RADIO

PROPAGATION

U. S. DEPARTMENT OF COMMERCE

National Bureau of Standards

j

i ll

NIST

PUBLICATtONS

NIST

RESEARCH INFOCEtfTER

GAITHERSBURG,MD 20899-0001

DATE DUE

rt.ii " ^ . b/5

MAY S 1978

llifti \ h \ W3

nrp

—

CAVLOUC l>RiNTeOINU-S.A.

XJNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary NATIONAL BUREAU OF STANDARDS # A. V. Astin, Director

Ionospheric Radio Propagation

Kenneth Davies

National Bureau of Standards Monograph 80

Issued April 1, 1965

For sale by the Sup>erintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 - Price $2.75
Library of Congress Catalog Card Number: 64-60061
IONOSPHERIC RADIO PROPAGATION

Corrtents

Chapter 1 The Earth's Atmosphere, Geomagnetism, and the Sun

Page

1.1. Nomenclature 1

1.2. Pressure and Density Variations 2

1.3. Chemical Composition 5

1.4. Formation of Ionized Layers 8

1.4.1. Ion Production 8

1.4.2. Ion Disappearance 8

1.4.3. Formation of a Chapman Layer 12

1.4.4. Electron Density Distribution 17

1.5. The Earth's Magnetic Field , 19

1.5.1. The Dipole Field 19

1.5.2. The Real Field 23

1.5.3. Magnetic Variations 26

1.5.4. Magnetic Indices 30

1.6. The Auroral Zones 36

L7. The Sun 36

1.7.1, Quiet Conditions 36

1.7.1.1. Structure 36

1.7.1.2. Ionizing Radiations 37

1.7.1.3. Radio Emissions 38

1.7.2. The Active Sun 40

1.7.2.1, Sunspots 40

1.7.2.2, The Sunspot Cycle 40

1.7.2.3, Flares 41

1.7.2.4, Radio Emissions 43

References 44 Chapter 2 Theory of Wave Propagation

2.1, Purpose 45

2.2. Electromagnetic Waves 45

2.2.1. Electrostatics and Magnetostatics 45

2.2.2. Ampere's Circuital Law 49

2.2.3. Faraday's Law 49

III
2.2.4. The Displacement Current 51

2.2.5. A Solution of Maxwell's Equations 53

2.2.6. Some Properties of Electromagnetic Waves 56

2.3. Magneto-ionic Theory 59

2.3.1. Motion of Ions in Electric and Magnetic Fields 59

2.3.1.1. Motion in an Electric Field 59

2.3.1.2. Motion in a Magnetic Field 61

2.3.1.3. Motion in Crossed Electric and Magnetic Fields 62

2.3.2. Derivation of the Appleton Formula 63

2.3.3. Some Properties of the Appleton Formula 71

2.3.3.1. No Magnetic Field, No Collisions 71

2.3.3.2. Magnetic Field, No Collisions 73

2.3.3.3. No Magnetic Field, With Collisions 80

2.3.3.4. Magnetic Field, With Collisions 82

2.3.4. Generalized Magneto-ionic Formulas 84

2.3.4.1. Collision Statistics 84

2.3.4.2. Dispersion 88

2.3.4.3. Absorption „ 88

2.4. Group Propagation 89

2.4.1. Phase Velocity 89

2.4.2. Group Velocity 91

2.5. Propagation in Anisotropic Media 93

2.5.1. Meaning of Anisotropy 93

2.5.2. Angle Between Phase and Ray Directions 95

2.5.3. Phase and Group Paths 96

References 99

Chapter 3

Synoptic Studies of the Ionosphere

3.1. Worldwide Soundings 101

3.2. Experimental Techniques „ 103

3.2.1. Height Recorders „ 103

3.2.1.1. The lonosonde 103

3.2.1.2. The Virtual Height-Time Recorder 108

3.2.2. Absorption Measurements 108

3.2.2.1. The Pulse Reflection Method 108

3.2.2.2. Continuous-Wave Field-Intensity Recordings 110

3.2.2.3. The Riometer Method 110

3.2.2.4. Minimum Frequency Observations 112

3.2.3. Phase Measurements '. 113

3.2.3.1. Relative Phase Changes 113

3.2.3.2. Frequency Changes 113

3.2.4. Angle of Arrival 114

3.2.4.1. Direction Finding 114

3.2.4.2. Vertical Angle 114

3.2.5. Rockets and Satellites 116

3.3. The Quiet Ionosphere 117

3.3.1. Purpose 117

3.3.2. lonograms and Their Interpretation 117

IV
3.3.3. Electron Density Profiles 124

3.3.3.1. Real Height Analysis 124

3.3.3.2. Diurnal Variations 125

3.3.3.3. Seasonal Variations 130

3.3.3.4. Solar Cycle Variations 130

3.3.3.5. Geographical Variation 130

3.3.4. Model Layers 134

3.3.4.1. Chapman Layer 134

3.3.4.2. Parabolic Layer 134

3.3.4.3. Linear Layer 136

3.3.4.4. Exponential Layer 136

3.3.5. Critical Frequency Variations 136

3.3.5.1. General Features 136

3.3.5.2. The E Layer 138

3.3.5.3. The Fi Layer 140

3.3.5.4. The F2 Layer 142

3.3.6. Variations in Ionospheric Absorption 144

3.3.6.1. Introductory Remarks 144

3.3.6.2. Frequency Dependence of Absorption 145

3.3.6.3. Solar Cycle Control 147

3.3.6.4. Diurnal Variations 147

3.3.6.5. Seasonal Variations 149

3.3.7. Sporadic E 150

3.3.8. Spread F 153

3.3.8.1. Description of Spread F 153

3.3.8.2. Diurnal Variations 153

3.3.8.3. Seasonal Variations 154

3.3.8.4. Solar Cycle Variations 156

3.3.8.5. Correlation with Magnetic Activity 156

References _' 156

Chapter 4

Oblique Propagation

4.1. Characteristics of HF Propagation 159

4.2. Equivalence Relationships 160

4.2.1. Plane Earth and Plane Ionosphere 160

4.2.1.1. The "Secant Law" 160

4.2.1.2. Breit and Tuve's Theorem 161

4.2.1.3. Martyn's (Equivalent Path) Theorem 162

4.2.1.4. Martyn's (Absorption) Theorem 163

4.2.2. Effect of the Curvature of the Ionosphere 163

4.3. Calculation of Maximum Frequencies 165

4.3.1. Plane Ionosphere 165

4.3.2. Curved Ionosphere 169

4.3.3. The Parabolic-Layer Method 172

4.4. Oblique lonograms 173

4.4.1. Experimental Technique 173

4.4.2. Conversion from Vertical to Oblique Incidence 174

4.4.3. Experimental Records 175

4.4.3.1. Medium Distances 175V
4.4.3.2. Long Distances 178

4.5. Definitions of MUF 179

4.6. Accuracy of MUF Calculations 180

4.6.1. Effect of the Earth's Magnetic Field 180

4.6.2. MUF Extention 182

4.6.3. Sporadic E 182

4.6.4. Ionospheric Scatter 184

4.6.5. Ground Scatter 184

4.6.6. Ionospheric Tilts 186

4.7. Some Problems in Long-Distance Transmission 188

4.7.1. Path Identification 188

4.7.2. E-hayer Cutoff Frequencies for F2 Propagation 190

4.7.3. Optimum Working Frequency 192

4.8. Multipath Propagation Times 192

4.9. Ray Paths 194

4.9.1. Without Magnetic Field 194

4.9.2. With Magnetic Field (Waves and Rays) 197

4.9.3. Some Sample Ray Paths 198

4.9.3.1. Vertical Propagation 198

4.9.3.2. ObUque Paths 201

4.9.3.3. Topside Soundings 204

4.9.3.4. Satellite-to-Ground Paths 207

4.9.4. Propagation Effects Associated with Ray Paths 210

4.9.5. Faraday Rotation 210

4.9.5.1. Rotation of the Plane of Polarization 210

4.9.5.2. Some Results of Faraday-Rotation Experiments 213

References 214

Chapter 5

Signal Strength

5.1. Meaning of Signal Strength 217

5.2. Factors Affecting Signal Strength 217

5.3. Path Loss 222

5.3.1. Components of Path Loss 222

5.3.2. Spatial Loss 223

5.3.3. Focusing 223

5.3.3.1. Effective Path Length 223

5.3.3.2. Skip Distance Focusing 226

5.3.3.3. Antipodal Focusing 229

5.3.3.4. Horizon Focusing 229

5.3.3.5. Ionospheric Distortion 229

5.3.3.6. Defocusing Due to Underlying Ionization 230

5.3.4. Absorption 231

5.3.4.1. The Absorption Coefficient 231

5.3.4.2. Martyn's Absorption Theorem 232

5.3.4.3. Variation of Absorption with Distance 232

5.3.4.4. Deviative Absorption 234

5.3.4.5. Geographic Considerations 235

5.3.5. Polarization Mismatch Factors 236

VI
5.3.6. Antenna Gain 241

5.4. Fading 242

5.4.1. General Characteristics 242

5.4.2. Interference Fading 242

5.4.3. The Fading Power Spectrum 245

5.4.4. Scintillations 248

5.4.5. Fading Correlation Band>vidth 253

5.4.6. Reciprocity 253

5.4.7. Diversity 255

References 255

Chapter 6 Ionospheric Disturbances

6.1. Types of Disturbance 257

6.2. Sudden Ionospheric Disturbances 258

6.2.1. D-Region Absorption 258

6.2.2. Sudden Phase AnomaHes 262

6.2.3. Sudden Frequency Deviations 262

6.2.4. Effects on Very High Frequencies 265

6.3. Ionospheric Storms 265

6.3.1. Association w-ith Magnetic Storms 265

6.3.2. Depression of Fo Critical Frequencies 266

6.3.3. Absorption 267

6.3.3.1. Blackout Statistics 267

6.3.3.2. Time of Maximum Occurrence 271

6.3.3.3. Total Time of Occurrence 272

6.3.3.4. Latitude Variation 274

6.3.3.5. Magnetic Correlation 274

6.3.3.6. Sunspot Variation 274

6.3.4. Sporadic E 276

6.4. Polar Cap Absorption 277

6.4.1. Duration 277

6.4.2. Temporal Variations 278

6.4.3. Geographical Extent 280

6.4.4. Frequency Dependence of the Absorption 281

6.5. Effects on Radio Communications in High Latitudes 281

6.5.1. Some General Considerations 281

6.5.2. WWV Monitoring 282

6.5.3. Some Path-Loss Data 282

6.5.4. Remedial Measures 284

6.6. Radio Propagation Forecasting 285

References 287

Chapter 7 Ionospheric Propagation Predictions

7.1. Aim of the Chapter 289

7.2. Purposes of Predictions 289

VII
7.3. Predictable Characteristics 290

7.3.1. Sunspot Number 290

7.3.2. Maximum Frequencies 291

7.3.3. Radiation Angle 293

7.3.4. System Loss 294

7.3.4.1. The Elements of System Loss 294

7.3.4.2. Ground Loss 294

7.3.4.3. Distance Loss 294

7.3.4.4. Ionospheric Absorption 297

7.3.4.5. Allowance for Fading, Polarization, Etc 300

7.3.4.6. Antenna Gain 301

7.4. Frequency Prediction Systems 301

7.4.1. Monthly Predictions 301

7.4.2. Permanent Predictions 303

7.5. Radio Noise Predictions 310

7.5.1. Importance of Noise 310

7.5.2. Presentation of Noise Data 311

7.5.2.1. Long-Term Characteristics 311

7.5.2.2. Short-Term Characteristics 314

7.5.2.3. Application of Noise Data 314

7.6. Calculation Procedures for Distances Less Than 4000 km 315

7.6.1. Introduction 315

7.6.2. Problem 1 315

7.6.3. Determination of Optimum Frequency 317

7.7. Calculation Procedures for Distances Greater Than 4000 km 330

7.7.1. Control Points 330

7.7.2. Statement of Problem 2 330

7.7.3. Control Points and Midpoint 331

7.7.4. Frequency Calculations 331

7.7.5. Path Structure 335

7.7.6. System Loss 337

7.7.6.1. Path Loss 337

7.7.6.2. Antenna Loss 338

7.7.6.3. Total System Loss 338

7.7.7. Noise Power 338

7.7.8. Required Carrier Power at the Receiver 339

7.7.9. Required Transmitter Power Pt 339

7.8. Choice of Operating Frequency 339

7.8.1. Optimum Working Frequency 339

7.8.2. Lowest Usable Frequency 340

7.8.3. Operating Frequency 341

References 341

Chapter 8

Scatter Propagation on Very High Frequencies

8.1. Scattering from Ionospheric Irregularities 343

8.2. Characteristics of Propagation on Very High Frequencies 343

8.3. D-Region Scattering 344

8.3.1. Scattering from Irregularities in the D Region 344

VIII
8.3.2. Height of Scattering 346

8.3.3. Signal Strengths in Middle and High Latitudes 347

8.3.3.1. Long-Term Variations 347

8.3.3.2. Frequency Dependence 347

8.3.3.3. Short-term Variations 348

8.3.3.3.1. Amplitude Distribution and Fading Rate 348

8.3.3.3.2. Space Correlation 348

8.3.3.3.3. Frequency Correlation 349

8.3.3.4. Geographical Variations 349

8.3.4. Abnormal Behavior 349

8.3.4.1. Sudden Ionospheric Disturbances 349

8.3.4.2. Correlation with Auroral Phenomena 350

8.3.4.3. Sputter 351

8.3.4.4. Polar Cap Absorption Effects 351

8.4. Meteor Scatter 351

8.4.1. Ionization by Meteors 351

8.4.2. Meteor Data 353

8.4.3. Reflection from a Meteor Trail 356

8.4.3.1. Important Parameters 356

8.4.3.2. Long Wavelength Reflections from Low-Density Trails 357

8.4.3.3. Long Wavelength Reflections from High-Density Trails 359

8.4.3.4. Short Wavelength Reflections from Low-Density Trails 361

8.4.3.5. Short Wavelength Reflections from High-Density Trails 363

8.4.4. Other Aspects of Reflections from Meteor Ionization 363

8.4.4.1. Long Wavelength Reflections During Trail Formation 363

8.4.4.2. Trail Drift and Distortion 364

8.4.4.3. Diversity Effects 365

8.4.5. Short-Term Statistical Characteristics 365

8.4.5.1. General Remarks 365

8.4.5.2. Peak Amplitude Distribution 366

8.4.5.3. Duty Cycle versus Threshold 367

8.4.5.4. Apparent Location of Trails 369

8.4.6. Long-Term Statistical Characteristics 370

8.4.6.1, Diurnal Variations 370

8.4.6.2, Monthly Variations 372

8.4.6.3, Geographical Variation 374

8.4.6.4, Abnormal Absorption 374

8.4.7. Use of Meteor Reflections for Intermittent Radio Communications. _ 375

8.4.7.1. General Characteristics 375

8.4.7.2. Channel Capacity 376

8.4.8. Concluding Remarks on Meteor Propagation 376

8.5. Equatorial F Scatter 377

8.5.1. History... 377

8.5.2. Characteristics of F Scatter 377

8.5.2.1. Diurnal Variation 377

8.5.2.2. Seasonal Variation 377

8.5.2.3. Geographical Variation 377

8.5.2.4. Fading 378

8.5.2.5. Geophysical Factors 378

8.5.3. Flutter Fading 378

IX
8.6. Auroral Scatter 379

8.6.1. Radio Aurora 379

8.6.2. Bistatic Observations 380

8.6.3. Monostatic (Radar) Observations 381

8.7. Incoherent Scatter 384

8.7.1. Historical Note 384

8.7.2. Scattering from an Individual Electron 384

8.7.3. Electron Density Profiles 386

References 390

Chapter 9

Propagation of Low and Very Low Frequency Waves

9.1. Purpose 393

9.2. Theoretical Considerations 394

9.2.1. Ray Theory 394

9.2.2. Waveguide Theory 394

9.2.2.1. Meaning of Mode. 394

9.2.2.2. Basic Concepts 395

9.2.2.3. Modifications for Imperfect Reflection 400

9.2.2.4. Effect of Earth Curvature 402

9.2.2.5. Effect of the Earth's Magnetic Field 404

9.2.2.6. Modes and Rays on Very Low Frequencies 408

9.2.2.7. Effect of Ionospheric Stratification 410

9.2.3. Ionospheric Coupling on Low Frequencies . 411

9.3. Sources of Very Low Frequency Signals 413

9.3.1. Atmospherics 413

9.3.2. Manmade Signals 413

9.3.3. VLF Signals Associated with the Exosphere 413

9.4. Phase Variations on Very Low Frequencies 414

9.4.1. Method of Observing Phase Changes 414

9.4.2. Regular Diurnal Changes Over Short Distances 414

9.4.3. Regular Diurnal Changes Over Long Distances 416

9.4.4. Influence of Geographical Location 418

9.4.5. Determination of Phase Velocity 420

9.4.6. Effects of Meteors 421

9.4.7. Effects of Solar Flares 421

9.4.8. Effects of Magnetic Disturbance 421

9.4.8.1. Sudden Commencements 421

9.4.8.2. Magnetic Storm Effects 423

9.5. Amplitude Variations on Very Low Frequencies 423

9.5.1. Reflection Coefficients 423

9.5.2. Amplitude 425

9.5.3. Attenuation Rate 425

9.5.4. Polarization 427

9.6. Phase Variations on Low Frequencies 427

9.6.1. Normal Behavior over Short Distances 427

9.6.2. Normal Behavior over Long Distances 427

9.6.3. Effects of Solar Flares 428

9.6.4. Polar Cap Disturbances 429 X
9.7. Amplitude Variations on Low Frequencies 429

9.7.1. Normal Behavior over Short Distances 429

9.7.2. The Reflection Coefficient 431

9.7.3. Normal Behavior over Long Distances 433

9.7.3.1. Diurnal Variation 433

9.7.3.2. Seasonal Variation 433

9.7.4. Efifects of Solar Flares 434

9.7.5. Polar Cap Disturbances 435

9.7.6. Magnetic Storm Effects 437

9.7.7. Nocturnal Anomalies 437

9.7.8. The Winter Anomaly 437

9.7.9. Variation of Amplitude with Distance 438

9.7.9.1. Short Distances 438

9.7.9.2. Long Distances 438

9.8. Use of Very Low Frequencies in Frequency Comparison 440

9.9. Uses of Very Low and Low Frequencies 441

References 441

Index 445 Author index 465

Place index 469

XI
I

I

(

I

f
IONOSPHERIC RADIO PROPAGATION

Preface

The purpose of this book is to replace, in part, a previous pubUcation

of the National Bureau of Standards (Circular 462) with the same title. Since the publication of the earlier work in 1948, the whole subject has

undergone a considerable transformation. This is partly due to the special

geophysical efforts known as the International Geophysical Year (1957-8)

and the International Year of the Quiet Sun (1964-5) and to the advent

of the Space Age. The scope of the present work has therefore been

broadened to include aspects of ionospheric radio propagation which

were not treated in the earlier publication.

Such topics as electron -layer production, the geomagnetic field, magneto-ionic theory, and oblique propagation have been expanded with

respect to the earlier treatment. On the other hand, such topics as fre- quency prediction and atmospheric noise have been less thoroughly

dealt with because they have been well treated in other publications

[1, 2, 3].^ Thus, those persons interested in the purely practical aspects

of ionospheric radio communications should use this book in conj unction

with these other publications.

The bulk of the material in the book is taken from the published liter- ature. However, a certain amount has been based on, or taken verbatim

from, certain of the lecture notes prepared by the CRPL staff for the

courses in Radio Propagation held in Boulder, Colorado, during the summers of 1961 and 1962. Recognition of the sources of the material

has been given in the text (or as footnotes). I wish to express my deepest

appreciation to those lecturers who have given me permission to use their notes. Of course, it is impossible to list the names of all those who have

contributed in an indirect manner and I apologize for any inadvertent

omissions. My thanks are also expressed to the many authors and publishers who have given generous permission for the reproduction of their

illustrations. The work of the following authors has been particularly

helpful in the preparation of the respective chapters.

Chapter 1: S. Chapman, T. E. VanZandt.

Chapter 3: J. S. Belrose, R. W. Knecht, J. M. Watts, J. W. Wright.

Chapter 4: T. N. Gautier, R. S. Lawrence, R. K. Salaman.

1 Figures in brackets indicate the literature references on p. XIV.

XllI
Chapter 5: H. J. A. Chivers, T. N. Gautier.

Chapter 6: V. Agy, R. W. Knecht, C. G. Little. Chapter 7: W. Q. Crichlow, G. W. Haydon, M. Leftin, S. Ostrow.

Chapter 8: K. L. Bowles, R. S. Cohen, R. C. Kirby, G. Sugar.

Chapter 9: J. S. Belrose, C. J. Chilton, J. H. Crary, D. D. Crombie,

A. Glenn Jean, W. L. Taylor, J. R. Wait.

It is intended that the reader who wishes to pursue the subject further

will consult the references cited. To this end, whenever possible, the most

recent references are cited, as the older (and sometimes more important)

works are invariably listed therein. The reference lists are augmented by

acknowledgments to the sources of published figures and the reader is advised to consult these references also. An excellent bibliography of

ionospheric work has been compiled by Dr. L. A. Manning [4].

While the book is devoted mostly to the propagation of high-frequency radio waves, two chapters have been included in order to give

the reader a better perspective of the relationship of the high-frequency

band to the lower frequency (LF and VLF) bands and upper (VHF)

frequency band.

The book was prepared during a visit to the Radio Research Station

of the Department of Scientific and Industrial Research in Slough,

England. I want to extend my appreciation to Mr. J. A. Ratcliffe, Director of the Radio Research Station, and his staff for their kindness and

help in the preparation of the manuscript and in supplying certain illus- trations. In particular, I should like to thank J. W. King, L. Thomas,

and W. R. Piggott.

Finally, I should like to thank Mr. J. W. Finney, Mrs. T. Simpson,

Dr. J. R. Lebsack, and the staffs of the Technical Information Office (NBS, Boulder) and of the Technical Publications Division (NBS,

Washington) for their help in the preparation of the typescript, and my

colleagues in the Central Radio Propagation Laboratory and the University of Colorado who kindly read and criticized the earlier versions.

It is hoped that the book will be of use both to research workers and

to communications engineers who already have some background knowledge of radio propagation via the ionosphere.

REFERENCES

[1] Haydon, G. W., and D. L. Lucas, Technical Considerations in the Selection of Optimum Frequencies for High Frequency Sky Wave Communications Services (unpublished).

[2] World Distribution and Characteristics of Atmospheric Radio Noise (1964), CCIR Report 322.

[3] Radio Spectrum Conservation (Revised) (1964), IEEE and Joint Technical Advisory Committee of IEEE and EIA.

[4] Manning, L. A. (1962), Bibliography of the Ionosphere, Stanford University Press. XIV
!

CHAPTER 1

The Earth's Atmosphere,

Geomagnetism, and the Sun

1.1. NOMENCLATURE

Throughout this book, the terminology used to describe the various

regions of the upper atmosphere will be that based upon the temperature

distribution of the neutral atmosphere [1].^ This distribution is shown in

figure 1.1, and the following terminology is widely used.

The mesosphere, which lies in the height range of 50 to 85 km, is a region of decreasing temperature with height.

The thermosphere, above 85 km, is a region in which the temperature increases with height.

These "regions" are not well defined and the transition regions are

called "pauses." In addition to the terminology based on temperature, others have

been devised based on alternative physical quantities and processes. Two of these are illustrated in figure 1.1. For example, one terminology

is based on the fact that turbulence predominates below about 100 km,

whereas diffusive separation sets in above about 110 km. Above about

500 km is a region called the exosphere.

The term ionosphere was first applied by Sir Robert Watson-Watt

to that part of the atmosphere in which free ions exist in sufficient quantities to affect the propagation of radio waves. The ionosphere can,

therefore, be considered as lying between about 40 to 50 km and several earth radii. This definition is essentially that adopted by the Institute of

Radio Engineers [2].

