Two-dimensional nonlinear cylindrical equilibria with reversed magnetic shear and sheared flow

Abstract

Nonlinear translational symmetric equilibria with up to quartic flux terms in free functions, reversed magnetic shear, and sheared flow are constructed in two ways: (i) quasi-analytically 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. This latter case presented in Sec. 4 is relevant to the International Thermonuclear Experimental Reactor project. The equilibrium characteristics are then examined by means of 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.