Misc,
Magnetic helicity estimations in models and observations of the solar magnetic field. Part I: Finite volume methods
(Oct 7, 2016)
Abstract
Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics
characterized by an inverse turbulent cascade. Accordingly, it is often invoked
as one of the basic physical quantities driving the generation and structuring
of magnetic fields in a variety of astrophysical and laboratory plasmas. We
provide here the first systematic comparison of six existing methods for the
estimation of the helicity of magnetic fields known in a finite volume. All
such methods are reviewed, benchmarked, and compared with each other, and
specifically tested for accuracy and sensitivity to errors. To that purpose, we
consider four groups of numerical tests, ranging from solutions of the
three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical
simulations. Almost all methods are found to produce the same value of magnetic
helicity within few percent in all tests. In the more solar-relevant and
realistic of the tests employed here, the simulation of an eruptive flux rope,
the spread in the computed values obtained by all but one method is only 3\%,
indicating the reliability and mutual consistency of such methods in
appropriate parameter ranges. However, methods show differences in the
sensitivity to numerical resolution and to errors in the solenoidal property of
the input fields. In addition to finite volume methods, we also briefly discuss
a method that estimates helicity from the field lines' twist, and one that
exploits the field's value at one boundary and a coronal minimal connectivity
instead of a pre-defined three-dimensional magnetic-field solution.
