scholarly journals Hammond versus Ford radiation reaction force with the attractive Coulomb field

2018 ◽  
Vol 64 (2) ◽  
pp. 187
Author(s):  
G. Ares de Parga ◽  
S. Domínguez-Hernández ◽  
E. Salinas-Hernández
Keyword(s):  
Reaction Force ◽  
Coulomb Field ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Central Field ◽  
Force Term ◽  
Point Particles ◽  
Charged Point ◽  
Relativistic Equations ◽  
Radiation Reaction Force

The classical central field is analyzed within the Hammond theory of radiation reaction force. For the attractive Coulomb field, the trajectories deduced from Ford and Hammond equations are numerically obtained. Ford and Hammond equations are rewritten by using a recent correction to the non-relativistic equations for charged point particles which include a radiation reaction force term. Also, for the attractive Coulomb case, the trajectories are numerically obtained for both corrected equations. A comparison between all these trajectories is made. It is proved that Hammond equation satisfies the constraint proposed by Dirac of getting an equation of motion which should make the electron in the hydrogen atom spiralling inwards and ultimately falling into the nucleus. A further analysis of the applicability of such a theory is described for experiments particularly in Plasma Physics and some comments are made for the generalization of Hammond equation to General Relativity.

scholarly journals A New Derivation for the Radiation Reaction Force

1997 ◽  
Vol 50 (4) ◽  
pp. 815
Author(s):  
W. N. Hugrass
Keyword(s):  
Point Charge ◽  
Reaction Force ◽  
Plane Waves ◽  
Wave Spectrum ◽  
Coulomb Field ◽  
Radiation Reaction ◽  
Inhomogeneous Plane ◽  
Homogeneous Plane ◽  
Inhomogeneous Plane Waves ◽  
Radiation Reaction Force

A new derivation for the radiation reaction on a point charge is presented. The field of the charge is written as a superposition of plane waves. The plane wave spectrum of the field consists of homogeneous plane waves which propagate away from the charge at the speed of light, and inhomogeneous plane waves which constitute the Coulomb field of the point charge. The radiation field is finite at the orbit of the point charge. The force acting on the charge due to this field is the well known Abraham-Lorentz radiation reaction.

scholarly journals Maxwell-Lorentz without self-interactions: Conservation of energy and momentum

2022 ◽  
Author(s):  
Jonathan Gratus
Keyword(s):  
Reaction Force ◽  
Radiation Reaction ◽  
Point Particle ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Conservation Of Energy ◽  
Stress Energy ◽  
Energy And Momentum ◽  
Charged Point ◽  
Radiation Reaction Force

Abstract Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.

scholarly journals On the Schott Term in the Lorentz-Abraham-Dirac Equation

2020 ◽  
Vol 4 (4) ◽  
pp. 34
Author(s):  
Tatsufumi Nakamura
Keyword(s):  
Charged Particle ◽  
Reaction Force ◽  
Time Derivative ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Relative Difference ◽  
Field Energy ◽  
Derivative Term ◽  
Radiation Reaction Force ◽  
Classical Radiation

The equation of motion for a radiating charged particle is known as the Lorentz–Abraham–Dirac (LAD) equation. The radiation reaction force in the LAD equation contains a third time-derivative term, called the Schott term, which leads to a runaway solution and a pre-acceleration solution. Since the Schott energy is the field energy confined to an area close to the particle and reversibly exchanged between particle and fields, the question of how it affects particle motion is of interest. In here we have obtained solutions for the LAD equation with and without the Schott term, and have compared them quantitatively. We have shown that the relative difference between the two solutions is quite small in the classical radiation reaction dominated regime.

Radiation-reaction force on a moving mirror

1993 ◽  
Vol 3 (11) ◽  
pp. 2151-2159 ◽  
Author(s):  
Claudia Eberlein
Keyword(s):  
Reaction Force ◽  
Radiation Reaction ◽  
Radiation Reaction Force

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

scholarly journals Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
E. Hirvijoki ◽  
J. Decker ◽  
A. J. Brizard ◽  
O. Embréus
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Uniform Magnetic Field ◽  
Reaction Force ◽  
Charged Particles ◽  
Collision Operator ◽  
Radiation Reaction ◽  
Transform Method ◽  
Lie Transform ◽  
Radiation Reaction Force

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

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