It is convenient to define a region as a section of the atmosphere

within which there can exist ion distributions called layers. A division

1 Figures in brackets indicate the literature references on p. 44. I
2 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

of the ionosphere into regions is given in table 1.1 together with the layers

which may exist within these regions. The electron distribution within

a region may not contain a peak of electron density.

1.2. PRESSURE AND DENSITY VARIATIONS

The relationship between pressure p and density p at any height h

is given by the "barometric equation," which is derived as follows: con- Table 1.1. Ionospheric regions and layers

Height range (km) Region Layers 50-90 D D

90- (120-140) E El, E2, Es Above (120-140) F Fl, Fl., F2

E

5000 IONOSPHERE NEUTRAL ATMOSPHERE

i

' \ '

'

1 TEMPERATURE PROCESSES

\ PROTONOSPHERE

2000 2000

1000 EXOSPHERE _ 1000 \ HELIOSPHERE

500 \\\

s X

THERMOSPHERE /

-—(500 -700)-

500

200 /

DIFFUSOSPHERE _ 200

100

—

/

J

' ( v.^ J ^> ^^^.-^

FlED (—-MES0PAUSE(85)

\ MESOSPHERE

TURBOPAUSE

(100-120) _ TURBOSPHERE " 100

50

1 1 1 1 \ MES0PEAK(50)

1 1 i 50

2 3 4 5 6 0 500 1000 1500 L0G,QNg(cm-3) T (°K) Figure 1.1. Atmospheric nomenclature.

f (After T. E, VanZandt and R. W. Knecht. See fig. 1.3.)
PRESSURE AND DENSITY VARIATIONS 3

sider an elementary cylinder of height dh and unit cross section. The net

pressure difference dp between the top and bottom surfaces must equal

the downward force due to the weight of the fluid in the cylinder, and

is given by

dp= —pg dh

(1.1) = —Nmgdh,

where g is the acceleration due to gravity, N is the number density of

molecules and m is the mean molecular mass. It should be remembered

that A^, m, and g are all functions of height; e.g., g varies inversely as the

square of the radius vector. The perfect gas law is p = NkT, (1.2)

where k is Boltzmann's Constant ( = 1.372 X 10~^^ erg/deg) and T is the

absolute temperature.

From (1.1) and (1.2) we obtain

^=-p|,,= (1.3)

p kT H

where H=kT/mg is known as the ""scale height" of the atmosphere, which

again is height dependent. At the earth's surface the value of H is about

8 km.

In an isothermal atmosphere, integration of (1.3) gives

/ h-h\ p=poexp{ —I (a)

or (1.4)

p = PoexpI —j, (b)

where p is the pressure at a height h corresponding to a pressure po at a height ho. Similarly for the density p. The quantity (h — ho)/H, which

is the height difference in scale height units, is often denoted by z. Below

about 100 km it is possible to measure T(h) and m{h) directly, by means

of rockets, and hence to determine H. Above about 100 km, however,

it is much easier to measure p{h) and determine H from (1.3) expressed
4 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

in the form

f Pgdh

J I,

The following formulas are useful in calculating the scale height at any

altitude:

M(gm/mole) Hikm) =0.848 ^

, ,

, (1.6)

where a is the earth's radius (6370 km approximately). Equation (1.6) can be approximated by

H=0.93 J, (1.7)

which is correct to within 7.5 percent between 50 km and 500 km. It is exact at 300 km.

The temperature or scale height structure gives rise to the ter- minology indicated in the column labeled "temperature" in figure 1.1. Although the terminology is self-explanatory, the causes of the observed

temperature structure deserve comment. The mesosphere is heated by

the absorption by ozone of solar ultraviolet light with wavelengths between 2550 A and 1650 A. The thermosphere is heated by the dissociation

and ionization of the atmospheric gases by solar ultraviolet light with

wavelengths less than 1760 A. Up to about 100 km, heat is lost mainly

by infrared radiation. Above 100 km, on the other hand, heat is lost mainly by conduction downward towards the mesopause.

Below about 100 km, the specific heat of the atmosphere is so large

that even though the rate of heat input almost vanishes at night, the

temperature changes very little. Above 100 km the temperature is in- creasingly variable, both diurnally and with solar activity. For example,

at 300 km the temperature decreases by about one third from day to night

and probably by about half from sunspot maximum to sunspot minimum.

The temperature may also increase by a factor of two during large ionospheric storms. These variations of the structure of the thermosphere are complex and poorly understood, but they are now the object of intensive

research.
CHEMICAL COMPOSITION

1.3. CHEMICAL COMPOSITION

5

Below about 85 km, turbulent mixing keeps the relative composition of the atmosphere essentially the same as that at the ground, which

is given in table 1.2. In addition to the primary constituents, there are

traces of other chemicals in the atmosphere, chief of which are water

vapor, carbon dioxide, ozone, nitric oxide, and hydrogen.

Above about 90 km, dissociation of O2 becomes important. This re- sults in a marked decrease in the mean molecular weight and hence an

increase in the scale height of the atmosphere.

The variation with height of some atmospheric properties are shown

in tables 1.3 and 1.4. Table 1.3 is based upon the 1959 ARDC Model

Atmosphere [3]. Table 1.4 is that given by Norton, Van Zandt, and

Denison [4]. The differences between the values given in these tables are due to the different assumptions made with respect to the degree of

dissociation of O2 and the reference level used, etc. The differences may

be taken as an indication of the degree of uncertainty to which the pa- rameters are known.

It is impossible to construct a model of the atmosphere between 90

and 200 km which hes within the range of observations of total density,

temperature, mean molecular weight, and density of O2. For example, if a model agrees with the observations of total density and temperature,

then deduced composition cannot agree with the observed composition,

etc. It appears that the observations of at least one of these quantities are systematically wrong. Thus atmospheric models differ widely according

to which observations have been accepted and which are ignored.

Table 1.2. Chemical composition at the ground

Concentration Total per cm^

Molecule Mass Percentage per cm3 column N2 28.022 78.084 2.098 (19) 1.678 (25) O2 32.009 20.946 5.629 (18) 4.501 (24) A 39.960 0.934 2.510 (17) 2.007 (23) CO2 44.024 0.33 8.870 (15) 7.090 (21) Air 28.973 100 2.687 (19) 2.148 (25) He 1.41 (14) 1.13 (20) Ne 4.89 (14) 3.89 (20) Kr 3.06 (13) 2.45 (19) Xe 2.34 (12) 1.89 (18)

Note that the figures in ( ) represent the exponent of 10 by which the number shown must be multiplied.
EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

CO vO On CO CO

rfi LO CO 00

(N I—( CO ' Tf vO CO ON ' lO (M VO to CO O CO ON(N CO 00

i-H (N O ' ^ CO ^ "O \o i> CO NO lo ^ NO CO

1—I CSl CO

CO © (N lO 1—I CO

NO t> CO O I—

I

'O ^ ^ ^ ^ NO NO NO

On On O^ On 0^

vo NO NO

NO NO NO

0^ O^ O^ O^ O^

<M LO NO CO (N CO

CO On LO CNl LO O

00 CO CO CO CO

CN) CNl CNl CNJ CNJ 00 00 CO 00 00

(M (N CNl CNl CNl CO CO CO CO «><M CNl CNl CNl csi ^ i-H ON CO i>

CNl CNl pH f-H !—I 1—

I

O CO rH CO CSI NO ON Tft

CNl CO CO

I I I LO NO NO OI I I I I NO l> CO CO 0\ ON

I I I I I I O O I—I I—I fH LO CO rH 1—I r-H CO rH

(N rH rH O ON

CNl CNl CNl CM 1—

I

COI>NONONO LO LO CO CO CNl

CNl CO

CNl CO rH CO CO

rH ON CO 'J? CO l>- C^l CNl rH

CNl CNl LO I> CO NO CNl rH CO rH CN| CN| CO

.2 c ON ON 00 NO NO LO CO CNl CN| CO ON o

O O rH NO rH O

CO ON CNl o o o

NO CNl ON CNl NOrHTfONrH LO O O O O O

CO ir- NO LO

I I I I I LO Tf< Tf* CO CN|

I I I I I CO o © o o NO © rH LO ©

© T* © © © lO CO rH 00 On NOCNION-^CNl tr- CNl CO CO CNl

00 © © © ON ON CO © CNl © rH CNl lO

rH NO CO 1^

CNl ©CNl

ON © CO rH LO © ON rH CO

CO

rH rH 00 00

LO CO On ^ Tf ^ ^ CO CO CO

CNl CO LO LO © 00 O^ 0\ LO CO

CO LO t> ON ©

CNl CN| NO rH ON rH NO !>• NO LO CNl © © rH CNl CO LO

CNl CNl CN| CNl CNl CO Tj< © NO VO

00 LO pH NO NO

CNl CNl C^l rH rH © O © O rH LO © CNl CO CNl CO

T* CO © NO rH CNl © CNl CO t— ON rH

Tf< T^H LO NO CO

H CNl CNl CO MM CO LO NO M M I M M I MM

C^lTtONCO© COrH©CNl-^ COCOCNICNlrH r^lO©©CNl©

CN| rH OO © © LO © rH 00 l> © rH © NO O © CN| NO CO

rH rj< 00 rH rH CO rH CN| CNJ CO rH CO rH NO CO On CNl NO CNl

© © © © © ©CNIT^NOCO ©©©©' r-^^^^,^ CM CO Tf< LO NO
CHEMICAL COMPOSITION

(M <N (N i-H I—I OO'^-^-^'^ ^^^^^^ ^^^^^ I—ii—ir—Ii-Hi-H 1—Hi—(0^0^0^^ O^^OOOOOOOO COOOCOOOOO

l> lO <M lO CO 1—I 'O LO O (N O tJ" OmO (rq CO (N <—I ^ r-i CO CO \0 Cm—I I—I CO LO LO CO \0 r-H 1—I ^ lO r-rH\OCOO

CO 1—I CO rH r-l OMO CO <M i—I rH CO ^ Tf< CO (N i—I i—I rH

asCOCOCOCOI> l> l> tr- vO^OvOOMD

0^ ^ LO O l> ^ Qs CO

lO vO CO

CO ^ O CO On

vo 1—I (N i> cq ON

1

Tj< CO csj ph I—I CO ^ Lo CO

C* C^ C^ C\ C^ C^ C\ O** C^ C^ S VO 1—I Tf< O CO 1—• <M Tf ON t— " VO (N ON O COOONCOCOlO

VO ON <N to (N O ON i> ON tr^ CO VO ON lO O O ON O <N 1—

I

LO CO 1—1 1—I ON lo CO CO csj cq

O © O f-i(N 77777

CNJ CO CO CO CO 777777

CO CO CO CO ^ 777777 77777

I CO Tt © r-l t— © © vO to

r- © VO ON Tf

<^t CNi CO I—

I

CO o CO

CO CO r—I CO

CO © ^ CO (N to to ON

(N I—I cNi CO CO 1—I ON o Tj* CO CNj I—1 1—1 1—I ON \o to CO CO

^ f-H rH (M Csl g I I I I I CO CO CO CO CO CO

I I I I I I CO ^*I I I I I I I I I I I CO CO ^ ON tJ< O rH © <N ,-1 CO © ON 1—I l> CO © «M CO tJ* ON © r—I rH \0 l>- vo ^ vo Tf* © to © CO

r-H Cq rH VO CSJ CI i—I i—I i—I ON On ^ tO Tf< CO CO (N CN)

1—I Tf CO ON to

to i> I—I \o CN) ON

1—I ON ON CNJ o O Tf< rH ON CO

CO CO CO i> i> t> t-

© r-ON©i>ONr^

CO vOON©COi—1^

vO O CO © CO © vo i> i>

c CO to i>

iti ON 1-1 CO 00 VO

o rH (rq (N CO

CO vo Tf CNl CO CO

t> © © CO o CO ON o\

CO vo CNi

tJ< © to © l> © i-H 1—I cq (N 0\ CO © CO CO ©

CO CO CO CO

- ©to©©© ©©©©©© ©©©©©© Q©©©© g © © I—I CNi CO ^ to i> 00 ON © ph cNj CO to vot— COON©

I rH I—I r—I ph i—1 1—I i—I i—1 1—I i—I cq cq CN| csi cq (N cq cq CN| CO
8 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

1.4. FORMATION OF IONIZED LAYERS

1.4.1. Ion Production

Ions are believed to be produced in the earth's atmosphere partly

by cosmic rays but mostly by solar radiation. The latter may include

particle radiation (during storm periods), ultraviolet light, and x rays. By far the predominant agent appears to be solar ultraviolet light and

soft X rays. With a suitable atmospheric model together with a knowledge

of the solar flux, absorption cross section, and ionization efficiency of

the various constituents, it is possible to compute the rate of ion production in the atmosphere. Some relevant photoionization data are included

in table 1.5 for the major constituents of the E and F regions; i.e., O, O2,

and N2. The ionization efficiency (ion pairs per photon absorbed) is the

ratio of the ionization cross section to the absorption (yoss section. For

a more extensive discussion of this subject, the reader is referred else- where [1, 5, 6].

1.4.2. Ion Disappearance

When electrons are produced in the upper atmosphere, they tend

to reunite with positive ions (recombination) and to attach themselves

to neutral molecules to form negative ions such as 02~ (attachment).

The 02~ ion is later neutralized by further reactions. Electrons can also leave a given volume by moving out of it (diffusion and/or drift).

For our present purposes we shall consider recombination and at- tachment only. Let the number densities of electrons, of positive ions,

and of molecules to which attachment is possible be denoted by N{e),

A^(^+), and N(A), respectively. The rate at which electrons are lost by

recombining with positive ions is given by

d—N(e) ^=-aN(e)N{A+), (1.8)

dt where a is the recombination coefficient. If we assume that there are few negative ions compared with the electron concentration, we have

N{e)^N{A+) so that

^=-„liV(.)lV (1.9)

at
FORMATION OF IONIZED LAYERS 9 Consider the process of attachment; the rate of disappearance will be

proportional to both electron concentration and the neutral atom concentration, that is d—N(p) -bN{e)N(A), (1.10)

at where 6 is a constant of proportionality. If we assume that the number of

neutral molecules is enormously greater than the number of electrons, so that it does not change appreciably when a few of the atoms are con- yerted into negatiye ions, we may write

yiV(e) = -/3iV(e), (1.11)

at where 0 is known as the attachment coefficient. For a fuller discussion of

this subject, the reader is referred to other works on the subject [6].

The coefficients a and (3 may yary with height because the reactions

usually inyolye three bodies rather than two. The rate of change of electron density N is, therefore, giyen by

the following continuity equations for the cases of recombination and

attachment, respectively:

^= q-aN\ (1.12)

dN—= q-0N, (1.13)

where q is the rate of electron production, i.e., number of electrons pro- duced per second.

It should be noted here that if electrons are produced at a rate q and are lost by attachment to neutral atoms to form negative ions, and

if these ions are subsequently lost by ionic recombination, it can be shown

that the continuity equation assumes the form —dN

= q.ii-oc,uN\ (1.14)

dt

^

where q^n and a^u are eifective rates of production and disappearance

[6]. Thus the net effect is to make the process appear as simple recom-
10 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

o "8 ^ CO

I

0.2 a

re

© ^ ON ON (NO©LOeOCOO(NLO

CO 00 CO O t> ^

rHO'sfvofocor-oc^

QN On vooo^Ofor^coot^oqoioioooTj'oo'^'^ccomcooLOfc ©CCfMOOONt-OLOfOr-HOCOeCONODOfOi—lCOLOLCOvOvOvOfO<N (NOOOOONONONONONONONCOCOt^t^Jr-^^OLCiOLCLOrJtfCfOCCCO

00 O (N O CO CO -"^inoNOOONCOcococooooo

©OOOOOOOOOOOOOOOOi-Hp-ldoOOOr-HpHi-JrH

tr- LO i> vO l> CO t> O I OOOOOOOOOOOOOOOOOOOOOOOOrHrHi-ir-l

ooooooooooooooooo©

©OOOOOOOOOi

f-H O O O O ON O O O O O i-H ©OOOrHi—lOOCOOT?LOLC(NiOinONCOLOONir5vO'«?'ir5CC(NOCO O 1—I CNJ 1—I I—I rH rH Cn| 1—1 I—I i-H I—I I—I rH

eO(0^0^0©t~- O LC o in lOi—ii—ii—l^J^coMO^J^ON^^l>oooect^lnLr^fO(NOcocoLO^-^-^-•^-

rH I—I pH CNl CNJ (N fC CSJ (N (M fH I—I r-H r—

I

vO CO ON (N CO r-l 1/5 CO CO CO in OOOO©OOOOOC^CN|CNjeCC0fCC0(N(Nf0CCfCC0e0OO\C0C0

111

CCS 0 0 0

U V u

<^«0 VLI >^ ;^ >^ t^O S ? >^ > >

eO^LOI>©CCt^-<*fO©©(N00LOCCfCC^ONTf©COi—IC^r--lTj<CCCOCNl LO CO I—I CO CO I—I rH

© ©ON O^ON C^©©lOCOC0©<NlO

i-H©'^VOCOC0t^©C<J

I—I O^ON ONONcococor^t^t^o ON ON CO CO CO l> O LO PO •<^o©voo©^'5^>co©^^-e^^©lAlO©©4*©©'*'^co©LOM ©CO(M©©Ost-^-iOCOi-H©COCOONCO©COi-lCOiOiO©vOO^COC^J c^©©©©o^a^ONa^ONO\ONOOoo^-t^^>"OvOLClOLOLOT^^cocococo

i-H (—I i-H 1—I I—

I
FORMATION OF IONIZED LAYERS

<N O CO O ^ © i/^ COvO(N©\OfO©©iO©(M'^

I I I I I I I I I I I I ^lC©OnC0©^©lO©lO©(N ©COCOi-0(N©>OfO©aNC— OlO

fC<NCSl(M(M(Mi—IpHi—I

©©©cgvooN'^i—icoioiovoi—

I

1—li—If-Hi-H^pHC^eOCO'^LO'OCO

©©©(NVOON-^rHCOli^LO^Oi—

:

pHi—ii—ii—ii-Hi—icsicoec^in^co

©©©(N^ON-^r-ICCiniOO^

1—irHi-Hi—ii—(^(rqfCfOTj<io^oco

© © © ©

LOI>l>©LC^CClO(Mr-l©©©

t^r-^co©r--^(Ni-Hi—I©©©

f<5 O © CO CO © lTS © I—I O lC CO csi a\cocoou:ifC(M^©©©©©

I J I I 1 I I I I I

Tjirtir5©©CO<N'^t^'^i

i-l CO (N

(M © CO © O © lO COO(M©OCO©©LO©(N'^

CSJ(M(N(Ni—IpHi—lOM— vOLO-^

I I I I I I I I I I I I ^lr5©o^co©so©LO©LC©l^^ ©COCOLOC^©OfO©OM>OLO
12 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

bination. The effective recombination coefficient aeff becomes relatively

large in the lower {D and E) regions of the atmosphere.

Another set of reactions which is thought to be of importance in the

upper atmosphere is electron disappearance first by atom-ion exchange

between a neutral molecule (XY) and the positive ion (^+), followed by

recombination between an electron and the XA'^ ion: Production ^ +photon—>^++e, (a)

A+-\-XY-^XA++Y, (b) (1.15)

Xy++e->X'+^'. (c) Loss

The primes indicate that the atoms X and A may be left in excited states. With these reactions it can be shown [6] that, if the number density

of X y is high in the F region and low in the E and D regions (as is thought

to be the case if A represents atomic oxygen and XY molecular oxygen),

the continuity equation takes the form

dN-- = q-l3enN, (1.16)

at where /3eff is an effective attachment coefficient. We now see that the forms of the continuity equation may not be

those expected from simple recombination and attachment.

1.4.3. Formation of a Chapman Layer

The simplest type of ionized layer that can be deduced from theoretical considerations is known as a Chapman Layer [7]. The derivation^

is based on the following assumptions:

(1) An atmosphere with only one type of gas.

(2) Plane stratification.

(3) A parallel beam of monochromatic ionizing radiation from the

sun.

(4) An isothermal atmosphere.

To start with, let us invoke assumptions (1), (2), and (3) only.

Let the ionizing radiation of intensity be incident, at a zenith angle

2 Due to Dr. T. E, Van Zandt.
FORMATION OF A CHAPMAN LAYER 13

ZENITH

UNIT AREA

h + dh

h

Figure 1.2. Absorption of radiation in a slab of gas.

X, on the top of the atmosphere. As the radiation is absorbed, as it penetrates into the atmosphere, its intensity diminishes. Let S be the energy

flux at a height h and S-{-dS the flux at a height h-{-dh as sketched in

figure 1.2. Let a be the absorption cross section of the atoms of the gas and N their number density. The energy absorbed c?S in a cyhnder of

unit cross section and axis parallel to the direction of the incident beam

is given by

Note that (1.17) merely states that the energy absorbed is proportional

to the total cross section and to the intensity of the incident radiation.

Upon integration we obtain

dS = SaN dh sec x- (1.17)

(1.18)

where

(1.19)

is the optical depth of the atmosphere down to the height h. The minus

sign arises because r increases in the opposite direction to h.
14 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

At great heights, S-^S^^ as r—>0 and (1.18) gives

S=S^exp (-rsec x). (1.20)

The energy absorbed per unit volume is given by

dS

dh sec X = NaS = NaS^exp f-rsecx). (1.21)

Let 7] be the number of ion pairs produced per unit quantity of energy

absorbed, i.e., the ionization efficiency. The number of ion pairs pro- duced per unit volume per second is q{x.h)=NaS^Vexp (-rsecx). (1.22)

Now T is a function of x and h. Using (1.1), (1.2), and (1.3), we

obtain

r = a f Ndh = — f dp = ^= ^^= aNH. (1.23)

J mgJ mg mg

Substitution of (1.23) into (1.22) yields

tS

q{x. h) V exp (l-r sec x), (1-24)

lie where e = 2.718 • • •. Note that we have neglected the variation of g with

height.

Notice that (1.24) holds for any temperature distribution. To obtain

Chapman's formula we invoke assumption (4) , an isothermal atmosphere,

where H is independent of height.

We can define a quantity z by the relation z= — In T, (a)

i.e., (1.25) r= exp (-z). (b)

Substitution of (1.25b) into (1.24) gives

S 7] 9(x, 2) exp {1 — 2— sec X exp (—2) j (a) en
FORMATION OF A CHAPMAN LAYER 15

(1.26) = ^0 exp {1 — z— sec X exp ( — z) }, (b)

where

9^ = ^

(1-27)

is the rate of production of ion pairs at the level z=0 when the sun is overhead, i.e., when ro= 1, and where tq is the value of r at the level z=0.

From (1.23), (1.25b), and (1.4a) we get

r p / h-h,\

exp {-z)=-- = -= exp\^--^j,

To Pq

I.e.,

(1.28)

The reference height ho is, therefore, the height of maximum ion pro- duction when the sun is overhead.

If, in (1.26b), we replace z by z— In sec x and put x^O? obtain

q(zQ, z— In sec x) = sec x qix^ z) . (1-29)

Equation (1.29) gives us an important scaling rule. That is, the curve

qiXt z) has the same shape as ^(0, 2), but is moved upwards by In sec x and is diminished by cos x- The height of the peak of ion production

Zm or hm is given by

Zm= \n sec X, (a) or (1.30)

hm = ho-\-H In sec x- (h)

The variation of q{x) for various values of z is shown in figure 1.3. It can be seen that the use of a logarithmic scale for q makes the shapes

of the q curves identical. The peak rate of production is given by

qm = qocosx- (1-31)

The intensity of the ion production is determined by the flux of ionizing

radiation and the efficiency 77. Changing the flux does not alter the height
16 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

0.1 0.15 0.2 0.3 0.4 0.6 08 N(z)/No

Figure 1.3. Normalized rate of photoionization q(z)/qo and electron density N{z)/No

according to Chapman theory.

