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Additivity of relative magnetic helicity in finite volumes View all abstracts by submitter

Gherardo Valori   Submitted: 2020-08-04 02:51

Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, i.e., that it is an additive quantity. A limited number of very specific applications have shown that this is not the case. Progress in understanding the non-additivity of relative magnetic helicity requires removal of restrictive assumptions in favour of a general formalism that can be used both in theoretical investigations as well as in numerical applications. We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite-volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge. he non-additivity of relative magnetic helicity in finite volumes is proven in the most general, gauge-invariant formalism, and verified numerically. More restrictive assumptions are adopted to derive known specific approximations, yielding a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the non-additivity term in the partition equation is, in general, non-negligible. The non-additivity of relative magnetic helicity can potentially be a serious impediment to the application of relative helicity conservation as a constraint to the complex dynamics of magnetized plasmas. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of non-additivity on global helicity budgets of complex physical processes.

Authors: Gherardo Valori, Pascal Démoulin, Etienne Pariat, Anthony Yeates, Kostas Moraitis and Luis Linan
Projects: None

Publication Status: Accepted for publication in Astronomy & Astrophysics
Last Modified: 2020-08-05 14:12
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