The propagation of radio waves

Frontmatter......Page 1
Contents......Page 5
Preface......Page 13
1.1 The earth\'s atmosphere......Page 17
1.3 Waves in ion plasmas......Page 19
1.4 Relation to other kinds of wave propagation......Page 21
1.5 Height dependence of electron concentration: the Chapman layer......Page 23
1.6 Collision frequencies......Page 26
1.7 Observations of the ionosphere......Page 28
1.8 The structure of the ionosphere......Page 30
1.9 The magnetosphere......Page 33
1.10 Disturbances of the ionosphere and magnetosphere......Page 35
Problems 1......Page 36
2.1 Units and symbols......Page 38
2.2 Definitions of electric intensity e and magnetic intensity h......Page 39
2.3 The current density j and the electric polarisation p......Page 40
2.5 Harmonic waves and complex vectors......Page 41
2.6 Maxwell\'s equations......Page 43
2.7 Cartesian coordinate system......Page 44
2.8 Progressive plane waves......Page 45
2.10 The notation [SCRIPT CAPITAL H] and H......Page 47
2.11 The power input to the plasma from a radio wave......Page 48
2.12 The flow of energy. The Poynting vector......Page 49
2.13 Complex refractive index......Page 50
2.15 Inhomogeneous plane waves......Page 51
Problems 2......Page 53
3.2 Free, undamped electrons......Page 54
3.3 The Lorentz polarisation term......Page 56
3.4 Electron collisions. Damping of the motion......Page 58
3.5 The Debye length......Page 60
3.6 Effect of the earth\'s magnetic field on the motion of electrons......Page 61
3.7 Effect of the magnetic field of the wave on the motion of electrons......Page 62
3.8 Electric neutrality of the plasma. Plasma oscillations......Page 64
3.9 The susceptibility matrix......Page 65
3.10 Complex principal axes......Page 66
3.11 Properties of principal axis elements of the permittivity. Effect of ions......Page 69
3.12 Collisions. The Sen--Wyller formulae......Page 73
3.13 Electron--electron collisions. Electron--ion collisions......Page 77
Problems 3......Page 78
4.1 Plane wave and homogeneous plasma......Page 82
4.2 Isotropic plasma......Page 83
4.3 Anisotropic plasma. The wave polarisation......Page 84
4.4 Properties of the polarisation equation......Page 87
4.5 Alternative measure of the polarisation. Axis ratio and tilt angle......Page 89
4.6 Refractive index 1. The dispersion relation......Page 90
4.7 Longitudinal component of electric polarisation and electric field......Page 91
4.8 The flow of energy for a progressive wave in a magnetoplasma......Page 92
4.9 Refractive index 2. Alternative derivations and formulae......Page 93
4.10 Zeros and infinity of refractive index. Equal refractive indices......Page 95
4.11 Dependence of refractive index on electron concentration 1. Y < 1......Page 96
4.12 Dependence of refractive index on electron concentration 2. Y > 1......Page 100
4.14 The transition collision frequency......Page 102
4.15 The terms `ordinary\' and `extraordinary\'......Page 104
4.16 Dependence of refractive index on electron concentration 3. Collisions allowed for......Page 105
4.17 Approximations for refractive indices and wave polarisations......Page 110
Problems 4......Page 115
5.1 Introduction......Page 119
5.2 Refractive index surfaces......Page 120
5.3 The ray. Ray surfaces......Page 124
5.4 Properties of ray surfaces......Page 127
5.5 Crystal optics......Page 129
5.6 Classification of refractive index and ray surfaces. C.M.A. type diagrams......Page 132
5.7 Dependence of refractive index on frequency......Page 140
5.8 Group velocity......Page 144
5.9 Properties of the group velocity......Page 147
5.10 Effect of electron collisions on the group refractive index......Page 153
Problems 5......Page 155
6.1 Introduction......Page 157
6.2 The variable q......Page 158
6.3 The Booker quartic. Derivation......Page 160
6.4 Some properties of the Booker quartic......Page 162
6.5 Some special cases of the Booker quartic......Page 167
6.6 The discriminant of the Booker quartic......Page 168
6.7 The Booker quartic for east--west and west--east propagation......Page 169
6.8 The Booker quartic for north--south and south--north propagation......Page 171
6.9 Effect of electron collisions on solutions of the Booker quartic......Page 176
6.10 The electromagnetic fields......Page 178
Problems 6......Page 179
7.1 Introduction......Page 181
7.2 The differential equations for an isotropic ionosphere......Page 182
7.3 The phase memory concept......Page 183
7.4 Loss-free medium. Constancy of energy flow......Page 184
7.5 W.K.B. solutions......Page 185
7.6 The W.K.B. method......Page 186
7.7 Discrete strata......Page 188
7.8 Coupling between upgoing and downgoing waves......Page 190
7.9 Liouville method and Schwarzian derivative......Page 191
7.10 Conditions for the validity of the W.K.B. solutions......Page 193
7.11 Properties of the W.K.B. solutions......Page 194
7.12 W.K.B. solutions for oblique incidence and vertical polarisation......Page 196
7.13 Differential equations for anisotropic ionosphere......Page 197
7.14 Matrix theory......Page 199
7.15 W.K.B. solutions for anisotropic ionosphere......Page 203
7.16 The matrices S and S[MINUS SIGN]1......Page 206
7.17 W.K.B. solutions for vertical incidence......Page 208
7.18 Ray theory and `full wave\' theory......Page 209
7.19 The reflection coefficient......Page 210
Problems 7......Page 211
8.2 Linear height distribution of electron concentration and isolated zero of q......Page 213
8.3 The differential equation for horizontal polarisation and oblique incidence......Page 215
8.4 The Stokes differential equation......Page 216
8.5 Qualitative discussion of the solutions of the Stokes equation......Page 217
8.6 Solutions of the Stokes equation expressed as contour integrals......Page 218
8.7 Solutions of the Stokes equation expressed as Bessel functions......Page 220
8.9 Zeros and turning points of Ai([GREEK SMALL LETTER ZETA]) and Bi([GREEK SMALL LETTER ZETA])......Page 221
8.11 Asymptotic expansions......Page 222
8.13 Stokes lines and anti-Stokes lines......Page 225
8.14 The Stokes diagram......Page 227
8.16 Furry\'s derivation of the Stokes multipliers for the Stokes equation......Page 228
8.17 The range of validity of asymptotic approximations......Page 229
8.18 The choice of a fundamental system of solutions of the Stokes equation......Page 230
8.19 Connection formulae, or circuit relations......Page 231
8.20 Stratified ionosphere. Uniform approximation......Page 232
8.21 The phase integral method for reflection......Page 234
8.22 The intensity of light near a caustic......Page 239
Problems 8......Page 243
9.2 Some properties of complex variables and complex functions......Page 245
9.3 Saddle points......Page 247
9.4 Error integrals and Fresnel integrals......Page 249
9.5 Contour maps......Page 253
9.6 Integration by the method of steepest descents......Page 254
9.7 Application to solutions of the Stokes equation......Page 257
9.8 The method of stationary phase......Page 263
9.9 Higher order approximation in steepest descents......Page 265
9.10 Double steepest descents......Page 267
Problems 9......Page 268
10.1 Introduction......Page 270
10.2 The ray path......Page 271
10.3 Wave packets......Page 273
10.4 Equations of the ray path......Page 275
10.6 The reflection of a wave packet......Page 277
10.7 An example of a ray path at oblique incidence......Page 279
10.8 Poeverlein\'s construction......Page 280
10.9 Propagation in magnetic meridian plane. The `Spitze\'......Page 282
10.10 Ray paths for the extraordinary ray when Y < 1......Page 284
10.11 Extraordinary ray when Y > 1......Page 286
10.12 Lateral deviation at vertical incidence......Page 289
10.13 Lateral deviation for propagation from (magnetic) east to west or west to east......Page 291
