In this presentation, an analysis of the conservation of currents in a full-F electromagnetic gyro-kinetic model in the long-wavelength limit will be presented. This equation corresponds to what is usually named "vorticity equation”. In the presentation, reasons to not keep using this name will be presented. These results are relevant to reduced plasma descriptions like gyro-kinetic, drift-kinetic, gyro-fluid and drift-fluid models for tokamaks and stellarators. The equation describes the change of the polarization charge density (often called "vorticity") in terms of the polarization stress due to the ExB flow, external sources and three currents: the parallel current, the curvature current and a current related to the magnetic field fluctuations. The derived equation is compared with previous drift- and gyro-fluid equations and find general agreement except in the vorticity source terms where previous drift-fluid models fail to capture the heating and density sources. The role of the currents in the dynamics of diamagnetic and \ExB flow shear and the possible connection between these currents with phenomena observed in experiments that influence the radial electric field in the edge of tokamak plasmas, like resonant magnetic perturbations, different magnetic field configurations and shapes, is presented.
[mehr]