Advanced Theoretical and Numerical Electromagnetics: Static, stationary and time-varying fields (Electromagnetic Waves)

Description

This comprehensive and self-contained resource conveniently combines advanced topics in electromagnetic theory, a high level of mathematical detail, and the well-established ubiquitous Method of Moments applied to the solution of practical wave-scattering and antenna problems formulated with surface, volume, and hybrid integral equations. Originating from the graduate-level electrical engineering course that the author taught at the Technical University of Eindhoven (NL) from 2010 to 2017 this well-researched two-volume set is an ideal tool for self-study. The subject matter is presented with clear, engaging prose and explanatory illustrations in logical order. References to specialized texts are meticulously provided for the readers who wish to deepen and expand their mastery of a specific topic. This book will be of great interest to graduate students, doctoral candidates and post-docs in electrical engineering and physics, and to industry professionals working in areas such as design of passive microwave/optical components or antennas, and development of electromagnetic software. Thanks to the detailed mathematical derivations of all the important theoretical results and the numerous worked examples, readers can expect to build a solid and structured knowledge of the physical, mathematical, and computational aspects of classical electromagnetism. Volume 1 covers fundamental notions and theorems, static electric fields, stationary magnetic fields, properties of electromagnetic fields, electromagnetic waves and finishes with time-varying electromagnetic fields. Volume 2 starts with Integral formulas and equivalence principles, the moves to cover spectral representations of electromagnetic fields, wave propagation in dispersive media, integral equations in electromagnetics and finishes with a comprehensive explanation of the Method of Moments. Cover Contents List of figures List of tables List of examples About the author Foreword Preface Acknowledgements 1 Fundamental notions and theorems 1.1 The electromagnetic field 1.2 The Maxwell equations 1.2.1 Integral or global form 1.2.2 Differential or local or point form 1.3 The Faraday law for slowly moving conductors 1.4 Displacement current 1.5 Time-harmonic fields and sources 1.6 Constitutive relationships 1.7 Boundary conditions for fields and currents 1.8 Wave equations 1.8.1 Time domain 1.8.2 Frequency domain 1.9 Electromagnetic radiation 1.10 Conservation of electromagnetic energy 1.10.1 Poynting theorem in the time domain 1.10.2 Poynting theorem in the frequency domain 1.11 Conservation of electromagnetic momentum 1.12 Conservation of electromagnetic angular momentum References 2 Static electric fields I 2.1 Laws of electrostatics 2.2 Scalar potential and the Poisson equation 2.3 Physical meaning of the scalar potential 2.4 Boundary conditions for the scalar potential 2.5 Uniqueness of the static solutions 2.5.1 Scalar potential 2.5.2 Electrostatic field 2.6 The three-dimensional static Green function 2.6.1 Unbounded homogeneous isotropic medium 2.6.2 Unbounded homogeneous anisotropic medium 2.7 Integral representation of the scalar potential 2.8 Volume potential 2.9 Double-layer potential 2.10 Single-layer potential References 3 Static electric fields II 3.1 Scalar potential due to surface charges 3.2 Integral representation of the electrostatic field 3.3 Other Green functions for static problems 3.3.1 The Dirichlet Green function 3.3.2 The Neumann Green function 3.4 Properties of the static Green functions 3.5 Laplace equation and boundary value problems 3.5.1 Polar spherical coordinates 3.5.2 Circular cylindrical coordinates 3.6 Multipole expansion of the scalar potential 3.6.1 Taylor series of the Green function 3.6.2 Spherical harmonics 3.7 Polarization vector 3.8 The Kelvin and Earnshaw theorems 3.9 Image principle in electrostatics 3.10 Singular electric fields References 4 Stationary magnetic fields I 4.1 Stationary limit of Maxwell's equations 4.2 Vector potential and the vector Poisson equation 4.3 Boundary conditions for the vector potential 4.4 Magnetic scalar potential 4.5 Magnetic dipoles 4.6 Energy and momentum in the stationary limit 4.7 Uniqueness of the stationary solutions 4.7.1 Vector potential 4.7.2 Magnetic entities in the presence of magnetic media 4.7.3 Magnetic entities in the presence of conductors References 5 Stationary magnetic fields II 5.1 Integral representations 5.1.1 Vector potential in an isotropic medium 5.1.2 Magnetic induction and magnetic field 5.1.3 Vector potential and magnetic entities in an anisotropic medium 5.2 Vector potential due to surface currents 5.3 Physical meaning of the vector potential 5.4 Geometrical meaning of the scalar potential 5.5 Multipole expansion of the vector potential 5.6 Magnetization vector 5.7 Magnetic forces between steady currents References 6 Properties of electromagnetic fields 6.1 Principle of superposition 6.2 Well-posedness of the Maxwell equations 6.3 Uniqueness in the time domain 6.3.1 Bounded regions 6.3.2 Unbounded regions 6.4 Uniqueness in the frequency domain 6.4.1 Bounded regions 6.4.2 Unbounded regions 6.5 Magnetic charges and currents 6.6 Boundary conditions with magnetic sources 6.7 Duality transformations 6.8 Reciprocity theorems 6.8.1 Frequency domain 6.8.2 Non-reciprocal media 6.8.3 Time domain 6.9 Other symmetry relationships 6.9.1 Electrostatic fields 6.9.2 Stationary fields and steady currents References 7 Electromagnetic waves 7.1 Time-domain uniform plane waves 7.2 Time-harmonic plane waves 7.2.1 Lossless isotropic medium 7.2.2 Lossy isotropic medium 7.3 Polarization of plane waves 7.4 Plane-wave propagation in layered isotropic media 7.4.1 Reflection and transmission at a planar interface 7.4.2 Network equivalent of a multi-layered medium 7.5 Time-domain uniform cylindrical waves 7.6 The two-dimensional time-domain Green function 7.7 Time-domain transverse electric-magnetic spherical waves 7.8 Non-radiating sources References 8 Time-varying electromagnetic fields I 8.1 The Helmholtz decomposition 8.1.1 Unbounded regions 8.1.2 Bounded regions 8.2 Electrodynamic potentials and gauge transformations 8.3 Boundary conditions for the electrodynamic potentials 8.4 Hertzian potentials 8.5 The scalar Helmholtz equation 8.5.1 Polar spherical coordinates 8.5.2 The Rellich theorem 8.5.3 Conservation of `energy' 8.5.4 Uniqueness in unbounded regions 8.5.5 Uniqueness in bounded regions 8.6 Uniqueness of solutions to the D'Alembert equation 8.6.1 Bounded regions 8.6.2 Unbounded regions 8.7 The three-dimensional time-dependent Green function 8.7.1 Frequency domain 8.7.2 Time domain References 9 Time-varying electromagnetic fields II 9.1 Integral representations of the potentials 9.1.1 Frequency domain 9.1.2 Time domain 9.2 Potentials and fields of a point charge in uniform motion 9.2.1 Velocity smaller than c 9.2.2 Velocity equal to c 9.2.3 Velocity larger than c 9.3 Electrodynamic potentials due to surface sources 9.4 Time-harmonic dyadic Green functions 9.4.1 Observation points away from the sources 9.4.2 Observation points in the source region 9.4.3 Governing equation of G-EJ 9.4.4 Governing equation of G-HJ 9.5 Regions of a localized time-harmonic source 9.6 Fields in the Fraunhofer region of a time-harmonic source 9.7 Symmetry properties of dyadic Green functions 9.8 Quasi-static electromagnetic fields 9.8.1 Electro-quasi-static regime 9.8.2 Magneto-quasi-static regime References Index Back Cover