(After T. E. VanZandt and R. W. Knecht, 1964, Ch. 6, Space Physics, John Wiley & Sons.)
ELECTRON DENSITY DISTRIBUTION 17

of maximum production. Thus, if there are several wavelengths present

in the incident radiation for which the ionization coefficients are markedly

different, several distinct layers will result. The most strongly absorbed

radiation produces the uppermost layer and vice versa. Likewise, different

ionized layers would result with different gases in the atmosphere.

1.4.4. Electron Density Distribution

To determine the electron density distribution, we must assume some

process of electron disappearance. Under certain circumstances the left- hand sides of (1.12) and (1.13) are small (quasi-equilibrium conditions).

If, therefore, the loss of ions is due to a recombinationlike process, then

q=aN^ and

N=Noexpi{l-z- secxexp (-z)}, (1.32)

where a is independent of height and

Nl=^. (1.33)

Oi The peak density

iV_= '-^

(1.34)

and the height of the peak is given by (1.30).

When the loss process is "attachmentlike," which is independent of

height, we have

q=m, (1.35)

which gives

7V=7V'exp {1-2- secxexp (-z)}, (1.36)

where

N' = ^. (1.37)

/3 This gives

A^max = |"cOSX. (1-38)
18 EARTH*S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

If we assume that ^ depends directly on the molecular density,

q = l3oNexp (-z), (1.39)

where /3o is the value of ^ at the level ho. This gives, for the electron density

distribution,

iV=iVoexp {1- secxexp (-z)}. (1.40)

This type of ion distribution has no maximum for the steady state except

at very great heights where saturation occurs because all the molecules

are ionized. Hence we see that with recombination the maximum electron

density varies as cos^ x whereas with attachment it varies as cos x* It

is of interest to note that the maximum densities in the E and Fi layers

tend to follow the cos' x law, as will be seen later. It is of interest to examine the dependence on height of the solar control of a Chapman layer. Low down in the layer, below the peak, z

is negative and so the term sec x exp ( —2) is relatively large so that there

will be a marked solar control of the diurnal variation. This is illustrated in figure 1.4 by the 2= —4 curve. On the other hand, high up in the layer

SOLAR ZENITH ANGLE, X

F^iGURE 1.4. Ion production as a function of solar zenith angle.

(After T. E. VanZandt and R. W. Knecht. See fig. 1.3.)
DIPOLE FIELD 19 where z is positive and large, the sec x exp ( — z) term is small and so the

production increases rapidly near smirise and remains almost constant

until sunset, when it drops rapidly (fig. 1.4, curve z=4). This is the type

of diurnal variation to be expected when electron production is due to photodetachment of electrons from negative ions by visible hght.

Although the theory given above is useful for purposes of discussion,

it should be borne in mind that, in practice, almost all the basic assumptions need quaUfication. Thus the earth's atmosphere consists of several

species of gases, and the incoming radiation has a broad spectrum. The

assumption of an isothermal atmosphere is certainly invalid. Cos X can be found for any location on the earth from the following

equation

:

cos x= sin 0 sin 5+ cos 0 cos 5 cos (1-41)

where 0 is the geographic latitude, 5 is the solar declination, and h is the

local hour angle of the sun measured westwards from apparent noon (mean noon corrected for the equation of time and the standard time used

at the location) . Tables of hourly values of cos x from sunrise to sunset

for the fifteenth day of each month for most of the ionospheric vertical incidence sounding stations are givei^ in the URSI Ionosphere Station

Manual [8].

Near grazing incidence (x greater than about 80°), the assumption

of plane stratification breaks dowTi, and it is necessary to replace sec x by the Chapman function of Ch{R-\-z, x)? where R= {a-\-h) /H. Tables

of Ch(R-\-z, x) have been pubUshed by Wilkes [9].

Finally, it should be realized that the recombination coefficient (effective) is not independent of height. In view of all the above qualifications, it is remarkable that the E and Fi layers behave approximately

as predicted.

1.5. THE EARTH'S MAGNETIC FIELD'

1.5.1. The Dipole Field

To a first approximation, the earth's magnetic field is that of a sphere

uniformly magnetized in the direction of the centered dipole axis. The

centered dipole axis cuts the surface of the earth at two points A and B

known as the south and north dipole poles, as shown in figure 1.5. The

* Based on a lecture by Dr. S. Chapman.
20 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

GEOMAGNETIC AXIS\

BOREAL MAGNETIC POLE B

AXIS OF ROTATION

THE EARTH

A AUSTRAL MAGNETIC POLE

Figure 1.5. Earth's dipole magnetic poles. A—austral pole; B—^boreal pole.

best fit between the earth-centered dipole and the actual magnetic field

is obtained by taking A at 78.3°S, 111°E and B at 78.3°N, 69°W. It

will be seen that the axis of the dipole does not coincide with the axis

of rotation. The plane through the center of the earth O perpendicular

to BA is called the dipole equatorial plane, and the circle in which it cuts the sphere is called the dipole equator. Dipole latitude <l> is reckoned

relative to this equator. The semicircles joining B and A are called the

dipole meridians; the one passing through the dipole and south geo- graphic pole is chosen as the zero of dipole longitude A. The relationships

between the dipole coordinates (<I> the latitude and A the longitude)

and the corresponding geographic coordinates (0, X) at a point P are given by

sin sin <f> sin 0o+ cos 0 cos 0o cos (X — Xq)

sm A =

cos 0 sin (X — Xo) cos $

(1.42)

(1.43)

where 0o and Xq are the geographical latitude and longitude of the north
DIPOLE FIELD 21

dipole pole ((^o = 78.3°N, Xo = 291.0°E). The magnetic potential F of the

dipole, of moment M at any point P whose position vector relative to 0 is r, is given by

M-r Af sin $ K=— = —-, (1.44)

where $ denotes the dipole latitude. This is also the potential of the

external field of the uniformly magnetized sphere.

The radial (vertical) component Z of the field, reckoned positive

when inward, is given by ^ dV 2Msin$ , Z= —= . (1.45)

dr 7^ The horizontal (tangential) component H at P hes in the meridian

through P and is directed towards B. It is given by

dV Mcos^ H= = . (1.46)

The magnetic dip or inclination / is given by

tan I = — = 2 tan (1.47) H

Because this is independent of r, the dip is the same at all points along

any radius OP. Note that / is positive when the field direction is below

the horizontal. Also,

F^ = H'+Z\ (1.48)

At the pole B, F=Z, and at the equator, F=H. Let Hq denote the equatorial value of H at the surface of the sphere (r = a). Then we have the

following relationships:

cos ^>, (a)

Z=2Ho(-] sin$, (b) (1.49) 0

-•(;) l+3sin2<l>p. (c)
22 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

EARTH

RADII Figure 1.6. Lines of force and of equal intensity of a uniformly

magnetized sphere.

(After S. Chapman, 1964, Geophysics—The Earth's Environment, Part III, Solar Plasma, Geomagnetism and Aurora, Gordon and Breach, N.Y.)

It will be seen, from (1.49), that the magnetic intensity at the poles is twice that at the same radial distance (height) at the equator.

The lines of force of the dipole field are given by dr/Z=rd^/H;

hence their equation is r = A:a cos2 (1.50)

Here k is the equatorial radius measured in earth radii. The product ka

is the distance at which the line of force crosses the equatorial plane. The

points where it meets the sphere are given by $ = $o and <I> = — «i>o where

cos ^0 = k~^. The lines of force, together with the isosurfaces of F (on which F

is constant) , are given by

r = A:'a(l+3sin2<J>)i, (1.51)

and are shown in figure 1.6. The parameter k' of the F isosurface is thus
REAL FIELD 23

related to the value of F for the surface: k'={H,/F)K (1.52)

It is interesting to note that the strength of the magnetic field decreases

as the cube of the distance from the earth's center. Thus at one earth

radius above the surface, the field is only 0.125 of that at the surface. Thus it may be important to consider the variation of field strength when

large distances are involved (e.g., earth-space propagation)

.

1.5.2. The Real Field

The magnetic intensity F at any point P on the earth's surface can

be specified by its downward vertical component Z and its vector hori- zontal component H, or by H and the angle I by which F dips below the

horizontal. On the earth, the direction of H is specified by the angle D

between H and the geographic north; D is called the magnetic (or compass) declination and is reckoned positive if eastward. The northward

and eastward components of H are denoted by X, Y, respectively, and

tanZ) = ^, X= HcosD, Y=H sin H'=X'+Y\ (1.53)

The seven quantities F, Z, H, /, D, X, and Y are called the magnetic

elements, and any set of three independent elements serves to specify F; i.e., F, 7, D; H, /, D; if, Z, D; X, Y, Z. (1.54)

The elements F, if, Z, and I are called intrinsic because their only refer- ence to direction is to the natural direction characteristics of P, namely,

the vertical. The other three elements, D, X, Y, are called relative be- cause they are defined relative to the geographical (or rotational) axis iVS, which has no necessary relation to the geomagnetic field. In geomagnetism, field intensity is measured in gauss units F, despite

the internationally agreed use of the term oersted for intensity and

gauss for induction. A smaller unit, the gamma (7), is used, especially

in connection with the variations in the geomagnetic field where

1^ = 10-5F. (L55)
24 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

Figure 1.7. World map of total magnetic intensity (F).

(After J. C. Cain and J. R. Neilon, 1963, J. Geophys. Res. 68, 4689.)
Figure 1.8. World map of magnetic dip (1). (After J. C. Cain and J. R. Neilon, 1963, J. Geophys. Res. 68, 4689.)
26 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

In practice, the magnetic field of the earth departs somewhat from

that of a uniformly magnetized sphere. Maps have been prepared showing

the distribution of the various magnetic elements over the earth's surface. The worldwide variation of the total intensity F is shown in figure

1.7 and of the magnetic dip / in figure 1.8. Both of these elements are of

importance in ionospheric radio propagation. From the latter figure it will be seen that the magnetic dip poles (north) and Ps (south) are not at opposite ends of a diameter. Their locations are not accurately

known because they move around. Approximate positions for 1945 were: Pn 76.0°N; 102.0°W

Ps 68.2°S; 145.4°E

The antipode of Ps is about 1600 km from Pn, and the line PnPs misses

the earth center by about 1150 km.

The distribution of the earth's magnetic potential V (from which

the vector field can be derived) can be expressed by a mathematical

process called spherical harmonic analysis [10]. The potential V can be

expressed as a sum of orthogonal functions of the type

Pr(cos 6) {a^ cos sin mX),

where d is the north co-latitude (i.e., angular distance from the north

pole) and X is the east longitude. The functions P^ have been tabulated

[11]. Using this technique, it has been shown that most of the field originates from within the earth. A small part (less than 0.1 percent) has

its origin outside the earth.

1.5.3. Magnetic Variations

Owing to electric currents flowing above the earth's surface, the

magnetic field at any point on the surface varies diurnally, seasonally,

and with solar activity. The net variation at the earth's surface is due

partly to the external currents and partly to induced earth currents. Days on which the transient magnetic variations are "smooth" and

regular are called q days, q

signifying magnetically quiet. The others,

d days, are said to be magnetically disturbed. On q days the magnetic variations proceed mainly according to

local solar time, but they also contain a part, usually small, controlled

by the moon. These two parts are called the solar daily and the lunar daily
MAGNETIC VARIATIONS 27 magnetic variations. They, and the fields of which they are the manifestation, are denoted by Sq and L ( S = solar, L = lunar) . Both are caused

by currents flowing in the ionosphere, mainly in the E layer. An example

of a quiet day magnetogram for a middle latitude station is given in

figure 1.9. The Sq currents are stronger by day than by night, stronger in summer than in winter, and about 50 percent stronger at sunspot maximum than at sunspot minimum.

Of particular interest, from the point of view of the ionosphere, is the concentration of enhanced currents in a narrow strip along the magnetic equator which is known as the "equatorial electrojet."

During a magnetic disturbance, additional currents circulate in the

ionosphere. They are superposed on the Sq and L currents. Unlike the

latter, they are strong in high latitudes and are often stronger over the

night than over the day hemisphere. They are denoted by DP (Z) = dis- turbance, P= polar). They are especially concentrated along the auroral zones (i.e., the region of overhead visible aurora), and hence the currents

there are called the auroral electrojet. A strong auroral electrojet may

carry a current of the order of a million amperes. The return current flows

mainly over the polar cap, but some flows between the north and south

auroral zones. The DP currents are believed to be one of the many effects caused by the impact of a solar stream or cloud of ionized gas upon the

earth's magnetic field. Some of the gas finds its way into the polar at- mosphere and causes the luminescence of the aurora. A magnetogram

taken during a magnetic storm is shown in figure 1.10. Many magnetic storms, particularly the big storms, begin suddenly

and almost simultaneously, to within a minute, all over the earth. The

sudden commencement is ascribed to the impact of solar ionized gas on

the outer part of the geomagnetic field, at a distance of several earth

radii.Though much of the solar gas is turned away from the earth, some

is trapped by the field and the trapped particles spiral round the lines of force, between the northern and southern hemispheres; they also drift round the earth under the influence of the magnetic field. The total motion is equivalent to an electric current in the form of a ring around

the earth. The net effect at the earth is to decrease the horizontal field, and in many storms the decrease soon overpowers the initial increase.
EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

1 y

1

1

i

('

1

i

j

j

CSi

t

;

<M

j

-

j

j

1 /

^

1

i j i

1

t!n f o

\

BOULDI SEPT. I

SI

1

I

s.

1

I
MAGNETIC VARIATIONS 29
30 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

1.5.4. Magnetic Indices

The degree of magnetic disturbance during each Greenwich day is indicated by a variety of indices, according to internationally adopted

plans.^ Many magnetic observatories throughout the world take part in these plans. They assign local indices of magnetic activity. These are

sent to an international center at De Bilt, The Netherlands. This is linked with a Permanent Service of Geomagnetic Indices at Gottingen,

Germany.^ There the local indices are used as the basis for world indices. Each participating observatory assigns to each Greenwich day its own ^'daily figure" C. This is one of the numbers 0, 1, or 2, to indicate

ascending degrees of disturbance of its records. This local daily index

is assigned by simple inspection of the records. Naturally there are many

borderline cases where the choice between 0 and 1, or between 1 and 2,

is difficult; but the choice is made.

The values of C from all observatories for each day are averaged to one decimal place. This gives Ci, the "international daily character figure."

It provides a 21 -fold classification of Greenwich days, from 0.0 on days

of extreme calm, to 2.0 on days that are magnetically highly disturbed.

By a more detailed and precise method, a local index K is assigned

to each three-hourly interval of Greenwich time, 0-3, 3-6, • • • ; K is one

of the integers 0 to 9, giving a tenfold classification of these intervals. The records of the three elements are examined, and for each an estimate

is made of the range r during the interval, allowing for the part of the

change caused by Sq and L and, when necessary, by SFE ( Sq current augmented by solar flare effect) and the recovery phase of the ring cur- rent field. Such allowance calls for experience and judgment. The largest

of the three ranges is taken as the basis for K; the element concerned

may vary from interval to interval, or from one observatory to another.

For each observatory a table is assigned, giving limits of r corre- sponding to each of the ten values of K. The lower limit of r for K= 9

may have any of the values 300, 350, 500, 600, 750, 1000, 1200, 1500,

and 2000 y. The first applies to very-low-latitude observatories (outside

the belt of the equatorial electrojet; sec. 1.5.3). The last applies to the

most disturbed stations, in the auroral zone. The limit 500 refers to

stations in about geomagnetic latitude 50°. The table for this latitude is

* The plans are under the auspices and supervision of the Committee on Characterization of Magnetic

disturbances of lAGA (International Association of Geomagnetism and Aeronomy), a part of lUGG

(International Union of Geodesy and Geophysics); the present Chairman is J. Bartels.

5 Addresses: C+K Centre, Kon. Ned. Meteor. Inst., De Bilt, The Netherlands; and Geophysikalisches

Institut, 180 Herzberger Landstr., (34) Gottingen, Germany.
MAGNETIC INDICES 31

as follows: Range of r: 0 5 10 20 40 70 120 200 330 500

012345 6 7 8 9

For other latitudes, the lower values of the range limits of r are scaled

up or down proportionately to the lower limit for K= 9. The C and K figures for some observatories appear currently in their own or other publications. A volume containing the complete set for all participating observatories, together with much other data, including

the world indices, is pubhshed annually as an issue of lAGA Bulletin 12. These volumes, formerly issued as lATME^ Bulletins 12, are now dis- tributed by the North Holland Publishing Co., Amsterdam, from whom

information as to the availability of back issues can be obtained^.

The values of K for any one observatory show statistically a daily

variation, depending on its local time. To obtain a world index this local influence must be eliminated. Corrected or standardized values Kg of K

are prepared at the Permanent Service at Gottingen for each of 12 selected observatories, northern and southern, lying between geomagnetic lati- tudes 48° and 63°. The mean of the 12 values of Ks for these 12 observatories is denoted by Kp, and is called the planetary 3-hr index; it is ex- pressed in a scale of thirds.

Oo, 0+, 1-, lo, 1+, 2-, 2o, • • •, 9-, 9o. Thus it is a 28-fold classification. By cooperation between De Bilt and Gottingen, it is possible to issue monthly tables of Kp before the end of the following month. The values

are also published in the CRPL F Series, Part B, Solar-Geophysical Data

and in the Journal of Geophysical Research. Quarterly Bulletins containing the Kp figures and other magnetic data are issued from De Bilt. A sample table of Kp indices is given in table 1.6. Along with the values of Kp^ values of two daily world indices Ap

and Cp are given. These are derived from the eight values of Kp for each

day. The values of Cp range like those of d, from 0.0 to 2.0 at intervals

of 0.1. A table of range limits for the daily sums of Kp has been formed,

such that the frequency distributions of C^ and Cp for the 10 years 1940-49

6 lATME signifies International Association of Terrestrial Magnetism and Electricity, the former name of lAGA.

' This publication and the work of the two centers for geomagnetic indices, at De Bilt and Gottingen,

are sponsored by ICSU (International Council of Scientific Unions) with financial support from UNESCO.
32 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

Table 1.6. Geomagnetic activity indices (June 1963)

Values Kp

June c Sum Final

1963 Three-hour Gr. interval selected 12 days

3 4 5 6 7 8

1 0.6 2-4- 2+ 2o 34- 3+ 1— 1+ 3 — 2O0 11 Five

2 0.7 2o 3o 2+ 2 + 3- 3o 2+ lo 19- 10 quiet

3 0.4 2- 2- 2o 2o 2+ 1- 2- 2- 14- 6

4 0.2 lo lo 3-1- 1+ 1- 1- 1- 9- 5 4

5 0.0 0+ lo Oo 0 + 0+ 1- 0+ 0 + 34- 2 5

16

6 1.1 Oo 1-0+ lo 1+ 2+ 5- 6- I60 16 22

7 1.5 7o 6- 5- 3 + 4- 4- 3+ 4o 35 + 43 23

8 0.8 2o 2o 2o 3o 2- 3- 3- 4+ 20 + 12

9 0.6 3+ 3- 2+ 3- 2+ 2- 1+ 2o 18 + 10

10 0.4 1+ 1- lo 2- 2- 1+ 2o 1 + llo 5

11 0.4 2o 2-1- 1-1- lo loXV/ 2-1-14-1-1- ^ 1 X 1 X 1 13- 6 Five

12 0.1 2- 2o lo 2- 0+ lo 1+ 1- 10- 5 disturbed

13 0.3 2o 1+ lo 2- 1+ lo 1+ 2- 11 + 5

14 0.2 3- Oo lo 2o 2- 2o 0+ 1 + llo 5 7

15 0.6 2- 3+ 3+ l-f- 1+ 1+ 2- 2o I60 9 18

25

16 0.1 O-h Oo Oo OH- Oo 2- 1+ 1 + 5o 2 26

17 0.8 2-H 2- 2+ 2o 2+ 3o 2+ 2 + 18 + 9 27

18 1.1 lo 3-1-3- 3o 44- 3o 5o 4o 26 + 21

19 0.7 3+ 3- 2- 1- 2- 2+ 3+ 3- 18 + 10

20 0.9 4o 3o 3o 3o 2+ 2o 2o 2- 2I0 13

21 0.4 24- 2-\- 3— 3o 0+ 1+ 1+ lo 14+ 8 Ten

22 0.1 2- 2- l-h lo lo lo 1- lo 9 + 4 quiet

23 0.1 lo 1—1—1-1- 0+ lo lo lo 7o 4

24 0.3 0+ 1+ 2- lo 2+ 3- 1+ 2o 13- 6 4

25 1.1 3o 4o 4+3- 2+ 2+ 4o 5 + 28o 23 5

10

26 1.3 6- 5- 5o 3+ 2+ 2o 2+ 3- 28o 26 11

27 0.9 4- 4o 3+ 3o 2+ 1- 4- 3o 24- 16 12

28 0.7 3- 2- 3+ 3o 3- 3+ 3o 1 + 2I0 13 13

29 0.6 1+ lo 2+ lo 2o 3+ 3+ 2 + 17- 9 14

30 0.8 2+ 3- 3- 2 + 2+ 2o 4- 2 + 20 + 11 16

22

23

Mean: 0.59 Mean: 11

are nearly identical. The indices of d and Cp are approximately logarithmically related to the ranges r of the magnetic elements during the disturbance (corrected for S and L) . The indices Ap are more nearly linearly

related to these ranges.

The planetary index Kp is designed to measure solar particle radiation by its magnetic effects, specifically to meet the needs of research

workers in the ionospheric field.

The K tables for the individual observatories, in the lAGA Bulletins

12, give a very detailed indication of the incidence, in time and place.
MAGNETIC INDICES 33
34 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

Figure 1.12. Location of the northern zone of maximum frequency of occurrence of overhead aurora on magnetically quiet and on magnetically disturbed days.

(After Y. I. Feldstein, Investigations of the Aurora, Moscow, I960.)

of the magnetic effects of the solar eruptions. The Kp^ Cp, Ap, and d

tables give a concise indication of the overall world effects 1^11]. These

tables are now available from the time of the Second International Polar

Year (1932/3) to date. The tables of C go back still further. Details

regarding these publications are given in Bulletin 12(1) (pp. iv and 268)

;

see also IGY Annals, vol. 4, pp. 227-236, where also, on pp. 220-226, an account is given of the quarter-hourly indices Q to be issued, covering

the period of the IGY. These will permit studies of correlations between

magnetic disturbance and other phenomena in much more time detail than is possible with the daily and three-hourly indices.
35

Figure 1.13. South auroral zone.

(After O. Schneider, 1961, Institute Antarctico Argentine 55, Buenos Aires,)

Finally, note in this connection the publication of diagrams (Bartels'

"musical scales") graphically illustrating the sequence of the Kp values,

figure 1.11. These are arranged in rows so as to show the 27-day recur- rence tendency of magnetic disturbance, arising from the solar rotation.

The diagrams are issued monthly along with the Kp tables, in time to be

helpful in making 27 -day recurrence forecasts. The monthly diagrams issued during the IGY have been combined

into a diagram for the whole IGY period, and since then annual diagrams

have been issued (see Bulletins 12 for further information).
36 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

1.6. THE AURORAL ZONES

These regions of the earth where visible aurora occurs overhead are of particular importance to the radio communicator because of the fre- quent occurrence there of ionospheric disturbance, as will be discussed

in a later chapter.

As was mentioned in section 1.5.3 above, aurora is thought to be the

result of the entry into the atmosphere of charged corpuscles. Owing to the interaction between the moving charges and the geomagnetic field, the corpuscles are deflected north and south of the equatorial plane and

are deposited in a relatively narrow ring situated between dipole latitudes

of about 64° and about 70°. Maps showing lines of constant frequency

of occurrence (called isochasms) have been prepared for the northern

and southern auroral zones and are shown in figures 1.12 and 1.13. The

north auroral isochasms are not quite circular, but are elongated along

the Siberia -North American axis. The geographical areas encVsed by the

auroral rings are often called "polar caps."

It should be borne in mind that the auroral zone is not fixed but moves with varying magnetic activity. Thus during strong magnetic

storms the auroral zones, both north and south, move towards the equator.

