Additivity of relative magnetic helicity in finite volumes 

Gherardo Valori Submitted: 20200804 02:51
Relative magnetic helicity is conserved by magnetohydrodynamic 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 nonadditivity 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 gaugeinvariant expression for the partition of relative magnetic helicity between contiguous
finitevolumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge.
he nonadditivity of relative magnetic helicity in finite volumes is proven in the most general, gaugeinvariant 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 nonadditivity term in the
partition equation is, in general, nonnegligible.
The nonadditivity 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 nonadditivity 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: 20200805 14:12


