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Vortex nucleation in strongly sheared poloidal rotation and effects on velocity saturation and generation of ELM modes

The vorticity field in tokamak evolves to self organization and is concentrated in a narrow layer at the edge. The particle density and the current density have local maxima on the same layer, leading to destabilization of the rotation, breaking up of the layer and filamentation. We propose this as a basic model for the Edge Localized Modes. Large scale vorticity is injected in tokamak plasma via external heating (NBI, ICRH) and evolves to an equilibrium profile via the balance of torque. The drive-dissipation is not the unique factor in the dynamics since the vorticity cannot have an arbitrary equilibrium profile in a 2D plasma. It has natural profiles corresponding to the spatial distributions of the streamfunction ψ of the poloidal velocity which are extrema of a particular action functional [1]. The extrema of that action functional are governed by a differential equation Δψ + 1 2 sinhψ (coshψ −1) = 0 (1) Solving this equation one identifies natural profiles of the vorticity which in the phase space represent attractors. Essentially the vorticity separates into two regions with opposite signs: in the center it is collected the vorticity of one sign and at the perifery it is expelled the vorticity of the opposite sign. This is a particular form of dipolar structure, of the same nature as, for example, the Larichev-Reznik modon, but in cylindrical geometry it has superior stability compared to the situation where the regions of opposite vorticity are side-by-side, and it is compatible with global rotation. The states consisting of this radial separation are actually not stationary, they continue to evlove on a slow time scale toward the strict localisation of the vorticity of the appropriate sign in a region close to the edge, leading to a narrowing of the layer of poloidal rotation. An