10.14 Lateral deviation in the general case......Page 292
10.15 Calculation of attenuation, using the Booker quartic......Page 293
10.16 Phase path. Group or equivalent path......Page 294
10.17 Ray pencils......Page 295
10.18 Caustics......Page 297
10.19 The field where the rays are horizontal......Page 301
10.20 The field near a caustic surface......Page 302
10.21 Cusps. Catastrophes......Page 303
10.22 The skip distance......Page 304
10.23 Edge focusing......Page 305
Problems 10......Page 308
11.2 The reference level for reflection coefficients......Page 311
11.3 The reference level for transmission coefficients......Page 313
11.4 The four reflection coefficients and the four transmission coefficients......Page 314
11.5 Reflection and transmission coefficient matrices......Page 315
11.6 Alternative forms of the reflection coefficient matrix......Page 316
11.7 Wave impedance and admittance......Page 317
11.8 Reflection at a sharp boundary 1. Isotropic plasma......Page 320
11.9 Properties of the Fresnel formulae......Page 322
11.10 Reflection at a sharp boundary 2. Anisotropic plasma......Page 323
11.11 Normal incidence. Anisotropic plasma with free space below it......Page 324
11.12 Normal incidence. Two anisotropic plasmas......Page 325
11.13 Probing the ionosphere by the method of partial reflection......Page 327
11.14 Spherical waves. Choice of reference level......Page 329
11.15 Goos--Hönchen shifts for radio waves......Page 331
11.16 The shape of a pulse of radio waves......Page 336
Problems 11......Page 341
12.1 Introduction......Page 344
12.2 Vertically incident pulses......Page 345
12.3 Effect of collisions on phase height h(f) and equivalent height h[PRIME](f)......Page 346
12.4 Equivalent height for a parabolic height distribution of electron concentration......Page 348
12.5 Effect of a `ledge\' in the electron height distribution......Page 352
12.6 The calculation of electron concentration N(z), from h[PRIME](f)......Page 353
12.7 Ray paths at oblique incidence......Page 358
12.8 Equivalent path P[PRIME] at oblique incidence......Page 361
12.9 Maximum usable frequency, MUF......Page 364
12.10 The forecasting of MUF......Page 365
12.11 Martyn\'s theorem for attenuation of radio waves......Page 368
Problems 12......Page 369
13.1 Introduction......Page 372
13.2 Reflection levels and penetration frequencies......Page 373
13.3 The calculation of equivalent height, h[PRIME](f)......Page 375
13.4 Ionograms......Page 378
13.5 Topside sounding......Page 381
13.6 The calculation of electron concentration N(z) from h[PRIME](f)......Page 384
13.7 Faraday rotation......Page 388
13.8 Whistlers......Page 392
13.9 Ion cyclotron whistlers......Page 396
13.10 Absorption, non-deviative and deviative......Page 407
13.11 Wave interaction 1. General description......Page 409
13.12 Wave interaction 2. Outline of theory......Page 411
13.13 Wave interaction 3. Kinetic theory......Page 413
Problems 13......Page 414
14.1 Introduction......Page 416
14.2 The eikonal function......Page 418
14.3 The canonical equations for a ray path......Page 419
14.4 Properties of the canonical equations......Page 421
14.5 The Haselgrove form of the equations......Page 423
14.6 Fermat\'s principle......Page 425
14.7 Equivalent path and absorption......Page 428
14.8 Signal intensity in ray pencils......Page 430
14.9 Complex rays. A simple example......Page 433
14.10 Real pseudo rays......Page 438
14.11 Complex rays in stratified isotropic media......Page 440
14.12 Complex rays in anisotropic absorbing media......Page 441
14.13 Reciprocity and nonreciprocity with rays 1. The aerial systems......Page 444
14.14 Reciprocity and nonreciprocity with rays 2. The electric and magnetic fields......Page 447
14.15 Reciprocity and nonreciprocity with rays 3. Applications......Page 449