For example, a great aurora on September 25, 1909, was observed in Singapore, latitude 1°N. Even during magnetic storms of moderate

strength there is a close connection between the position of the aurora and the strength of the magnetic disturbance. In addition to the visible aurora, radio techniques have revealed the

existence of enhanced ionization in the ionosphere in these latitudes [12].

This enhanced ionization is manifested as sporadic E (sec. 6.3.4) , Z)-region

absorption (sec. 6.3.3), and radio aurora (sec. 8.6.1). However, it may

not necessarily follow that the various auroral zones coincide.

1.7. THE SUN

1.7.1. Quiet Conditions

1.7.1.1. Structure

For our present purposes it will be sufficient to consider the sun as made up of four parts:
QUIET CONDITIONS 37

(1) the interior;

(2) the photosphere, or visible surface;

(3) the chromosphere, the bright region above the photosphere,

seen during total solar echpses; and

(4) the corona, the outer atmosphere of the sun. Although the various sections merge into one another, the radiation

from the photosphere comes entirely from a layer about 400 km thick

compared to a solar radius of about 700,000 km so that the concept of

a solar surface has a fairly well-defined meaning. Approximate values of

the heights and temperatures of the various regions are given in table

1.7. For further information the reader should consult "The Sun" [13].

The sim is composed chiefly of the elements hydrogen and helium

together with smaller amounts of the heavier elements, notably calcium.

Table 1.7. Approximate heights and temperatures of the sun's outer layers

Solar layer h (km) T °K Outer corona 1,400,000 1,500,000

Middle corona 700,000 1,500,000

Inner corona 21,000 to 140,000 1,000,000

Upper chromosphere 7,000 to 14,000 25,000 to 300,000 Lower chromosphere 1000 5300 Photosphere 6000 effective

1.7.1.2. Ionizing Radiations

To a first approximation, the quiet sun radiates as a blackbody at a temperature aroimd 6000° Kelvin. Superimposed on the blackbody

continuum are certain lines characteristic of the elements in the sun. Some of the more important lines are hydrogen a (6563 A), Lyman a

(1216 A), and helium i (584 A). These radiations are responsible for the

ionization of the upper atmosphere discussed in section 1.4. A number

of lines in the ultraviolet part of the solar spectrum are given in table 1.5. For example, it is thought that Lyman a radiation is the major source

of ionization in the quiet D region. The quiet E region is believed to be

produced by x rays (10-100 A), Lyman (3 (1025.7 A), Cm (977 A),

and the Lyman continuum (910 to 980 A) [14]. The primary source of

ionization in the F region appears to be the Lyman continuum and the

band 350 to 200 A (which includes the He iii 304 A resonance line).
38 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

The amount of visible light from the sun changes very little from

one day to the next. On the other hand, the day to day variability of

the quiet ionosphere suggests that the solar emissions in the ultraviolet

and x-ray regions vary appreciably. In addition to the wave radiations, the quiet sun emits a stream of

charged corpuscles (mostly electrons and protons) which is called the

"solar wind."

1.7.1.3. Radio Emissions

The sun is a source of radiation on radio frequencies. These emissions

are caused by plasma oscillations (see sec. 2.3.1.1) and gyro-oscillations

Figure 1.14a. Photograph of the sun at sunspot minimum (1954).
QUIET CONDITIONS 39

(see sec. 2.3.1.2) in the solar atmosphere, as well as "noise" originating

in random collisions of the electrons [15]. The noise from the quiet sun

is of the last type.

The flux of solar radio noise at the earth's surface is monitored at a number of observatories, and the data are available in the CRPL F

Series Part B [16] and in Quarterly Bulletin on Solar Activity of the

International Astronomical Union [17]. There are several methods of

recording, such as fixed frequency, sweep frequency, total flux, inter- ferometers for exploring the distribution of radio sources on the solar

disk, etc. A hst of observing stations, the frequencies (or frequency bands)

of observation, and the universal times of recording are listed in the

Bulletin [17]. The unit of measurement of flux is 10~^^ watts per square

Figure 1.14b. Photograph of the sun at sunspot maximum (1958).
40 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

meter per cycle per second. In general, the flux increases with frequency

in the range 100 Mc/s to 10,000 Mc/s, but the day to day variability

is much greater on the lower frequencies as can be seen on pages 464-6

of the Bulletin [17].

1.7.2. The Active Sun

1.7.2.1. Sunspots

One of the most notable phenomena on the sun's surface is the ap- pearance, and disappearance, of certain dark areas known as sunspots.

The life of a sunspot is highly variable; some spots last only a few days,

whereas a few may survive four or five solar rotations (of about 27 days

each). Their exact nature is not known, but they appear to be vortices

in the matter comprising the photosphere. Sunspots Appear dark because

the surface temperature is only about 3000 °K, compared with the

6000 °K of the quiet photosphere. Sunspots tend to group together. A

group may contain a few isolated spots or dozens of spots.

One of the more interesting features of sunspots is their unusually

strong magnetic fields. These may approach 0.4 Wb/m^ (weber per square

meter) (4000 G) for the larger spots.

1.7.2.2. The Sunspot Cycle

The appearance of the sun in 1954 and in 1958 can be seen in figures

1.14a and 1.14b. Clearly, there is a variation in the sunspot "activity."

To measure this activity an index is required. The most common index

of sunspot activity is the Wolf number R given by

i? = A:(10g+s), (1.56)

where g is the number of groups and s is the number of observable indi- vidual spots. The factor it is a correction factor to take into account the

equipmental and observer characteristics. It will be seen that this number

is weighted heavily in favor of groups, so that its value as an index of

sunspot activity is questionable. Nevertheless, it is valuable because

of its availability for a period of about 200 yr. It thus provides a large

homogeneous sample of data. Sunspot numbers are available on a daily

basis and as monthly and yearly averages.
ACTIVE SUN 41 When the yearly sunspot numbers are plotted, for a long period of

time, such as is shown in figure 1.15, it is clear that the sunspot activity

has a periodicity of about 11 yr. The duration of an individual cycle may

vary over much wider limits; thus the periods between minima range from

about 8.5 yr to about 14 yr and those between maxima range from 7.3 yr to about 17 yr. Furthermore, the annual minima of R lie in the range

0 to 10, whereas the maxima range from about 50 to about 190. The

daily values of R vary between 0 and 355 or more. In addition to the 11 -yr period, there are periods, particularly near

the 11-yr minima, when a 27-day (approximate) recurrence is evident.

This period corresponds to a solar rotation.

Many attempts have been made to represent, analytically, the exist- ing sunspot data with a view to the prediction of future cycles. The predictions have never been particularly successful. In addition to the relatively dark sunspots, bright areas often appear on the solar disk. These areas, called plages, are observed in the light

of calcium K and are intimately associated with sunspots. Plages are comparatively long-lived active regions; they precede in appearance the

spots, which develop in them, and persist after the spots have disappeared.

1.7.2.3. Flares A solar flare is a burst of ^^light" occurring in the chromosphere near

a sunspot. It is most easily observed in the Ha light (6563 A), although,

in some rare cases, flares have been seen in white light. At present, solar patrol observations are almost continuous and so most of the flares oc- curring on the solar hemisphere facing the earth are detected. Flares are frequent occurrences, particularly at the peak of the sunspot cycle.

Flares are divided into classes of importance 1 — , 1, 1+, 2, 2+, 3, and 3+, according to area and brightness. The average duration of a

flare increases with its importance; thus 1 flares last about 20 min, 2

flares last about 30 min, and 3 flares last about 60 min. Of course, the

life of an individual flare may vary greatly from the mean value. Flares

smaller than importance 1 are referred to as subflares. The development of a flare is somewhat as follows: a rapid rise (flash) to peak intensity, a brief period of peak intensity, followed by a steady

decline. There is a close statistical relation between the number of flares per solar rotation, A^^, and the corresponding mean sunspot numbers R,

given by

NF = a(R-lO). (1.57)
42 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

g § § 8 g 8 9 8 op g 8 g 8 § 8 8 9 8

°

g § 8 § g s § k o<^k ^sg^grigo

Figure 1.15. Sunspot activity in the years 1700 to 1960.

(After M. Waldmeier, 1961, Schulthess, Zurich.)
ACTIVE SUN 43

The mean values of a for the sunspot cycles having peaks in 1937 and

1947 are 1.98 and 1.47 respectively [18].

During some flares there is a marked increase in the flux of solar

ionizing radiation in the far ultraviolet and soft x-ray regions of the

spectrum. This results in enhancements in the electron densities in the

D and E regions, as will be seen later. Data on the duration and importance of flares, etc., can be found in the F Series Part B [16] and in the

lAU Bulletin [17].

1.7.2.4. Radio Emissions

The amplitude of the solar signals may remain relatively constant

for long periods of time and then will be greatly enhanced during a ^^noise

storm." These storms are often associated with solar flares and certain

geophysical disturbances and may last for a period of hours or days.

Noise bursts are categorized as follows:

Type /, or noise storms, occur most frequently on frequencies less

than about 300 Mc/s. Type I bursts extend over a narrow frequency

range, 5 to 30 Mc/s, for instance, while their lifetimes range from 0.2 sec to 1 min or so. During the lifetime of a single burst, the frequency of

emission may drift with time to higher or to lower frequencies.

Certain outbursts, which last for the order of several minutes, are

associated with the larger solar flares and may involve signal enhancements of the order of a million times the quiet values.

The chief characteristic of Type II (slow drift) and Type III (fast

drift) bursts is the drift of the emission to lower frequency with time.

This drift can be explained as due to a source moving outwards through

the corona, emitting at the plasma frequency, which decreases as the

electron density decreases (see sec. 2.3.1.1). Type III events are very

frequent.

Type IV events are long-lived emissions emanating from a source of

large extent that moves to heights of the order of a solar radius. Radiation occurs over a broad band of frequencies at each height. The characteristics of type IV radiation can be explained by synchrotron emission

of electrons. From the point of view of sun-earth relationships, type IV

events are particularly important because of the strong association with

solar corpuscular radiation, evidenced by polar cap absorption events

[19, ch. 6], ground-level cosmic ray increases, and great magnetic storms.

Type V is continuum emission of shorter duration, following a type

III burst.
44 EARTH'S ATMOSPHERE, GEOMAGNETISM, AND THE SUN

A considerable amount of data is made available every month in the

F Series Part B [16].

REFERENCES

[1] VanZandt, T. E., and R. W. Knecht (1964), The structure and physics of the upper atmosphere. Space Physics (ed. A. Rosen and D. P. LeGallery) (John

Wiley & Sons).

[2] Standards on wave-propagation, definition of terms, (1950) Proc. IRE 38, 1264.

[3] Minzner, R. A., K. S. W. Champion, and H.L . Pond (1959), The ARDC model

atmosphere, Air Force Surveys in Geophysics No. 115, Bedford, Mass.

[4] Norton, R. B., T. E. VanZandt, and J. S. Denison (1962), A model of the atmosphere, and ionosphere in the E and Fi regions, Proc. Intern. Conf. on the Ionosphere, Inst. Phys. and Phys. Soc, London.

[5] Nawrocki, P. J., and R. Papa (1961), Atmospheric Processes, Geophysics Corporation of America, Bedford, Mass., AFCRL-595, GCA Number 61-37-A.

[6] RatclifFe, J. A., and K. Weekes (1960), The Ionosphere, chap. 9, Physics of the Upper Atmosphere (ed. J. A. Ratcliffe) (Academic Press).

[7] Chapman, S. (1931), The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth, Proc. Phys. Soc. 43,

26.

[8] Wright, J. W., R. W. Knecht, and K. Davies (1957), Annals of the International Geophysical Year, Vol. Ill, Part 1.

[9] Wilkes, M. V. (1954), A table of Chapman's grazing incidence integral Ch(ji;, %)? Proc. Phys. Soc. 67B, 304.

[10] Chapman, S., and J. Bartels (1962), Geomagnetism, ch. 17 (Oxford Univ. Press).

[11] Bartels, J. (1957), The geomagnetic measures for the time variations of solar corpuscular radiation, described for use in correlation studies in other geo- physical fields, IGY Annals 4, 227.

[12] Booker, H. G. (1960), Radar studies of the aurora. Physics of the Upper Atmosphere (ed. J. A. Ratcliffe) (Academic Press).

[13] The Sun (1953) (ed. G. P. Kuper) (Univ. of Chicago Press).

[14] Friedman, H. (1960), The sun's ionizing radiations. Physics of the Upper Atmosphere (ed. J. A. Ratcliffe) (Academic Press).

[15] Pawsey, J. L., and S. F. Smerd (1953), Solar radio emission. The Sun (ed. G. P. Kuper) (Univ. of Chicago Press).

[16] CRPL F Series, Part B, Solar Geophysical Data, issued monthly by the National Bureau of Standards, Boulder, Colo.

[17] Quarterly Bulletin on Solar Activity, International Astronomical Union, (ed. M.

Waldmeier) (Schulthess and Co., Zurich).

[18] Kiepenheuer, K. O. (1953), Solar activity. The Sun (ed. G. P. Kuper) (Univ. of Chicago Press).

[19] Athay, R. G., and C. S. Warwick (1961), Indices of solar activity. Advances in Geophysics (ed. H. E. Landsberg and J. Van Mieghem), Vol. 8 (Academic Press).
CHAPTER 2

Theory of Wove Propagation

2.1. PURPOSE

The purpose of this chapter is to acquaint the reader with the basic

ideas needed for an understanding of the propagation of radio waves in the ionosphere. In the presence of the earth's magnetic field, the ionosphere

behaves as a birefringent medium and so it is necessary to discuss the

properties of such a medium. These properties include the decomposition

of a plane polarized wave into ordinary and extraordinary waves and the

deviation of the direction of energy flow away from the direction of phase

propagation.

We shall consider first the early history of the subject leading to the

formulation of Maxwell's equations and their experimental verification by Hertz. Next we shall derive the Appleton formula for the complex

refractive index of a magneto-ionic medium and consider its properties.

The weakness of the Appleton theory will be considered and more

generalized formulas will be discussed. Finally, we shall discuss the

propagation of wave packets in a magneto-ionic medium.

2.2. ELECTROMAGNETIC WAVES

2.2.1. Electrostatics and Magnetostatics

The principles underlying the propagation of radio waves are based on the relationships between electricity and magnetism which were dis- covered in the eighteenth and nineteenth centuries. It is now generally

known that the attractive and repulsive properties of electrified bodies

and of lodestone were first recorded by the ancient Greeks. Little further progress was made until the eighteenth century, when attempts were made to establish laws of electrical and magnetic forces similar to the

45
46 THEORY OF WAVE PROPAGATION

gravitational law of Newton. This search bore fruit when, in 1785, the

French scientist Coulomb, using a torsion balance, showed that the

mechanical force between two small electrified spheres varies inversely as the square of the distance r between them. Later work showed that the

force was proportional also to the amounts of charge qu ^2 on the two

bodies and so we obtain the relationship

F=^'-f, (2.1) 4x60 where eo is the permittivity of free space (8.85 X10~^^ F/m).

A relationship similar to (2.1) was found to hold for the mutual

forces exerted by long bar magnets.

It is useful to introduce the concept of electric field E at this point.

Let us assume that the charge 92 produces an electric field E at the site of qi and that this field exerts the force F on qi where

F = giE. (2.2)

Thus the electric field E at a point may be defined as the force experienced

by a small unit test charge. It is assumed that the test charge itself does not alter the field. The field at a vector distance r from a point charge q is, therefore,

given by

E = r-%. (2.3) 4x60 H

so that the vector E is in the direction of r. If the charge is distributed

throughout a volume of space, we have

where dq is an element of charge and Ar is a unit vector in the direction

from dq.

Many electrical and magnetic problems, particularly static field problems, are best tackled through the idea of potential difference. The

potential difference between two points A and B can be defined as the

work done by an external force on a unit test charge in moving it from ^ to B as shown in figure 2.1. The zero of potential is, therefore, arbitrary;
ELECTROSTATICS AND MAGNETOSTATICS

ELECTRIC FIELD E

47

B ds

Figure 2.1. Potential difference. and it is sometimes convenient to define the zero at infinity. The work

done on the test charge in moving it from ^ to B is

and hence

— Va=— E cos <f)ds=— E'ds,

J A J A

dV E=- --=-gradV.

ds

(2.5)

(2.6)

Gauss showed that the integral of the electric field over a surface A

enclosing a medium of permittivity e is given by

:( E'dA= f pdV=Q, (2.7)

where p is the charge density, V is the volume enclosed, and Q is the total charge enclosed.

Similarly, for a magnetic field of induction B Wb/m^ (webers per

square meter).

f B'dA = 0.

''a This follows since there are no free magnetic poles.

(2.8)
48 THEORY OF WAVE PROPAGATION

Before proceeding to a consideration of current electricity let us

consider some elementary properties of dielectrics. Consider a parallel

plate capacitor with a large area of cross section (so that edge effects are negligible), and distance d between plates, connected to a voltage

source and let a be the charge density on one of the plates. From (2.7) we can show that the field E between the plates is given by

eoE=(7, (2.9)

and, by definition,

E=^. (2.10)

Now on the introduction of a slab of dielectric, of thickness </, between the plates, the positive nuclei in the atoms of the dielectric will tend to be displaced in the direction of smaller field while the negative

charges (electrons) will tend to be displaced up the field, i.e., the medium

becomes polarized. Thus a back electromotive force is set up which will tend to decrease the field between the plates.

Now the total field E, as given by (2.10), is independent of the dielectric. Hence, the charge density on the plates must increase by an amount for instance. We can regard the polarization of the dielectric as conferring on it an effective permittivity e so that from (2.7) we obtain

eE=(T-\-(Ti. (2.11)

Imagine a cylinder of dielectric of unit cross section with its axis perpendicular to the plates. At the end surfaces will be charges -{-ai and — ai at a distance d apart. Hence we have the equivalent of a dipole of

moment Ci d. The electric moment per unit volume is, therefore, ai which

is called the polarization P. The total quantity tr+ai is known as the dis- placement D. Hence we have the relationship

D = eoE+P. . (2.12)

Now in certain media (anisotropic) the application of an electric field in one direction gives rise to a polarization in some other direction. Under

these circumstances (2.12) has to be expressed as a vector equation:

D = eoE+P. (2.13)
FARADAY'S LAW 49 This relation is of great importance in ionospheric radio propagation as

will be seen later.

2.2.2. Ampere's Circuital Law

One of the most important observations in the study of electro- magnetism was that of Oersted, who found, in 1819, that a piv^ed magnet was deflected when in the vicinity of an electric current. This experiment demonstrated that a current of electricity produced a magnetic

field. As in the case of static electricity and magnetism, it was found that

the magnetic field produced by a current element decreased as the square

of the distance from the element. This led Ampere to formulate his

circuital law, namely, that the line integral of the tangential magnetic

field H( taken around a current i was equal to the component of the

current flowing normal to the surface A enclosed (see fig. 2.2),

j Urds = I

J'dA = U (2.14)

where J is the current density through the surface A enclosed by the path

of integration S. Note that H refers to magnetic intensity which, in a medium of magnetic permeability /x, is related to magnetic induction B

by the formula

B = mH. (2.15)

2.2.3. Faraday's Law

Efforts to observe the electrical effects of magnetic fields bore fruit in 1831 when Faraday found that a current was produced in a coil of

J

Figure 2.2. Ampere's circuital law.
50 THEORY OF WAVE PROPAGATION

wire by the following processes: (1) when a magnet was moving near it and/or (2) when a current in an adjacent coil was switched on and off. Faraday carried out a large number of beautiful experiments to

verify the phenomena of electromagnetic induction and the serious reader

is recommended to read Faraday's account in his book Experimental

Researches in Electricity [1].^

Faraday's results may be summed up in the following two laws:

(a) When the flux of magnetic induction through a coil is changing, an electromotive force is induced in the circuit. (b) The magnitude of the emf 8 is proportional to the rate of change

of flux. The sign of the emf is given by Lenz's law, which states that it is such that any current flow is in the direction which would oppose the

flux change causing the emf.

Therefore

dN 8=--, (2.16)

where N is the total flux through the coil, i.e., induction times area, normal to the surface, that is N= f

B'dA. (2.17)

-'a Consider now the integral of the electric field round a loop which,

as shown in figure 2.3, has a small gap CD and through which is threaded

a time-varying magnetic field. The integral

/,

D E-ds

c

is the total voltage between C and D, that is, the induced emf, S. Hence, when C and D are brought together we arrive at the formula

jE-ds=- B'dA. (2.18)

It must be stressed that this relationship is quite general in spite of

the fact that we have derived it for a particular case only.

Figures in brackets indicate the literature references on p.
DISPLACEMENT CURRENT 51

Figure 2.3. Faraday's electromagnetic induction law.

It is convenient, at this point, to summarize the essential equations

obtained above. They are:

The electric field e j f E'dA= f

A ''V pdK (a)

The magnetic field

j f B'dA = 0, A

(b)

Magnetic field of

a current jll-ds = j

J'dA, (c) Electromagnetic

induction j E'ds=-

d r - / B'dA.

dt J (d)

2.2.4. The Displacement Current

It would appear, at first sight, as if eqs (2.19) are complete in themselves and define the electromagnetic field uniquely. However, that this

is not so was discovered by Maxwell in the course of his studies on the

charging of a capacitor (Leyden jar).
52 THEORY OF WAVE PROPAGATION

Consider the charging of a parallel plate capacitor with an insulator

as dielectric so that no current can flow between the plates. Let us apply

(2.19c) to a closed loop around the wire to a plate. If the surface enclosed

by the loop cuts the wire, then J"H.'ds around the loop is non-zero. Now

it is possible to construct a surface which envelopes the plate of the ca- pacitor and which passes between the plates. Since there is no flow of

electricity between the plates, application of (2.19c) shows that ^H'ds

around the loop is zero. We thus arrive at a contradiction. James Clerk

Maxwell's great contribution to electromagnetic theory was his assertion

that the circuit through a capacitor should be considered as closed. He

showed, furthermore, that the current density through the insulator

between the plates is due to the time rate of change of the displacement

jD, i.e., ^

i I dq I d , . dD

A Adt Adt^^^""'^^' dt

' (2.20)

where q is the charge on the plate.

Maxwell maintained that as far as the electromagnetic field was concerned, the displacement current was just as important as a flow of elec- tricity and that it must be added to the current on the right hand side of (2.19c). This enables us to write Maxwell's equations in integral form

as follows:

[ T>'dA= [ pdV,

-'a •'f

[ B-c/A = 0,

J A

(a)

(b)

j H-ds = j J-'i^+jJ D-rfA, (c)

(d)

(2.21)

For Maxwell's own account of the derivation of these formulas the

reader should consult his "A Treatise on Electricity and Magnetism" [2].
SOLUTION OF MAXWELL'S EQUATIONS

2.2.5. A Solution of Maxwell's Equations

53

In order to solve the set of eqs (2.21) , it is necessary to express them

in their differential forms. This can be achieved by means of the following

two vector theorems:

Green's Theorem

Let F be any vector function and V a volume bounded by the closed

surface A: then

f F-dA= [ divFdV. (2.22)

Stokes"* Theorem

Let F be a vector function and A a surface (not closed) bounded by

simple closed curve S; then

curlF-(iA. (2.23)

Applying these transformations to (2.21) we obtain

div D = p, (a)

divB = 0, (b)

curlH = J+D, (c) curlE=-B=-A<H, (d)

(2.24)

where the dot signifies the time derivative.

Let us consider a solution of these equations in a medium having the

following properties:

(i) Magnetically and electrically isotropic, that is, having the same

properties in all directions.

(ii) Electrically neutral, no net space charge so that p = 0.

(iii) Electrically nonconducting, i.e., J=0.

(iv) A field varying in the 1 -direction only in a right-handed orthog-
54 THEORY OF WAVE PROPAGATION

onal system of axes (1, 2, 3), so that

dx2 dxz With these restrictions, we obtain

curlH=+D, (a)

curlE=-MH. (b)

(2.25)

Taking the curl of (2.25a) we have

curl curl H = +curl D

= +e curl E = -enK.

Now it can be shown that, for any vector F,

curl curl F = grad div F — div grad F.

