Idemen Discontinuities in the Electromagnetic Field

1. Auflage 2011
ISBN: 978-1-118-05790-2
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 250 Seiten, E-Book

Reihe: IEEE/OUP Series on Electromagnetic Wave Theory

A multifaceted approach to understanding, calculating, andmanaging electromagnetic discontinuities
Presenting new, innovative approaches alongside basic results,this text helps readers better understand, calculate, and managethe discontinuities that occur within the electromagnetic field.Among the electromagnetic discontinuities explored in this volumeare:
* Bounded jump discontinuities at the interfaces between two mediaor on the material sheets that model very thin layers
* Unbounded values at the edges of wedge-type structures
* Unbounded values at the tips of conical structures
The text examines all the key issues related to the bodies thatcarry the interfaces, edges, or tips, whether these bodies are atrest or in motion with respect to an observer. In addition to itsclear explanations, the text offers plenty of step-by-step examplesto clarify complex theory and calculations. Moreover, readers areencouraged to fine-tune their skills and knowledge by solving thetext's problem sets.
Three fundamental, classical theories serve as the foundationfor this text: distributions, confluence, and the special theory ofrelativity. The text sets forth the fundamentals of all three ofthese theories for readers who are not fully familiar with them.Moreover, the author demonstrates how to solve electromagneticdiscontinuity problems by seamlessly combining all three theoriesinto a single approach.
With this text as their guide, readers can apply a uniquephilosophy and approach to the investigation and development ofstructures that have the potential to enhance the capabilities ofelectronics, antennas, microwaves, acoustics, medicine, and manymore application areas.

Autoren/Hrsg.

Idemen, M. Mithat

Inhaltsverzeichnis

Preface ix
1. Introduction 1
2. Distributions and Derivatives in the Sense of Distribution 7
2.1 Functions and Distributions, 7
2.2 Test Functions. The Space C infinity 0 , 9
2.3 Convergence in D, 14
2.4 Distribution, 16
2.5 Some Simple Operations in D, 21
2.5.1 Multiplication by a Real Number or a Function, 21
2.5.2 Translation and Rescaling, 21
2.5.3 Derivation of a Distribution, 22
2.6 Order of a Distribution, 26
2.7 The Support of a Distribution, 31
2.8 Some Generalizations, 33
2.8.1 Distributions on Multidimensional Spaces, 33
2.8.2 Vector-Valued Distributions, 38
3. Maxwell Equations in the Sense of Distribution 49
3.1 Maxwell Equations Reduced into the Vacuum, 49
3.1.1 Some Simple Examples, 53
3.2 Universal Boundary Conditions and Compatibility Relations, 54
3.2.1 An Example. Discontinuities on a Combined Sheet, 57
3.3 The Concept of Material Sheet, 59
3.4 The Case of Monochromatic Fields, 62
3.4.1 Discontinuities on the Interface Between Two
Simple Media that Are at Rest, 64
4. Boundary Conditions on Material Sheets at Rest 67
4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet, 67
4.2 Some General Results, 69
4.3 Some Particular Cases, 70
4.3.1 Planar Material Sheet Between Two Simple Media, 70
4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media, 91
4.3.3 Conical Material Sheet Located Between Two Simple Media, 93
5. Discontinuities on a Moving Sheet 109
5.1 Special Theory of Relativity, 110
5.1.1 The Field Created by a Uniformly Moving Point Charge, 112
5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle, 114
5.1.3 Lorentz Transformation Formulas, 115
5.1.4 Transformation of the Electromagnetic Field, 118
5.2 Discontinuities on a Uniformly Moving Surface, 120
5.2.1 Transformation of the Universal Boundary Conditions, 123
5.2.2 Transformation of the Compatibility Relations, 126
5.2.3 Some Simple Examples, 126
5.3 Discontinuities on a Nonuniformly Moving Sheet, 138
5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself, 139
5.3.2 Boundary Conditions on the Interface of Two Simple Media, 143
6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149
6.1 Introduction, 149
6.2 Singularities at the Edges of Material Wedges, 153
6.3 The Wedge with Penetrable Boundaries, 154
6.3.1 The H Case, 156
6.3.2 The E Case, 171
6.4 The Wedge with Impenetrable Boundaries, 174
6.5 Examples. Application to Half-Planes, 175
6.6 Edge Conditions for the Induced Surface Currents, 176
7. Tip Singularities at the Apex of a Material Cone 179
7.1 Introduction, 179
7.2 Algebraic Singularities of an H-Type Field, 185
7.2.1 Contribution of the Energy Restriction, 185
7.2.2 Contribution of the Boundary Conditions, 186
7.3 Algebraic Singularities of an E-Type Field, 191
7.4 The Case of Impenetrable Cones, 193
7.5 Confluence and Logarithmic Singularities, 195
7.6 Application to some Widely used Actual Boundary Conditions, 197
7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index, 200
7.7.1 The Case of Very Sharp Tip, 200
7.7.2 The Case of Real-Valued Minimal v, 201
7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v, 203
8. Temporal Discontinuities 209
8.1 Universal Initial Conditions, 209
8.2 Linear Mediums in the Generalized Sense, 211
8.3 An Illustrative Example, 212
References 215
Index 219
IEEE Press Series on Electromagnetic Wave Theory

Über Autor(innen)

M. Mithat Idemen, PhD, is Professor in the MathematicsDepartment of Yeditepe University (Istanbul, Turkey) and honorarymember of the Turkish Academy of Sciences (TüBA). He hasserved as editor and associate editor for various scientificjournals, including the International Series of Monographs onAdvanced Electromagnetics.