Conception of the scalar-vector potential in contemporary electrodynamics

We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space, there are solutions to Maxwell's equations representing the propagation of electromagnetic fields as waves. We introduce electromagnetic potentials, and show how they can be used to simplify the calculation of the fields in the presence of...

Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is considered. The link between the longitudinal electromagnetic waves and the system of Maxwell equations is demonstrated. The longitudinal wave component of the electric field strength vector is found as the exact solution of the standard Maxwell...

{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notations such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc int...

The analytical and numerical analysis of the dynamics of charged particles in the field of an intensive transverse electromagnetic wave in a vacuum presented in the article. Identifies the conditions for resonant acceleration of particles. These conditions are formulated. The features and the mechanism of this acceleration are discussed.

On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the direction of the wave vector {\bf k}. The concepts of wave motion, causality, scalar and vector potentials and their gauge transfo...

In this work we further advance theoretical investigation of radiation by the electric dipole under the assumption that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation. The electric dipole considered in this paper is the one with fixed charge positions, but oscillating charge magnitudes. Specifically, two cases were considered. In the first case phase delay between o...

In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method is sometimes more effective than the scalar and vector potential-based relations. Finally, the measurable field variables, the electric and magnetic fields, can be deduced by direct calculation from the Hertz vector. However, right now, the ...

We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the familiar Maxwell equations as a special case but, in other cases, can predict birefringence, charge non-conservation, wave damping and other effects that the familiar Maxwell equations do not. It follows that observational constraints on such effe...

The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the physical reality of the vector potential.

Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \emph{unphysical}. However, these scalar expressions might have the meaning ...