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Nonlinear tranlational symmetric equilibria with up to quartic flux terms in the free functions, reversed magnetic shear and sheared flow are constructed in two ways: i) quasianalytically by an ansatz which reduces the pertinent generalized Grad-Shafranov equation to a set of ordinary differential equations and algebraic constraints which is then solved numerically, and ii) completely numerically by prescribing analytically a boundary having an X-point. The equilibrium characteristics are then examined by means of the pressure, safety factor, current density and electric field. For flows parallel to the magnetic field the stability of the equilibria constructed is also examined by applying a sufficient condition. It turns out that the equilibrium nonlinearity has a stabilizing impact which is slightly enhanced by the sheared flow. In addition, the results indicate that the stability is affected by the up-down asymmetry., Comment: 16 pages, 12 figures

The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of two-fluid model. The study is based on exact self-consistent solutions in cylindrical geometry by means of which the impact of the magnetic shear, s, and the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components on the radial electric field, its shear and the shear of the ExB velocity is examined. For a wide parametric regime of experimental concern it turns out that the contributions of the toroidal and poloidal velocity and pressure gradient terms to the electric field, its shear and ExB velocity shear are of the same order of magnitude. The impact of s on ExB velocity shear through the pressure gradient term is stronger than that through the velocity terms. The results indicate that, alike MHD, the magnetic shear and the sheared toroidal and poloidal velocities act synergetically in producing electric fields and therefore ExB velocity shear profiles compatible with ones observed in discharges with ITBs; owing to the pressure gadient term, however, the impact of s on the electic field, its shear and the shear of ExB velocity is stronger than that in MHD., 25 pages, 21 figures

We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).

A necessary condition for the existence of general dissipative magneto-hydrodynamic equilibria is derived. The derivation comprises Ohm's law and the existence of magnetic surfaces, only in the sense of the Kolmogorov–Arnold–Moser (KAM) theorem. All other equations describing the system are only required for evaluating the condition for a specific case.