The paper on magnetic helicity and its conservation has been accepted in Astronomy & Astrophysics :
E. Pariat, G. Valori, P. Démoulin, K. Dalmasse:
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 magnetised plasmas.
Theoretical estimations indicate that magnetic helicity is also essentially conserved with non-ideal MHD processes, e.g. magnetic reconnection. This conjecture has however been barely tested, either experimentally or numerically. Thanks to recent advances in magnetic helicity estimation methods, it is now possible to test numerically its dissipation level in general three-dimensional datasets.
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 are made. We introduce a method to precisely estimate its dissipation independently of the type of non-ideal MHD processes occurring. In a solar-like eruptive event simulation, using different gauges, we compare its estimation in a finite volume with its time-integrated flux through the boundaries, hence testing the conservation and dissipation of helicity.
We provide an upper bound of the real dissipation of magnetic helicity: It is quasi-null during the quasi-ideal MHD phase. Even when magnetic reconnection is acting the relative dissipation of magnetic helicity is also very small (<2.2%), in particular compared to the relative dissipation of magnetic energy (>30 times larger). We finally illustrate how the helicity-flux terms involving velocity components are gauge dependent, hence limiting their physical meaning.
Our study paves the way for more extended and diverse tests of the magnetic helicity conservation properties. Our study confirms the central role that helicity can play in the study of MHD plasmas. For instance, the conservation of helicity can be used to track the evolution of solar magnetic fields, from its formation in the solar interior until their detection as magnetic cloud in the interplanetary space.