On the gravitational influence of direct particle fields

1964 ◽  
Vol 282 (1389) ◽  
pp. 184-190 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Vector Potential ◽  
Particle Interaction ◽  
Energy Tensor ◽  
Green Functions ◽  
Charge Conservation ◽  
Usual Procedure ◽  
Unique Result ◽  
Gravitational Influence ◽  
Gravitational Equations

The problem of the contribution of direct particle interaction of the Fokker type to the gravitational equations is solved. It is shown that the usual procedure for obtaining the gravitational equations, of making small variations of geometry, g ik + δg ik replacing g ik in finite regions, with δg ik = 0 on their boundaries, and of requiring that the action be stationary for such variations, can be carried through with the aid of Green functions. This procedure, due to Hilbert, serves to define the energy tensor T ik associated with each of the fields. That for the C -field turns out exactly the same as we have used in the macroscopic form of the theory. That for the electromagnetic field turns out to have some new features. These are terms containing the vector potential and its derivative when world-lines are broken, although these terms vanish when there is charge conservation. The terms in the field F ik are identical with the usual tensor if the field is calculated from retarded potentials. In former work no decision has been made on the form the tensor should take when the potentials are ½ (retarded + advanced). Wheeler & Feynman showed that alternative choices are possible and that a decision cannot be made from electromagnetic considerations alone. Our analysis leads to a unique result, the Frenkel tensor.

Propagation of ultrashort optical pulses in anisotropic optical media with carbon nanotubes

2021 ◽  
pp. 2150197
Author(s):  
N. N. Konobeeva ◽  
M. B. Belonenko
Keyword(s):  
Carbon Nanotubes ◽  
Electromagnetic Field ◽  
Vector Potential ◽  
Pulse Shape ◽  
Electromagnetic Waves ◽  
Optical Pulses ◽  
Effective Equation ◽  
Ultrashort Optical Pulses ◽  
Optical Media ◽  
Crystal Type

In this paper, we investigate the evolution of electromagnetic waves in a nonlinear anisotropic optical medium with carbon nanotubes (CNTs). Based on Maxwell’s equation, an effective equation is obtained for the vector potential of the electromagnetic field, which takes into account different values of the velocity and polarization with two directions. The dependence of the pulse shape on the crystal type, as well as the angle between the electric field and the CNTs axis is revealed.

A Proposed Experiment of Direct Detecting of the Vector Potential within Classical Electrodynamics

1997 ◽  
Vol 11 (12) ◽  
pp. 531-540
Author(s):  
V. Onoochin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Vector Potential ◽  
Energy Exchange ◽  
Short Pulse ◽  
Classical Electrodynamics ◽  
Direct Influence ◽  
Ultra Short Pulse ◽  
The Magnetic Field

An experiment within the framework of classical electrodynamics is proposed, to demonstrate Boyer's suggestion of a change in the velocity of a charged particle as it passes close to a solenoid. The moving charge is replaced by an ultra-short pulse (USP), whose characteristics should depend on the current in the coil. This dependence results from the exchange of energy between the electromagnetic field of the pulse and the magnetic field within the solenoid. This energy exchange could only be explained, by assuming that the vector potential of the solenoid has a direct influence on the pulse.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

Direct Measurement of Excitation and Growth of Large Amplitude Cyclotron Waves by Reflected Ion Beams in Front of Shock

2020 ◽  
Author(s):  
Jiansen He ◽  
Chuanpeng Hou ◽  
Xingyu Zhu ◽  
Qiaowen Luo ◽  
Daniel Verscharen ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Electromagnetic Field ◽  
Phase Space ◽  
Large Amplitude ◽  
Particle Interaction ◽  
Field Vector ◽  
Ion Beams ◽  
Magnetic Field Vector ◽  
Wave Particle Interaction

<p>Wave-particle interaction plays a critical role in producing the newborn waves/turbulence in the foreshock region in front of supercritical shock, which is prevalent in the heliosphere. It has been a long-lasting goal to catch and witness the excitation and growth of waves/turbulence by identifying the ongoing process of wave-particle interaction. This goal cannot be fulfilled until the arrival of the MMS’s era, during which we can simultaneously measure the electromagnetic fields and particle phase space densities with the unprecedented data quality. By surveying the data of burst mode, we are lucky to find some good examples illustrating the clear signals of wave activities in front of the shock. The active waves are diagnosed to be right-handed cyclotron waves, being highly circularly polarized and rotating right-handed about the background magnetic field vector. The waves are large amplitude with dB being greatly dominant over B0, or in other words, almost the whole magnetic field vector is involved in the circular rotation. Furthermore, we investigate the growth evolution of the large-amplitude cyclotron waves by calculating the spectrum of dJ.dE and its ratio to the electromagnetic energy spectrum. As far as we know, it is the first time to provide the spectrum of growth rate from in-situ measurements. Interestingly, we find that the contribution to the growth rate spectrum mainly comes from dJ<sub>e,perp</sub>·dE<sub>perp</sub> rather than dJ<sub>e,para</sub>·dE<sub>para</sub> or d<strong>J</strong><sub>i</sub>·d<strong>E</strong>. Although the eigen mode to couple the oscillating electromagnetic field is the electron bulk oscillation, the ultimate free energy to make the eigen mode unstable comes from the ion beams, which are reflected from the shock. The dynamics of 3D phase space densities for both ion and electron species are also studied in detail together with the fluctuating electromagnetic field, demonstrating the ongoing energy conversion during the wave-particle process.</p><p> </p>

