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The Propagation of Radio Waves

The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere

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Paperback | 3 October 1988

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688 Pages

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This book is largely concerned with the ionosphere and the magnetosphere, and gives the theory of their effect on radio waves. It includes accounts of some mathematical topics that are now widely used in this study, particularly W.K.B. approximations, Airy integral functions and integration by steepest descents. The subject is in two main parts, usually called ray theory and full wave theory. The first is useful for high frequencies and includes ray tracing and caustic surfaces. The second is used for lower frequencies when the approximations of ray theory fail. Much of the book is concerned with the ionosphere treated as a horizontally stratified medium, but there is some discussion of the magnetosphere whose structure is more complicated. This includes an account of whistlers and ion cyclotron whistlers.

The book has been planned both for final year undergraduates and as a reference book for research. It is suitable as a course book on radio propagation for students of physics or electrical engineering or mathematics. Some of the topics are presented from an elementary viewpoint so as to help undergraduates new to the subject. The later parts are more advanced. The subject is very large and has seen many important recent advances. Some topics have had to be treated only briefly, but there is a full bibliography with about 600 references.

Industry Reviews

' ... the most significant ionosphere text for many years ... it is a masterpiece of lucidity and exposition.' Electronics and Power

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Non-Fiction Science Physics Applied Physics Geophysics Classical Mathematics Wave Mechanics including Vibration & Acoustics Engineering & Technology Electronics & Communications Engineering Communications Engineering & Telecommunications Radio Technology

