 23, 2209 (1982).