Frontmatter
Contents
Preface
1 - The ionosphere and magnetosphere
1.1 The earth's atmosphere
1.2 Plane and spherical radio waves
1.3 Waves in ion plasmas
1.4 Relation to other kinds of wave propagation
1.5 Height dependence of electron concentration: the Chapman layer
1.6 Collision frequencies
1.7 Observations of the ionosphere
1.8 The structure of the ionosphere
1.9 The magnetosphere
1.10 Disturbances of the ionosphere and magnetosphere
Problems 1
2 - The basic equations
2.1 Units and symbols
2.2 Definitions of electric intensity e and magnetic intensity h
2.3 The current density j and the electric polarisation p
2.4 The electric displacement d and magnetic induction b
2.5 Harmonic waves and complex vectors
2.6 Maxwell's equations
2.7 Cartesian coordinate system
2.8 Progressive plane waves
2.9 Plane waves in free space
2.10 The notation [SCRIPT CAPITAL H] and H
2.11 The power input to the plasma from a radio wave
2.12 The flow of energy. The Poynting vector
2.13 Complex refractive index
2.14 Evanescent waves
2.15 Inhomogeneous plane waves
Problems 2
3 - The constitutive relations
3.1 Introduction
3.2 Free, undamped electrons
3.3 The Lorentz polarisation term
3.4 Electron collisions. Damping of the motion
3.5 The Debye length
3.6 Effect of the earth's magnetic field on the motion of electrons
3.7 Effect of the magnetic field of the wave on the motion of electrons
3.8 Electric neutrality of the plasma. Plasma oscillations
3.9 The susceptibility matrix
3.10 Complex principal axes
3.11 Properties of principal axis elements of the permittivity. Effect of ions
3.12 Collisions. The Sen--Wyller formulae
3.13 Electron--electron collisions. Electron--ion collisions
Problems 3
4 - Magnetoionic theory 1. Polarisation and refractive index
4.1 Plane wave and homogeneous plasma
4.2 Isotropic plasma
4.3 Anisotropic plasma. The wave polarisation
4.4 Properties of the polarisation equation
4.5 Alternative measure of the polarisation. Axis ratio and tilt angle
4.6 Refractive index 1. The dispersion relation
4.7 Longitudinal component of electric polarisation and electric field
4.8 The flow of energy for a progressive wave in a magnetoplasma
4.9 Refractive index 2. Alternative derivations and formulae
4.10 Zeros and infinity of refractive index. Equal refractive indices
4.11 Dependence of refractive index on electron concentration 1. Y < 1
4.12 Dependence of refractive index on electron concentration 2. Y > 1
4.13 Effect of collisions included
4.14 The transition collision frequency
4.15 The terms ordinary' andextraordinary'
4.16 Dependence of refractive index on electron concentration 3. Collisions allowed for
4.17 Approximations for refractive indices and wave polarisations
Problems 4
5 - Magnetoionic theory 2. Rays and group velocity
5.1 Introduction
5.2 Refractive index surfaces
5.3 The ray. Ray surfaces
5.4 Properties of ray surfaces
5.5 Crystal optics
5.6 Classification of refractive index and ray surfaces. C.M.A. type diagrams
5.7 Dependence of refractive index on frequency
5.8 Group velocity
5.9 Properties of the group velocity
5.10 Effect of electron collisions on the group refractive index
Problems 5
6 - Stratified media. The Booker quartic
6.1 Introduction
6.2 The variable q
6.3 The Booker quartic. Derivation
6.4 Some properties of the Booker quartic
6.5 Some special cases of the Booker quartic
6.6 The discriminant of the Booker quartic
6.7 The Booker quartic for east--west and west--east propagation
6.8 The Booker quartic for north--south and south--north propagation
6.9 Effect of electron collisions on solutions of the Booker quartic
6.10 The electromagnetic fields
Problems 6
7 - Slowly varying medium. The W.K.B. solutions
7.1 Introduction
7.2 The differential equations for an isotropic ionosphere
7.3 The phase memory concept
7.4 Loss-free medium. Constancy of energy flow
7.5 W.K.B. solutions
7.6 The W.K.B. method
7.7 Discrete strata
7.8 Coupling between upgoing and downgoing waves
7.9 Liouville method and Schwarzian derivative
7.10 Conditions for the validity of the W.K.B. solutions
7.11 Properties of the W.K.B. solutions
7.12 W.K.B. solutions for oblique incidence and vertical polarisation
7.13 Differential equations for anisotropic ionosphere
7.14 Matrix theory
