Solution of the Einstein-Maxwell equations for a static distribution of massive charged particles

The linearization procedure is applied to the equations governing a beam-plasma system, in which the stream velocities and the wavevector are parallel to the external magnetic induction. No special constraints are imposed on the parameters characterizing the constituent fluids in the equilibrium state of this macroscopic picture. From the MAXWELL equations an expression for the electromagnetic field of the wave is obtained and substituted in the equations of motion. The components of the first-order pressure tensors are computed in the low-temperature approximation, but without recurring to the strong magnetic induction CGL hypothesis. Since the equations of motion are now expressed only in the components of the perturbations of the drift velocities, the dispersion relations follow immediately. These relations are applicable to all beam-plasma systems comprised between the now conventional multicomponent plasma and the system of beams of charged particles. Some known cold beam-plasma cases are included in the general dispersion equations.

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The symmetrization of Maxwell's equations, and fractionally charged particles

Canadian Journal of Physics ◽

10.1139/p70-038 ◽

1970 ◽

Vol 48 (3) ◽

pp. 279-282 ◽

Cited By ~ 1

Author(s):

Darryl Leiter

Keyword(s):

Electric Charge ◽

Maxwell’S Equations ◽

Maxwell Equations ◽

Maxwell's Equations ◽

Charged Particles ◽

Charge Ratio ◽

Model Universe ◽

Electromagnetic Interactions ◽

Electromagnetic Tensor ◽

Classical Point

It is shown that Maxwell's equations can be consistently symmetrized by the introduction of an additional vector 4-current as the source of the dual of the generalized electromagnetic tensor. The additional 4-current is related to a second type of electric charge which we shall call "m-electric charge," as distinguished from the conventional electric charge (denoted as "e-electric" charge). A Lagrangian formulation of this theory for classical point charges is constructed, yielding the symmetrized Maxwell equations, in which each particle is assumed to carry both an "e-electric" charge and an "m-electric" charge. We show that if the m-electric to e-electric charge ratio is the same for all particles in the model universe, then the predictions of the symmetrized Maxwell equations are the same as that of the unsymmetrized, conventional Maxwell equations. However, if all particles in a detector carry the same m-electric to e-electric charge ratio, not equal to zero, then a detected particle with different m-electric to e-electric charge ratio (than that of the detector) could appear to have only a fractional e-electric charge. This implies that fractionally charged particles could be generated even if only integral multiples of e-charge and m-charge were allowed in the symmetrized theory. This means that it might be experimentally difficult to distinguish between a differently "m-charged" particle, and an SU3-type "quark," in purely electromagnetic interactions alone.

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A Model for the Maxwell Equations Coupled with Matter Based on Solitons

Symmetry ◽

10.3390/sym13050760 ◽

2021 ◽

Vol 13 (5) ◽

pp. 760

Author(s):

Vieri Benci

Keyword(s):

Maxwell Equations ◽

Gordon Equation ◽

Mountain Pass Theorem ◽

Energy Charge ◽

Charged Particles ◽

Matter Field ◽

Linear Interaction ◽

Low Energies ◽

Klein Gordon ◽

Klein Gordon Equation

We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein–Gordon equation. A simple linear interaction and a nonlinear perurbation produces solutions to the equations containing hylomorphic solitons, namely stable, solitary waves, whose existence is related to the ratio energy/charge. These solitons, at low energy, behave as poinwise charged particles in an electromagnetic field. The basic points are the following ones: (i) the matter field is described by the Nonlinear Klein–Gordon equation with a suitable nonlinear term; (ii) the interaction is not described by the equivariant derivative, but by a very simple coupling which preseves the invariance under the Poincaré group; (iii) the existence of soliton can be proved using the tecniques of nonlinear analysis and, in particular, the Mountain Pass Theorem; (iv) a suitable choice of the parameters produces solitons with a prescribed electric charge and mass/energy; (v) thanks to the point (ii), the dynamics of these solitons at low energies is the same of classical charged particles.

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The Tesla Currents in Electrodynamics

Applied Physics Research ◽

10.5539/apr.v10n5p79 ◽

2018 ◽

Vol 10 (5) ◽

pp. 79

Author(s):

Andrew Chubykalo ◽

Viktor Kuligin

Keyword(s):

Maxwell Equations ◽

Semiconductor Devices ◽

Charged Particles ◽

Lorentz Gauge ◽

Conduction Electrons

The paper theoretically shows that the Maxwell equations in the Lorentz gauge deal with not only inertial charged particles, but also charged particles that do not have inertia (virtual charges). Virtual charges appear on the surface of metals. Their movement is the currents of Tesla. Experiments confirming their existence are presented, and some features that reveal them. The influence of virtual currents on the process of transfer of conduction electrons in p-n junctions of semiconductor devices is especially interesting. The results obtained can change our understanding of phenomena in the microcosm.

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Shock waves and Cerenkov radiation in electromagnetic substratum

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171291001047 ◽

1991 ◽

Vol 14 (4) ◽

pp. 769-788 ◽

Cited By ~ 2

Author(s):

H. E. Wilhelm

Keyword(s):

Shock Waves ◽

Relative Velocity ◽

Maxwell Equations ◽

Rest Frame ◽

Charged Particles ◽

Cerenkov Radiation ◽

Physical Vacuum ◽

Inertial Frames ◽

Theoretical Predictions

TheEMfields of charged particles moving with velocityvin a physical vacuum with wave carrier (substratum) are determined by means of the generalized, Galilei covariant Maxwell equations for inertial frames∑. with substratum floww. In this Galilean approach, all velocities have absolute meaning relative to the substratum rest frame∑o, and the relative velocity of material particles is given by the linear Galilean relationvG=v1−v2, permitting in principle superluminal relative velocities|vG|>co. Inter alias, the possibility ofEMshock waves and Cerenkov radiation in the vacuum substratum is discussed. Experiments are proposed to test the theoretical predictions.

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The Jovian ring

International Astronomical Union Colloquium ◽

10.1017/s0252921100101174 ◽

1984 ◽

Vol 75 ◽

pp. 203-209

Author(s):

Joseph A. Burns

Keyword(s):

Equatorial Plane ◽

Charged Particles ◽

Dynamical Evolution ◽

Main Band ◽

Small Grains ◽

Three Components

ABSTRACTLying in Jupiter's equatorial plane is a diaphanous ring having little substructure within its three components (main band, faint disk, and halo). Micron-sized grains account for much of the visible ring, but particles of centimeter sizes and larger must also be present to absorb charged particles. Since dynamical evolution times and survival life times are quite short (≲102-3yr) for small grains, the Jovian ring is being continually replenished; probably most of the visible ring is generated by micrometeoroids colliding into unseen parent bodies that reside in the main band.

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Atomic orientation effects in proton stopping at low velocity

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100077116 ◽

1983 ◽

Vol 41 ◽

pp. 708-709

Author(s):

Kin Lam

Keyword(s):

Polycrystalline Material ◽

Charged Particles ◽

Target Material ◽

Stopping Power ◽

Low Velocity ◽

Electronic Density ◽

Interatomic Distances ◽

Frame Work ◽

Image Position ◽

Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

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Inelastic scattering at surfaces and interfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143560 ◽

1986 ◽

Vol 44 ◽

pp. 392-393

Author(s):

R. H. Ritchie ◽

A. Howie

Keyword(s):

Inelastic Scattering ◽

Surface Properties ◽

Correlation Energy ◽

Condensed Matter ◽

Charged Particles ◽

Condensed Matter Physics ◽

Optical Phonons ◽

Exchange Correlation ◽

Surfaces And Interfaces ◽

Inelastic Interactions

An important part of condensed matter physics in recent years has involved detailed study of inelastic interactions between swift electrons and condensed matter surfaces. Here we will review some aspects of such interactions.Surface excitations have long been recognized as dominant in determining the exchange-correlation energy of charged particles outside the surface. Properties of surface and bulk polaritons, plasmons and optical phonons in plane-bounded and spherical systems will be discussed from the viewpoint of semiclassical and quantal dielectric theory. Plasmons at interfaces between dissimilar dielectrics and in superlattice configurations will also be considered.

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