Theory of self-generated vortex flows in a tokamak magnetic island

We present a gyrokinetic theory of an E × B vortex flow in a magnetic island self-generated from turbulence in a collisionless tokamak plasma. We have found that after fast collisionless damping, the self-generated vortex flow arrives at a residual level higher than the Rosenbluth-Hinton level predicted in the tokamak geometry. In the longer term, the residual vortex flow undergoes further damping with a deformation toward a zonal-vortex mixture, making open streamlines near the X-points that reduce the isolated region of the island. It is due to the helical symmetry breaking by the toroidal precession, expected to be stronger in higher-temperature plasmas and in lower aspect ratio tokamaks. A strong enough background vortex flow can significantly suppress the toroidicity-induced damping and deformation of the self-generated vortex flow, proposing that the island boundary is a key location for the bifurcation of the confinement state.