7.15 W.K.B. solutions for anisotropic ionosphere
7.16 The matrices S and S[MINUS SIGN]1
7.17 W.K.B. solutions for vertical incidence
7.18 Ray theory and full wave' theory
7.19 The reflection coefficient
Problems 7
8 - The Airy integral function and the Stokes phenomenon
8.1 Introduction
8.2 Linear height distribution of electron concentration and isolated zero of q
8.3 The differential equation for horizontal polarisation and oblique incidence
8.4 The Stokes differential equation
8.5 Qualitative discussion of the solutions of the Stokes equation
8.6 Solutions of the Stokes equation expressed as contour integrals
8.7 Solutions of the Stokes equation expressed as Bessel functions
8.8 Tables of the Airy integral functions. Computing
8.9 Zeros and turning points of Ai([GREEK SMALL LETTER ZETA]) and Bi([GREEK SMALL LETTER ZETA])
8.10 The W.K.B. solutions of the Stokes equation
8.11 Asymptotic expansions
8.12 The Stokes phenomenon of thediscontinuity of the constants'
8.13 Stokes lines and anti-Stokes lines
8.14 The Stokes diagram
8.15 Definition of the Stokes multiplier
8.16 Furry's derivation of the Stokes multipliers for the Stokes equation
8.17 The range of validity of asymptotic approximations
8.18 The choice of a fundamental system of solutions of the Stokes equation
8.19 Connection formulae, or circuit relations
8.20 Stratified ionosphere. Uniform approximation
8.21 The phase integral method for reflection
8.22 The intensity of light near a caustic
Problems 8
9 - Integration by steepest descents
9.1 Introduction
9.2 Some properties of complex variables and complex functions
9.3 Saddle points
9.4 Error integrals and Fresnel integrals
9.5 Contour maps
9.6 Integration by the method of steepest descents
9.7 Application to solutions of the Stokes equation
9.8 The method of stationary phase
9.9 Higher order approximation in steepest descents
9.10 Double steepest descents
Problems 9
10 - Ray tracing in a loss-free stratified medium
10.1 Introduction
10.2 The ray path
10.3 Wave packets
10.4 Equations of the ray path
10.5 The reversibility of the path
10.6 The reflection of a wave packet
10.7 An example of a ray path at oblique incidence
10.8 Poeverlein's construction
10.9 Propagation in magnetic meridian plane. The Spitze'
10.10 Ray paths for the extraordinary ray when Y < 1
10.11 Extraordinary ray when Y > 1
10.12 Lateral deviation at vertical incidence
10.13 Lateral deviation for propagation from (magnetic) east to west or west to east
10.14 Lateral deviation in the general case
10.15 Calculation of attenuation, using the Booker quartic
10.16 Phase path. Group or equivalent path
10.17 Ray pencils
10.18 Caustics
10.19 The field where the rays are horizontal
10.20 The field near a caustic surface
10.21 Cusps. Catastrophes
10.22 The skip distance
10.23 Edge focusing
Problems 10
11 - Reflection and transmission coefficients
11.1 Introduction
11.2 The reference level for reflection coefficients
11.3 The reference level for transmission coefficients
11.4 The four reflection coefficients and the four transmission coefficients
11.5 Reflection and transmission coefficient matrices
11.6 Alternative forms of the reflection coefficient matrix
11.7 Wave impedance and admittance
11.8 Reflection at a sharp boundary 1. Isotropic plasma
11.9 Properties of the Fresnel formulae
11.10 Reflection at a sharp boundary 2. Anisotropic plasma
11.11 Normal incidence. Anisotropic plasma with free space below it
11.12 Normal incidence. Two anisotropic plasmas
11.13 Probing the ionosphere by the method of partial reflection
11.14 Spherical waves. Choice of reference level
11.15 Goos--HΓΆnchen shifts for radio waves
11.16 The shape of a pulse of radio waves
Problems 11
12 - Ray theory results for isotropic ionosphere
12.1 Introduction
12.2 Vertically incident pulses
12.3 Effect of collisions on phase height h(f) and equivalent height h[PRIME](f)
12.4 Equivalent height for a parabolic height distribution of electron concentration
12.5 Effect of aledge' in the electron height distribution
12.6 The calculation of electron concentration N(z), from hPRIME
12.7 Ray paths at oblique incidence
12.8 Equivalent path P[PRIME] at oblique incidence
12.9 Maximum usable frequency, MUF
12.10 The forecasting of MUF
