Determination of a flow generating a neutral magnetic mode

TL;DR

This paper investigates how to reconstruct fluid flows that generate specific magnetic modes in conducting fluids, using magnetic induction equations and additional data, and shows limitations on possible neutral magnetic modes.

Contribution

It introduces a method to determine flows generating magnetic modes using differential equations along field lines and proves that not all solenoidal fields can be neutral modes.

Findings

Derived ODEs along magnetic field lines for flow reconstruction

Established conditions for flow generation of magnetic modes

Proved that some solenoidal fields cannot be neutral modes

Abstract

The problem of reconstruction of a flow of conducting incompressible fluid generating a given magnetic mode is considered. We use the magnetic induction equation to derive ordinary differential equations along the magnetic field lines, which give an opportunity to determine the generating flow, if additional data is provided on a two-dimensional manifold transversal to magnetic field lines, and show that an arbitrary solenoidal vector field can not be a neutral magnetic mode sustained by any flow of conducting fluid.