book

Non-Stationary Electromagnetics, 2nd Edition

by Alexander Nerukh, Trevor Benson

October 2018

Intermediate to advanced

474 pages

9h 49m

English

Jenny Stanford Publishing

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1.1 Generalized Wave Equation for an Electromagnetic Field in a Time-Varying Medium1.1.1 Generalized Derivatives1.1.2 Initial and Boundary Conditions for Electromagnetic Fields in a Time-Varying Medium1.1.3 Maxwell’s Equations in a Generalized Derivatives Representation1.1.4 Generalized Wave Equation for the Case of a Non-Dispersive Background1.1.5 Generalized Wave Equation for the Case of a Dispersive Background1.2 Fundamental Solutions to Maxwell’s Equations1.2.1 The Non-Dispersive Background1.2.2 The Dispersive Background1.2.3 A Rectangular Waveguide with Perfectly Conducting Walls1.3 Causal Time-Spatial Interpretation of Electromagnetic Field Interaction with Time-Varying Objects1.3.1 The Volterra Integral Equation for the Electromagnetic Field in a Non-Dispersive Background
1.3.3 Spatial-Temporal Interpretation of the Volterra Integral Equation1.3.4 Three Stages of Development of Electromagnetic Transients in a Bounded Medium with Time-Varying Parameters1.3.5 Three Stages of Solution of a Non-Stationary Problem1.4 The Resolvent Method for Solving the Integral Equation1.4.1 Operator Form of an Integral Equation Representation1.4.2 Kernels of the Integral Equations for Typical Media1.4.3 The Resolvent Method
2.1 Transformation of an Electromagnetic Wave in a Non-Dispersive Time-Varying Medium2.1.1 The Resolvent for an Unbounded Medium with a Jump Change in Its Properties2.1.2 Splitting of a Plane Harmonic Wave by a Time Jump in Medium Parameters2.1.3 Transformation of Extrinsic Source Radiation by a Jump in Medium Parameters2.2 Evolution of a Harmonic Wave in a Medium Modulated by Repetitive Identical Pulses2.2.1 Electromagnetic Waves in a Linear Modulated Medium2.2.2 “Intermittency” in Electromagnetic Wave Transients in a Time-Varying Linear Medium

