# Models of Particles and Moving Media

## 1st Edition

**Authors:**Donald Dunn

**eBook ISBN:**9780323156127

**Imprint:**Academic Press

**Published Date:**1st January 1971

**Page Count:**318

## Description

Models of Particles and Moving Media deals with the use of mathematical models to study electrical interactions with moving particles and moving media. Topics covered range from space-time and the Galilean transformation to the Lorentz transformation of time and space and of Maxwell's equations. Forces and wave interaction with uniformly moving circuits and continua are also considered, along with non-uniform motion of charged particles in prescribed electric and magnetic fields.

Comprised of seven chapters, this book begins with an overview of some of the ways in which motion can be described, with particular reference to the concept of space-time and the Galilean transformation. The discussion then turns to the Lorentz transformation of time and space, giving emphasis on the transformation of coordinates, time dilation and the Lorentz contraction, and conservation of mass and energy. After an analysis of the Lorentz transformation of Maxwell's equations, forces and wave interaction with uniformly moving circuits and continua are reviewed, along with non-uniform motion of charged particles in prescribed electric and magnetic fields. The book concludes by describing the use of the Lagrangian model and the Eulerian model to determine the motion of many interacting particles and the motion of charged and conducting fluids, respectively.

This monograph is written primarily for students and researchers in the fields of mathematics and physics.

## Table of Contents

Preface

Acknowledgments

Chapter 1 Space—Time and the Galilean Transformation

1.0 Introduction

1.1 Trajectories in Various Spaces

Example I Simple Harmonic Motion in a Moving Frame of Reference

1.2 Frames of Reference

Example II Doppler Effect for Acoustic Waves

1.3 Newton’s Laws and Galilean Invariance

References

Chapter 2 The Lorentz Transformation of Time and Space

2.0 Introduction

2.1 Transformation of Coordinates

2.2 Time Dilation and the Lorentz Contraction

2.3 Transformation of Velocity and Acceleration

2.4 Transformation of Mass

2.5 Transformation of Force

2.6 Conservation of Mass and Energy

2.7 Particle Accelerators

References

Chapter 3 The Lorentz Transformation of Maxwell’s Equations

3.0 Introduction

3.1 The Lorentz Transformation of Maxwell’s Equations in Free Space

3.2 The Fields of a Moving Point Charge in Free Space

3.3 The Lorentz Transformation of Maxwell’s Equations in Material Media

3.4 Wave Transformations

Example III A Moving Resonator

3.5 TEM Waves in a Moving Lossless Dielectric Medium

3.6 Poynting’s Theorem and the Conservation of Energy

Example IV A Radiation-Pressure Motor

References

Chapter 4 Forces and Wave Interaction with Uniformly Moving Circuits and Continua

4.0 Introduction

4.1 Self-Consistent Forces and Emfs in Wave Interactions with Moving Conducting Media—the TEM Mode

4.2 A Model of an Induction Motor—TE Mode in a Moving Conducting Medium

4.3 The Surface Charge Induction Motor—TM Mode in a Moving Conducting Medium

4.4 Quasi-Static Formulation of Maxwell’s Equations

4.5 Faraday’s Law for Moving Media

Example V Emfs in Slowly Moving Loops in a Magnetic Field

4.6 Forces on Prescribed Current Distributions in Prescribed Magnetic Fields—Conventional ac and dc Motors

4.7 Self-Consistent Forces and Emfs in Circuits Moving through Prescribed Magnetic Fields—the Induction Motor

References

Chapter 5 Nonuniform Motion of Charged Particles in Prescribed Electric and Magnetic Fields

5.0 Introduction

5.1 Motion of a Point Charge in a Static Magnetic Field Uniform in Space

5.2 Motion of a Point Charge in a Slowly Varying Magnetic Field Uniform in Space

5.3 Motion of a Point Charge in a Static, Nonuniform, Axially Symmetric Magnetic Field

5.4 Motion of a Point Charge in a Static Electric Field Uniform in Space

5.5 Motion of a Point Charge in Crossed Static Electric and Magnetic Fields Uniform in Space

5.6 Motion of Many Noninteracting Particles in a Static Electric Field Uniform in Space

5.7 Electron Guns and Lenses

References

Chapter 6 Motion of Many Interacting Particles—The Lagrangian Model

6.0 Introduction

6.1 Electric Field Calculations for Zero-Thickness Charge Sheets

Example VI A Problem of Many Interacting Particles That Can Be Solved Exactly—Plasma Oscillations

6.2 Finite-Difference Solutions to Particle-Trajectory Equations

6.3 Particle Ordering and Field Calculations Based on a Coarse-Grained Configuration Space

6.4 Particle Injection in the Lagrangian Model—Specifying the Initial Conditions

6.5 The Single-Species Diode with a dc Injection Velocity

6.6 The Single-Species Diode with Time-Varying Injection Velocity—Klystron Amplifiers and Oscillators

6.7 The Two-Species Diode with Infinite Spacing—Ion Propulsion Beam Neutralization

6.8 The Dual Problem—Interaction of Uncharged Current Sheets

References

Chapter 7 Motion of Charged and Conducting Fluids—The Eulerian Model

7.0 Introduction

7.1 Fundamental Equations for Charged and Conducting Fluids

7.2 Static Theory of a Charged Fluid in a Planar Diode—Single Velocity Injection of a Prescribed Current

7.3 Static Theory of a Neutralized Beam

7.4 Time-Varying Perturbations in a Neutralized Beam—Space Charge Waves

7.5 A Two-Fluid Problem—Growing Waves in a Plasma with Finite-Mass Ions

7.6 Interaction with a Circuit—Beam Loading in a Finite-Length Gap

7.7 Interaction with a Distributed Circuit—the Traveling-Wave Tube

7.8 Interaction with a Distributed Circuit—The Resistance-Wall Amplifier

7.9 The Magnetic Pinch Effect

References

Author Index

Subject Index

## Details

- No. of pages:
- 318

- Language:
- English

- Copyright:
- © Academic Press 1971

- Published:
- 1st January 1971

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323156127