On heteroclinic separators of magnetic fields in electrically conducting fluids

TL;DR

This paper investigates the existence of heteroclinic separators in magnetic fields within plasma, demonstrating their presence in specific 3-dimensional bodies and linking the problem to dynamical systems theory.

Contribution

It introduces a new approach to prove the existence of magnetic field separators in plasma with specific boundary conditions, connecting plasma physics and dynamical systems.

Findings

Heteroclinic separators exist in 3-annulus and 'fat' orientable surfaces with two holes.

The study links plasma magnetic field topology to dynamical systems theory.

The method provides a partial solution to the separator existence problem.

Abstract

In this paper we partly solve the problem of existence of separators of a magnetic field in plasma. We single out in plasma a 3-body with a boundary in which the movement of plasma is of special kind which we call an (a-d)-motion. We prove that if the body is the 3-annulus or the "fat" orientable surface with two holes the magnetic field necessarily have a heteroclinic separator. The statement of the problem and the suggested method for its solution lead to some theoretical problems from Dynamical Systems Theory which are of interest of their own.