scholarly journals Hamiltonian structure of the guiding-center Vlasov–Maxwell equations

2021 ◽  
Vol 28 (10) ◽  
pp. 102303
Author(s):  
Alain J. Brizard
Keyword(s):  
Maxwell Equations ◽  
Hamiltonian Structure

scholarly journals Lifting of the Vlasov–Maxwell bracket by Lie-transform method

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
A. J. Brizard ◽  
P. J. Morrison ◽  
J. W. Burby ◽  
L. de Guillebon ◽  
M. Vittot
Keyword(s):  
Single Particle ◽  
Maxwell Equations ◽  
Perturbation Methods ◽  
Hamiltonian Structure ◽  
Particle Dynamics ◽  
Magnetized Plasmas ◽  
Transform Method ◽  
Lie Transform ◽  
Dynamical Reduction

The Vlasov–Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation (‘lift’) of the Vlasov–Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to provide an explicit pathway to the Hamiltonian formulations for the guiding-centre and gyrokinetic Vlasov–Maxwell equations, which have found important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov–Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

New Approach to the Theory of Circular Dichroism

1998 ◽  
Vol 63 (8) ◽  
pp. 1187-1201 ◽  
Author(s):  
Jaroslav Zamastil ◽  
Lubomír Skála ◽  
Petr Pančoška ◽  
Oldřich Bílek
Keyword(s):  
Electromagnetic Wave ◽  
Circular Dichroism ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Optically Active ◽  
Semiclassical Approach ◽  
New Approach ◽  
Isotropic Media ◽  
New Formula ◽  
Circular Dichroïsm

Using the semiclassical approach for the description of the propagation of the electromagnetic waves in optically active isotropic media we derive a new formula for the circular dichroism parameter. The theory is based on the idea of the time damped electromagnetic wave interacting with the molecules of the sample. In this theory, the Lambert-Beer law need not be taken as an empirical law, however, it follows naturally from the requirement that the electromagnetic wave obeys the Maxwell equations.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

Sign in / Sign up

Export Citation Format

Share Document