scholarly journals The Field Of A Step–Like Accelerated Point Charge: Liénard–Wiechert Potentials And Čerenkov Shock Waves Revisited

2015 ◽  
Vol 66 (6) ◽  
pp. 317-322
Author(s):  
L’ubomír Šumichrast
Keyword(s):  
Electromagnetic Field ◽  
Shock Waves ◽  
Vector Potential ◽  
Point Charge ◽  
Solvable Problems

Abstract Scalar and vector potential as well as the electromagnetic field of a moving point charge is a nice example how the application of symbolic functions (distributions) in electromagnetics makes it easier to obtain and interpret solutions of otherwise hardly solvable problems.

scholarly journals The Inertia of Light. Newton's Law in 4 Dimensions.

2019 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Field Configuration ◽  
Energy Tensor ◽  
Electromagnetic Mass ◽  
Spatial Direction ◽  
Newtonian Physics ◽  
Isaac Newton ◽  
Spatial Coordinate ◽  
James Clerk Maxwell

Isaac Newton and James Clerk Maxwell were giants in the history of physics. Newton in his century (1643 – 1727) and Maxwell about 150 years later (1831 – 1879) in his own century. Newton has built his theories, based on the deep and profound wisdom in nature and religion. For this reason, Newton has been called the last magician in his time. Maxwell represents modern physics and he has built his theories only on pure mathematics. Based on Newtonian Physics it is possible to reach much further in physics than the achievements based on a simple Maxwell’s mathematical approach. Newtonian Physics gives a new insight in the fundamental physics of Light, Electromagnetic Fields, Dirac’s relativistic Quantum Physics and Einstein’s General Relativity. All we know about light, and in general about any electromagnetic field configuration, has been based only on two fundamental theories. James Clerk Maxwell introduced in 1865 the “Theory of Electrodynamics” with the publication: “A Dynamical Theory of the Electromagnetic Field” and Albert Einstein introduced in 1905 the “Theory of Special Relativity” with the publication: “On the Electrodynamics of Moving Bodies” and in 1913 the “Theory of General Relativity” with the publication ”Outline of a Generalized Theory of Relativity and of a Theory of Gravitation”. However, both theories are not capable to explain the property of electromagnetic mass and in specific the anisotropy of the phenomenon of electromagnetic mass. To understand what electromagnetic inertia and the corresponding electromagnetic mass is and how the anisotropy of electromagnetic mass can be explained and how it has to be defined, a New Theory about Light has to be developed. A part of this New Theory about Light will be published in this article.The New Theory about Light has been based on one single fundamental property of our Universe. The unique property that there has always been, is always and will always be a perfect equilibrium within our Universe. Isaac Newton has discovered this fundamental physical law already 300 years ago by his third law in physics. “For every action there is an equal and opposite reaction”. In the New Theory this law of Equilibrium has been extended for any arbitrary Electromagnetic Field Configuration, which requires the fundamental Universal Property: “The total algebraic sum of all force densities will always equal zero at any time at any spatial coordinate in any spatial direction”. To develop a set of 4 electromagnetic equations, describing all the force densities within any arbitrary electromagnetic field configuration, the Divergence of the 4-Dimensional Stress-Energy Tensor has been taken, resulting in the 4-Dimensional Electromagnetic Vector Equation with the fundamental requirement: “The the total algebraic sum of all force densities equals zero at any time at any spatial coordinate in any spatial direction”

scholarly journals 44. Electromagnetic acceleration of particles to cosmic ray energies

1958 ◽  
Vol 6 ◽  
pp. 428-440
Author(s):  
W. F. G. Swann
Keyword(s):  
Electromagnetic Field ◽  
Vector Potential ◽  
Cosmic Ray ◽  
Acceleration Of Particles ◽  
Gain Energy ◽  
Image Position

It has been demonstrated that if a particle is accelerated in an electromagnetic field between two points designated by subscripts (1) and (2), the particle will gain energy in passing from (1) to (2) provided that the quantity J defined by is positive, where ds is an element of path, Us1 and Us2 are the initial and final values of the vector potential along the path, and t is the time. Moreover, if the particle is at rest at the point (1), its energy W2 at the point (2) is such that here e is the charge on the particle.

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