Related papers: Introduction to Field Line Helicity
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two…
The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative…
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…
We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in…
Through a direct comparison between numerical simulations in two and three dimensions, we investigate topological effects in reconnection. A simple estimate on increase in reconnection rate in three dimensions by a factor of $\sqrt{2}$,…
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…
We study the evolution of a stochastic helical magnetic field generated in the early Universe after the electroweak phase transition, using standard magnetohydrodynamics (MHD). We find how the coherence length xi, magnetic energy E_M and…
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, $\emfb$. We show that the difference between kinetic and current helicities…
An expression for a third-order link integral of three magnetic fields is presented. It is a topological invariant and therefore an invariant of ideal magnetohydrodynamics. The integral generalizes existing expressions for third-order…
The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field…
Potential field extrapolations are widely used as minimum-energy models for the Sun's coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed)…
This pedagogical note revisits the concept of electromagnetic helicity in classical systems. In particular, magnetic helicity and its role in mean field dynamo theories is briefly discussed highlighting the major mathematical inconsistency…
We consider the evolution of primordial magnetic fields generated during cosmological, electroweak or QCD, phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological…
We make some remarks on reconnection in plasmas and want to present some calculations related to the problem of finding velocity fields which conserve magnetic flux or at least magnetic field lines. Hereby we start from views and…
In this paper, we introduce a new shape functional defined for toroidal domains that we call harmonic helicity, and study its shape optimization. Given a toroidal domain, we consider its associated harmonic field. The latter is the magnetic…
The definition and measurement of magnetic reconnection in three-dimensional magnetic fields with multiple reconnection sites is a challenging problem, particularly in fields lacking null points. We propose a generalization of the familiar…
We consider the possibility that cosmic magnetic field, instead of being uniformly distributed, is strongly correlated with the large scale structure of the universe. Then, the observed rotational measure of extra-galactic radio sources…
For the electromagnetic fields, hydrodynamic media and turbulent flows we consider the relationship between a topological characteristic of vector fields known as helicity and the angular momentum of the medium, and discuss, in this…
We present a first application of the recently proposed LITMUS test for magnetic helicity, as well as a thorough study of its applicability under different circumstances. In order to apply this test to the galactic magnetic field, the newly…
Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions…