Relativistic Dynamics of a Charged Sphere: Updating the Lorentz-Abraham Model

ISBN-13: 9783031060663 / Angielski / Twarda / 2022 / 207 str.

Arthur D. Yaghjian

Opis

In addition to expanding and clarifying a number of sections of the first edition, it generalizes the analysis that eliminates the noncausal pre-acceleration so that it applies to removing any pre-deceleration as well. It also introduces a robust power series solution to the equation of motion that produces an extremely accurate solution to problems such as the motion of electrons in uniform magnetic fields.

Spis treści

Foreword.- Preface To The First Edition.- Preface To The Second Edition.- Introduction and Summary of Results.- Lorentz-Abraham Force And Power Equations.- Derivation of Force And Power Equations.- Internal Binding Forces.- Electromagnetic, Electrostatic, Bare, Measured, and Insulator Masses.- Transformation and Redefinition of Forcepower and Momentum-Energy.- Momentum and Energy Relations.- Solutions to The Equation of Motion.- Derivation and Transformation of Smallvelocity Force and Power.- Derivation of Force and Power at Arbitrary Velocity.- Electric and Magnetic Fields in a Spherical Shell of Charge.- Derivation of The Linear Terms for the Self Electromagnetic Force.- References.

O autorze

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.

Blurb

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.