Electromagnetic Fields

Electromagnetic Fields......Page 0
Contents......Page 6
Preface......Page 11
1. Linear Analysis......Page 13
1.1 Linear Spaces......Page 14
1.2 Linear Transformations......Page 17
1.3 The Inversion Problem......Page 20
1.4 Green’s Functions......Page 23
1.5 Reciprocity......Page 26
1.6 Green’s Dyadics......Page 29
1.7 Convergence of a Series......Page 31
1.8 Eigenfunctions......Page 32
1.9 Integral Operators......Page 35
1.10 Eigenfunction Expansions......Page 38
1.11 Discretization......Page 42
1.12 Matrices......Page 45
1.13 Solution of Matrix Equations: Stability......Page 48
1.14 Finite Differences......Page 50
1.15 Perturbations......Page 55
2. Variational Techniques......Page 62
2.1 Stationary functionals......Page 63
2.2 A Suitable Functional for the String Problem......Page 64
2.3 Functionals for the General L Transformation......Page 66
2.4 Euler’s Equations of Some Important Functionals......Page 69
2.5 Discretization of the Trial Functions......Page 71
2.6 Simple Finite Elements for Planar Problems......Page 73
2.7 More Finite Elements......Page 76
2.8 Direct Numerical Solution of Matrix Problems......Page 80
2.9 Iterative Numerical Solution of Matrix Problems......Page 81
3.1 Volume Charges in Vacuum......Page 88
3.2 Green’s Function for Infinite Space......Page 91
3.3 Multipole Expansion......Page 94
3.4 Potential Generated by a Single Layer of Charge......Page 97
3.5 Potential Generated by a Double Layer of Charge......Page 102
3.6 Potential Generated by a Linear Charge......Page 105
3.7 Spherical Harmonics......Page 109
3.8 Dielectric Materials......Page 113
3.9 Cavity Fields......Page 116
3.10 Dielectric Sphere in an External Field......Page 119
3.11 Dielectric Spheroid in an Incident Field......Page 122
3.12 Numerical Methods......Page 126
4.1 Conductivity......Page 135
4.2 Potential Outside a Charged Conductor......Page 137
4.3 Capacitance Matrix......Page 143
4.4 The Dirichlet Problem......Page 144
4.5 The Neumann Problem......Page 147
4.6 Numerical Solution of the Charge Density Problem......Page 149
4.7 Conductor in an External Field......Page 152
4.8 Conductors in the Presence of Dielectrics......Page 156
4.9 Current Injection into a Conducting Volume......Page 158
4.10 Contact Electrodes......Page 163
4.11 Chains of Conductors......Page 168
5.1 Two-Dimensional Potentials in the Plane......Page 176
5.2 Field Behavior at a Conducting Wedge......Page 180
5.3 Field Behavior at a Dielectric Wedge......Page 184
5.4 Separation of Variables in Two Dimensions......Page 186
5.5 Two-Dimensional Integral Equations......Page 190
5.6 Finite Methods in Two Dimensions......Page 194
5.7 Infinite Computational Domains......Page 197
5.8 More Two-Dimensional Techniques......Page 201
5.9 Layered Media......Page 205
5.10 Apertures......Page 208
5.11 Axisymmetric Geometries......Page 212
5.12 Conical Boundaries......Page 216
6.1 Magnetic Fields in Free Space: Vector Potential......Page 229
6.2 Fields Generated by Linear Currents......Page 232
6.3 Fields Generated by Surface Currents......Page 235
6.4 Fields at Large Distances from the Sources......Page 237
6.5 Scalar Potential in Vacuum......Page 240
6.6 Magnetic Materials......Page 242
6.7 Permanent Magnets......Page 244
6.8 The Limit of Infinite Permeability......Page 247
6.9 Two-Dimensional Fields in the Plane......Page 252
6.10 Axisymmetric Geometries......Page 257
6.11 Numerical Methods: Integral Equations......Page 259
6.12 Numerical Methods: Finite Elements......Page 261
6.13 Nonlinear Materials......Page 266
6.14 Strong Magnetic Fields and Force-Free Currents......Page 268
7.1 Maxwell’s Equations......Page 284
7.2 The Wave Equation......Page 287
7.3 Potentials......Page 289
7.4 Sinusoidal Time Dependence: Polarization......Page 293
7.5 Partially Polarized Fields......Page 297
7.6 The Radiation Condition......Page 300
7.7 Time-Harmonic Potentials......Page 303
7.8 Radiation Patterns......Page 307
7.9 Green’s Dyadics......Page 310
7.10 Multipole Expansion......Page 314
7.11 Spherical Harmonics......Page 320
7.12 Equivalent Sources......Page 327
7.13 Linear Wire Antennas......Page 334
7.14 Curved Wire Antennas: Radiation......Page 340
7.15 Transient Sources......Page 344
8.1 Constitutive Equations......Page 364
8.2 Plane Waves......Page 377
8.3 Ray Methods......Page 384
8.4 Beamlike Propagation......Page 395
8.5 Green’s Dyadics......Page 399
8.6 Reciprocity......Page 404
8.7 Equivalent Circuit of an Antenna......Page 409
8.8 Effective Antenna Area......Page 416
9.1 Plane Wave Incident on a Plane Boundary......Page 430
9.2 Propagation Through a Layered Medium......Page 449
9.3 The Sommerfeld Dipole Problem......Page 455
9.4 Multilayered Structures......Page 459
9.5 Periodic Structures......Page 467
