Long Term Vortex Flow Evolution around a Magnetic Island in Tokamaks

We present a gyrokinetic analysis of the vortex flow evolution in a magnetic island in collisionless tokamak plasmas. In a short term ω[over ¯]_{D}t<1, where ω[over ¯]_{D} is the secular magnetic drift of the orbit center, initial monopolar vortex flow approaches to its residual level determined by the neoclassical enhancement of polarization shielding after collisionless relaxation. The residual level depends on the location inside an island and is higher than the Rosenbluth-Hinton level [M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett. 80, 724 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.724] due to finite island width. In a long term ω[over ¯]_{D}t>1, the residual vortex flow evolves to a dipolar zonal-vortex flow mixture due to toroidicity-induced breaking of a helical symmetry. The mixture forms localized flow shear layers near the island separatrix away from X points. The deviation of the streamlines of the mixture flows from magnetic surfaces allows turbulence advection across the island. We expect a small island w≲qρ_{Ti}/s[over ^] provides a favorable condition for this mixture flow formation, while the monopolar vortex flow persists for a larger island.