(2.26)

(2.27)

Since div B = 0, then div H = 0 and hence grad div H = 0. Furthermore,

under restriction (iv) we have

div grad xl =

^ dXi^ dXi" dXi" Equation (2.26) thus reduces to d^H, am

dxi^ ^ dx dxi'

e/i- Now

div H = H 1 = = 0, dxi 6x2 dxz dxi and if we select the 2- and 3 -axes so that i/2 = 0, we obtain

(2.28)

(2.29)

(2.30)

(2.31)
SOLUTION OF MAXWELL'S EQUATIONS 55 This is the equation of a plane transverse wave traveUng in the 1- direction with a phase velocity v where

1 (2.32)

Note that this can be shown by substituting a wave of the form

cos 27r\^ ftzL (^i/X)] and remembering that v=f\. The — sign represents a wave traveling in the positive 1 -direction and vice versa. The free space velocity c is given by

1 V.

(2.33)

Now the refractive index n of the medium is given by the ratio c/v, so that

c I Me

(2.34)

then

In media which have no particular magnetic properties, ii = iiq and

(2.35)

where K is the dielectric constant of the medium.

The equation of such a wave may be written in several different

forms, each of which has its peculiar advantages, such as

E= Eq cos 0)^—

V/

(a)

E= Eq cos ko{ct - nxi) , (b)

E= Eq cos {o)t — (c) E= Eq exp i{cot- (d)

(2.36)
56 THEORY OF WAVE PROPAGATION

where the propagation factor,

ko = — the phase constant,

Xo Xo= the free space wavelength.

X= actual wavelength in the medium.

It is of historical interest to note that Maxwell used a mixed (electrostatic and electromagnetic) system of units and he found that the

velocity c is given by the ratio of the electromagnetic to the electrostatic

unit of charge. This ratio was known to be about 3X10^ m/sec, or close to the velocity of light. This agreement led Maxwell to claim that light was indeed an electromagnetic phenomenon.

The existence of electromagnetic waves was demonstrated conclusively, around 1888, when Hertz [3] showed that the disturbances generated by a spark coil could be reflected, refracted, focused, and polarized.

2.2.6. Some Properties of Electromagnetic Waves

Let us consider some of the properties of a plane electromagnetic wave propagating in an isotropic nonconducting medium. If the wave is traveling in the 1 -direction we have d/dx2 = d/dxz = 0, since, for a given

value of Xi, the fields are constant over the whole 2-3 plane. Equation

(2.25) can be written

dX2

dH2

(a)

dHi

dxs dHz

dxi

(b) (2.37)

dxi

dHi

dX2

e (c) dt

'
PROPERTIES OF ELECTROMAGNETIC WAVES 57

dE2 dHi

(a) dX2 ^° dt

'

dEi dEz_

(b)

dxi dt

'

dEi

(c) dxi dX2

(2.38)

Let us rotate our system of axes so that the 2 -axis Ues parallel to the

E vector. Then E2= E, and £:3 = 0. Since d/dx2 = d/dxz = 0,{2.31) and

(2.38) become

dEi

dt

0, (a)

dH^ dE2 . dxi at (2.39)
58 THEORY OF WAVE PROPAGATION

From (2.39a) and (2.40a) we see that there is no time-varying

component of E or H in the 1 -direction. That is, the electromagnetic wave

is entirely transverse. Equations (2.39c) and (2.40b), respectively, tell us that H has no

space- or time-varying components in the 2 -direction. Hence E and H

are perpendicular to each other and to the direction of propagation. We

shall see later that this is not necessarily the case for propagation in the

ionosphere.

To determine the phase relationship between E and if, substitute

the expression E2—E20 cos {mt—hxi) in (2.39b) or (2.40c). This gives

Hz= —— co^ {o)t—kxi) ^ (a)

Hz = Hzo cos {uit—kxi) , (b)

(2.41)

where

V n

Hzo = —E20 = —£^20 = —E20' (2.42)

Equations (2.41) show that, if n is real, E and H are in phase. Equation (2.42) gives us the relationship between the peak amplitudes of E

and H in terms of the refractive index n of the medium.

The energy density Ue in the electric field is given by

Ue = iDE=ieE' (2.43)

and in the magnetic field

Hence the ratio of the energy densities is given by

Ue

(2.44)

(2.45)

so that the energy is divided equally between the electric and magnetic

fields.
MOTION OF IONS IN ELECTRIC AND MAGNETIC FIELDS 59 The flux of energy per unit area in the direction of propagation is given by the Poynting vector [4],

S = EXH. (2.46)

For a sinusoidally varying wave, S has to be averaged over a complete cycle. This gives

S.. = iEoHo. (2.47) In general, the E and H vectors will be complex quantities and, in

this case, it can be shown [4] that the average of the complex Poynting

vector is given by

Sav = iEXH* (2.48)

where H* is the complex conjugate of H.

2.3. Magneto-Ionic Theory

2.3.1. Motion of Ions in Electric and Magnetic Fields

2.3.1.1. Motion In an Electric Field

It will be recalled that, in chapter 1, we discussed the existence of

free electrons and ions in the earth's atmosphere (ionosphere) and, also,

the existence of the earth's magnetic field. It is the purpose of this section to discuss the propagation of radio waves in a conducting medium in the

presence of a superposed magnetic field. First of all, let us examine the motions of ions in the presence of

static fields. The equation of motion of an ion of charge e and mass m in an electric field E V/m, in the 2 -direction, is mx2 = eE, (2.49)

from which, by integration, we obtain the velocity

X2 =—Et

m

(2.50)
60 THEORY OF WAVE PROPAGATION

E= INDUCED ELECTRIC FIELD

, POSITIVE ION DISPLACEMENT

2- AXIS Figure 2.4. Force on an electron due to plasma displacement.

assuming that the ion starts from rest. If the ion concentration is N (per cubic meter), the current density

created is

7Ve2 J = Nex2 = Et. m

(2.51)

Consider now a slab of plasma (a medium containing free charges) in which the light electrons and the heavy positive ions are displaced, as shown in figure 2.4, by a distance X2. Such a displacement will produce

charges on the surface of the slab and an electric field E will be set up in the slab as in the case of a parallel plate capacitor.

The surface charge density is Nex2 so that from (2.9) the field is given by

Ne E= X2.

€0 (2.52)

The — sign arises because E is in the opposite direction to the displacement X2. There will be a restoring force due to the electrostatic attraction;

the equation of motion of an ion is

mx2 = eh= X2
MOTION OF IONS IN ELECTRIC AND MAGNETIC FIELDS 61

or

(2.53)

where co^v^ is called the angular plasma frequency.

2.3.1.2. Motion in a Magnetic Field The force F exerted on an ion of charge e moving with velocity v in a magnetic field B Wb/m- is

where 6 is the angle between v and B. Equation (2.56) shows that the

force on a moving charge is proportional to the component of the magnetic

field transverse to the direction of motion. Thus, if we shoot an ion into a region where there is a magnetic field, the component of motion parallel to the field will be unaltered whereas there will be a force, and hence an

acceleration, due to the component of motion perpendicular to the magnetic field. This acceleration tends to bend the path around the hnes of

force. The ion motion is, therefore, a helix. The projection on to a plane

perpendicular to the magnetic field is a circle of radius r//, which is deter- mined by balancing the centrifugal force mr//co^ against the centripetal

force evrB. Here oiH is the angular velocity and Vt is the transverse component of velocity rncoi/. Now mrH(^]j = erHOiHB, hence.

F = evXB, (2.55)

F=evE sin ^, (2.56)

(a)

(2.57)

Ztt m

(b)
62 THEORY OF WAVE PROPAGATION

Here/ff is called the gyro (or gyromagnetic) frequency and 03h the angular

Notice that fn is independent of the velocity of the ion. For electrons we have

Now in the ionosphere, B is on the order of 0.5 G or 0.5X10~^ Wb/cm"^;

therefore,/// =1.42X106 c/s"! or 1.42 Mc/s.

The numerical value of /// is of great importance in ionospheric

radio wave propagation because it lies in the band of frequencies, re- flected from the ionosphere, which are of use in radio communication.

2.3.1.3 Motion in Crossed Electric and Magnetic Fields

When magnetic and electric fields are present, the motion of an ion

is complicated except in the case where they are parallel.

When the fields are perpendicular, for example, when E is in the

1 -direction and B is in the 2 -direction, of a right-handed system of axes

(see fig. 2.5), the motion produced by the electric field is altered by the

magnetic field. The motion in the direction of the electric field does not

increase indefinitely, but the ion swings around and eventually moves

gyrofrequency.

Jh = 2.84 X WB= 3.57 X lOW. (2.58)

2

tH

E —

POSITIVE ON

3 Figure 2.5. Motion of ions in the presence of crossed electric and magnetic fields.
DERIVATION OF THE APPLETON FORMULA 63

against the electric field, as illustrated in figure 2.5. The average ion motion

is in the 3 -direction and is independent of the mass and charge of the ion

and even of the sign of the charge, negative and positive ions both moving

in the same direction. Hence, in an electrically neutral medium there is no resultant current in the 3 -direction, except insofar as these conditions

may be altered by collisions.

2.3.2. Derivation of the Appleton Formula

The formulas for the complex refractive index of a medium such as the ionosphere were derived by a number of people during the 1920's but the name most commonly associated with the theory is that of Sir Edward Appleton [5]. In 1931, D. R. Hartree [6] suggested that it was appropriate to include the Lorentz polarization term in the theory. Although the bulk

of both theoretical and experimental evidence indicates that the inclusion

of the term is unjustified, the formula for the complex refractive index is often referred to as the Appleton-Hartree formula.

The influence of heavy ions on the refractive index was considered

by Goubau [7] in 1935, and since then more realistic distributions of

collision statistics have been introduced by Phelps [8] and by Sen and

Wyller [9]. In order to derive the formula for the refractive index it is necessary

to define certain properties of both the wave and the medium. For our

present purposes we shall assume the following properties:

Wave Properties

(1) Simple harmonic progressive wave.

(2) Steady-state solution.

(3) Plane waves with given polarization. We shall call such waves

characteristic waves [10].

Properties of the Medium

(4) Electrically neutral.

(5) Charges distributed with statistical uniformity so that there is no resultant space charge.

(6) Uniform external magnetic field. (7) Electrons only are effective.

(8) Electronic collisions are independent of electron energy.

(9) The thermal motions of the electrons are unimportant. Such a medium is called a cold plasma.

( 10) The magnetic properties are those of free space.
64 THEORY OF WAVE PROPAGATION

Our procedure will now be as follows. First, we will apply Maxwell's

equations to the wave and, secondly, we shall impose the properties of

the medium, the so-called "constitutive relations." In our application of Maxwell's equations in the form given in (2.24) we are at liberty either to consider the medium as a conductor, so that

there is a conduction current (i.e., Jt^O), or we may consider it as a

polarizable medium in which the movement of the ions is included in the

P term of (2.13). It is most important to reahze that we cannot do both. For our present purposes let us use the second alternative, and express the refractive index in terms of the components of P and E. From (2.24) and condition 4 we have

divD (a)

divB (b)

(2.59)

curlH D = eoE+P, (c) curlE -B. (d)

CO-ORDINATE AXES

2

3

Figure 2.6. System of axes.
DERIVATION OF THE APPLETON FORMULA 65 Consider a characteristic wave, having properties (1), (2), and (3)

above, to be traveling along the 1-axis of a right-handed orthogonal

system with axes 1, 2, and 3 as shown in figure 2.6. The components of

the wave vary in time as exp {-{-icct) and in space as exp { — ikxi) and

do not vary in the 2- and 3 -directions. Since we are considering the charge oscillation as a polarization of

the medium then we have, from (2.13)

D = eoE+P,

which expresses the electrical anisotropy of the medium. The magnetic

properties, given by B = /zoH, are those of free space. A plane wave traveling in the positive 1 -direction can be expressed

by an equation of the form

E= Eq cos (oit—kxi) , (a)

or E= Eq exp i(cot—kxi) . (b)

(2.60)

Since the electric and magnetic vectors of the wave do not vary in the 2- and 3-directions we have, using the notation of (2.60b),

OXi

(a)

d d ^

dX2 dX2

(b)

d . — = ICO, dt

(c)

(d)
66 THEORY OF WAVE PROPAGATION

Substituting these in (2.59a) and (b) we obtain

A= eoEi +Pi = 0, (a)

Bi = Moi/i = 0. (b)

(2.62)

Before dealing with the curl equations, let us consider the implications of (2.62). Equation (2.62a) states that there is no component of D

in the direction of phase propagation. However Pi and Ei are not necessarily non-zero; this means that P and E may have components in the 1- direction. Furthermore, since the vector P is a measure of the electron

displacement from its mean position, the electron motion has a component in the direction of propagation. Equation (2.62b) implies that both

the B and H vectors are entirely transverse to the direction of propagation.

Substituting (2.61) in the curl equations (2.59c) and (d) we obtain

dxi = — ikHz = ioi ( €qE2 +P2)

= ikEz = —fioiccHir, dxi

dH2

dxi

dE2

dxi

= ikH2 = io)(eoE^-{-Pz)

= ikE2~ —fJioiooHs.

This is k

€qE2-\-P2= 1/3 = 1)2, (a)

60

k

eoEz +P3 = -H2 = (b)

CO

kEz = yLQwH2, (c) — kE2 = y-QOiH^. (d)

(2.63)
DERIVATION OF THE APPLETON FORMULA 67 Our next step is to express the refractive index in terms of the P's and £^'s. To do this we shall eliminate Hz from (2.63a) and (d). This

gives

or

eo E2 \co/ Moeo \ w /

(2.64)

From the definitions of A;, oj, and n it follows that

ck n = —

CO (2.65)

Hence

1 P2

(a)

similarly

«2 = 14— —

fb)

eo Ez

(2.66)

From these equations it follows that

E2^P2

Ez P3

and with (2.63) we obtain

H2_Ez_ Pz

Hz E2 P2

R, (2.67)

where R is called the tvave polarization.
68 THEORY OF WAVE PROPAGATION

3

MAGNETIC VECTOR

^) /-DISPLACEMENT VECTOR

-TAN

1 \

TAN"'

r 1 "2 ^2

2

Figure 2.7. Relationship between the instantaneous D and H vectors in the plane of the wavefront. Note that when /? is real, the E, D, and P vectors are linearly polarized along a direction making an angle tan~^ R with the 2 -axis. On the

other hand, the H vector is linearly polarized in a direction tan~^ { — R)

with the 3 -axis (see fig. 2.7). From this it follows that the H vector is perpendicular to the D vector and to the projections of the E and P

vectors on the 2-3 plane.

When R is complex the H and D vectors describe ellipses in the 2-3

plane as also do the projections on the wavefront of the E and P vectors. When the propagation factor k is real, equations (2.63) imply that

the H vector and the D vector, and hence the projections of the E and P

vectors on the wavefront, are always at right angles to each other and

rotate in the same sense. The above considerations apply to the propagation of characteristic waves in any medium. To find the refractive index we must now introduce

the properties of the magneto-ionic medium. These properties are embodied in the constitutive relations. We consider now the motion of electrons under the following

influences:

(1) The electric field of the wave.

(2) The imposed magnetic field Bq.

(3) Collisions between electrons and neutral molecules. For our

present purposes we shall neglect the motion of the heavy ions.
DERIVATION OF THE APPLETON FORMULA 69 The forces acting on an electron are

(a) The electric force eE.

(b) A force evXBo due to the electron motion v relative to the imposed magnetic field Bq.

(c) A force mvY which represents the average rate of loss of mo- mentum of the electron per colhsion.

(d) A force due to electron motion in the magnetic field of the wave.

This force is on the order of v/c of the force (a) above and will, therefore,

be neglected.

To obtain the constitutive relations, we write down the equations

of motion of the electrons under the combined influence of the electric

field of the wave and of the imposed magnetic field. If the direction of

propagation is along the 1-axis, as shown in figure 2.6, and the imposed

magnetic field Bo lies in the 2-3 plane making an angle 6 with the direction

of propagation, then the equations of motion are mxi = eEi —bxzBt — mvxu (a)

mx2 = eE2-\-exsBL — mvX2, (b)

mxi = eEz-\-exiBT — ex^BL — mvXz. (c)

(2.68)

We now proceed to transform these equations by the following

operations:

(i) Multiply throughout by A^e, where is the electron number

density;

(ii) Replace Xi by ioiXi^ Xi by —oi^Xi, etc;

(iii) Put Nexi= Pi, etc., the volume polarization.

With some rearrangement and introducing the accepted symbols, we

obtain the constitutive relations.

eoXEi=-Pi+iPiZ-\-iPzYT, (a)

€oXE2=-P2-\-iP2Z-iPzYL, (b)

eoXE,= -P,+iPzZ-iPiYT-hiP2YL, (c)

(2.69)
70 THEORY OF WAVE PROPAGATION

where X=Ne^/eomo3^, YL = eBL/mco, YT = eBT/mo:, and Z=v/o3.

The subscripts T and L refer to the transverse and longitudinal components of the imposed magnetic field with reference to the direction of

the wave normal (i.e., phase propagation).

The next step in our derivation is to express the ratio P2/E2 or Ps/Es in terms of the parameters X, Y, and Z. This is best done via the wave polarization term R as follows: From (2.62a),

eoXEi=-XPi.

Substitution in (2.69a) gives

Pi iYr

P3 l-X-iZ (2.70)

From (2.67) it follows that PiEz^ P^Ez so that by multiplying (2.69b)

by P3 and (2.69c) by P2 and subtracting, we end up with

PIYl^P^P^Yt-PIY:,. (2.71)

With a little rearrangement, and remembering that R=Pz/P2^ we have

from (2.70) and (2.71) the following quadratic expression in Ri

YlR'- ^ '1\ R-{-Yl = 0. (2.72)

l — X—iZ

There are, in general, two solutions of this quadratic which are given by

^=4l(i3i:^z)=^Va3fezr+^^4-

For the propagation of high-frequency radio waves through the E

and F regions of the ionosphere, Z is usually very small and can be neglected. For instance, with a frequency of 10 Mc/s at the 100-km level

(v = l.lSX Wfrom table 1.3) we have Z= 3 X lO"*. Under these conditions

R is given by

This formula tells us that, in general, there are two, and only two, char-
PROPERTIES OF THE APPLETON FORMULA 71

acteristic waves capable of propagation in our magneto-ionic medium.

From (2.69b) we obtain

(2.75) eoE2 l-iZ+iYLR'

which, on substituting, in (2.66a) gives

n'=l ^

, (2.76)

2(l-X-iZ) \4(l-X-iZ)2^ ^

which is the Appleton formula. In the upper regions of the ionosphere the collision frequency is sufficiently small so that, for frequencies greater than about 1 Mc/s, we may put Z=0, and hence the real part^ n of the refractive index is given by

^ 2X(1-X)

2{l-X)-Y}±y/YffI{r^XyYl'

In the absence of an imposed magnetic field {Yt= Yl = 0) and of colli- sions (Z=0) the refractive index is given by

(2.78) —(f)--'?-

where k = {e^/4>7r\m) =80.5 and / is in cycles per second.

2.3.3. Some Properties of the Appleton Formula

2.3.3.1. No Magnetic Field, No Collisions

In a discussion of the properties of the Appleton formula it is best

to start with the simplest case, that is, with (2.78). First it will be seen that the square of the refractive index must be equal to or less than unity.

Furthermore, for propagation of the wave, n must be real so that fx must

2 Henceforth the symbol fi will be used in this sense and not for magnetic permeability.
72 THEORY OF WAVE PROPAGATION

lie between 0 and 1. Secondly, we see that, for a given wave frequency,

the refractive index decreases with increase of electron density, and that,

for a given electron density, the refractive effects decrease with increase

of frequency but are independent of the amplitude of the wave. Curves depicting the variation of ^t^ (or fj,) with X are often called dispersion curves. The simplest dispersion curve is that representing

(2.78) and is shown in figure 2.8. This curve can be interpreted in terms

of ionospheric propagation as follows: Imagine a radio wave incident normally on a plane stratified ionosphere; at the bottom of the ionosphere (A^= 0) is unity. As we penetrate into levels of higher and higher electron concentration, fx falls lower

and lower. If the electron density is sufficiently high, then fx will go to

zero. To find what happens when fi reaches zero we apply SnelPs law to the wave. Snell's law states that for a wave incident at an angle 0o to the

normal, the angle 0 with the normal at a level where the refractive index

is fjL is given by

ju sin 0 = /zo sin <po. (2.79)

Now /xo = 1 outside the ionosphere and at reflection 0 must be 90° so that

the refractive index at reflection Hr must be equal to sin 0o. With normal

incidence (00 = 0) the condition of reflection becomes /Xr = 0. Thus we see that if the electron density is sufficiently large to reduce /x to zero then a wave (incident normally) will be reflected. Otherwise the wave will penetrate through the layer.

DISPERSION CURVE

Figure 2.8. Dispersion curve (no field, no collisions).
PROPERTIES OF THE APPLETON FORMULA 73

2.3.3.2. Magnetic Field, No Collisions

Dispersion. For a more complete discussion of the properties of the

refractive index formula, the reader should consult the excellent books

by J. A. RatcHffe [10], K. G. Budden [11], and J. M. Kelso [17]. However, we shall derive some formulas which will be needed in future chapters.

First consider the case of the reflection of a wave, of frequency /, incident normally in an ionospheric layer. Putting ^t = 0 in (2.77) and

solving for X we obtain the following:

With + sign X=l (2.80)

With - sign X=l-y, (a) or X=l+y. (b) (2.81)

where

Y'=Y}+Yl (c)

Equation (2.80) tells us that, for one of the magneto-ionic waves, the wave is reflected as in the absence of the magnetic field. This wave is called the "ordinary" wave. Equations (2.81) show that the level of

reflection of the other magneto-ionic wave (called the extraordinary) is dependent on the strength, but not on the direction, of the imposed

magnetic field. For waves of frequency greater than the gyrofrequency (fn) the usual level of reflection is given by X=l— Y whereas on frequencies below fn (so that y>l) the condition is X=lH-y.

The dispersion curves corresponding to (2.77) are shown in figures 2.9a and b for values of Y=i and y=2, respectively, and for ^;^45°

together with the limiting cases of longitudinal and transverse propagation. Note that these curves are not drawn to scale but are intended

merely to illustrate the general shapes.

Approximate formulas. Even in the absence of electronic collisions,

the refractive index formula (2.77) is complicated. There are certain

practical conditions under which considerably simpler approximations

are useful. Although, with the advent of electronic computers, the necessity for using approximations in numerical work has decreased, there is

still some need for them in practical work and, furthermore, they are widely used to simplify theoretical discussion.

The usual rules for determining whether the quasi-transverse (QT)

or the quasi-longitudinal (QL) approximations hold are.
0 = ORDINARY WAVE

X = EXTRAORDINARY WAVE

Figure 2.9. Dispersion curves for the general direction of propagation.

Cross-hatched areas represent the limits between transverse and longitudinal propagation. Curves shown

are for d «=45°. Vertical cross-hatch represents the + sign and the horizontal cross-hatch represents the — sign.
PROPERTIES OF THE APPLETON FORMULA 75 QT y^.»4(i- (a)

QL y^«4(i- (b)

(2.82)

It is important to notice that these conditions do not depend on the

value of 6 only. Thus QT may hold either for 6^90° or for X;^l which

is the value of X near the level of reflection (with normal incidence) of

the o-wave in almost all magnetic latitudes. Similarly the QL condition is good for the extraordinary wave, near its level of reflection (normal

incidence) at almost all magnetic latitudes. Davies and King [12] have

discussed the usefulness of the following approximations in the case of

the magnetic dipole field and vertical propagation.

