| Description |
1 online resource (474 pages) |
| Summary |
This book is devoted to the investigations of non-stationary electromagnetic processes. The investigations are undertaken analytically mainly using the Volterra integral equations approach. The book contains a systematic statement of this approach for the investigations of electrodynamics phenomena in the time domain and new results and applications in microwave techniques and photonics. Particular consideration is given to electromagnetic transients in time-varying media and their potential applications. The approach is formulated and electromagnetic phenomena are investigated in detail for a hollow metal waveguide, which contains moving dielectric or plasma-bounded medium, and dielectric waveguides with time-varying medium inside a core. |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Introduction -- 1: Basic Relations for an Electromagnetic Field in a Medium with Time-Varying Parameters and/or Moving Boundaries -- 1.1 Generalized Wave Equation for an Electromagnetic Field in a Time-Varying Medium -- 1.1.1 Generalized Derivatives -- 1.1.2 Initial and Boundary Conditions for Electromagnetic Fields in a Time-Varying Medium -- 1.1.3 Maxwell's Equations in a Generalized Derivatives Representation -- 1.1.4 Generalized Wave Equation for the Case of a Non-Dispersive Background -- 1.1.5 Generalized Wave Equation for the Case of a Dispersive Background -- 1.2 Fundamental Solutions to Maxwell's Equations -- 1.2.1 The Non-Dispersive Background -- 1.2.2 The Dispersive Background -- 1.2.3 A Rectangular Waveguide with Perfectly Conducting Walls -- 1.3 Causal Time-Spatial Interpretation of Electromagnetic Field Interaction with Time-Varying Objects -- 1.3.1 The Volterra Integral Equation for the Electromagnetic Field in a Non-Dispersive Background -- 1.3.2 Influence of a Dispersive Background on the Integral Equation Form -- 1.3.3 Spatial-Temporal Interpretation of the Volterra Integral Equation -- 1.3.4 Three Stages of Development of Electromagnetic Transients in a Bounded Medium with Time-Varying Parameters -- 1.3.5 Three Stages of Solution of a Non-Stationary Problem -- 1.4 The Resolvent Method for Solving the Integral Equation -- 1.4.1 Operator Form of an Integral Equation Representation -- 1.4.2 Kernels of the Integral Equations for Typical Media -- 1.4.3 The Resolvent Method -- 2: Transformation of an Electromagnetic Field in an Unbounded Medium with Time-Varying Parameters -- 2.1 Transformation of an Electromagnetic Wave in a Non-Dispersive Time-Varying Medium -- 2.1.1 The Resolvent for an Unbounded Medium with a Jump Change in Its Properties. |
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2.1.2 Splitting of a Plane Harmonic Wave by a Time Jump in Medium Parameters -- 2.1.3 Transformation of Extrinsic Source Radiation by a Jump in Medium Parameters -- 2.2 Evolution of a Harmonic Wave in a Medium Modulated by Repetitive Identical Pulses -- 2.2.1 Electromagnetic Waves in a Linear Modulated Medium -- 2.2.2 "Intermittency" in Electromagnetic Wave Transients in a Time-Varying Linear Medium -- 2.3 Wave Chaotic Behavior Generated by Linear Time-Varying Systems -- 2.3.1 Complexity of the Signals -- 2.3.2 Dependence of Electromagnetic Pulse Form on a Modulation Cycle Number -- 2.3.3 Wave Chaotic Behavior Generated by Linear Time-Varying Systems -- 2.4 Electromagnetic Wave in Isotropic Plasma with Step-Wise Change of Plasma Density -- 2.5 Plane Wave in Gyrotropic Plasma with "Switching On" of a Magnetizing Field -- 2.5.1 Basic Equations -- 2.5.2 The Resolvent for the Integral Equation -- 2.5.3 The Case of the Arbitrary Time-Varying Magnetic Field Approximation -- 2.5.4 The Transformation of a Plane Wave by a Jump of a Magnetic Field -- 2.5.5 The Transformation of the Plasma Oscillations -- 3: Influence of Medium Plane Boundaries on Electromagnetic Transients -- 3.1 A Resolvent for an Initial-Boundary-Value 1D Problem in a Dielectric -- 3.2 Electromagnetic Field in a Half-Restricted Time-Varying Medium -- 3.2.1 Transformation of a Plane Wave by a Jump Change of a Dielectric Permittivity -- 3.2.2 Splitting of a Pulse in a Half-Space with Time-Varying Conductivity -- 3.3 Jump Changes of Plasma Density in a Plasma Half-Space with a Plane Boundary -- 3.3.1 Plasma Density's Jump Change in a Half-Space -- 3.3.2 The Resolvent of the Second Stage of Evolution with Two-Step Change of Plasma Density -- 3.3.3 The Field after One Jump of Plasma Density -- 3.3.4 Transformation of an Electromagnetic Wave by Two-Step Change of the Plasma Density. |
