Chapter
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
4 Magnetoionic theory 1. Polarisation and refractive index
4.1 Plane wave and homogeneous 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' and 'extraordinary'
4.16 Dependence of refractive index on electron concentration 3. Collisions allowed for
4.17 Approximations for refractive indices and wave polarisations
5 Magnetoionic theory 2. Rays and group velocity
5.2 Refractive index surfaces
5.3 The ray. Ray surfaces
5.4 Properties of ray surfaces
5.6 Classification of refractive index and ray surfaces. C.M.A. type diagrams
5.7 Dependence of refractive index on frequency
5.9 Properties of the group velocity
5.10 Effect of electron collisions on the group refractive index
6 Stratified media. The Booker quartic
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
7 Slowly varying medium. The W.K.B. solutions
7.2 The differential equations for an isotropic ionosphere
7.3 The phase memory concept
7.4 Loss-free medium. Constancy of energy flow
7.8 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
7.15 W.K.B. solutions for anisotropic ionosphere
7.16 The matrices S and S-1
7.17 W.K.B. solutions for vertical incidence
7.18 Ray theory and 'full wave' theory
7.19 The reflection coefficient
8 The Airy integral function and the Stokes phenomenon
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(£) and Bi(()
8.10 The W.K.B. solutions of the Stokes equation
8.11 Asymptotic expansions
8.12 The Stokes phenomenon of the 'discontinuity of the constants'
8.13 Stokes lines and anti-Stokes lines
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
9 Integration by steepest descents
9.2 Some properties of complex variables and complex functions
9.4 Error integrals and Fresnel integrals
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
10 Ray tracing in a loss-free stratified medium
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
10.19 The field where the rays are horizontal
10.20 The field near a caustic surface
10.21 Cusps. Catastrophes
11 Reflection and transmission coefficients
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-Hanchen shifts for radio waves
11.16 The shape of a pulse of radio waves
12 Ray theory results for isotropic ionosphere
12.2 Vertically incident pulses
12.3 Effect of collisions on phase height h(f) and equivalent height h'(f)
12.4 Equivalent height for a parabolic height distribution of electron concentration
12.5 Effect of a 'ledge' in the electron height distribution
12.6 The calculation of electron concentration N(z), from h'(f)
12.7 Ray paths at oblique incidence
12.8 Equivalent path F 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
13 Ray theory results for anisotropic plasmas
13.2 Reflection levels and penetration frequencies
13.3 The calculation of equivalent height, h'(f)
13.6 The calculation of electron concentration N(z) from h'(f)
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
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
14.7 Equivalent path and absorption
14.8 Signal intensity in ray pencils
14.9 Complex rays. A simple example
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
15 Full wave solutions for isotropic ionosphere
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
16 Coupled wave equations
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
16.7 Phase integral method for coupling
16.10 Second order coupled equations
16.11 Forsterling's coupled equations for vertical incidence
16.12 Properties of the coupling parameter ψ
16.13 The method of'variation of parameters'
17 Coalescence of coupling points
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
18.3 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
19 Applications of full wave methods
19.2 Vertical incidence and vertical magnetic field
19.3 Oblique incidence and vertical magnetic field
19.4 Resonance and barriers
19.6 Resonance tunnelling
19.7 Inversion of ionospheric reflection measurements
19.8 Full wave solutions at higher frequencies
Index of definitions of the more important symbols
The Propagation of Radio Waves
：The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere
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