12.11 Martyn's theorem for attenuation of radio waves
Problems 12
13 - Ray theory results for anisotropic plasmas
13.1 Introduction
13.2 Reflection levels and penetration frequencies
13.3 The calculation of equivalent height, hPRIME
13.4 Ionograms
13.5 Topside sounding
13.6 The calculation of electron concentration N(z) from hPRIME
13.7 Faraday rotation
13.8 Whistlers
13.9 Ion cyclotron whistlers
13.10 Absorption, non-deviative and deviative
13.11 Wave interaction 1. General description
13.12 Wave interaction 2. Outline of theory
13.13 Wave interaction 3. Kinetic theory
Problems 13
14 - General ray tracing
14.1 Introduction
14.2 The eikonal function
14.3 The canonical equations for a ray path
14.4 Properties of the canonical equations
14.5 The Haselgrove form of the equations
14.6 Fermat's principle
14.7 Equivalent path and absorption
14.8 Signal intensity in ray pencils
14.9 Complex rays. A simple example
14.10 Real pseudo rays
14.11 Complex rays in stratified isotropic media
14.12 Complex rays in anisotropic absorbing media
14.13 Reciprocity and nonreciprocity with rays 1. The aerial systems
14.14 Reciprocity and nonreciprocity with rays 2. The electric and magnetic fields
14.15 Reciprocity and nonreciprocity with rays 3. Applications
Problems 14
15 - Full wave solutions for isotropic ionosphere
15.1 Introduction
15.2 Linear electron height distribution
15.3 Reflection at a discontinuity of gradient
15.4 Piecewise linear models
15.5 Vertical polarisation at oblique incidence 1. Introductory theory
15.6 Vertical polarisation 2. Fields near zero of refractive index
15.7 Vertical polarisation 3. Reflection coefficient
15.8 Exponential electron height distribution
15.9 Parabolic electron height distribution 1. Phase integrals
15.10 Parabolic electron height distribution 2. Full wave solutions
15.11 Parabolic electron height distribution 3. Equivalent height of reflection
15.12 The differential equations of theoretical physics
15.13 The hypergeometric equation and its circuit relations
15.14 Epstein distributions
15.15 Reflection and transmission coefficients for Epstein layers
15.16 Ionosphere with gradual boundary
15.17 The sech2' distribution
15.18 Other electron height distributions
15.19 Collisions. Booker's theorem
Problems 15
16 - Coupled wave equations
16.1 Introduction
16.2 First order coupled equations
16.3 Coupled equations near a coupling point
16.4 Application to vertical incidence
16.5 Coupling and reflection points in the ionosphere
16.6 Critical coupling
16.7 Phase integral method for coupling
16.8 The Z-trace
16.9 Additional memory
16.10 Second order coupled equations
16.11 FΓΆrsterling's coupled equations for vertical incidence
16.12 Properties of the coupling parameter [GREEK SMALL LETTER PSI]
16.13 The method ofvariation of parameters'
16.14 The coupling echo
Problems 16
17 - Coalescence of coupling points
17.1 Introduction
17.2 Further matrix theory
17.3 Coalescence of the first kind, C1
17.4 Coalescence of the second kind, C2
17.5 Ion cyclotron whistlers
17.6 Radio windows 1. Coalescence
17.7 Radio windows 2. Formulae for the transparency
17.8 Radio windows 3. Complex rays
17.9 Radio windows 4. The second window
17.10 Limiting polarisation 1. Statement of the problem
17.11 Limiting polarisation 2. Theory
18 - Full wave methods for anisotropic stratified media
18.1 Introduction
18.2 Integration methods
18.3 Alternative methods 1. Discrete strata
18.4 Alternative methods 2. Vacuum modes
18.5 Alternative methods 3. The matrizant
18.6 Starting solutions at a great height
18.7 Finding the reflection coefficient
18.8 Allowance for the earth's curvature
18.9 Admittance matrix as dependent variable
18.10 Other forms, and extensions of the differential equations
18.11 Numerical swamping
18.12 Reciprocity
18.13 Resonance
Problems 18
19 - Applications of full wave methods
19.1 Introduction
19.2 Vertical incidence and vertical magnetic field
19.3 Oblique incidence and vertical magnetic field
19.4 Resonance and barriers
19.5 Isolated resonance
19.6 Resonance tunnelling
19.7 Inversion of ionospheric reflection measurements
19.8 Full wave solutions at higher frequencies
Answers to problems
Bibliography
Index of definitions of the more important symbols
Subject and name index