Ordinary wave:

QT: (2.83)

QL:

X

1+ 1 |. (2.84)

Extraordinary wave:

M4 1-X' (2.85)

QL:

1- I Y (a)

(2.86)
76 THEORY OF WAVE PROPAGATION

Care must be taken when using these approximations, as the range of

vahdity may be very small. This is illustrated in figures 2.10a and b. Note

that the extraordinary wave curves are plotted in terms of the parameter

The following are suitable formulas for the refractive indices near

the levels of reflection with normal incidence. For the ordinary wave

ju+ = ( 1 — cot^ 6) cosec^ 6, (2.87)

where e = 1 — X, and for the extraordinary wave we have

-4 261 (i-y)(i+cos2 d) 1- €1 tan2 e 3+sec2^

4(l-y)(l+sec2 6')\ Y

ftan2 e

(2.88)

where ei = 1 — Y— X.

For further details the reader is referred to Budden [11, Ch. 12).

Note that if Y is replaced by — Y in (2.88) the refractive index is that

when X approaches 1 + Y. Other approximations of interest are those applicable to audio fre- quency waves (the whistler mode) . When X^ Y^l and | Yl | > 1, Storey [13] has shown that the + sign in (2.77) reduces to the following

approximations for a wide range of 6, not too near 90°:

X

(a)

Yl

or approximately ijl^ = X

(b)

Yl

(2.89)

Wave polarization. One other aspect of the Appleton formula which

is of interest is the wave polarization R given by (2.74). This gives the

amplitude ratio and the phase difference between the oscillations of the

D, E, and P vectors along the 2- and 3-axes. In general, the tips of these

vectors describe ellipses. The D ellipse is similar in shape to the projections of the E and P ellipses on to the 2-3 plane and the sense of rotation

is the same. The H ellipse is similar to the D ellipse (and lies wholly in
PROPERTIES OF THE APPLETON FORMULA 77

0 16.1 40.9 90

0.7 _

1 ORDINARY ^

\

• "^ """ -^

0.6 _ \\H-2

\

0.5

- \

0.4 -

\\

0.3

0.2 \

\

0.1

0

f = 2 000 Mc/s

fN = l.996Mc/s

1

(a)

1 i 1

0.55

0.50

045

H-4

\

\ 1 EXTRAORDINARY

f=2.0 Mc/s

fN/C=0.90

b) 90 75 60 45 30 15 0

(GEOMAGNETIC LAT.) X° Figure 2.10. Refractive index curves under quasi-longitudinal and quasi-transverse

conditions.

Vertical propagation, dipole magnetic field, (a) ordinary wave; (b) extra ordinary wave. The indices m+

and n- are from (2.77).
78 THEORY OF WAVE PROPAGATION

the 2-3 plane) but is rotated through 90° as shown in figure 2.11a and

the sense of rotation is the same. The relationship between the ordinary wave ellipses and the extraor- dinary wave ellipses can be deduced from (2.74), from which it follows

that

R(-)R(+)=l. (2.90)

Hence, in the absence of collisions, the ellipse of the extraordinary wave

can be obtained from the corresponding ellipse of the ordinary wave by

rotating it through 90°. Furthermore, the sense of rotation is reversed as shown in figure 2.11b. While the vectors D, B, and H lie in the plane of the wavefront

(2-3 plane), the P and E ellipses are tilted forward making angles <f> and

\f/ respectively with the 2-3 plane where

, (1-X)^

COt0 = -=—

(2.91)

where the + and — signs refer to the corresponding signs in (2.77), and

where

tan ;/'= — = I j—^ . (2.92)

From these equations we see that the forward tilt is different for the two

magneto-ionic waves.

It can be shown from (2.91) and (2.92) that, for waves incident

normally on the ionosphere, at reflection

(i) the E and P vectors of the ordinary wave vibrate linearly in the

direction of the imposed magnetic field, since cot </> = tan d = cot \f/. (ii) the E and P ellipses of the extraordinary wave are perpendicular

to the imposed magnetic field, since <l) = \l/= —6.

The following properties are of interest:

(1) With longitudinal propagation the two magneto-ionic waves are

circularly polarized, in opposite senses.

(2) With transverse propagation the ordinary wave is polarized

with the E and P vectors parallel to the imposed magnetic field, whereas

for the extraordinary wave the P and E ellipses lie entirely in the 1-3

plane.
PROPERTIES OF THE APPLETON FORMULA 79

D ELLIPSE AND PROJECTIONS

OF THE E AND P ELLIPSES

H ELLIPSE

(a)

0 ELLIPSE

<

(b)

X ELLIPSE

Figure 2.11. Polarization ellipses (no collisions).

(a) Wave polarization D and H ellipses, (b) Relation between the corresponding ellipses of the ordinary and the extraordinary waves.
80 THEORY OF WAVE PROPAGATION

2.3.3.3. No Magnetic Field, With Collisions

Meaning of a complex index. For the sake of simplicity we now set Yt= Yl = 0, but retain Z, in (2.76). This yields a complex refractive

index n given by

X X iXZ

(2.93)

where n and x are the real and imaginary parts of n respectively.

Let us pause for a moment to consider the meaning of a complex

refractive index. The equation for a wave traveling in the 1 -direction is of the form (see 2.36)

E=Eo exp i(^t— -nx^, (2.94)

or E= Eq exp ^x~^i^ exp i^cot— -/x^i^- (2.95)

Thus, if X is non-zero, this represents a wave whose amplitude is de- creasing exponentially with distance. The quantity (co/c)x is a measure

of the decay of amplitude per unit distance and is called the absorption

coefficient k (kappa).

K=-x. (2.96)

C

Dispersion. Consider first the real part of the refractive index. The

variation of fj.^ with X, for a series of values of Z, is shown in figure 2.12.

It will be seen that, for a given value of X, the effect of a large collision frequency is to diminish the refracting properties of the medium. It is important to notice also that, when collisions are present, the real part

of the refractive index never goes to zero but attains a minimum value

given by — , (2.97)

(1+Z2) ' ^

at X=2.
PROPERTIES OF THE APPLETON FORMULA 81

This means that in a lossy medium total reflection <Qever really occurs. However, strong reflections still occur near levels at which }i is small. Absorption. We shall return now to the absorption of the radio wave. From (2.93) and (2.96) we get

a; 1 XZ I Nv

'^ = -^7X^2=^^ (2.98)

This formula gives the absorption in nepers per meter, where 1 neper =

8.69 dB.

Equation (2.98) enables us to distinguish between two extreme types

of absorption, namely:

Non-deviative absorption occurs in the D region of the ionosphere; it predominates when ^ is near unity and when the product Nv is large.

Deviation absorption occurs near the level of reflection and whenever

there is marked bending of the ray, that is, when /jl tends to zero. For non-deviative absorption we have, when oo is much greater than i^,

e2 Nv

(2.99)

2eomc co
82 THEORY OF WAVE PROPAGATION

so that the absorption varies inversely as the square of the frequency.

For deviative absorption we have

(2.100)

Note that this type of absorption does not, in general, vary inversely as the square of the frequency.

Let us consider now the case when the angular wave frequency is small compared with the collision frequency (i.e., oi'^<^v'^) . With this condition we have from (2.98) for non-deviative absorption

e2 iV

(2.101)

2eomc v Under these conditions, the absorption may actually decrease with in- crease of collision frequency. The physical reason for this appears to be

that the electronic motions are so confined that little energy is extracted

from the wave. Absorption of this type is thought to occur during some

polar cap absorption events and certain solar flare effects. It is of interest to note that differentiation of (2.98) (for m^I)

shows that a maximum of absorption occurs when v = oi.

2.3.3.4. Magnetic Field, With Collisions

Dispersion. With one exception, the inclusion of a magnetic field and collisions introduces great complication into the dispersion and absorption relationships. The one exception is that of transverse propagation of the ordinary wave which is the same as the "no field" case. The dispersion curves for the general case of any angle of propagation are discussed usually in terms of the so-called critical collision fre- quency Vc where

-^lll^l^, (2.102) 2 Yl 2 COS d The curves are sketched in figure 2.13 and show how profound are the

effects of collisions (in comparison with figure 2.9), especially near X=l.

Collisions play an important part in modifying the QT and QL conditions.

Thus QL conditions may hold even near X=l for the ordinary wave
PROPERTIES OF THE APPLETON FORMULA 83

DISPERSION CURVES WITH COLLISIONS

20°

ORDINARY

EXTRAORDINARY

Figure 2.13. Dispersion curves with maffietic field and collisions for a fixed 6=20°.
84 THEORY OF WAVE PROPAGATION

whereas QT conditions may apply near X=l=Fy for the X-wave. The

interested reader can find more information on this in Mr. RatcHffe's

book [10].

Polarization. As far as polarization is concerned, the introduction of

colHsions causes the polarization ellipses (in the 2-3 plane) to rotate about the 1-axis. All the ellipses associated with one magneto-ionic wave

rotate in the same direction and through the same angle as shown in figure 2.14a. The ellipses associated with the other wave rotate in the

opposite direction through the same angle (figure 2.14b). Hence, for the projections of the ellipses onto the wavefront, we may deduce the ellipses of one magneto-ionic tvave from that of the other as follows: Rotate the ellipse

through 90° about the direction of phase propagation and then reflect in the magnetic meridian. It may be noted that one ellipse is the reflection of the other in the plane making an angle of 45° with the magnetic meridian.

Absorption. In principle it is possible to express the complex refrac- tive index in terms of its real and imaginary parts and thus to obtain the

absorption. In practice the expressions which would be obtained by this procedure are so complex as to be of little or no value. For a variety of

conditions, however, the propagation conditions are quasi-longitudinal

and the non-deviative absorption coefficient is then given, approximately,

by

e2 /Y "-^ , ^ ",2 , 2

- (2.103)

The + and — signs refer to the ordinary and extraordinary waves re- spectively. From this we see that the ordinary wave suffers less absorption, and the extraordinary suffers more absorption, than the corresponding wave in the absence of a magnetic field.

2.3.4. Generalized Magneto-Ionic Formulas

2.3.4.1. Collision Statistics

In our derivation of the Appleton formula it was assumed that the

electrons all possessed the same average velocity and that the collision frequency v was independent of the electron velocity. Now the question

of finding an ^^average" velocity while not important in the upper regions

of the ionosphere, where v is small, is of considerable importance in the

D region where v may be equal to or greater than the angular wave
GENERALIZED MAGNETO-IONIC FORMULAS 85

D ELLIPSE AND PROJECTIONS

OF THE E AND P ELLIPSES

H ELLIPSE

(a)

\

\

\

\

\

\

/

X

^

Y

\

/ / V L / \ / ' 0'

\

\^

\7 ^

' \

\

\ \

\

(b)

Figure 2.14. Polarization ellipses with collisions.

(a) Polarization D and H ellipses, (b) Relation between the corresponding ellipses of ordinary and

extraordinary waves.
86 THEORY OF WAVE PROPAGATION

frequency. The method of averaging collisions is indeed the weakest

point in the theory developed above, and to improve upon the above

theory it is necessary to consider the energy distribution of the electrons

and the dependence of collision frequency on electron energy. Thus a few

y.00 Table 2.1. Table of Cpix) =—, ^f^.

p

X

3/2 5/2 p

X

3/2 5/2

0.00 1.333 0.2667 3.00 0.07034 0.05454

ft ftC ft C\'74 A ft OAl c 3 Oft ft Cl^AfiA ft ftCft/l/l 0.10 0.8425 0.2542 3.40 0.05854 0.04677

0.15 0.7502 0.2463 3.60 0.05369 0.04347

0.20 0.6786 0.2384 3.80 0.04941 0.04048

0.25 0.6202 0.2306 4.00 0.04562 0.03778

ft 9ft ft C71 ft ft 009ft A Oft ft ft/lOOU ft fto coo 0.35 0.5289 0.2156 4.40 0.03920 0.03311

0.40 0.4922 0.2085 4.60 0.03647 0.03107

0.45 0.4598 0.2017 4.80 0.03402 0.02921

0.50 0.4310 0.1951 5.00 0.03179 0.02751

0.55 ft /< ftC" O ft 1 OOft C Oft A A0ft'70 ft ftOCft/( 0.60 0.3818 0.1828 5.40 0.02794 0.02450

0.65 0.3607 0.1771 5.60 0.02627 0.02317

0.70 0.3414 0.1715 5.80 0.02474 0.02195

0.75 0.3237 0.1662 6.00 0.02333 0.02081

ft Oft 0 . oO ft 9 ATT ft 1 ^1

1

U. loll ^ Oft A AOOA/I ft fti nn^ 0.85 0.2926 0.1563 6.40 0.02085 0.01878

0.90 0.2787 0.1516 6.60 0.01976 0.01787

0.95 0.2659 0.1471 6.80 0.01874 0.01702

1.00 0.2540 0.1428 7.00 0.01780 0.01623

1 . 10 0.2325 0. 1347 7.20 0.01693 0.01549

1.20 0.2137 0.1273 7.40 0.01612 0.01480

1.30 0.1971 0.1204 7.60 0.01536 0.01415

1.40 0.1824 0.1140 7.80 0.01466 0.01355

1.50 0.1693 0.1081 8.00 0.01400 0.01298

1.60 0.1576 0.1026 8.20 0.01339 0.01244

1.70 0.1471 0.09750 8.40 0.01281 0.01194

1.80 0.1376 0.09275 8.60 0.01227 0.01146

1.90 0.1289 0.08831 8.80 0.01176 0.01101 2.00 0.1211 0.08417 9.00 0.01128 0.01059

2.10 0.1139 0.08030 9.20 0.01084 0.01019

2.20 0.1073 0.07668 9.40 0.01041 0.009811

2.30 0.1013 0.07328 9.60 0.01001 0.009453

2.40 0.09580 0.07009 9.80 0.009635 0.009114

2.50 0.09070 0.06710 10.00 0.009278 0.008792

2.60 0.08599 0.06428 10.50 0.008468 0.008059

2.70 0.08164 0.06163 11.00 0.007758 0.007408

2.80 0.07759 0.05913 11.50 0.007132 0.006833 2.90 0.07384 0.05677 12.00 0.006578 0.006321
GENERALIZED MAGNETO-IONIC FORMULAS 87 Table 2.1

Continued

V

3 2 5/2 p

3 2 5/2

12.50 0.006086 0 005864 28 00 0 001262 0 001251

13.00 0.005647 0 005453 29 00 0 001177 0 001168

13.50 0.005252 0 005084 30 00 0 001101 0 001092

14.00 0.004898 0 004750 32 00 0 0009684 0 0009620

14.50 0 . 004578 0.004448 34 00 0.0008586 0 0008536

15.00 0.004287 0 004173 36 00 0 0007665 0 0007625

15.50 0 . 004024 0 003922 38 00 0 0006884 0 0006851

16.00 0.003784 0 003693 40 00 0 0006216 0 0006190

16.50 0.003564 0 003484 42 00 0 0005641 0 0005619

17.00 0.003363 0 003291 44.00 0 0005142 0.0005124

17.50 0.003179 0 003114 46 00 0 0004707 0 0004691

18.00 0 . 003009 0 002950 48 00 0 0004324 0 0004311

18.50 0.002852 0 002799 50 00 0 0003986 0 0003975

19.00 0.002707 0 002660 55 00 0 0003296 0 0003289

19.50 0.002573 0 002530 60 00 0 0002771 0 0002766

20.00 0.002448 0.002409 65 00 0.0002362 0.0002358

21.00 0.002225 0 002192 70 00 0 0002037 0 0002034

22.00 0.002031 0 .002003 75 00 0 0001775 0 0001773

23.00 0.001860 0 .001837 80 .00 0 0001560 0 0001559

24.00 0.001711 0 .001691 85 .00 0 .0001382 0 0001381 25.00 0.001578 0 .001562 90 .00 0 .0001233 0 .0001232 26.00 0.001461 0 .001446 95 .00 0 .0001107 0 .0001106 27.00 0.001356 0 .001343 100 .00 0 .0000999 0 .0000998

electrons with high energy may lose as much energy as a large number of

electrons with low energy.

Little was kno^vTi about the energy dependence of v until Phelps

and Pack [14] and Phelps [8] established, experimentally, that for slow

electrons in nitrogen, the frequency of collisions for momentum transfer was directly proportional to electron energy. Margenau [15] has shown that, to include the distribution of elec- tron energies, it is necessary to use the Boltzmann transfer equation.

This theory has been extended to the case of a magneto-ionic medium by

Sen and Wyller [9] but their development is beyond the scope of this book. We shall, however, consider their results in the important case where

there is no imposed magnetic field. This case applies also to transverse propagation of the ordinary wave. With a Maxwellian velocity distribu- tion and with a collision frequency which varies linearly with electron energy, the complex refractive index is given by the expression
88 THEORY OF WAVE PROPAGATION

in which Zm = Vm/oi. Here Vm is the electron collision frequency associated

with the most probable energy rather than with the mean energy. -rn! A

exp ( — e) de (2.105)

The values of 63/2 (a:) and 65/2 (^) given in table 2.1 are taken from Burke

and Hara [16] and are published by permission of the Superintendent,

Defence Research Telecommunications Establishment, Ottawa, Canada.

2.3.4.2. Dispersion

For the sake of simplicity let us consider the case where the absorption is relatively small so that x^<J^M^- Under this condition we have

(2.106)

From (2.105) it can be seen that when x is small, i.e., when Vm'^oi', 63/2(0) Substitution of this value into (2.106) gives ^l'^=l— (co^A^)

which is similar to (2.97) with Z^l. Thus it is possible to use the classical formula provided that v= {'\fS/2)vm' When x is large, i.e., when oy^Vm^

(2.106) reduces to (2.78).

2.3.4.3. Absorption

The non-deviative absorption per unit length (x^<^M^) is obtained

from the imaginary part of (2.104), namely
PHASE VELOCITY 89

Sco 1 X

or

5 1 co!^ /w\

(a)

(b)

(2.107)

To see how the absorption from the generahzed theory compares with

that from the Appleton equation, we need to compare the following

function:

KG

5 1 /co\

=--e5/2(-K

^ Vm \Vm/

(2.108)

with

C02 +i;2 (2.109)

This comparison is made in figure 2.15. As in the case of the dispersion

curves, it is not possible to use a single effective collision frequency v^a across the entire frequency band. Nevertheless, on high frequencies the

Appleton theory can be used with j^eff = 2.5 Vm^ whereas on low frequencies

it is necessary to use VQii=\.'D Vm- It must be realized, however, that on

intermediate frequencies appreciable error is involved in using one or the other of these values of z^eff2.4. GROUP PROPAGATION

2.4.1. Phase Velocity

From (2.78) it follows that the phase velocity (f) of a wave in a plasma containing no imposed magnetic field and in which electronic

collisions are negligible is given by

c

v = - = c (2.110)

meoco r
90 THEORY OF WAVE PROPAGATION

Mc/s

Figure 2.15. Comparison of absorption curves of Appleton theory and of generalized

theory.

This indicates that the phase velocity, in the medium, is greater than that

of hght. It might be thought, at first sight, that this is a violation of the

special theory of relativity. However, this is not so; all it means is that

the wavelength (i.e., the distance between one wave crest and the next)

is greater in the medium than in free space. It does not mean that energy

is propagated faster than light.

The relationships between phase velocity (i;), wavelength X, and

refractive index fi are given by
GROUP VELOCITY 91

(a)

and - = — , (b) X Xo

(2.111)

where Xo is the free space wavelength.

2.4.2. Group Velocity

When the phase velocity of a wave in a medium is a function of the wave frequency, the medium is said to be "dispersive." This term arose

in the dispersion of colors by a prism. Inspection of (2.110) reveals that,

for radio waves, the ionosphere is dispersive. This means that two waves

differing sHghtly in frequency will travel with slightly different velocities. It is the interference pattern produced by two such waves that determines

where, and with what velocity, the energy in the composite wave will travel. This is what happens when we modulate a wave and it introduces

the concept of "group velocity" which, for our present purposes, may be

regarded as the velocity with which the modulation envelope travels or the velocity of the energy. It should be realized that this concept is applicable only when the modulation envelope retains its shape. It is not applicable under conditions of severe distortion as can occur in highly

dispersive media. For a more detailed discussion of this subject the reader

should consult Stratton [4, sec. 5.17J. For our present purpose it will suffice to consider the superposition

of two harmonic waves and 1/^2 of equal amplitude which differ slightly in frequency and wave number.

\l/i= cos (kxi — cot),

yp2= cos {{k +8k)xi— (o:-^do:)t}

4^ = ^1+^2 = 2 cosi(xi8k-t8o:) cos [(^+y)^i~(^+y)^

(a)

(b)

(c)

(2.112)
92 THEORY OF WAVE PROPAGATION

Figure 2.16. Interference pattern produced by two waves of equal amplitudes and slightly different frequencies.

This is shown diagrammatically in figure 2.16. The superposition pro- duces a "beat" signal, the envelope of which is given by

A = 2 cos ^{xi 8k —t 5co)

.

(2.113)

It follows from (2.113) that the velocity of propagation of the envelope

(i.e., the group velocity u) is given by

u =

8ct) (2.114)

This contrasts with the phase velocity v given by

(2.115)

For a non-dispersive medium, in which cx)/k is constant, u = v. In the limit as 5co—>0 and 8k—^0 we obtain the differential form

(2.116)

where ko is the value of k at which the gradient (dco/dk) is evaluated.

It is convenient to define a group refractive index ji' in a manner

similar to a phase index namely.
MEANING OF ANISOTROPY 93

It is important to remember that the group velocity as defined above is the component in the direction of phase propagation. Furthermore,

under normal dispersion conditions, its magnitude is always less than the velocity of light. Substituting m = Vl - ( /iv//) ' in (2.117) we find that

M =j>/)=-. (2.118)

df M

In the presence of an imposed magnetic field the group refractive

index m'(±) is given by substituting the expression for /x from (2.77) in (2.117). This gives

/(±)=m(±) + {(1-m^(±)P

J 1 , 2(l-XyYl-XY^ 1 ^LXm(±)%(±)(1-X)2 2XM(±)(l-X)Vy^ + 4y|(l-X)2j'

(2.119)

where the + and — signs refer to the ordinary and extraordinary waves

respectively. The more complete expression, involving collisions, is given

by Budden [11, ch. 12].

2.5. PROPAGATION IN ANISOTROPIC MEDIA

2.5.1. Meaning of Anisotropy

A homogeneous medium is said to be isotropic if the phase velocity

at any given point in the medium is independent of the direction of

propagation. A two-dimensional illustration of this is seen in figure .2.17. Consider a disturbance, originating at the origin 0; after a time t the

wavefront will be a circle of radius r = vt. At a point P on the wave the

wavefront is tangent to the circle and hence the wave normal lip, which

is perpendicular to the front, is radial. Now, since the disturbance is traveling out from 0 in all directions, it is not hard to see that the direc- tion of energy flow (ray direction) is always radial. Hence, in an isotropic

medium, the direction of phase propagation and of energy propagation

coincide. Now consider a magneto-ionic medium. Equation (2.77) shows that

the refractive index fj. depends upon Yt and Yl, that is, upon the direction
94 THEORY OF WAVE PROPAGATION

Figure 2.18. Wavefront in an anisotropic medium.

of phase propagation with respect to the magnetic field. A medium such

as this, in which the phase velocity at a point is a function of direction, is said to be ^^anisotropic." Again consider a disturbance originating at a point O in such a medium as illustrated in figure 2.18. Since the phase

velocity is a function of the angle 0 made with the reference axis, the

wavefront at a time t is not circular but shaped somewhat similar to that

shown in figure 2.18. As before, the wavefront at a point P is tangential to the surface of constant phase and so the wave normal rip is no longer

radial. Since the energy is radiating from the point 0, the ray direction

XYr is still radial. Hence, in an anisotropic medium, the direction of phase

propagation differs, in general, from that of energy propagation.
ANGLE BETWEEN PHASE AND RAY DIRECTIONS

2.5.2. Angle Between Phase and Ray Directions

95

Let a be the angle measured from the wave normal Hp to the ray iir, i.e., in same sense as ^, as shown in figure 2.18. Our next step is to find a

relationship for a in terms of the refractive properties of the medium.

