Axisymmetric equilibria with pressure anisotropy and plasma flow

TL;DR

This paper derives a comprehensive equation for axisymmetric plasma equilibrium considering pressure anisotropy and flow, providing analytical solutions relevant to tokamaks like ITER and NSTX, and analyzing their effects.

Contribution

It introduces a generalized Grad-Shafranov equation incorporating anisotropic pressure and flow, with analytical solutions and analysis of their impacts on tokamak equilibria.

Findings

Pressure anisotropy can be paramagnetic or diamagnetic.

Flow and anisotropy have stronger effects on NSTX than ITER.

Analytical solutions for plasma equilibria with X-point and separatrix.

Abstract

A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones.