Rigorous new limits on magnetic helicity dissipation in the solar corona

TLDR

Determining the free energy in magnetic structures is difficult due to constraints imposed by magnetic helicity conservation. The study uses the Cauchy–Schwarz inequality to derive geometry‑independent limits on magnetic helicity dissipation in resistive plasmas. The authors apply the inequality to relate helicity dissipation to plasma energy, dissipation rate, and mean diffusion coefficient. The limits depend only on total energy, dissipation rate, and diffusion coefficient; for isolated plasmas they set a minimum helicity decay time, and in solar coronal loops the limits imply decay on a diffusion timescale too long to affect most coronal processes, while rapid reconnection likely conserves helicity.

Abstract

Abstract The Cauchy-Schwarz inequality is employed to find geometry-independent limits on the magnetic helicity dissipation rate in a resistive plasma. These limits only depend upon the total energy of the plasma, the energy dissipation rate, and a mean diffusion coefficient. For plasmas isolated from external energy sources, limits can also be set on the minimum time necessary to dissipate a net amount of helicity ΔH. As evaluated in the context of a solar coronal loop, these limits strongly suggest that helicity decay occurs on a diffusion timescale which is far too great to be relevant to most coronal processes. Furthermore, rapid reconnection is likely to approximately conserve magnetic helicity. The dilliculties involved in determining the free energy residing in a magnetic structure (given the constraint of magnetic helicity conservation) are discussed.