Related papers: A Force-Free Magnetic Field Solution in Toroidal C…
Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal and toroidal magnetic fields are obtained numerically. Because of the mixed components of the magnetic field, the underlying stationary and…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
The force on a macroscopic polarizable body in an inhomogenous electromagnetic field is calculated for three simple exactly solvable situations. Comparing different approaches we pinpoint possible pitfalls and resolve recent confusion about…
3D picture of the coronal magnetic field remains an outstanding problem in solar physics, particularly, in active regions. Nonlinear force-free field reconstructions that employ routinely available full-disk photospheric vector magnetograms…
The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation…
The paper describes ways that the computation of the volume enclosed by an invariant torus (flux surface) for a magnetic field can be reduced from a 3D integral to a 2D integral.
We report on a remarkable class of exact solutions to force-free electrodynamics that has four-current along the light cones of an arbitrary timelike worldline in flat spacetime. No symmetry is assumed, and the solutions are given in terms…
We consider a free boundary problem for the axially symmetric incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. Both the plasma magnetic field and vacuum magnetic field are tangent along…
We study the motion of a charge on a conformally flat Riemannian torus in the presence of magnetic field. We prove that for any non-zero magnetic field there always exist orbits of this motion which have conjugate points. We conjecture that…
In previous work constant magnetic field strength solutions for SU(2) gauge theory on a torus were found, which somewhat surprisingly turned out to be classically stable. This was called marginal stability, as moving along one of its…
The structure of steady axisymmetric force-free magnetosphere of a Kerr black hole (BH) is governed by a second-order partial differential equation of $A_\phi$ depending on two "free" functions $\Omega(A_\phi)$ and $I(A_\phi)$, where…
We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish.…
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a…
Magnetic fields in the solar corona are responsible for a wide range of phenomena. However, any direct measurements of the coronal magnetic fields are very difficult due to lack of suitable spectral lines, weak magnetic fields, and high…
An analytical approximation of a nonlinear force-free magnetic field (NLFFF) solution was developed in Paper I, while a numerical code that performs fast forward-fitting of this NLFFF approximation to a line-of-sight magnetogram and coronal…
We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing…
Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global…
We construct self-similar, axisymmetric, time-independent solutions to Einstein's field equations for an isothermal gas with a flat rotation curve in the equatorial plane. The metric scales as $ds^2 \to a^2 ds^2$ under the transformation…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
A numerical method is presented which allows to compute the spectrum of the Schroedinger operator for a particle constrained on a two dimensional flat torus under the combined action of a transverse magnetic field and any conservative…