Problems 14......Page 452
15.1 Introduction......Page 454
15.2 Linear electron height distribution......Page 455
15.3 Reflection at a discontinuity of gradient......Page 457
15.4 Piecewise linear models......Page 459
15.5 Vertical polarisation at oblique incidence 1. Introductory theory......Page 462
15.6 Vertical polarisation 2. Fields near zero of refractive index......Page 464
15.7 Vertical polarisation 3. Reflection coefficient......Page 466
15.8 Exponential electron height distribution......Page 469
15.9 Parabolic electron height distribution 1. Phase integrals......Page 472
15.10 Parabolic electron height distribution 2. Full wave solutions......Page 476
15.11 Parabolic electron height distribution 3. Equivalent height of reflection......Page 480
15.12 The differential equations of theoretical physics......Page 482
15.13 The hypergeometric equation and its circuit relations......Page 483
15.14 Epstein distributions......Page 486
15.15 Reflection and transmission coefficients for Epstein layers......Page 488
15.16 Ionosphere with gradual boundary......Page 489
15.17 The `sech2\' distribution......Page 491
15.18 Other electron height distributions......Page 492
15.19 Collisions. Booker\'s theorem......Page 493
Problems 15......Page 495
16.1 Introduction......Page 496
16.2 First order coupled equations......Page 498
16.3 Coupled equations near a coupling point......Page 501
16.4 Application to vertical incidence......Page 505
16.5 Coupling and reflection points in the ionosphere......Page 508
16.6 Critical coupling......Page 511
16.7 Phase integral method for coupling......Page 515
16.8 The Z-trace......Page 518
16.9 Additional memory......Page 521
16.10 Second order coupled equations......Page 523
16.11 Försterling\'s coupled equations for vertical incidence......Page 525
16.12 Properties of the coupling parameter [GREEK SMALL LETTER PSI]......Page 526
16.13 The method of `variation of parameters\'......Page 530
16.14 The coupling echo......Page 533
Problems 16......Page 534
17.1 Introduction......Page 536
17.2 Further matrix theory......Page 537
17.3 Coalescence of the first kind, C1......Page 539
17.4 Coalescence of the second kind, C2......Page 541
17.5 Ion cyclotron whistlers......Page 546
17.6 Radio windows 1. Coalescence......Page 548
17.7 Radio windows 2. Formulae for the transparency......Page 550
17.8 Radio windows 3. Complex rays......Page 556
17.9 Radio windows 4. The second window......Page 558
17.10 Limiting polarisation 1. Statement of the problem......Page 559
17.11 Limiting polarisation 2. Theory......Page 562
18.1 Introduction......Page 566
18.2 Integration methods......Page 568
18.3 Alternative methods 1. Discrete strata......Page 569
18.4 Alternative methods 2. Vacuum modes......Page 572
18.5 Alternative methods 3. The matrizant......Page 574
18.6 Starting solutions at a great height......Page 576
18.7 Finding the reflection coefficient......Page 578
18.8 Allowance for the earth\'s curvature......Page 579
18.9 Admittance matrix as dependent variable......Page 582
18.10 Other forms, and extensions of the differential equations......Page 585
18.11 Numerical swamping......Page 590
18.12 Reciprocity......Page 592
18.13 Resonance......Page 595
Problems 18......Page 597
19.1 Introduction......Page 599
19.2 Vertical incidence and vertical magnetic field......Page 600
19.3 Oblique incidence and vertical magnetic field......Page 603
19.4 Resonance and barriers......Page 607
19.5 Isolated resonance......Page 609
19.6 Resonance tunnelling......Page 612
19.7 Inversion of ionospheric reflection measurements......Page 618
19.8 Full wave solutions at higher frequencies......Page 622
Answers to problems......Page 625
Bibliography......Page 628
Index of definitions of the more important symbols......Page 659
Subject and name index......Page 668