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

TL;DR

This paper constructs and analyzes nonlinear two-dimensional cylindrical plasma equilibria with reversed magnetic shear and sheared flow, exploring their stability and the effects of nonlinearity and asymmetry.

Contribution

It introduces two methods for constructing nonlinear equilibria with reversed shear and flow, and examines their stability and characteristics.

Findings

Nonlinear equilibrium nonlinearity stabilizes the plasma.

Sheared flow slightly enhances stability.

Up-down asymmetry influences stability.

Abstract

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.