Overview
- Re-examines Lorentz's model of the electron, serving as both a review of the subject and as a context for new material
- Updated and expanded with added historical context, simplified derivations, and new results
- Provides the final equations of motion in different formats to allow them to be used by scientists and mathematicians
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book takes a fresh, systematic approach to determining the equation of motion for the classical model of the electron introduced by Lorentz 130 years ago. The original derivations of Lorentz, Abraham, Poincaré, and Schott are modified and generalized for the charged insulator model of the electron to obtain an equation of motion consistent with causal solutions to the Maxwell-Lorentz equations and the equations of special relativity. The solutions to the resulting equation of motion are free of pre-acceleration and pre-deceleration. The generalized method is applied to obtain the causal solution to the equation of motion of a charge accelerating in a uniform electric field for a finite time interval. Alternative derivations of the Landau-Lifshitz approximation are given as well as necessary and sufficient conditions for the Landau-Lifshitz approximation to be an accurate solution to the exact Lorentz-Abraham-Dirac equation of motion. Binding forces and a total stress-momentum-energy tensor are derived for the charged insulator model. Appendices provide simplified derivations of the self-force and power at arbitrary velocity.
In this third edition, some of the history has been made more accurate and some of the derivations have been simplified and clarified. A detailed three-vector exact solution to the Landau-Lifshitz approximate equation of motion is given for the problem of an electron traveling in a counterpropagating plane-wave laser-beam pulse. Semi-classical analyses are used to derive the conditions that determine the significance of quantum effects not included in the classical equation of motion.
The book is a valuable resource for students and researchers in physics, engineering, and the history of science.
Authors and Affiliations
About the author
Arthur D. Yaghjian works primarily as a research engineer in the area of electromagnetic theory. His work has led to the determination of electric and magnetic fields in natural materials and metamaterials, as well as to the development of exact, numerical, and high-frequency methods for predicting and measuring the near and far fields of antennas and scatterers in both the time and frequency domains. His contributions to the determination of the classical equations of motion of accelerated charged particles have found recognition in a number of texts such as the latest edition of Jackson's "Classical Electrodynamics." He has published two books, several chapters in other books, and about 120 archival journal articles, four of which received IEEE best paper awards. He is an IEEE Life Fellow, has received an Honorary Doctorate from the Technical University of Denmark, the IEEE Electromagnetics Award, the IEEE-APS Distinguished Achievement Award, and has served as an IEEE-APS Distinguished Lecturer.
Bibliographic Information
Book Title: Relativistic Dynamics of a Charged Sphere
Book Subtitle: Updating the Lorentz-Abraham Model
Authors: Arthur D. Yaghjian
DOI: https://doi.org/10.1007/978-3-031-06067-0
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-06066-3Published: 30 September 2022
Softcover ISBN: 978-3-031-06069-4Published: 02 October 2023
eBook ISBN: 978-3-031-06067-0Published: 29 September 2022
Edition Number: 3
Number of Pages: XVII, 207
Number of Illustrations: 2 b/w illustrations, 17 illustrations in colour
Additional Information: First edition published as Lecture Notes in Physics Monographs: Vol. 11, 1992; Second edition published as Lecture Notes in Physics: Vol. 686, 2006
Topics: Classical Electrodynamics, Mathematical Physics, Theoretical, Mathematical and Computational Physics, Particle Acceleration and Detection, Beam Physics, Analysis, Classical Mechanics