Radial penetration of flux surface shaping in tokamaks

TL;DR

This paper analytically investigates how flux surface shaping penetrates in tokamaks, highlighting the roles of magnetic field variation, flux surface shape, and current profiles in shaping the plasma core.

Contribution

It introduces a method to analyze the effects of magnetic pressure and tension on flux surface shaping penetration in tokamaks.

Findings

Shaping penetration depends on poloidal magnetic field variation.

Hollow current profiles better transmit edge shaping to the core.

A technique to separate magnetic pressure and tension effects is developed.

Abstract

Using analytic calculations, the effects of the edge flux surface shape and the toroidal current profile on the penetration of flux surface shaping are investigated in a tokamak. It is shown that the penetration of shaping is determined by the poloidal variation of the poloidal magnetic field on the surface. This fact is used to investigate how different flux surface shapes penetrate from the edge. Then, a technique to separate the effects of magnetic pressure and tension in the Grad-Shafranov equation is presented and used to calculate radial profiles of strong elongation for nearly constant current profiles. Lastly, it is shown that more hollow toroidal current profiles are significantly better at conveying shaping from the edge to the core.