Role of the mean curvature in the geometry of magnetic confinement configurations

TL;DR

This paper explores how the geometric concept of mean curvature influences magnetic confinement configurations, linking it to magnetic field variations and identifying optimal surfaces for plasma confinement.

Contribution

It demonstrates the application of mean curvature to magnetic field configurations and identifies surfaces that optimize plasma confinement in specific systems.

Findings

Mean magnetic curvature relates to magnetic field variation along lines.

Magnetic surfaces of constant mean curvature are optimal for plasma confinement.

Examples include multimirror systems and rippled tori.

Abstract

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curvature are optimum for plasma confinement in multimirror open confinement systems and rippled tori.