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The main issue of the pulsar magnetosphere is how the rotation power is converted into both particle beams which causes pulsed emissions, and a highly relativistic wind of electron-positron plasmas which forms surrounding nebulae shining in…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
Electron plasmas confined by an external magnetic field exhibit variations in a two-dimensional plane orthogonal to the confining magnetic field. A nonlinear fluid simulation code to investigate the properties of 2-D electron plasma wave…
We develop a general methodology for numerical computations of electromagnetic (EM) fields and forces in matter, based on solving the macroscopic Maxwell's equations in real space and adopting the Maxwell Stress Tensor formalism. Our…
The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
An exact analogy of electromagnetic fields and particles can be found in mechanics of a turbulent ideal fluid with voids. The system is supposed to form a fine dispersion of voids in the fluid. This microscopically discontinuous medium is…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
The sets ${\Phi({F}^{\mu \nu})}, {\Phi(\tilde {F}^{\mu \nu})}$ of linear functionals on the space $< F,+,\cdot >$ represent themself linear space $< \Phi,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space $< F,+,\cdot…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
In the limit of extremely intense electromagnetic fields the Maxwell equations are modified due to the photon-photon scattering that makes the vacuum refraction index depend on the field amplitude. In presence of electromagnetic waves with…
In this paper the proofs are given that the electric and magnetic fields are properly defined vectors on the four-dimensional (4D) spacetime (the 4-vectors in the usual notation) and not the usual 3D fields. Furthermore, the proofs are…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
Effective Riemann space effect of vacuum nonlinear electrodynamics is considered in the context of theory for unified gravitation and electromagnetism. The electromagnetic four-vector potential in the scope of Born-Infeld nonlinear…
Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if…
We study Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star and find analytical solutions for the exterior electric fields after separating the equations of electric field into angular and radial…
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…
More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the relativistic mechanics of many particles.…
In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…