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.

Transient response from a planar acoustic interface by a new point‐source decomposition into plane waves

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 766-774 ◽  
Author(s):  
Peter Hubral ◽  
Martin Tygel
Keyword(s):  
Point Source ◽  
Wave Field ◽  
Plane Waves ◽  
Planar Interface ◽  
Integration Limit ◽  
Inhomogeneous Plane ◽  
Homogeneous Plane ◽  
Acoustic Interface ◽  
New Formula ◽  
Inhomogeneous Plane Waves

For the wave field of a point source in full space there currently exist two classical decompositions into plane waves. The wave field can be decomposed into either (a) homogeneous and horizontally propagating (vertically attenuated) inhomogeneous plane waves by using the so‐called Sommerfeld‐Weyl integral, or (b) upgoing and downgoing homogeneous plane waves only using the Whittaker integral. Transient representations of both integrals exist. We propose a new decomposition integral that has a greater flexibility than both classical decompositions. Solutions for the point‐source reflection/transmission response from a planar interface, if based on the Sommerfeld‐Weyl integral, have for instance inherently an infinite integration limit. With the new formula, by which the wave field of a transient point source is decomposed into upgoing and downgoing homogeneous as well as horizontally propagating inhomogeneous transient plane waves, the point‐source response is directly obtained in the form of an integral with a finite integration limit. It can also be interpreted in terms of certain plane waves by which the point source is simulated in a new manner. For that matter, solutions based on the new integral readily reveal the “evanescent” or “nonray” character of the point source. The new formula may be considered an extension of the Sommerfeld‐Weyl or Whittaker integral. It can be used to compute reflection/transmission responses in a compact form in situations where the Sommerfeld‐Weyl integral was hitherto considered fundamental.

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.

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.

Scattering of inhomogeneous plane waves by a truncated cylindrical cap

2015 ◽  
Vol 62 (19) ◽  
pp. 1555-1560
Author(s):  
Husnu Deniz Basdemir
Keyword(s):  
Plane Waves ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Waves

scholarly journals New capabilities of Chetaev´s model

2016 ◽  
Vol 2 (2) ◽  
pp. 104-114
Author(s):  
Михаил Савин ◽  
Mihail Savin ◽  
Юрий Израильский ◽  
Yuriy Izrailsky
Keyword(s):  
Experimental Data ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Geomagnetic Pulsations ◽  
Energy Fluxes ◽  
Field Recordings ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Wave ◽  
S Model ◽  
Inhomogeneous Plane Waves

This paper considers anomalies in the magnetotelluric field in the Pc3 range of geomagnetic pulsations. We report experimental data on Pc3 field recordings which show negative (from Earth’s surface to air) energy fluxes Sz<0 and reflection coefficients |Q|>1. Using the model of inhomogeneous plane wave (Chetaev’s model), we try to analytically interpret anomalies of energy fluxes. We present two three-layer models with both electric and magnetic modes satisfying the condition |Qh|>1. Here we discuss a possibility of explaining observable effects by the resonance interaction between inhomogeneous plane waves and layered media.

scholarly journals Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190478
Author(s):  
N. H. Scott
Keyword(s):  
Energy Density ◽  
Energy Flux ◽  
Plane Waves ◽  
Time Averaging ◽  
Complex Frequency ◽  
Hereditary Viscoelasticity ◽  
Inhomogeneous Plane ◽  
Dissipative Material ◽  
Comparable Magnitude ◽  
Inhomogeneous Plane Waves

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω , and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2 ω . The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω . A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2 ω . It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2 ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.

scholarly journals Finite Size Corrections to the Radiation Reaction Force in Classical Electrodynamics

2010 ◽  
Vol 105 (9) ◽  
Author(s):  
Chad R. Galley ◽  
Adam K. Leibovich ◽  
Ira Z. Rothstein
Keyword(s):  
Reaction Force ◽  
Finite Size ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Finite Size Corrections ◽  
Radiation Reaction Force
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