Referring to the geometry in figure 2.19 we see that

\dr tanQ;=-- — , (2.120)

r a0

and

(l> = d-a. (2.121)

It is now necessary to introduce the concept of ray velocity Vr. The

distance OP=r, in figure 2.18, is proportional to the velocity of P in the ray direction iir, whereas the phase velocity v is measured in the direction of phase propagation n^. By letting the wavefront advance a short

distance it can be seen that the relation between v and Vr is V=VrGOSa. (2.122)

Solution of (2.120), (2.121), and (2.122) gives

Bq reference axis Figure 2.19. Derivation of formula tan a = {\/ix){dfj./dd).
96 THEORY OF WAVE PROPAGATION

The sign convention used here is important because some authors use

(2.123) with a reversal of sign. The convention used here is that angles

measured in the same direction as 6 (i.e., from wave normal to magnetic

field) are positive. It is important to remember also that in the above

derivation of tan a, it was tacitly assumed that the medium was homogeneous^ that is the wave velocity in a given direction is independent of

position in the medium. Hence no distortion of the wavefront is brought

about by variations in the medium due to position.

2.5.3. Phase and Group Paths

For some purposes, it is convenient to use the concepts of phase and

group paths which may be defined with reference to the transit times of a

surface of constant phase and of a wave packet, respectively, between a sender and a receiver. It must be remembered that these are not paths in space but are distances which would have been covered if the wave (and wave packet) had traveled with the free space velocity.

Referring to the ray path between sender S and receiver R in figure

2.20, the time dTp required for a surface of constant phase (see fig. 2.20b)

to travel from P to Q is given by

,^ PM PQ ds cos a 1 , dTp = =—= = -fi cos ads. (2.124)

V Vr V C The total transit time

I p

where

Tp = - f ficosads = -, (2.125)

cJs c

.R P= /* M COS a ds, (2.126)

is defined as the phase path.

The quantity K= (27r/Xo)P is called the angular phase path length. It is simply the number of radians of phase between sender and receiver.

If K changes with time, either because of a change of real distance and/or

a change in refractive index, the angular frequency of the received wave

will differ from that transmitted by an amount Aco. If K increases then

the received frequency decreases because more radians are needed in the
PHASE AND GROUP PATHS 97

Hp WAVE NORMAL

RAY DIRECTION

Figure 2.20. Phase and group paths in an anisotropic medium.

medium between S and R. Therefore the angular Doppler frequency

Aco is

dt Xo dt (2.127)
98 THEORY OF WAVE PROPAGATION

In terms of linear frequency the Doppler shift A/ is given by

A/- - —

Xo dt fdp

c dt (2.128)

The group path may be defined in terms of the time of flight of a

pulse. It will be recalled that in section 2.4.2 we defined the group velocity u in the direction of phase propagation. In an anisotropic medium the wave packet will, in general, have a velocity component parallel to the

wavefront. The time dTg for the packet to travel from P to ^ (fig. 2.20)

is given by

dT,=

ds cos a

(2.129)

The quantity u sec a is called the ray group velocity and represents the

velocity of the wave packet along the ray path.

The total time of flight between sender and receiver is:

1 /-^ 1 Tg = -

J ^' COS a ds = -P',

C J o c where

P'= / m'cosq;

J a ds

(2.130)

(2.131)

is called the group path. Another useful relationship between these

quantities is

aco (a)

or P' = 4-(^P)-

dec (b)

(2.132)
REFERENCES 99 REFERENCES

[1] Faraday, M. (1855), Experimental Researches in Electricity, Vols. I, II, and

III (London).

[2] Maxwell, J. C. (1873), A Treatise on Electricity and Magnetism, Vols. I and II (Oxford).

[3] Hertz, H. (1892), Ausbreitung der Elektrischen (Kraft, Leipzig).

[4] Stratton, J. (1941), Electromagnetic theory, sec. 2.19 (McGraw-Hill Book Co.,

Inc., New York).

[5] Appleton, E. V. (1927), URSI Proc, Washington.

[6] Hartree, D. R. (1931), The propagation of electro-magnetic waves in a refracting

medium in a magnetic field, Proc. Cambridge Phil. Soc. 27, 143.

[7] Goubau, G. (1935), Dispersion in einem Electronen-Ionen-Gemisch dass unter dem Einfluss eines ausseren Magnetfeldes staht, Hochfrequenz u. Electroakust

46, 37.

[8] Phelps, A. V. (1960), Propagation constants for electromagnetic waves in weakly

ionized dry air, J. Appl. Phys. 31, 1723.

[9] Sen, H, K., and A. A. Wyller (1960), On the generalizations of the AppletonHartree magnetoionic formulas, J. Geophys. Res. 65, 3931.

[10] Ratcliffe, J. A. (1959), The magnetoionic theory (Cambridge Univ. Press).

[11] Budden, K. G. (1961), Radio waves in the ionosphere (Cambridge Univ. Press).

[12] Davies, K., and G. A. M. King (1961), On the validity of some approximations to the Appleton-Hartree formula, J. Res. NBS 65D, (Radio Prop.), No. 4, 323.

[13] Storey, L. R. O. (1953), An investigation of whistling atmospherics, Phil. Trans. Roy. Soc. London, A 246, 113.

[14] Phelps, A. v., and J. L. Pack (1959), Electron collision frequencies in nitrogen and

in the lower ionosphere, Phys. Rev. Letters 3, 340.

[15] Margenau, H. (1946), Conduction and dispersion of ionized gases at high fre- quencies, Phys. Rev. 69, 508.

[16] Burke, M. J., and E. Hara (May 1963), A table of C—script integrals for use with

the generahzed Appleton-Hartree magneto-ionic formulas, DRTE Report 1113.

[17] Kelso, J. M. (1964), Radio Ray Propagation in the Ionosphere, (McGraw-Hill

Co., Inc., New York).
i

I
CHAPTER 3

Synoptic Studies of the Ionosphere

3.1. WORLDWIDE SOUNDINGS

For purposes of radio communications, it is necessary to have in- formation about the ionosphere on a global scale. Since the spatial and

temporal fluctuations in the ionosphere are so great, geographic coverage

may be much more important than accuracy of measurement. This point

should be borne in mind whenever one is judging the value of ionospheric

data. For instance, the lack of accuracy to which a critical frequency can

be measured may make it of little value to the scientist, yet it may be of

value to the radio operator.

Before World War II, there were only a few sounding stations in existence, e.g.. Slough, England; Washington, D.C., U.S.A.; Huancayo,

Peru; Watheroo, Australia; and Slutsk, U.S.S.R. The need for more

reliable high-frequency communications led to the installation of many

more stations during the war (40 or 50). During the International Geophysical Year (IGY) still more stations were added, making a total of

about 150. The distribution of stations during the IGY is shown in figure

3.1. During this latter period considerable uniformity was introduced

into the scaling and reporting of ionospheric data [1],^ which has turned

out to be valuable from the point of view of both the radio communicator

and the scientific worker.

Much of the impetus for ionospheric research has come from certain

international organizations such as the International Scientific Radio

Union (URSI) and the Consultative Committee on Ionospheric Radio

(CCIR). These organizations have encouraged investigations into the

spatial and temporal variations in the electron distribution in the ionosphere, the measurement of ionospheric absorption of radio waves,

ionospheric movements, noise, and the scattering of radio waves from

ionospheric irregularities.

Figures in brackets indicate the literature references on p. 156. 101
102 SYNOPTIC STUDIES OF THE IONOSPHERE

IONOSPHERIC VERTICAL SOUNDING STATIONS

• = 1959 DATA !N WDC-A

= 1961 DATA IN WDC-A

Figure 3.1. Map of world distribution of sounding stations.
EXPERIMENTAL TECHNIQUES 103 In the present chapter, we shall consider some of the techniques

used in ionospheric investigations and a few of the results obtained.

When making measurements on a medium such as the ionosphere it is necessary to distinguish clearly between controlled experiments, such

as can be carried out in a laboratory, and those over which we have no

control. Except for certain modeling techniques involving laboratory

plasmas and microwaves, ionospheric research must be carried out in its own environment and, hence, any control must be "demote control."

3.2. EXPERIMENTAL TECHNIQUES

There are many possible ways of classifying radio techniques for investigating the ionosphere. For instance, we can divide them into pulse versus continuous wave (CW) techniques, or into fixed frequency versus sweep frequency, or again into intermittent versus continuous methods

and so on. In the present treatment, we shall start by studying the most

widely used technique (the ionosonde) and follow in order of decreasing

usage, such as the techniques for measuring absorption, phase, etc. It is not to be construed that this order is in any sense one of relative importance.

3.2.1. Height Recorders

3.2.1.1. The Ionosonde

The ionosonde is essentially a pulsed radar device in which the ex- ploring frequency can be varied over a wide range from 1 Mc/s, say, up

to 25 Mc/s. Of course the entire sweep may have to be covered in a series of frequency bands. A detailed description of ionosondes is given by

Wright, Knecht, and Davies [2]. The equipment is designed to measure

directly the time t taken for a pulse of radio waves to travel up to the

ionosphere and back as a function of frequency. That is, it measures the

group height h' of the ionosphere, where

/^' = ici=0.15«, (3.1)

t being in microseconds. This group height is also known as equivalent

height and virtual height. The transmitter and receiver are kept in tune by suitable electronic or mechanical linkage and the receiver output is
104 SYNOPTIC STUDIES OF THE IONOSPHERE

displayed on a cathode ray oscilloscope together with suitable frequency

and time (height) markers. These signals are usually applied in the form

of narrow blanking pulses which interrupt the sweep-trace every J, f or 6f msec corresponding to group heights of 50, 100, and 1000 km, respectively. In addition, as the frequency of the transmitter is varied, the

entire sweep-trace may be blanked for a short interval as the frequency

passes through each megacycle (or 0.1 Mc/s). Thus a grid of reference

lines is produced with which the group height at any frequency can be

determined.

An ionosonde embodying these principles is the NBS C-4 lonosonde.

Essentially it consists of a pulse transmitter (of peak power about 10

kW) and a wide-band receiver as shown in the block diagram in figure

3.2. The pulse transmitter is composed of a heterodyning CW oscillator,

sweeping from 31 to 55 Mc/s; a pulsed oscillator on a frequency of 30

Mc/s; a balanced mixer producing the difference frequency of the two

(variable-frequency oscillator VFO and fixed-frequency oscillator FFO)

;

and a power amplifier of the broadband video-coupled type. Note that

the difference frequency varies by a factor of 25 to 1, although the sweeping oscillator variation is less than 2 to 1. The receiver uses the same

heterodyning oscillator as the transmitter in another balanced mixer

which converts the frequency of incoming echoes to 30 Mc/s. This fre- quency is constant throughout the band and is amplified and detected in a straightforward way. Antennas are usually vertical deltas or vertical

rhombics which, although they possess fairly constant and resistive impedance, are not very efficient at the low frequency end of the sweep.

Log periodic antennas, which are better in this respect, are coming into

use. A pulse generator provides pulses for triggering the transmitter and

display, and employs a stable crystal at 1.0 Mc/s together with frequencydividing circuits to obtain frequencies of 3 kc/s from which, by suitable

shaping, the 50 km height markers are obtained. Further division to 1500 c/s and 300 c/s yields 100 km and 500 km markers respectively.

The frequency calibration marks are obtained as the receiver is tuned through the harmonics of the 1.0 Mc/s oscillator. Various types of display are used:

A scan: This is illustrated in figure 3.3a. The time base of the cathode

ray oscilloscope is synchronized with the pulse repetition frequency of the

transmitter, and a stationary pulse pattern is obtained. The time base is applied to the x plates and the receiver output is applied to the y plates,

together with the height marker pips. For photographic recording a

screen is placed in front of the tube. The motion of the film past the slit provides the frequency base. As the frequency increases, the time delay
HEIGHT RECORDERS 105

ou

Figure 3.2. Block diagram of a typical ionosonde.
106 SYNOPTIC STUDIES OF THE IONOSPHERE

G = DIRECT PULSE, A,,A2. A3 = ONCE. TWICE, THRICE

REFLECTED SIGNALS

(a) A-SCAN

Figure 3.3a. Types of ionosonde display—A scan.

OSCILLOSCOPE-^

G A| A2 A3

(b) B-SCAN

Figure 3.3b. Types of ionosonde display—B scan.

generally increases and the echo breaks in the time base move to the

right. The cams controlling the frequency of the transmitter and receiver are suitably shaped so as to give the desired frequency scale on the film

(e.g., linear or logarithmic).

B scan: This is similar to the A scan except that the receiver output

and height pips are applied as blanking pulses to the oscilloscope and the

y plates are grounded. The output is as shown in figure 3.3b.
HEIGHT RECORDERS 107

MAY 3, 1962

POINT BARROW

1345 (150° WMT)

III

ill

MC/S

(C) PANORAMIC DISPLAY

Figure 3.3c. Types of ionosonde display—panoramic.

Panoramic displays: The B scan is used with the time base appUed

to the y plates and a voltage applied to the x plates which is a function

of transmitter frequency. The whole h'—f picture is photographed on a

single frame of 16 mm movie film as illustrated in figure 3.3c. The ionosonde is a versatile equipment and, in one form or another,

is used at every ionospheric observatory. It has the advantage that the

quantity measured (virtual height) does not depend upon the output of

the transmitter or the gain of the receiver, which means that it can be

operated by relatively inexperienced operators. It is programmed, automatically, to make sweeps at certain intervals (e.g., every 15 min). The

duration of a sweep depends on the mechanical design of the ionosonde

but there are practical limits. If the sweep is too fast, the receiver is out

of tune with the echo which has been reflected from the ionosphere.

Sweeps of duration less than about 15 sec suffer from this. On the other

hand, if the sweep takes too long, the ionosphere itself may have changed

appreciably between the beginning and end of the sweep. Furthermore,

the ionosonde may produce excessive interference with other radio

systems.
108 SYNOPTIC STUDIES OF THE IONOSPHERE

3.2.1.2. The Virtual Height-Time Recorder

This is a fixed -frequency device using a B scan display which operates

continuously. Provided that the signal does not penetrate the ionosphere,

this system has the advantage of continuous monitoring of the ionosphere

and is useful in detecting "one-shot" events such as the effect of a solar

flare. It has the added advantage of extreme simplicity.

3.2.2. Absorption Measurements

The ionosonde gives very little information about the D region

because reflections from this region tend to be of the partial type rather

than the refractive type. Also, the lower frequencies are heavily absorbed

in the lower ionosphere because of the high collision frequency there. This absorption is, of course, very important to the radio operator be- cause it sets a lower limit to the power and/or the frequency with which

he can operate. Thus absorption measurements are of practical importance

and, in addition, they give information on the total electron content of

the D region. Some of the methods used will be discussed below. These

methods have been described, in more detail, by Piggott, Beynon, Brown,

and Little [3].

3.2.2.1. The Pulse Reflection Method

This method has been used extensively in England [4] and elsewhere

and involves the measurement of the amplitudes of successive echoes

with an A scan display. The amplitudes are usually read off visually,

either by noting the gain required to bring the tops of the oscilloscope

traces to a fiduciary mark or else by calibrating the face of the oscilloscope.

It is convenient to express the amplitude ratios in terms of an ap- parent reflection coefficient p. This parameter is the ratio of the amplitude

/ of a wave which is reflected once in the ionosphere to the amplitude Fq

which would have been received in the absence of dissipative attenuation

(3.2)

(3.3)
ABSORPTION MEASUREMENTS 109 In practice, the absorption is usually measured in terms of a loss in

decibels, L, where

L= - 20 log p = -8.7 In p. (3.4) In the absence of absorption, the amplitude / of a wave reflected from a group height h' is given by

Ih' = Ioho (3.5)

where 7o is the amplitude which would have been received if reflection had occurred at a standard height Hq. When absorption is present the

amplitudes of the first /i, second and rth order Ir reflections are given

by — pltjhfj — pG, (a)

2hh' (b)

rlrh' -- p'p/-^G, (c)

where pg is the apparent reflection coefficient of the ground and G( = /o^o) may be regarded as a calibration constant. The calibration factor, G, can be found by measuring the amplitudes

of multiple reflected signals when the absorption is low (at night) and

can then be used to measure p when the absorption is high, i.e., when

there is one reflection only.

When G is known, p can be found from the group height and amplitude of the reflected echo.

The chief practical problem in the measurement of absorption by

this technique is that introduced by the continuous fading of the reflected

signal. This question is too complex to be considered here but it requires

that a suitable statistical sample be used to derive a mean amplitude.

For vertical incidence measurements in the HF band, periods between

15 and 20 min are common, and it is desirable to average over such

periods. Of course, if the averaging period is excessive, the absorption

itself may have changed during the interval. The chief disadvantage of this system is that the measurements are tedious to make and/or reduce to L values. Furthermore, inaccuracies

arise because of noise and interference, polarization, pulse dispersion,

partial reflection, and scattering (see ref. [3]).
110 SYNOPTIC STUDIES OF THE IONOSPHERE

3.2.2.2. Continuous-Wave Field-Intensity Recordings

In this method a continuous wave sender is used. A communicationstype receiver is fed by a cahbrated antenna and the output is registered on a pen recorder. The CW recording method of measuring ionospheric absorption

has the advantage of continuous recording, but it suffers from the dis- advantage of not being able to separate the various echoes. The total

field received at any instant is the resultant of different order echoes and

of ordinary and extraordinary waves, all fading independently of each

other. Approximately, the resultant median field intensity is the square

root of the sum of the squares of the median values of all of its components. From a knowledge of the differential absorption of the ordinary

and extraordinary waves, and using the root-sum-square rule, the field intensity of the ordinary wave, first echo, can (in principle) be obtained.

If transmitter and receiver are close together, so that the incidence

is essentially normal, it is possible to calibrate the equipment (roughly)

by assuming that the nighttime signals are not absorbed in the ionosphere.

3.2.2.3. The Riometer Method

The riometer (rio = relative ionospheric opacity) is simply a receiver

that measures the intensity of the random noise which impinges on the

earth from deep space. The use of cosmic radio noise for the measurement

of ionospheric absorption has been developed by Little and his co- workers. The principle is as follows: The radio noise power incident at a point outside the earth's atmosphere from a given direction in space is assumed to be constant with

respect to time. The noise power received on a fixed receiving system at the earth's surface should, therefore, be a function of sidereal time only,

since each day the aerial beam will explore the same strip of sky as the

earth rotates. The transparency of the atmosphere at a particular in- stant of time is, therefore, given by the ratio of the signal strength actually

received to that received at the same sidereal time under conditions of

little ionospheric absorption.

The simplest equipment capable of measuring cosmic noise consists

of a gain stable receiver connected to an antenna (input) and a pen

recorder (output), as illustrated in the block diagram in figure 3.4, to- gether with a noise diode, for calibration purposes, and stabilized power
ABSORPTION MEASUREMENTS 111

rf

switch

Receiver Pen

recorder

Noise

diode

Stabilized

supplies

Figure 3.4. Block diagram of riometer.

(After C. G. Little, 1957, in The Measurement of Ionospheric Absorption, Annals of the IGY, Vol. Ill, Part II, Pergamon Press.)

supplies. The calibration is carried out, automatically, by periodically

disconnecting the antenna and feeding into the receiver, a known quantity

of noise power from the diode.

To understand how the method works, consider an antenna looking

at the sky, the temperature of which is Tg. If the bandwidth of the re- ceiving system is -B, the available power is

Pi = kTsB. (3.7)

If now some absorbing medium (such as the ionosphere) with a power

transmission coefficient a and temperature Ti is inserted over the whole

of the antenna beam, the power received from the sky would be reduced

to ak TsB. The absorbing medium would, however, itself radiate noise in proportion to its temperature and its effectiveness as an absorber. The

antenna would receive an additional signal P2 = k{l — a) TiB from the

absorbing medium.

In the case where the signal is transferred to the receiver via a trans- mission cable, the power transmission coefficient of which is E, the

transmission line itself will act as an attenuator and a generator of radio

noise Pc- The noise reaching the receiver will be given by:

Elak TsB-\-k{l-a) TiB^ -\-il-E)k TeB,

where Tc is the temperature of the transmission line. It is assumed that

the antenna and receiver are both matched to the transmission line, and

that the power transfer from the antenna to the receiver is complete,

apart from the effect of absorption within the transmission line. This received power will add to the noise generated within the
112 SYNOPTIC STUDIES OF THE IONOSPHERE

receiver, which is given by

Pr=(F-l)kTB, (3.8)

where T is the room temperature and F is the noise factor of the receiver.

If the above system receives cosmic radio noise, the output power

Po of the receiver may be written as

where Ps = noise power from the sky = EaTgkB^

Pi = noise power from the ionosphere = — a) TikB,

Ts, Ti = effective temperatures of sky and ionosphere,

Pc = noise power from cable = (1 — J^) TckB,

Pr = noise power from receiver = (F— 1) TkB,

1 = interference.

G = power gain of the receiver. The problem introduced by interference can be partially removed by

recording the minimum signal received while the receiver frequency is swept over a small frequency range (but many bandwidths). Various

other refinements are discussed in reference [3].

It should be realized that the riometer is of use on frequencies above

the penetration frequency only. A typical frequency is about 30 Mc/s.

The disadvantage of such high frequencies is that the ionospheric absorption is low and it is necessary, therefore, to measure small changes in absorption. A riometer can usually measure absorption changes down to about 0.1 dB.

3.2.2.4. Minimum Frequency Observations

In (2.99) it was shown that non-deviative absorption varies in- versely as the square of the wave frequency. Thus, when sounding the

ionosphere with a conventional ionosonde, the minimum frequency observed, /min, is roughly, a function of the ionospheric absorption. The

characteristic /min has been used quite widely as an index of ionospheric

absorption and its use is justified provided that the absorption changes

are large compared with the other variable characteristics of the

ionosphere.

Po = G{P, +Pi+P, +Pr+I) (3.9)
PHASE MEASUREMENTS 113 3.2.3. Phase Measurements

3.2.3.1. Relative Phase Changes

Although it is not possible to determine the absolute phase of a

reflected signal it is possible to measure, accurately, changes in phase.

This can be done by mixing the incoming signal of frequency fe with a

local oscillator signal of frequency fr of about the same amplitude and

differing from it in frequency by a small amount ife—fr)- The phase of

the signal from the reference oscillator must be highly stable or else must be locked to that of the radiated signal. With the advent of portable

stable crystal oscillators and atomic frequency standards the former

alternative is possible. The echo and the reference signal beat together

in the detector stage of the receiver and give a beat signal of frequency

{fe~fr)' This gives a sinusoidal trace on the screen of an oscilloscope

when the output of the receiver is applied to the y plates and a linear time base is applied to the x plates. The movements of the sinusoidal trace depict the varying phase of the echo. Such a method has been

described by Findlay [5]. Suitable modification of this arrangement

enables the phase changes to be tracked electronically and displayed on a pen recorder instead of on photographic paper.

3.2.3.2. Frequency Changes

When the changes of phase with time are slow, the above method is very suitable; on the other hand, if the phase changes rapidly with time,

there is a Doppler change in the received frequency and it is often con- venient to measure frequency changes rather than phase changes. The

technique is essentially the same as that described above; the beat fre- quency signal may be recorded directly on a pen recorder and the fre- quency changes determined by inspection. In a slight modification used

by Ogawa [6] and by Fenwick and Villard [7], the beat frequency is fed to a frequency meter the output of which is recorded on an inked chart. One disadvantage of both the above presentations is that they give

the frequency variation of the composite sky wave. An improvement on

this is the technique developed by Watts and Davies [8] which is of

interest also in that it provides one solution to a data storage problem.

This method involves the spectral analysis of the beat signal. The beat

signal is fed directly to the recording head of a magnetic tape recorder
114 SYNOPTIC STUDIES OF THE IONOSPHERE

the speed of which is 0.02 ips (inches per second). At this speed an 1800-ft

roll of tape can store data continuously for more than one week, at the

end of which the tape is played into an audio spectrum analyzer at a speed of 30 ips, say. This results in a frequency multiplication of 1500

and so converts the beat frequency of a few cycles per second into an

audio tone. A commercial 420 channel analyzer having a total bandwidth

of 10.5 kc/s and a channel bandwidth of 32 c/s is used for analysis; the

output is displayed on a continuously fed facsimile attachment. With

such a system the frequency resolution is about 0.2 c/s and the time reso- lution is less than 1 min. This method of recording is suitable for studying transient phenomena such as the ionospheric effects associated with

solar flare and sudden magnetic commencements. A sample record taken

during a solar flare is shown in figure 3.5.

