Conservation of currents in reduced full-F electromagnetic kinetic and fluid models

In this paper, we present an analysis of the conservation of currents in a full-F electromagnetic gyro-kinetic model in the long-wavelength limit. This equation corresponds to what is usually called the 'vorticity equation', which is not strictly correct as it cannot be formulated as the curl of a velocity equation. In the paper, we will therefore use the term 'current conservation equation' instead. Our 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 E x B flow, external sources and three currents: the parallel current, the curvature current and a current related to the magnetic field fluctuations. We compare this equation 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. We discuss the role of currents in the dynamics of diamagnetic and E x B flow shear. 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, and different magnetic field configurations and shapes, is presented.