# Terrestrial Propagation of Long Electromagnetic Waves

## 1st Edition

### International Series of Monographs in Electromagnetic Waves

**Authors:**Janis Galejs

**Editors:**A. L. Cullen V. A. Fock J. R. Wait

**eBook ISBN:**9781483159560

**Imprint:**Pergamon

**Published Date:**1st January 1972

**Page Count:**376

## Description

Terrestrial Propagation of Long Electromagnetic Waves deals with the propagation of long electromagnetic waves confined principally to the shell between the earth and the ionosphere, known as the terrestrial waveguide. The discussion is limited to steady-state solutions in a waveguide that is uniform in the direction of propagation. Wave propagation is characterized almost exclusively by mode theory. The mathematics are developed only for sources at the ground surface or within the waveguide, including artificial sources as well as lightning discharges.

This volume is comprised of nine chapters and begins with an introduction to the fundamental concepts of wave propagation in a planar and curved isotropic waveguide. A number of examples are presented to illustrate the effects of an anisotropic ionosphere. The basic equations are summarized and plane-wave reflection from a dielectric interface is considered, along with the superposition of two obliquely incident plane waves. The properties of waveguide boundaries are implicitly represented by Fresnel reflection coefficients. Subsequent chapters focus on boundaries of the terrestrial guide; lightning discharges as a natural source of extremely-low-frequency and very-low-frequency radiation; and the mode theory for waves in an isotropic spherical shell.
This book will be a useful resource for students and practitioners of physics.

