The two-dimensional Vlasov–Maxwell system, for a plasma with mobile, magnetised electrons and ions, is investigated numerically. A previously developed method for solving the two-dimensional electrostatic Vlasov equation, Fourier transformed in velocity space, for mobile electrons and with ions fixed in space, is generalised to the fully electromagnetic, two-dimensional Vlasov–Maxwell system fo...

A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physic...

We find the Lax pair for a system of reduced Maxwell–Bloch equations that describes the propagation of twocomponent extremely short electromagnetic pulses through the medium containing two-level quantum particles with arbitrary dipole moments.

The numerical solution of very large 3D electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the 3D Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov-Maxwell equations, widely used to si...

Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse-graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are ...