Related papers: Exact non-symmetric closed line vacuum magnetic fi…
Stellarators are generically small current and low plasma beta ($\beta= p/B^2\ll1$) devices. Often the construction of vacuum magnetic fields with good magnetic surfaces is the starting point for an equilibrium calculation. Although in…
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…
A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a…
We present a new range of solutions of the Maxwell equations in vacuum in which the topology of the field lines is that of the whole torus knots set. Knotted electromagnetic fields are solutions of the Maxwell equations in vacuum in which…
We investigate the vacuum expectation value of a complex scalar field on a two-dimensional torus with quantized magnetic flux $M$. A characteristic feature of this system is the emergence of a critical area: when the area of the torus…
Contrary to the electric charge that generates the electric field, magnetic charge (namely magnetic monopoles) does not exist in the elementary electromagnetism. Consequently, magnetic flux lines only form loops and cannot have a source or…
A simple approach allowing to construct closed-form analytical zero-field magnetization distributions in cylindrical particles of a small thickness and an arbitrary shape (not necessarily circular) is presented. The approach is based on…
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…
We construct two classes of magnetohydrostatic (MHS) equilibria for an axisymmetric vertical flux tube spanning from the photosphere to the lower part of the transition region within a realistic stratified solar atmosphere subject to solar…
We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric…
Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field,…
We develop an effective field theory approach to inspect the electromagnetic interactions in an electrically neutral plasma, with an equal number of negative and positive charge carriers. We argue that the static equilibrium configurations…
The non-uniform magnetostatic field produced by the equilibrium and non equilibrium magnetic states of magnetic nanotubes has been investigated theoretically. We consider magnetic fields produced by actual equilibrium states and transverse…
A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…
A system of multiple open magnetic flux tubes spanning the solar photosphere and lower corona is modelled analytically, within a realistic stratified atmosphere subject to solar gravity. This extends results for a single magnetic flux tube…
We explore the existence of quasisymmetric magnetic fields in asymmetric toroidal domains. These vector fields can be identified with a class of magnetohydrodynamic equilibria in the presence of pressure anisotropy. First, using Clebsch…
For any axisymmetric toroidal domain $\Omega \subset \mathbf{R}^3$ we prove that there is a locally generic set of divergence-free vector fields that are not topologically equivalent to any magnetohydrostatic (MHS) equilibrium in $\Omega$.…
We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. (2008). Our method is based on the solution of the relativistic Grad-Shafranov equation, to…