Two-dimensional shaping of Solov'ev equilibrium with vacuum using external coils

TL;DR

This paper presents a method for shaping Solov'ev equilibrium with arbitrary 2D boundary using external coils, applicable to tokamak plasma shaping in vacuum regions.

Contribution

It introduces a novel computational approach combining Green function method and matching conditions for flexible 2D plasma boundary shaping.

Findings

Accurate and robust construction of 2D plasma shapes.

Efficient computation of magnetic fields in vacuum regions.

Applicable to general tokamak plasma shaping scenarios.

Abstract

In this work, we demonstrate a method for constructing the Solov'ev equilibrium with any given 2D shape surrounded by a vacuum region using external poloidal field coils. The computational domain consists of two parts: the plasma region, where the solution is the same as the Solov'ev solution, and the vacuum region, where the magnetic field generated by external coils as well as plasma current is determined using the Green function method through a matching condition near the separatrix. However, the method is not limited to the Solov'ev equilibrium in particular. The accuracy, efficiency, and robustness of such a scheme suggest that this method may be applied to the 2D shaping of tokamak plasma with vacuum region using external coils in general.