## Table of Contents

Other Titles in the Series

Acknowledgments

List of Principal Symbols

1. Introduction

1.1 Scope and Limitations of the Treatment

1.2 Basic Equations

1.3 Plane Waves

1.4 Reflection of Plane Waves

1.5 Planar Waveguide

1.5.1 Modal Equation

1.5.2 Field Components

1.6 References

2. Boundaries of the Terrestrial Waveguide

2.1 Ground Surface

2.1.1 Stratified Ground

2.1.2 Equivalent Anisotropy of a Stratified Medium

2.1.3 Two-Layer Ground

2.2 The Ionospheric Boundary

2.2.1 Electron and Ion Densities

2.2.2 Collision Frequencies

2.2.3 Conductivity Tensor

2.2.4 The Conductivity of a Partly Ionized Gas

2.3 References

3. Natural Sources of Radiation

3.1 Introduction and Summary

3.2 Description of a Lightning Discharge

3.3 Mathematical Models of Lightning Discharges

3.3.1 Amplitude Distribution of Return Strokes

3.3.2 Current Waveforms and Dipole Moments

3.3.3 Spectra of Individual Atmospherics

3.4 Statistical Models for Relating Source and Receiver Waveforms

3.4.1 Probability Distribution of the Received Signal

3.4.2 Amplitude Distributions of Lightning Waveforms

3.5 References

4. Waves in a Spherical Guide

4.1 Introduction and Summary

4.2 Formal Solution

4.2.1 Field Components

4.2.2 Modal Equation

4.2.3 Vertical Electric or Magnetic Dipoles

4.2.4 Horizontal Electric Dipole

4.2.5 Horizontal Magnetic Dipole

4.3 Exponential or Thin-Shell Approximations

4.3.1 Modal Equation

4.3.2 Field Expressions

4.4 Taylor Series Expansion of the Radial Functions

4.5 Airy Function Approximation of the Radial Functions

4.5.1 Modal Equation

4.5.2 Field Components

4.6 Fields in the Vicinity of Sources

4.6.1 Vertical Electric Dipole

4.6.2 Horizontal Electric Dipole

4.7 Fields Near the Antipode

4.7.1 Vertical Electric Dipole

4.7.2 Horizontal Electric Dipole

4.8 Overall Field Variations

4.9 Appendix. Series of Zonal Harmonics and the Watson Transformation

4.9.1 Series of Zonal Harmonics

4.9.2 Watson Transformation

4.10 References

5. Waves in a Cylindrical Guide

5.1 Introduction

5.2 Formal Solution

5.2.1 Field Components

5.2.2 Modal Equation

5.2.3 Excitation by Line Source

5.3 Exponential or Thin-Shell Approximations

5.3.1 Modal Equation

5.3.2 Field Expressions

5.4 Airy Function Approximation of the Cylindrical Functions

5.4.1 Modal Equation

5.4.2 Field Expressions

5.5 Multilayer Representations

5.5.7 Formulation

5.5.2 Second-Order or Debye Approximation

5.5.3 Taylor Series Expansion

5.5.4 Thin-Shell Approximations

5.5.5 Impedance Calculations

5.5.6 The Modal Condition

5.6 Fields Below an Anisotropic Ionosphere

5.6.1 Modal Equation

5.6.2 Field Components

5.6.3 Application to Dipole Sources

5.7 Appendix. Excitation of the Air Space below an Anisotropic Ionosphere

5.7.1 The Primary Fields

5.7.2 Fields at the Anisotropic Ionosphere

5.7.3 The Harmonic Series

5.7.4 The Residue Series

5.8 References

6. Fields in Stratified and Anisotropic Media

6.1 Introduction and Summary

6.2 Isotropic Ionosphere Models with a Diffuse Lower Boundary

6.2.1 Exponential Changes of the Refractive Index

6.2.2 Exponential Changes of the Conductivity

6.3 Propagation Transverse to a Horizontal Static Magnetic Field in a Cylindrical Geometry

6.3.1 Differential Equation for a Continuously Varying Medium

6.3.2 Multilayer Representations

6.4 Spherical Layers with a Radial Static Magnetic Field

6.5 Cylindrical Layers with a Dipping Static Magnetic Field

6.5.1 Fields of a Homogeneous Layer

6.5.2 Multilayer Representations

6.6 Exponential Approximation for Arbitrary Directions of Propagation below an Anisotropic Ionosphere

6.6.1 Fields of a Homogeneous Layer

6.6.2 Multilayer Representations

6.7 Anisotropy of the Ground

6.7.1 Fields in the Anisotropic Ground

6.7.2 Fields of the Airspace and the Modal Equation

6.8 Appendix

6.8.1 Reflection Coefficients

6.8.2 Solution of the Quartic Equation

6.8.3 Solutions for the Lower Ionosphere

6.8.4 Shift of the Antenna Pattern

6.9 References

7. E.L.F. Propagation and Schumann Resonances

7.1 Introduction and Summary

7.2 Field Representations for a Uniform Cavity

7.3 Propagation Parameters

7.3.1 Models of One and Two Isotropic Layers

7.3.2 Exponential Isotropic Ionosphere

7.3.3 Composite Electron Density Profiles

7.3.4 Ions of the Lower Ionosphere

7.3.6 Models of a Perturbed Ionosphere

7.4 Schumann Resonances

7.4.1 Observed Waveforms and Frequency Estimates

7.4.2 Resonance Frequencies and Quality Factors

7.4.3 Noise Spectra

7.4.4 Fields in a Nonuniform Cavity

7.4.5 Variations of Resonance Frequencies

7.5 Appendix. Combined T.M. and T.E. Fields

7.6 References

8. V.L.F. Propagation

8.1 Introduction and Summary

8.2 Propagation Parameters for a Sharply Bounded Homogeneous Ionosphere Model

8.3 Propagation Parameters for Exponential Ionosphere Models

8.4 Propagation Parameters for Composite Ionosphere Models

8.5 Wave Polarization

8.6 Mode Interference

8.7 Perturbed Ionosphere

8.8 Elevated Sources

8.8.1 Field Expressions

8.8.2 Horizontal and Vertical Dipoles

8.8.3 The Inclined Dipole

8.9 References

9. L.F. Propagation

9.1 Introduction

9.2 Ground Waves

9.3 Waves in the Earth-to-Ionosphere Waveguide

9.4 References

Author Index

Subject Index

## Details

- No. of pages:
- 376

- Language:
- English

- Copyright:
- © Pergamon 1972

- Published:
- 1st January 1972

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483159560