Preface	p. xiii
The ionosphere and magnetosphere	p. 1
The earth's atmosphere	p. 1
Plane and spherical radio waves	p. 3
Waves in ion plasmas	p. 3
Relation to other kinds of wave propagation	p. 5
Height dependence of electron concentration: the Chapman layer	p. 7
Collision frequencies	p. 10
Observations of the ionosphere	p. 12
The structure of the ionosphere	p. 14
The magnetosphere	p. 17
Disturbances of the ionosphere and magnetosphere	p. 19
Problems 1	p. 20
The basic equations	p. 22
Units and symbols	p. 22
Definitions of electric intensity e and magnetic intensity h	p. 23
The current density j and the electric polarisation p	p. 24
The electric displacement d and magnetic induction b	p. 25
Harmonic waves and complex vectors	p. 25
Maxwell's equations	p. 27
Cartesian coordinate system	p. 28
Progressive plane waves	p. 29
Plane waves in free space	p. 31
The notation [script capital H] and H	p. 31
The power input to the plasma from a radio wave	p. 32
The flow of energy. The Poynting vector	p. 33
Complex refractive index	p. 34
Evanescent waves	p. 35
Inhomogeneous plane waves	p. 35
Problems 2	p. 37
The constitutive relations	p. 38
Introduction	p. 38
Free, undamped electrons	p. 38
The Lorentz polarisation term	p. 40
Electron collisions. Damping of the motion	p. 42
The Debye length	p. 44
Effect of the earth's magnetic field on the motion of electrons	p. 45
Effect of the magnetic field of the wave on the motion of electrons	p. 46
Electric neutrality of the plasma. Plasma oscillations	p. 48
The susceptibility matrix	p. 49
Complex principal axes	p. 50
Properties of principal axis elements of the permittivity. Effect of ions	p. 53
Collisions. The Sen-Wyller formulae	p. 57
Electron-electron collisions. Electron-ion collisions	p. 61
Problems 3	p. 62
Magnetoionic theory 1. Polarisation and refractive index	p. 66
Plane wave and homogeneous plasma	p. 66
Isotropic plasma	p. 67
Anisotropic plasma. The wave polarisation	p. 68
Properties of the polarisation equation	p. 71
Alternative measure of the polarisation. Axis ratio and tilt angle	p. 73
Refractive index 1. The dispersion relation	p. 74
Longitudinal component of electric polarisation and electric field	p. 75
The flow of energy for a progressive wave in a magnetoplasma	p. 76
Refractive index 2. Alternative derivations and formulae	p. 77
Zeros and infinity of refractive index. Equal refractive indices	p. 79
Dependence of refractive index on electron concentration 1. Y [ 1	p. 80
Dependence of refractive index on electron concentration 2. Y ] 1	p. 84
Effect of collisions included	p. 86
The transition collision frequency	p. 86
The terms 'ordinary' and 'extraordinary'	p. 88
Dependence of refractive index on electron concentration 3. Collisions allowed for	p. 89
Approximations for refractive indices and wave polarisations	p. 94
Problems 4	p. 99
Magnetoionic theory 2. Rays and group velocity	p. 103
Introduction	p. 103
Refractive index surfaces	p. 104
The ray. Ray surfaces	p. 108
Properties of ray surfaces	p. 111
Crystal optics	p. 113
Classification of refractive index and ray surfaces. C.M.A. type diagrams	p. 116
Dependence of refractive index on frequency	p. 124
Group velocity	p. 128
Properties of the group velocity	p. 131
Effect of electron collisions on the group refractive index	p. 137
Problems 5	p. 139
Stratified media. The Booker quartic	p. 141
Introduction	p. 141
The variable q	p. 142
The Booker quartic. Derivation	p. 144
Some properties of the Booker quartic	p. 146
Some special cases of the Booker quartic	p. 151
The discriminant of the Booker quartic	p. 152
The Booker quartic for east-west and west-east propagation	p. 153
The Booker quartic for north-south and south-north propagation	p. 155
Effect of electron collisions on solutions of the Booker quartic	p. 160
The electromagnetic fields	p. 162
Problems 6	p. 163
Slowly varying medium. The W.K.B. solutions	p. 165
Introduction	p. 165
The differential equations for an isotropic ionosphere	p. 166
The phase memory concept	p. 167
Loss-free medium. Constancy of energy flow	p. 168
W.K.B. solutions	p. 169
The W.K.B. method	p. 170
Discrete strata	p. 172
Coupling between upgoing and downgoing waves	p. 174
Liouville method and Schwarzian derivative	p. 175
Conditions for the validity of the W.K.B. solutions	p. 177
Properties of the W.K.B. solutions	p. 178
W.K.B. solutions for oblique incidence and vertical polarisation	p. 180
Differential equations for anisotropic ionosphere	p. 181
Matrix theory	p. 183
W.K.B. solutions for anisotropic ionosphere	p. 187
The matrices S and S[superscript -1]	p. 190
