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Format: XI, 17 p. 19 illus., 17 illus. in color. , online resource.

Edition: 3rd ed. 2022.

ISBN: 9783031060670

Content: 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.

Note: Chapter 1. Introduction and Summary of Results -- Chapter 2. Lorentz-Abraham Force and Power Equations -- Chapter 3. Derivation of Force and Power Equations -- Chapter 4. Internal Binding Forces -- Chapter 5. Electromagnetic, Electrostatic, Bare, Measured, and Insulator Masses -- Chapter 6. Transformation and Redefinition of Force-Power and Momentum-Energy -- Chapter 7. Momentum and Energy Relations -- Chapter 8. Solutions to the Equation of Motion.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031060663

Additional Edition: Printed edition: ISBN 9783031060687

Additional Edition: Printed edition: ISBN 9783031060694

Language: English

DOI: 10.1007/978-3-031-06067-0

URL: https://doi.org/10.1007/978-3-031-06067-0

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URL: Volltext  (URL des Erstveröffentlichers)

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Format: 1 online resource (211 pages)

Edition: 3rd ed.

ISBN: 9783031060670

Note: Intro -- Foreword -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Introduction and Summary of Results -- 2 Lorentz-Abraham Force and Power Equations -- 2.1 Force Equation of Motion -- 2.2 Power Equation of Motion -- 3 Derivation of Force and Power Equations -- 3.1 General Equations of Motion from Proper-Frame Equations -- 4 Internal Binding Forces -- 4.1 Poincaré Binding Forces -- 4.2 Binding Forces at Arbitrary Velocity -- 4.2.1 Electric Polarization Producing the Binding Forces -- 5 Electromagnetic, Electrostatic, Bare, Measured,and Insulator Masses -- 5.1 Bare Mass in Terms of Electromagnetic and Electrostatic Masses -- 5.1.1 Extra Momentum-Energy in Newton's Second Law of Motion for Charged Particles -- 5.1.2 Reason for Lorentz Setting the Bare Mass Zero -- 6 Transformation and Redefinition of Force-Power and Momentum-Energy -- 6.1 Transformation of Electromagnetic, Binding, and Bare-Mass Force-Power and Momentum-Energy -- 6.1.1 Total Stress-Momentum-Energy Tensor for the Charged Insulator -- 6.2 Redefinition of Electromagnetic Momentum and Energy -- 7 Momentum and Energy Relations -- 7.1 Hyperbolic Motion -- 7.2 Runaway Motion -- 8 Solutions to the Equation of Motion -- 8.1 Solution to the Equation of Rectilinear Motion -- 8.2 Formal Solution to the General Equation of Motion -- 8.3 Cause and Elimination of the Pre-acceleration -- 8.3.1 Cause of the Pre-acceleration -- 8.3.2 Elimination of the Pre-acceleration -- 8.3.3 Determination of the Transition Force for Rectilinear Motion -- 8.3.4 Motion of Charge in a Uniform Electric Field for a Finite Time -- 8.3.5 Conservation of Momentum-Energy in the Causal Equation of Motion -- 8.3.6 Causal Solution to the Parallel-Plate Capacitor -- 8.4 Power Series Solutions to the Equation of Motion. , 8.4.1 Power Series Solution to Rectilinear Equation of Motion -- 8.4.2 Power Series and Landau-Lifshitz Solution to General Equation of Motion -- 8.5 Charge Moving in a Uniform Magnetic Field -- 8.6 Electron in a Counterpropagating Laser Beam -- 8.6.1 Linearly Polarized Plane Wave -- Solution for γ(1+uz/c) -- Solution for γux/c -- Solution for the Relativistic Factor γ, the Longitudinal Velocity uz/c, and the Transverse Velocity ux/c -- Determination of the Time t in Terms of ξ -- Uniform Plane Wave -- Sinusoidal Envelope -- 8.6.2 Circularly Polarized Plane Wave -- Solution for γ(1+uz/c): Circular Polarization -- Solution for γux/c and γuy/c: Circular Polarization -- Solution for the Relativistic Factor γ, the Longitudinal Velocity uz/c, and the Transverse Velocities ux/c and uy/c: Circular Polarization -- Uniform Plane Wave: Circular Polarization -- Sinusoidal Envelope: Circular Polarization -- 8.6.3 Conditions for the Accuracy of the LL Approximate Solution to the LAD Equation of Motion -- 8.6.4 The Lorentz-Force Equation of Motion -- 8.6.5 Quantum Effects -- Quantum-Vacuum Electron-Positron Pair Production -- Compton Scattering -- Electron Quantum Recoil from Photon Emission -- 8.6.6 Regions of Validity of the Different Solutions -- 8.6.7 Brief Summary of the LL Solution to the Electron in a Laser Beam -- 8.7 The Finite Difference Equation of Motion -- 8.8 Renormalization of the Equation of Motion -- A Derivation and Transformation of Small-Velocity Force and Power -- A.1 Derivation of the Small-Velocity Force and Power -- A.1.1 Derivation of the Proper-Frame Force -- A.1.2 Derivation of the Small-Velocity Power -- A.2 Relativistic Transformation of the Small-Velocity Forceand Power -- A.2.1 Relativistic Transformation of the Proper-Frame Force -- A.2.2 Relativistic Transformation of the Small-Velocity Power. , A.3 Noncovariance of the Power Equation -- B Derivation of Force and Power at Arbitrary Velocity -- B.1 The 1/a Terms of Self Electromagnetic Force and Power -- B.1.1 Evaluation of 1/a Term of Self Electromagnetic Force -- B.1.2 Evaluation of 1/a Term of Self Electromagnetic Power -- B.2 Radiation Reaction of Self Electromagnetic Force and Power -- B.2.1 Evaluation of the Radiation Reaction Force -- B.2.2 Evaluation of the Radiation Reaction Power -- -- C Electric and Magnetic Fields in a Spherical Shell of Charge -- D Derivation of the Linear Terms for the Self Electromagnetic Force -- References -- Index.

Additional Edition: Print version: Yaghjian, Arthur D. Relativistic Dynamics of a Charged Sphere Cham : Springer International Publishing AG,c2022 ISBN 9783031060663

Language: English