2.3.1 Complexity of the Signals2.3.2 Dependence of Electromagnetic Pulse Form on a Modulation Cycle Number2.3.3 Wave Chaotic Behavior Generated by Linear Time-Varying Systems2.4 Electromagnetic Wave in Isotropic Plasma with Step-Wise Change of Plasma Density2.5 Plane Wave in Gyrotropic Plasma with “Switching On” of a Magnetizing Field2.5.1 Basic Equations2.5.2 The Resolvent for the Integral Equation2.5.3 The Case of the Arbitrary Time-Varying Magnetic Field Approximation2.5.4 The Transformation of a Plane Wave by a Jump of a Magnetic Field2.5.5 The Transformation of the Plasma Oscillations
3.1 A Resolvent for an Initial-Boundary-Value 1D Problem in a Dielectric3.2 Electromagnetic Field in a Half-Restricted Time-Varying Medium3.2.1 Transformation of a Plane Wave by a Jump Change of a Dielectric Permittivity3.2.2 Splitting of a Pulse in a Half-Space with Time-Varying Conductivity3.3 Jump Changes of Plasma Density in a Plasma Half-Space with a Plane Boundary3.3.1 Plasma Density’s Jump Change in a Half-Space
3.3.3 The Field after One Jump of Plasma Density3.3.4 Transformation of an Electromagnetic Wave by Two-Step Change of the Plasma Density3.4 The Evolution of an Electromagnetic Field in the Dielectric Layer after Its Creation3.5 Electromagnetic Field in a Layer with Non-Linear and Time-Varying Medium3.5.1 Integral Equation Representation for Numerical Calculation3.5.2 Numerical Algorithm for Solving Integral Equations
3.5.4 Comparison of the FDTD and Volterra Integral Equations in Time Domain Approaches3.6 Triple Asymmetry in Time-Spatial Structure of an Airy Pulse in Non-Stationary Environment3.6.1 The Problem Equations3.6.2 Transformed Pulses
4.1 The 3D Resolvent for a Problem with a Plane Boundary of a Dielectric Half-Space4.1.1 The Resolvent for the Inner Problem4.1.2 The Resolvent for the External Problem4.2 Fresnel’s Formulae in Time-Domain for a Plane Interface between Two Dielectrics4.3 Inclined Incidence of a Plane Wave on a Plane Boundary of the Time-Varying Medium4.3.1 The Field Caused by the Permittivity Time Jump4.3.2 The Field Caused by the Boundary Presence Only
4.3.4 The Field Outside the Non-Stationary Medium4.4 Refocusing of Point Source Radiation by the Plane Boundary of a Time-Varying Dielectric4.5 Formation of Point Source Image by Time Change of Plasma4.6 Frequency Change of Partial Spherical Waves Induced by Time Change of Medium Permittivity4.6.1 Field Representation4.6.2 Analysis of the Inner Field4.6.3 Analysis of the Exterior Field4.7 Evolution of Waves after Plasma Ignition in a Sphere4.7.1 Solution to the Problem4.7.2 The Evolutionary Process
5.1 Transformation of an Electromagnetic Wave by a Uniformly Moving Boundary of a Medium5.1.1 Discrepancy of Secondary Waves and Boundary Conditions Numbers5.1.2 Resolution of Moving Boundaries “Paradoxes”5.2 Evolution of an Electromagnetic Wave after the Beginning of Medium Boundary Movement5.3 Relativistic Uniform Accelerated Movement of a Medium Boundary5.4 Electromagnetic Field Energy Accumulation in a Collapsing Dielectric Layer5.4.1 Increase of the Wave Amplitudes in the Collapsing Layer5.4.2 The Energy Accumulation in the Layer5.4.3 Generation of Electromagnetic Pulses by the Collapsing Layer
6.1 Expansion of an Electromagnetic Field by Non-Stationary Eigen-Functions of a Waveguide6.2 Equations for a Field in the Waveguide with a Non-Stationary Insertion6.3 Vibration of a Boundary of a Plane Dielectric Resonator6.4 Uniform Movement of a Dielectric Layer in Presence of Waveguide Dispersion6.5 Penetration of an Electromagnetic Wave through Plasma Boundary after Its Start in a Waveguide
6.6.1 Main Ratios for Electromagnetic Waves in a Waveguide with a Relativistic Moving Plasma Bunch6.6.2 Characteristic Matrix for Waves in a Waveguide with a Plasma Layer6.7 Frequency Multiplication and Amplitude Amplification6.7.1 Enhanced Reflectivity from the Moving Plasma Bunch6.8 Resonance Effects in a Stratified Plasma Cluster Moving in a Waveguide6.8.1 The Characteristic Matrix for Stratified Plasma Cluster6.8.2 Resonance Effects
7.1 Wave Equations for Longitudinal and Transverse Components in Generalized Functions7.2 Volterra Integral Equations for Non-Stationary Electromagnetic Processes in Time-Varying Dielectric Waveguides7.2.1 Integral Equations for the Fields7.2.2 Harmonic Waves in a Waveguide7.3 Solution for the Problem with a Time Jump Change in the Waveguide Core Permittivity7.4 Harmonic Wave Transformation Caused by a Permittivity Change in the Waveguide Core7.4.1 The Early Stage of the Transient7.4.2 Waves Spectra Generated by a Permittivity Time Jump7.5 Transformation of a Wave in a Non-Linear Dielectric Waveguide7.5.1 Step-Like Description of Field Evolution7.5.2 The Step-Resolvent Method for the Waveguide
7.5.4 Evolution of the Electromagnetic Wave after Switching of Non-Linearity in the Waveguide7.6 Two Ways for Calculating Field Evolution in a Dielectric Waveguide: Via Brillouin- or Eigen-Waves7.6.1 Elastic Oscillations7.6.2 Differential Formulation of Initial and Boundary Value Electromagnetic Problem in a Dielectric Waveguide7.6.3 Flat Dielectric Resonator7.6.4 Field Evolution in a Dielectric Waveguide

Overview

This book is devoted to the investigations of non-stationary electromagnetic processes. The investigations are undertaken analytically mainly using the integral Volterra equation approach. The book contains a systematic statement of the Volterra integral equation method for the investigations of electrodynamics phenomena.