W.K.B. solutions for vertical incidence	p. 192
Ray theory and 'full wave' theory	p. 193
The reflection coefficient	p. 194
Problems 7	p. 195
The Airy integral function and the Stokes phenomenon	p. 197
Introduction	p. 197
Linear height distribution of electron concentration and isolated zero of q	p. 197
The differential equation for horizontal polarisation and oblique incidence	p. 199
The Stokes differential equation	p. 200
Qualitative discussion of the solutions of the Stokes equation	p. 201
Solutions of the Stokes equation expressed as contour integrals	p. 202
Solutions of the Stokes equation expressed as Bessel functions	p. 204
Tables of the Airy integral functions. Computing	p. 205
Zeros and turning points of Ai([characters not producible]) and Bi([small zeta])	p. 205
The W.K.B. solutions of the Stokes equation	p. 206
Asymptotic expansions	p. 206
The Stokes phenomenon of the 'discontinuity of the constants'	p. 209
Stokes lines and anti-Stokes lines	p. 209
The Stokes diagram	p. 211
Definition of the Stokes multiplier	p. 212
Furry's derivation of the Stokes multipliers for the Stokes equation	p. 212
The range of validity of asymptotic approximations	p. 213
The choice of a fundamental system of solutions of the Stokes equation	p. 214
Connection formulae, or circuit relations	p. 215
Stratified ionosphere. Uniform approximation	p. 216
The phase integral method for reflection	p. 218
The intensity of light near a caustic	p. 223
Problems 8	p. 227
Integration by steepest descents	p. 229
Introduction	p. 229
Some properties of complex variables and complex functions	p. 229
Saddle points	p. 231
Error integrals and Fresnel integrals	p. 233
Contour maps	p. 237
Integration by the method of steepest descents	p. 238
Application to solutions of the Stokes equation	p. 241
The method of stationary phase	p. 247
Higher order approximation in steepest descents	p. 249
Double steepest descents	p. 251
Problems 9	p. 252
Ray tracing in a loss-free stratified medium	p. 254
Introduction	p. 254
The ray path	p. 255
Wave packets	p. 257
Equations of the ray path	p. 259
The reversibility of the path	p. 261
The reflection of a wave packet	p. 261
An example of a ray path at oblique incidence	p. 263
Poeverlein's construction	p. 264
Propagation in magnetic meridian plane. The 'Spitze'	p. 266
Ray paths for the extraordinary ray when Y [ 1	p. 268
Extraordinary ray when Y ] 1	p. 270
Lateral deviation at vertical incidence	p. 273
Lateral deviation for propagation from (magnetic) east to west or west to east	p. 275
Lateral deviation in the general case	p. 276
Calculation of attenuation, using the Booker quartic	p. 277
Phase path. Group or equivalent path	p. 278
Ray pencils	p. 279
Caustics	p. 281
The field where the rays are horizontal	p. 285
The field near a caustic surface	p. 286
Cusps. Catastrophes	p. 287
The skip distance	p. 288
Edge focusing	p. 289
Problems 10	p. 292
Reflection and transmission coefficients	p. 295
Introduction	p. 295
The reference level for reflection coefficients	p. 295
The reference level for transmission coefficients	p. 297
The four reflection coefficients and the four transmission coefficients	p. 298
Reflection and transmission coefficient matrices	p. 299
Alternative forms of the reflection coefficient matrix	p. 300
Wave impedance and admittance	p. 301
Reflection at a sharp boundary 1. Isotropic plasma	p. 304
Properties of the Fresnel formulae	p. 306
Reflection at a sharp boundary 2. Anisotropic plasma	p. 307
Normal incidence. Anisotropic plasma with free space below it	p. 308
Normal incidence. Two anisotropic plasmas	p. 309
Probing the ionosphere by the method of partial reflection	p. 311
Spherical waves. Choice of reference level	p. 313
Goos-Hanchen shifts for radio waves	p. 315
The shape of a pulse of radio waves	p. 320
Problems 11	p. 325
Ray theory results for isotropic ionosphere	p. 328
Introduction	p. 328
Vertically incident pulses	p. 329
Effect of collisions on phase height h(f) and equivalent height h'(f)	p. 330
Equivalent height for a parabolic height distribution of electron concentration	p. 332
Effect of a 'ledge' in the electron height distribution	p. 336
The calculation of electron concentration N(z), from h'(f)	p. 337
Ray paths at oblique incidence	p. 342
Equivalent path P' at oblique incidence	p. 345
Maximum usable frequency, MUF	p. 348
The forecasting of MUF	p. 349
Martyn's theorem for attenuation of radio waves	p. 352
Problems 12	p. 353
Ray theory results for anisotropic plasmas	p. 356
Introduction	p. 356
