Testing magnetic helicity conservation in a solar-like active event^⋆

¹ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
e-mail: etienne.pariat@obspm.fr
² UCL-Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK
³ CISL/HAO, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000, USA

Received: 5 February 2015
Accepted: 18 June 2015

Abstract

Context. Magnetic helicity has the remarkable property of being a conserved quantity of ideal magnetohydrodynamics (MHD). Therefore, it could be used as an effective tracer of the magnetic field evolution of magnetized plasmas.

Aims. Theoretical estimations indicate that magnetic helicity is also essentially conserved with non-ideal MHD processes, for example, magnetic reconnection. This conjecture has been barely tested, however, either experimentally or numerically. Thanks to recent advances in magnetic helicity estimation methods, it is now possible to numerically test its dissipation level in general three-dimensional datasets.

Methods. We first revisit the general formulation of the temporal variation of relative magnetic helicity on a fully bounded volume when no hypothesis on the gauge is made. We introduce a method for precisely estimating its dissipation independently of which type of non-ideal MHD processes occurs. For a solar-like eruptive-event simulation, using different gauges, we compare an estimate of the relative magnetic helicity computed in a finite volume with its time-integrated flux through the boundaries. We thus test the conservation and dissipation of helicity.

Results. We provide an upper bound of the real dissipation of magnetic helicity: It is quasi-null during the quasi-ideal MHD phase. Even with magnetic reconnection, the relative dissipation of magnetic helicity is also very low (<2.2%), in particular compared to the relative dissipation of magnetic energy (>30 times higher). We finally illustrate how the helicity-flux terms involving velocity components are gauge dependent, which limits their physical meaning.

Conclusions. Our study paves the way for more extended and diverse tests of the magnetic helicity conservation properties. Our study confirms the central role of helicity in the study of MHD plasmas. For instance, the conservation of helicity can be used to track the evolution of solar magnetic fields from when they form in the solar interior until their detection as magnetic clouds in the interplanetary space.