Axisymmetric equilibria with pressure anisotropy and plasma flow

TL;DR

This thesis develops a generalized Grad-Shafranov equation to analyze how pressure anisotropy and plasma flow influence equilibrium states in axisymmetric toroidal plasmas, with solutions relevant to ITER and NSTX tokamaks.

Contribution

It introduces a new generalized Grad-Shafranov equation incorporating pressure anisotropy and flow, and constructs analytical solutions for specific plasma boundary conditions.

Findings

Pressure anisotropy can be paramagnetic or diamagnetic depending on its shape.

Flow and anisotropy have stronger effects on NSTX than on ITER equilibria.

The effects of anisotropy and flow may influence plasma stability and confinement transitions.

Abstract

In this Master thesis we investigate the influence of pressure anisotropy and incompressible flow of arbitrary direction on the equilibrium properties of magnetically confined, axisymmetric toroidal plasmas. The main novel contribution is the derivation of a pertinent generalised Grad-Shafranov equation. 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, through an anisotropy function assumed to be uniform on the magnetic surfaces, and plasma flow, via the variation of an Alfvenic Mach function, 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. We conjecture that these effects may have an influence on plasma stability and transport, and play a role in the transitions to the improved confinement regimes in tokamaks.