Quadratic helicities and the energy of magnetic fields

TL;DR

This paper introduces two non-local invariants of magnetic fields in ideal magnetohydrodynamics, estimates their variation in non-ideal conditions, and explores their role in magnetic field relaxation.

Contribution

It presents new non-local invariants called quadratic helicities and analyzes their significance in magnetic field dynamics and relaxation processes.

Findings

Invariants help understand magnetic field spectra.

Variation estimates for non-ideal MHD.

Discussion on higher magnetic helicities in relaxation.

Abstract

Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A possible role of higher magnetic helicities during a relaxation of magnetic fields is discussed.