Related papers: Relative Magnetic Helicity Based on a Periodic Pot…
We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to…
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the…
Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By…
Magnetic helicity is approximately conserved in resistive MHD models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both the dynamo in the solar interior and…
The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy…
Magnetic helicity, $H$, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in $\mathcal{V}$ bounded by $\mathcal{S}$. For magnetically closed systems,…
The discovery of clear criteria that can deterministically describe the eruptive state of a solar active region would lead to major improvements on space weather predictions. Using series of numerical simulations of the emergence of a…
Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic…
We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the…
We prove Taylor's conjecture which says that in 3D MHD, magnetic helicity is conserved in the ideal limit in bounded, simply connected, perfectly conducting domains. When the domain is multiply connected, magnetic helicity depends on the…
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process…
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In…
The coupling between a primordial magnetic field and the cosmic axion field generates a helical component of the magnetic field around the time in which the axion starts to oscillate. If the energy density of the seed magnetic field is…
Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution…
Helicity measures complexity in the field. Magnetic helicity is given by a volume integral over the scalar product of magnetic field {\bf B} and its vector potential {\bf A}. A direct computation of magnetic helicity in the solar atmosphere…
We compute magnetic helicity and energy spectra from about 2485 patches of about 100 megameters (Mm) side length on the solar surface using data from Hinode during 2006--2017. An extensive database is assembled where we list magnetic energy…
In this paper we investigate the dynamics of magnetic helicity in magnetohydrodynamic (MHD) turbulent flows focusing at scales larger than the forcing scale. Our results show a nonlocal inverse cascade of magnetic helicity, which occurs…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the…
The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different…