9.6 Field Penetration Through Apertures......Page 485
9.7 Edge Diffraction......Page 497
10.1 Eigenvectors for an Enclosed Volume......Page 516
10.2 Excitation of a Cavity......Page 521
10.3 Determination of the Eigenvectors......Page 524
10.4 Resonances......Page 532
10.5 Open Resonators: Dielectric Resonances......Page 536
10.6 Aperture Coupling......Page 547
10.7 Green’s Dyadics......Page 551
11.1 The Scattering Matrix......Page 569
11.2 Cross Sections......Page 574
11.3 Scattering by a Sphere......Page 580
11.4 Resonant Scattering......Page 588
11.5 The Singularity Expansion Method......Page 592
11.6 Impedance Boundary Conditions......Page 604
11.7 Thin Layers......Page 607
11.8 Characteristic Modes......Page 610
12.1 The Electric Field Integral Equation......Page 622
12.2 The Magnetic Field Integral Equation......Page 629
12.3 The T-Matrix......Page 634
12.4 Numerical Procedures......Page 638
12.5 Integral Equations for Penetrable Bodies......Page 644
12.6 Absorbing Boundary Conditions......Page 651
12.7 Finite Elements......Page 656
12.8 Finite Differences in the Time Domain......Page 659
13.1 Physical Optics......Page 675
13.2 Geometrical Optics......Page 680
13.3 Geometric Theory of Diffraction......Page 685
13.4 Edge Currents and Equivalent Currents......Page 693
13.5 Hybrid Methods......Page 696
13.6 Low-Frequency Fields: The Rayleigh Region......Page 699
13.7 Non-Conducting Scatterers at Low Frequencies......Page 700
13.8 Perfectly Conducting Scatterers at Low Frequencies......Page 703
13.9 Good Conductors......Page 711
13.10 Stevenson’s Method Applied to Good Conductors......Page 715
13.11 Circuit Parameters......Page 719
13.12 Transient Eddy Currents......Page 723
14.1 E and H Waves......Page 737
14.2 Scattering by Perfectly Conducting Cylinders......Page 742
14.3 Scattering by Penetrable Circular Cylinders......Page 747
14.4 Scattering by Elliptic Cylinders......Page 750
14.5 Scattering by Wedges......Page 753
14.6 Integral Equations for Perfectly Conducting Cylinders......Page 755
14.7 Scattering by Penetrable Cylinders......Page 763
14.8 Low-Frequency Scattering by Cylinders......Page 768
14.9 Slots in a Planar Screen......Page 774
14.10 More Slot Couplings......Page 782
14.11 Termination of a Truncated Domain......Page 790
14.12 Line Methods......Page 796
15. Cylindrical Waveguides......Page 816
15.1 Field Expansions in a Closed Waveguide......Page 817
15.2 Determination of the Eigenvectors......Page 821
15.3 Propagation in a Closed Waveguide......Page 825
15.4 Waveguide Losses......Page 835
15.5 Waveguide Networks......Page 840
15.6 Aperture Excitation and Coupling......Page 846
15.7 Guided Waves in General Media......Page 862
15.8 Orthogonality and Normalization......Page 868
15.9 Dielectric Waveguides......Page 876
15.10 Other Examples of Waveguides......Page 885
16.1 Field Expansions for Axisymmetric Geometries......Page 907
16.2 Scattering by Bodies of Revolution: Integral Equations......Page 910
16.3 Scattering by Bodies of Revolution: Finite Methods......Page 914
16.4 Apertures in Axisymmetric Surfaces......Page 917
16.5 The Conical Waveguide......Page 920
16.6 Singularities at the Tip of a Cone......Page 928
16.7 Radiation and Scattering from Cones......Page 932
17.1 Fields Generated by a Moving Charge......Page 944
17.2 The Lorentz Transformation......Page 947
17.3 Transformation of Fields and Currents......Page 951
17.4 Radiation from Sources: the Doppler Effect......Page 956
17.5 Constitutive Equations and Boundary Conditions......Page 959
17.6 Material Bodies Moving Uniformly in Static Fields......Page 961
17.7 Magnetic Levitation......Page 963
17.8 Scatterers in Uniform Motion......Page 967
17.9 Material Bodies in Nonuniform Motion......Page 973
17.10 Rotating Bodies of Revolution......Page 975
17.11 Motional Eddy Currents......Page 980
17.12 Accelerated Frames of Reference......Page 985
17.13 Rotating Comoving Frames......Page 989
Appendix 1. Vector Analysis in Three Dimensions......Page 1002
Appendix 2. Vector Operators in Several Coordinate Systems......Page 1011
Appendix 3. Vector Analysis on a Surface......Page 1025
Appendix 4. Dyadic Analysis......Page 1034
Appendix 5. Special Functions......Page 1042
Appendix 6. Complex Integration......Page 1061
Appendix 7. Transforms......Page 1073
Appendix 8. Distributions......Page 1087
Appendix 9. Some Eigenfunctions and Eigenvectors......Page 1102
Appendix 10. Miscellaneous Data......Page 1108
General Texts on Electromagnetic Theory......Page 1113
Texts that Discuss Particular Areas of Electromagnetic Theory......Page 1114
General Mathematical Background......Page 1118
Mathematical Techniques Specifically Applied to Electromagnetic Theory......Page 1119
Acronyms and Symbols......Page 1122
Author Index......Page 1128
Subject Index......Page 1143