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3.4 The Evolution of an Electromagnetic Field in the Dielectric Layer after Its Creation -- 3.5 Electromagnetic Field in a Layer with Non-Linear and Time-Varying Medium -- 3.5.1 Integral Equation Representation for Numerical Calculation -- 3.5.2 Numerical Algorithm for Solving Integral Equations -- 3.5.3 Numerical Results -- 3.5.4 Comparison of the FDTD and Volterra Integral Equations in Time Domain Approaches -- 3.6 Triple Asymmetry in Time-Spatial Structure of an Airy Pulse in Non-Stationary Environment -- 3.6.1 The Problem Equations -- 3.6.2 Transformed Pulses -- 4: 3D+T Problems with Electromagnetic Transients -- 4.1 The 3D Resolvent for a Problem with a Plane Boundary of a Dielectric Half-Space -- 4.1.1 The Resolvent for the Inner Problem -- 4.1.2 The Resolvent for the External Problem -- 4.2 Fresnel's Formulae in Time-Domain for a Plane Interface between Two Dielectrics -- 4.3 Inclined Incidence of a Plane Wave on a Plane Boundary of the Time-Varying Medium -- 4.3.1 The Field Caused by the Permittivity Time Jump -- 4.3.2 The Field Caused by the Boundary Presence Only -- 4.3.3 The Evolution of the Refracted Field -- 4.3.4 The Field Outside the Non-Stationary Medium -- 4.4 Refocusing of Point Source Radiation by the Plane Boundary of a Time-Varying Dielectric -- 4.5 Formation of Point Source Image by Time Change of Plasma -- 4.6 Frequency Change of Partial Spherical Waves Induced by Time Change of Medium Permittivity -- 4.6.1 Field Representation -- 4.6.2 Analysis of the Inner Field -- 4.6.3 Analysis of the Exterior Field -- 4.7 Evolution of Waves after Plasma Ignition in a Sphere -- 4.7.1 Solution to the Problem -- 4.7.2 The Evolutionary Process -- 5: Non-Stationarity of Electromagnetic Waves Caused by the Movement of a Medium Boundary -- 5.1 Transformation of an Electromagnetic Wave by a Uniformly Moving Boundary of a Medium. |
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5.1.1 Discrepancy of Secondary Waves and Boundary Conditions Numbers -- 5.1.2 Resolution of Moving Boundaries "Paradoxes -- 5.2 Evolution of an Electromagnetic Wave after the Beginning of Medium Boundary Movement -- 5.3 Relativistic Uniform Accelerated Movement of a Medium Boundary -- 5.4 Electromagnetic Field Energy Accumulation in a Collapsing Dielectric Layer -- 5.4.1 Increase of the Wave Amplitudes in the Collapsing Layer -- 5.4.2 The Energy Accumulation in the Layer -- 5.4.3 Generation of Electromagnetic Pulses by the Collapsing Layer -- 6: An Electromagnetic Field in a Metallic Waveguide with a Moving Medium -- 6.1 Expansion of an Electromagnetic Field by Non-Stationary Eigen-Functions of a Waveguide -- 6.2 Equations for a Field in the Waveguide with a Non-Stationary Insertion -- 6.3 Vibration of a Boundary of a Plane Dielectric Resonator -- 6.4 Uniform Movement of a Dielectric Layer in Presence of Waveguide Dispersion -- 6.5 Penetration of an Electromagnetic Wave through Plasma Boundary after Its Start in a Waveguide -- 6.6 Interaction of an Electromagnetic Wave with a Plasma Bunch Moving in a Metallic Waveguide -- 6.6.1 Main Ratios for Electromagnetic Waves in a Waveguide with a Relativistic Moving Plasma Bunch -- 6.6.2 Characteristic Matrix for Waves in a Waveguide with a Plasma Layer -- 6.7 Frequency Multiplication and Amplitude Amplification -- 6.7.1 Enhanced Reflectivity from the Moving Plasma Bunch -- 6.8 Resonance Effects in a Stratified Plasma Cluster Moving in a Waveguide -- 6.8.1 The Characteristic Matrix for Stratified Plasma Cluster -- 6.8.2 Resonance Effects -- 7: Non-Stationary Electromagnetic Processes in Time-Varying Dielectric Waveguides -- 7.1 Wave Equations for Longitudinal and Transverse Components in Generalized Functions. |
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7.2 Volterra Integral Equations for Non-Stationary Electromagnetic Processes in Time-Varying Dielectric Waveguides -- 7.2.1 Integral Equations for the Fields -- 7.2.2 Harmonic Waves in a Waveguide -- 7.3 Solution for the Problem with a Time Jump Change in the Waveguide Core Permittivity -- 7.4 Harmonic Wave Transformation Caused by a Permittivity Change in the Waveguide Core -- 7.4.1 The Early Stage of the Transient -- 7.4.2 Waves Spectra Generated by a Permittivity Time Jump -- 7.5 Transformation of a Wave in a Non-Linear Dielectric Waveguide -- 7.5.1 Step-Like Description of Field Evolution -- 7.5.2 The Step-Resolvent Method for the Waveguide -- 7.5.3 Calculation Scheme for Time Steps Approximation -- 7.5.4 Evolution of the Electromagnetic Wave after Switching of Non-Linearity in the Waveguide -- 7.6 Two Ways for Calculating Field Evolution in a Dielectric Waveguide: Via Brillouin- or Eigen-Waves -- 7.6.1 Elastic Oscillations -- 7.6.2 Differential Formulation of Initial and Boundary Value Electromagnetic Problem in a Dielectric Waveguide -- 7.6.3 Flat Dielectric Resonator -- 7.6.4 Field Evolution in a Dielectric Waveguide -- Index. |
| Subject |
Electromagnetism.
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Électromagnétisme. |
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electromagnetism. |
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Electromagnetism |
| Added Author |
Benson, Trevor, author.
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| Other Form: |
Print version: 9814774952 |
| ISBN |
0429027737 |
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9780429027734 |
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0429648316 |
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9780429648311 |
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0429650957 |
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9780429650956 |
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9780429645679 (electronic bk. ; Mobipocket) |
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0429645678 (electronic bk. ; Mobipocket) |
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