Reflection levels and penetration frequencies	p. 357
The calculation of equivalent height, h'(f)	p. 359
Ionograms	p. 362
Topside sounding	p. 365
The calculation of electron concentration N(z) from h'(f)	p. 368
Faraday rotation	p. 372
Whistlers	p. 376
Ion cyclotron whistlers	p. 380
Absorption, non-deviative and deviative	p. 391
Wave interaction 1. General description	p. 393
Wave interaction 2. Outline of theory	p. 395
Wave interaction 3. Kinetic theory	p. 397
Problems 13	p. 398
General ray tracing	p. 400
Introduction	p. 400
The eikonal function	p. 402
The canonical equations for a ray path	p. 403
Properties of the canonical equations	p. 405
The Haselgrove form of the equations	p. 407
Fermat's principle	p. 409
Equivalent path and absorption	p. 412
Signal intensity in ray pencils	p. 414
Complex rays. A simple example	p. 417
Real pseudo rays	p. 422
Complex rays in stratified isotropic media	p. 424
Complex rays in anisotropic absorbing media	p. 425
Reciprocity and nonreciprocity with rays 1. The aerial systems	p. 428
Reciprocity and nonreciprocity with rays 2. The electric and magnetic fields	p. 431
Reciprocity and nonreciprocity with rays 3. Applications	p. 433
Problems 14	p. 436
Full wave solutions for isotropic ionosphere	p. 438
Introduction	p. 438
Linear electron height distribution	p. 439
Reflection at a discontinuity of gradient	p. 441
Piecewise linear models	p. 443
Vertical polarisation at oblique incidence 1. Introductory theory	p. 446
Vertical polarisation 2. Fields near zero of refractive index	p. 448
Vertical polarisation 3. Reflection coefficient	p. 450
Exponential electron height distribution	p. 453
Parabolic electron height distribution 1. Phase integrals	p. 456
Parabolic electron height distribution 2. Full wave solutions	p. 460
Parabolic electron height distribution 3. Equivalent height of reflection	p. 464
The differential equations of theoretical physics	p. 466
The hypergeometric equation and its circuit relations	p. 467
Epstein distributions	p. 470
Reflection and transmission coefficients for Epstein layers	p. 472
Ionosphere with gradual boundary	p. 473
The 'sech[superscript 2]' distribution	p. 475
Other electron height distributions	p. 476
Collisions. Booker's theorem	p. 477
Problems 15	p. 479
Coupled wave equations	p. 480
Introduction	p. 480
First order coupled equations	p. 482
Coupled equations near a coupling point	p. 485
Application to vertical incidence	p. 489
Coupling and reflection points in the ionosphere	p. 492
Critical coupling	p. 495
Phase integral method for coupling	p. 499
The Z-trace	p. 502
Additional memory	p. 505
Second order coupled equations	p. 507
Forsterling's coupled equations for vertical incidence	p. 509
Properties of the coupling parameter [small psi]	p. 510
The method of 'variation of parameters'	p. 514
The coupling echo	p. 517
Problems 16	p. 518
Coalescence of coupling points	p. 520
Introduction	p. 520
Further matrix theory	p. 521
Coalescence of the first kind, C1	p. 523
Coalescence of the second kind, C2	p. 525
Ion cyclotron whistlers	p. 530
Radio windows 1. Coalescence	p. 532
Radio windows 2. Formulae for the transparency	p. 534
Radio windows 3. Complex rays	p. 540
Radio windows 4. The second window	p. 542
Limiting polarisation 1. Statement of the problem	p. 543
Limiting polarisation 2. Theory	p. 546
Full wave methods for anisotropic stratified media	p. 550
Introduction	p. 550
Integration methods	p. 552
Alternative methods 1. Discrete strata	p. 553
Alternative methods 2. Vacuum modes	p. 556
Alternative methods 3. The matrizant	p. 558
Starting solutions at a great height	p. 560
Finding the reflection coefficient	p. 562
Allowance for the earth's curvature	p. 563
Admittance matrix as dependent variable	p. 566
Other forms, and extensions of the differential equations	p. 569
Numerical swamping	p. 574
Reciprocity	p. 576
Resonance	p. 579
Problems 18	p. 581
Applications of full wave methods	p. 583
Introduction	p. 583
Vertical incidence and vertical magnetic field	p. 584
Oblique incidence and vertical magnetic field	p. 587
Resonance and barriers	p. 591
Isolated resonance	p. 593
Resonance tunnelling	p. 596
Inversion of ionospheric reflection measurements	p. 602
Full wave solutions at higher frequencies	p. 606
Answers to problems	p. 609
Bibliography	p. 612
Index of definitions of the more important symbols	p. 643
Subject and name index	p. 652
Table of Contents provided by Syndetics. All Rights Reserved.

The Propagation of Radio Waves

The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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