Minimum Quadratic Helicity States

TL;DR

This paper investigates specific minimum quadratic helicity states in magnetohydrodynamics, demonstrating they are eigenfunctions of the curl operator and solutions to the ideal MHD equations, with minimal quadratic helicity.

Contribution

It introduces a class of eigenfunction solutions to the MHD equations that minimize quadratic helicity, extending previous theoretical results.

Findings

Eigenfunctions of the curl operator serve as minimum quadratic helicity states.

These states are solutions to quasi-stationary incompressible ideal MHD equations.

Minimum quadratic helicity states are characterized and proven to be optimal.

Abstract

Building on previous results on the quadratic helicity in magnetohydrodynamics (MHD) we investigate particular minimum helicity states. Those are eigenfunctions of the curl operator and are shown to constitute solutions of the quasi-stationary incompressible ideal MHD equations. We then show that these states have indeed minimum quadratic helicity.