3.2.4. Angle of Arrival

3.2.4.1. Direction Finding

Ionospheric tilts and irregularities give rise to radio rays which lie outside the great circle path through the transmitter, the receiver, and

the center of the earth. Various techniques have been developed for measuring the azimuthal angles of arrival of signals and an account of

the modern techniques used can be found in reference p].

3.2.4.2. Vertical Angle

There are three principal methods of measuring vertical angle of

arrival: (1) the phase measurement method, (2) the use of "musa" or multi-wnit steerable antenna, and (3) the use of two antennas having

different radiation patterns in the vertical plane.

The most common system is (1) and depends on the fact that when

a radio wave (of wavelength X) from a given direction arrives at two

receiving antennas, separated by a known distance e?, the phase angle 0

between the induced voltages is

2,Tr d

(f) = cos A cost/' (3.10) X where A is the vertical angle measured from the horizontal and }f/ is the
ANGLE OF ARRIVAL 115
116 SYNOPTIC STUDIES OF THE IONOSPHERE

azimuthal angle, measured from a line joining the centers of the two

antennas. In practice the antennas are oriented with their centers in the great

circle plane passing through the transmitter and receiver so that \f/^0.

For accurate measurements it is necessary to correct for the variation of xf/. The musa system for measuring a vertical angle consists of an antenna

array having a very sharp lobe which can be steered up and down in the

vertical plane. The vertical angle is determined by the position of the

lobe at which the received signal is a maximum.

In the third system the antennas may be a pair of identical ones at

different heights above ground or one can be a horizontal and the other a

vertical. In either case the antenna patterns must be known. One useful application of this method is in normal incidence sounding where dipoles are located at such heights as to give (1) a maximum, (2) a null in the

zenith direction. This arrangement enables a determination to be made

of whether echoes are returned from overhead or scattered obliquely.

3.2.5. Rockets and Satellites

In recent years it has become possible to explore the ionosphere by

sending up radio equipment in rockets and satellites. In particular, elec- tron density profiles have been deduced from measurements in rockets of

the differential absorption [10] between ordinary and extraordinary waves. In 1961 an h't recorder was flown in a rocket to study the topside

of the F region [11] and more recently an ionosonde has been flown in a

satellite [12] to study the same region.

By moving the observing stations to artificial satellites three important advantages are gained:

1. Probes can be used to measure some ionospheric parameters in

situ^ thereby checking previous radio measurements and adding new ones.

2. Radio soundings can be obtained from above the level of maximum

density, thereby extending our knowledge greatly.

3. Geographic scanning of these parameters can be achieved to an

extent and degree of detail never possible with scattered ground stations.
lONOGRAMS AND THEIR INTERPRETATION 117 3.3. THE QUIET IONOSPHERE

3.3.1. Purpose

The purpose of this section is to describe the principal observational

features of the ionosphere. These features wdll iaclude the interpretation

of ionograms

h'{f) curves—and the geographical and temporal variations in the electron density distributions.

3.3.2. Ionograms and Their Interpretation

An ionogram is the photographic output of an ionosonde. The simplest

ionogram (nighttime) is of the type showTi in figure 3.6. It will be seen

that the group height h' increases with frequency until penetration occurs and that there are two distinct traces. The trace having the lower penetration frequency /oF is the ordinary wave trace and the other having the

higher penetration frequency fxF is due to the extraordinary wave. The

penetration frequencies are frequently referred to as the critical frequenFORT BELVOIR

APRIL 18, 1962 0115 LST

2 3 4 5 Mc/s

Figure 3.6. Ionogram on a quiet night in middle latitudes.
118 SYNOPTIC STUDIES OF THE IONOSPHERE

FORT BELVOIR

JUNE 3, 1962 1415 (75° WMT)

foF2 fxF2

E

MC/S

Figure 3.7. lonogram on a quiet summer day in middle latitudes.

cies. An ionogram taken in middle latitudes during a summer day (fig. 3.7) indicates reflections from the Fi, and F2 layers for both ordinary

and extraordinary waves. Note that just above the critical frequencies of

the E and Fi layers the group height decreases with increase of frequency.

This arises because the retardation below the level of reflection is decreasing with frequency more rapidly than the retardation near reflection is increasing with frequency. The minimum heights of the ordinary wave

traces are called the minimum virtual heights of the respective layers

[1]. Figure 3.8 shows an example of a high-latitude ionogram which has an additional z trace which can occur at high values of magnetic dip.

Notice also the trace near the 120 km level marked Eg. This is believed

to be a reflection from a thin layer, at about the same height as the normal

E layer, which varies in an unpredictable manner and, hence, is called sporadic E. Sometimes this layer is sufficiently thick to give rise to well- defined critical frequencies (foEg and fxEs).

The relationship between the z, o, and x critical frequencies can

be obtained from the fact that they are reflected at the levels X= 1+ Y,

X=l, and X=l— y, respectively. If /at max is the value of the plasma
lONOGRAMS AND THEIR INTERPRETATION 119

UU>(

Figure 3.8. High-latitude ionogram. Baker Lake, ApHl 22, 1949, 1530 90° WMT.

(By permission of the Chief Superintendent, DRTE, Ottawa, Canada.)
120 SYNOPTIC STUDIES OF THE IONOSPHERE

frequency at the peak of the layer, we have:

max (a)

/ max (b) (3.11)

max (c)

from which we get

(a)

(3.12)

and (b)

Equation (3.12a) can be solved for fx in terms of /o and/n. If/o and fx are much larger thaufn, however, so that fx-\-fQ^2fx we obtain

We see that, for a given/// (given altitude and geographic location), the

difference between fx and fz is independent of critical frequency and the

difference between fx and /o is approximately so. Hence, from measure- ments of the separations of the critical frequencies of a given layer we

can, in principle, determine the magnetic field strength (from fn) at the

height of the layer peak. The fx—fa separation as a function of frequency

is shown in figure 3.9. Most ionosondes have a lower frequency limit of about 1.0 Mc/s or

1.5 Mc/s for practical reasons such as high daytime absorption, broadcast interference, antenna limitations, and lack of height resolution (at

the lowest frequencies the radio frequency period is comparable to that

of the pulse duration; for instance, a SO-^tsec pulse would contain only

five cycles at 100 kc/s). Low and medium frequency ionograms have

been made by several workers, notably by Watts [13, 14], at the CRPL.

An example of a nighttime low -frequency ionogram is shown in figure 3.10, which shows reflections from heights of about 90 to 100,

120 to 150, and 220 to 230 km. The layers, or ledges, which produce

these reflections will be referred to as Eg, and F respectively. The

reason for calling the ^^150 km" echo E rests on the observed continuity

(3.13)
lONOGRAMS AND THEIR INTERPRETATION 121

0-51-

1 2 3 4 5 6 7 8

fo/fH

Figure 3.9. Critical frequency separation between ordinary and extraordinary traces.

(After J. W. Wright, R. W. Knecht, and K. Davies, 1957, Annals of the IGY, Vol. Ill, Part I, Pergamon Press.)

BOULDER, COLORADO

DECEMBER 2, 1959 2250 (105^ WMT)

0.1 0.5 1.0 1.5 2.0 Mc/s

Figure 3.10. Low-frequency ionogram.

with the daytime E echo over the sunrise period. The Es layer appears

to be patchy (transparent) and must be fairly thin because no group

retardation is evident at its upper frequency limit. Note that the critical frequency of the extraordinary Z trace is less than that of the ordinary,

which is to be expected on the theory given in sec. 2.3.3.2. lonograms vary in appearance depending upon the geographic

location of the station. A great many more ionograms are available for study in the IGY Atlas of lonograms [15] and in the Annals of the

IGY [2].
Figure 3.11a. Sample f plot for Adak, Alaska—summer.

r
lONOGRAMS AND THEIR INTERPRETATION 123

Figure 3.11b. Sample f plot for Adak, Alaska—winter.
124 SYNOPTIC STUDIES OF THE IONOSPHERE

Ionospheric data are available, in several different forms, in one of

the four World Data Centers. These forms may be the original ionograms

or scaled hourly values of the various parameters (e.g., critical frequencies

and minimum virtual heights) or simply monthly median values of these

parameters as published in the CRPL F Series, Part A [16]. The latter publication contains monthly medians of ionospheric parameters from

about 80 stations in tabular and graphical form. Another form of presentation (due to J. H. Meek) is the / plot. The / plot is a daily graph of the

frequency characteristics of the ionograms as a function of time, using

internationally agreed conventions for interstation comparison. It was

originally developed to enable the complicated and rapidly changing

ionograms from high latitudes to be reduced with the minimum of inter- pretation by the scaling individual. It was also introduced to obviate the

necessity of repeated plotting from tabulated data. Its use has now be- come worldwide. Some sample / plots are shown in figure 3.11.

3.3.3. Electron Density Profiles

3.3.3.1. Real Height Analysis

Conventional ionograms contain a direct measure of the electron

densities of the ionosphere within a range determined by the lowest and

highest radio frequencies employed in the sounding. The total retardation

depends upon the unknown electron density profile. However, it is not

immediately obvious how the actual height of reflection of each frequency

is to be determined, for the reason that the apparent (virtual) height

depends in an involved way on the group retardation imposed on the

probing pulses at each point below the level of reflection. The group height h' is given by the integral of the group refractive

index n' along the ray path. In the case of vertical propagation this is given by

h'^l f,'dh= n' — d4> (3.14)

where K is the real height of reflection and 0 is an arbitrary monotonic

function of the electron density distribution; for instance, in Budden's

method [17] </> is /at, whereas in King's method [18] 0 is logf^- It is not

possible to solve this integral analytically, except under certain limiting

conditions (transverse and longitudinal). However, a solution can be
ELECTRON DENSITY PROFILES 125 found by dividing the range of integration into n small intervals within

each of which dh/d<j> is assumed constant. Equation (3.14) can then be

replaced by

« /dh\ /"^^ ^'=Z(t7) / (3.15)

Since the integrals are now dependent on n' and <f> and the interval width,

they may be evaluated once and for all as a set of coefficients. Equation

(3.15) then represents a set of linear equations in dh/d<^. By dividing the

observed h'f curve into intervals of equal ranges of 0, this system of

equations can, in principle, be solved and the real height intervals

obtained. In the above theory, it was assumed that </> increased monotonically

with height. It does not give us any information about a "valley" which

may exist in the profile between the E and Flayers, say. Some information on the existence of a valley can be inferred from the extraordinary wave

trace [19, 20]. Another limitation on the experimental data is that con- ventional ionograms give no information on frequencies below about 1.0 Mc/s. Once again the extraordinary trace can sometimes be used to give

information concerning unobserved ionization [19, 21]. A good review

of this subject has been made by Thomas [22].

3.3.3.2. Diurnal Variations

Sample day and night N(h) profiles for middle latitudes are shown

in figures 3.12a and b respectively. Large diurnal changes occur particularly in the lower ionosphere. The daytime structure may be thought of

as a single bank of electrons beginning around 100 km and having a peak

density around 300 km. The various lower "layers" E and Fi may be

only inflections, or ledges, in the electron distribution.

At night, all vestige of the F^ layer disappears and the E-layer

densities drop by a factor of 100 or so, thus producing a simpler structure. The electron density in the D region is not directly observable by the

conventional ionosonde and probably falls from about 10^ per cm^ at 80

km at noon to less than 10^ per cm^ at night. Some tentative N{h) profiles

(obtained from cross modulation experiments) for the D region are shown

in figure 3.13. Additional features of the diurnal variation in ionospheric structure

are illustrated in figure 3.14. Note that the E layer appears promptly at
126 SYNOPTIC STUDIES OF THE IONOSPHERE

J L ELECTRON DENSITY (ELECTRONS/cm^

)

Figure 3.12. Sample electron density profiles at White Sands, New Mexico, April 1961.

(a) Noon; (b) midnight. (After R. W. Knecht, unpublished.)

km

65

07

16 -08 / ^

08-09^ 09-10/^ ^ 12-

-11-12

II, 3,13-14

--14-15 5-16

/ ////

NUMBERS

ARE TIME

"ANDARD

" ON GRAP

S OF DA

riME 15°

H

Y

E) J

50 100 200 500 1000 ELECTRON DENSITY Cm'^ —2000 5000

Figure 3.13. Yi-region profiles. (By permission of the Norwegian Defense Research Establishment.)
!

ELECTRON DENSITY PROFILES 127

AVERAGE QUIET-DAY PROFILES MARCH 1959

0 4 8 12

1 I I I I I I xIQS ELECTRONS /cm3

Figure 3.14. Diurnal changes in ionospheric profiles.

(After J. W. Wright, unpublished.) sunrise and disappears promptly at sunset (except for the residual nighttime ionization) . The electron densities are greater at all heights by day

than by night except at Huancayo, where the density continues to in- crease for a few hours after sunset. There is a general tendency for the height of the F2 peak, hmfi, to

fall at dawn, and then to rise during the afternoon or evening. In low

latitudes, hm /2 reaches a very high level by about 1900 and then falls such that at midnight it is about 100 km lower than at noon. In middle

latitudes, hmF2 rises after sunset and is 50 to 100 km higher at midnight

than at noon. This height variation is especially noticeable at Huancayo

where at 1900 to 2000 the F region may rise to very great heights indeed.
128 SYNOPTIC STUDIES OF THE IONOSPHERE

At the highest latitudes, the ionosphere may be in continuous sunlight or darkness for long periods, depending upon the season. In these

circumstances the ionosphere will be typical of daylight or nighttime

conditions, respectively. A moderate diurnal variation may be due to small variations of the solar zenith angle, but a diurnal variation is still detectable at the south pole, where the solar zenith angle is diurnally

MIDNIGHT MEAN N(h) PROFILES

800

600

400 h

200

0

800

E 600

T m I I I

'59

\

^ 400- ) X 200 h

0

800

600

400

200

0

'59

\

\

\

1 1 1

1 1 1

N^EWFOUNDLAND

\

\

\

MAY JULY SEPT NOV JAN

'59 '59 '59 '60

MAR

'59

MAY JULY SEPT NOV JAN

'59 '59 '59 '60

\' ' ' GRAND BAHAMA

MAR

'59

I I I I

MAY JULY SEPT NOV JAN

0 4 8 12

1 I I I I I I xlO^ ELECTRONS /cm3

Figure 3.15. Seasonal changes in midnight N(h) profiles.

(After J. W. Wright, unpublished.)
ELECTRON DENSITY PROFILES 129 constant [24], confirming that, at high latitudes at least, other factors besides solar illumination play a role in determining the diurnal variations

of the ionosphere. The topside profiles, represented by the broken lines,

figures 3.14 through 3.17, are extrapolated on the basis of a Chapman

type distribution (1.32).

NOON MEAN N(h) PROFILES

xlO^ ELECTRONS /cm3

Figure 3.16. Seasonal changes in noon N(h) profiles.

(After J. W. Wright, unpublished.)
130 SYNOPTIC STUDIES OF THE IONOSPHERE

3.3.3.3. Seasonal Variations

The seasonal variation in N{h) profiles is illustrated in figures 3.15

and 3.16 for midnight and noon conditions respectively. The nighttime F

layer tends to be at higher heights in summer than in winter, the tendency

being accentuated in lower latitudes. The nighttime F layer tends to be

thicker when higher. In general, the maximum electron density and the

total electron content of the nighttime F region are greater in summer

than in winter. Turning to the noon profiles, the most distinctive feature

is that the peak density is considerably larger in winter than in summer;

this is called the seasonal anomaly. It is more evident at high latitudes

than at low latitudes. In the summer months, in middle latitudes, the F

layer bifurcates into the Fi and F2 layers. Under these conditions the F2

peak density is fairly small and is located at a relatively great altitude. The Fi layer is not so much a distinct layer but rather a minor inflection

in the profile at about 200 to 220 km.

3.3.3.4. Solar Cycle Variations

In sec. 1.7.3 we discussed the long-term variation in sunspot activity.

This variation has a profound effect on the noon electron distribution, as can be seen from figure 3.17. The graphs are arranged to show increments

in ionization corresponding to increments of 100 in sunspot number. The

electron densities above the peak are extrapolated. A striking feature of

this variation is that the most significant increases in electron density occur at successively higher heights.

3.3.3.5. Geographical Variation

The expense of reducing all ionograms to N{h) profiles has meant

that the worldwide distribution is not yet available. Some idea of the

latitudinal variations can be obtained from the iso-ionic contours obtained

at CRPL [24], examples of which are shown in figure 3.18. Profile data

taken near the 75° west geographic meridian were used and the iso-ionic contours are for fixed values of plasma frequency. The height of the F2

maximum is shown by a dotted line. The following features are important:

(1) The F layer is much thicker near the magnetic equator than

elsewhere.
ELECTRON DENSITY PROFILES 131

in

UJ

Figure 3.17. Solar cycle changes in noon N(h) profiles.

(After J. W. Wright, 1962, Dependence of the ionospheric F region on the solar cycle. Nature 194, 461.)

(2) There are regions of high electron concentration at geomagnetic

latitudes of about d=20° during the afternoon and early evening. This

distortion of the ionosphere is of importance in transequatorial radio

propagation, and will be considered later.
SYNOPTIC STUDIES OF THE IONOSPHERE

Figure 3.18. Ionospheric sections along the 75th geographical meridian.

(After J. W. Wright, 1959, Note on quiet-day vertical cross sections of the ionosphere along 75° west geographic meridian, J. Geophys. Res. 64, 1631.)
ELECTRON DENSITY PROFILES 133

Figure 3.18—Continued. Ionospheric sections along the 75th geographic meridian.
134 SYNOPTIC STUDIES OF THE IONOSPHERE

3.3.4. Model Layers

For many purposes, particularly computational purposes, it is convenient to approximate the N{h) profile by analytical expressions which

are amenable to integration, differentiation, etc. Various models can be

used as approximations to the Chapman layer; for instance, near the peak

the distribution is approximately parabolic, whereas high up in the layer

the distribution is roughly exponential. Over short ranges of height it is often sufficiently accurate to assume a linear variation of N with h. Some

relevant formulas derived from certain models are given below.

3.3.4.1. Chapman Layer

From (1.32) we have

A^= A^o exp J { 1 — z— sec X exp ( — z) )

.

The total non-deviative absorption suffered by a wave of angular

frequency co in one complete vertical transit through the layer (in which

oj^^v^) is given by

L= Kds = \/27rexp (1)-— -. (3.16)

^_co eomc (coitcoL)^

Here Nq is the electron concentration at the level of maximum electron

production when x = 0 (i.e., at z=0), vq is the collision frequency at the same height, and H is the constant scale height. It is assumed that the

propagation conditions are quasi-longitudinal, col being the gyrofrequency

corresponding to the component of the earth's magnetic field in the direc- tion of phase propagation.

3.3.4.2. Parabolic Layer

When X and z are very small (1.32) reduces to N=No exp § I izM = iVo jl - Q)] = iV„ jl - (^yj, (3.17)

which is the equation of a parabola with semithickness (i.e., distance
MODEL LAYERS 135 from base to level of maximum density) of jm = 2H:

This can be written in terms of plasma frequency:

f%-fl\i-{^\ (3.19)

where fp is the penetration frequency of the layer. In the absence of an imposed magnetic field, the refractive index

within the layer is given by

f)H'-(f(-(0)l'

The group height for reflection within the layer is given by

h'= f m' dh = K-y^+hy„^ FrJ' (3.21) JP JP J and the phase height for the same conditions is

h, = f

M dA = fto-iy„-ir"(y - f)

In J^. (3.22)

Note that h' = ho for a frequency 0.834/p. This shows that the height of

the maximum electron density is equal to the group height on a frequency

of 0.834 /p.

For transmission through a layer, the contributions to the group and

phase heights are

h' = h-y„+{-y^lJ-^' , (3.23) JP J JP
136 SYNOPTIC STUDIES OF THE IONOSPHERE

3.3.4.3. Linear Layer

If TV increases linearly with height h from a base at /^o above ground,

since TV is proportional to/jj, we have

f^ = aih-ho), (3.25)

where a is the constant height gradient of f^. The virtual and phase

heights are given by

h' = ho~^-f (3.26) a K= h,+^f. (3.27)

3.3.4.4. Exponential Layer

The equation for this layer can be written:

/^ = F^exp(az) (3.28)

where z= {h — hR)/H and F is the plasma frequency at the level Hr. Note

that, for propagation in the medium, the wave frequency must be greater

than F. The group and phase heights are given by

and

3.3.5. Critical Frequency Variations

3.3.5.1. General Features

For many purposes, including radio communication, the most important characteristics of the ionospheric layers are their critical fre-
CRITICAL FREQUENCY VARIATIONS 137 quencies and virtual heights. In this section we shall consider the temporal

and geographical variations in critical frequencies. In figure 3.19 are shown the monthly mean noon critical frequencies

of the E, Fi, and F2 layers as observed at Slough, England, over a 30-

Figure 3.19. Monthly mean noon critical frequencies at Slough, 1932-1962.

(Reproduction is by permission of the Controller of Her Brittannic Majesty's Stationery

Office and is by arrangement with the Director of Radio Research.)
138 SYNOPTIC STUDIES OF THE IONOSPHERE

yr period. These graphs bring out some important features, namely:

(a) The seasonal variation of foE and /oFi are in phase with solar zenith angle % whereas /0F2 is in antiphase (winter anomaly).

(b) The Fi layer disappears in some winters.

(c) There is a marked increase in the critical frequencies in sympathy with the 11 -yr sunspot cycle.

3.3.5.2. The E Layer

To a first approximation the critical frequencies of the E layer are given by

/oE=0.9[(180+1.44/?) cosx?-^ (3.31)

where R is the Ziirich sunspot number. The exponent may vary between

0.1 and 0.4 for the diurnal variation but (3.31) is a reasonably good fit for seasonal and diurnal variations. Values offoE determined from (3.31) are usually within 0.2 Mc/s of the observed values. During the night /o-E reaches a minimum of about 0.5 Mc/s at sunspot maximum or about

foE-1958 FORT BELVOIR

LST

Figure 3.20. Diurnal and seasonal variations of /qE at Fort Belvoir, 1958.

Contours in Mc/s. (After R. W. Knecht, unpublished.)
CRITICAL FREQUENCY VARIATIONS 139

foE - MARCH, 1958

00 04 08 12 16 20 24

foE - JUNE. 1958

X 80 ' 2'8l '

'

'

/^GROUND

DAY- NIGHT

LINE

I I I I I I I 00 04 24

Figure 3.21. Maps of foE, March, June 1958.

(After R. W. Knecht, unpublished.)
140 SYNOPTIC STUDIES OF THE IONOSPHERE

0.25 Mc/s at sunspot minimum. The temporal variation of /o-E during

1958 at Fort Belvoir is shown in figure 3.20. The local time variations of

foE with latitude for March and June 1958 are shown in figure 3.21.

3.3.5.3. The Fi Layer

The Fi layer is observed only during the day; it is more pronounced

during the summer than during the winter, and at high sunspot number,

and during ionosphere storms, i.e., when/oF2 is low.

To a first approximation:

/oFi= (4.3+O.Oli?) cosO-2 X. (3.32)

Here again the exponent varies from place to place and with season. For

example, at Fort Belvoir it is about 0.18 in summer and about 0.25 in winter. Furthermore, it appears to be lower at sunspot minimum than at sunspot maximum. The diurnal and seasonal variations in JqFi at Fort

Belvoir are shown in figure 3.22 and the latitude variation is illustrated in figure 3.23.

fo E-1958 FORT BELVOIR

Figure 3.22. Diurnal and seasonal variations of /oFi at Fort Belvoir, 1956.

(After R. W. Knecht, unpublished.)
CRITICAL FREQUENCY VARIATIONS 141

foFi - JUNE, 1954

X 80

40

§ 60

H

20

b 0

§ 20

40 ^ 60

CO 80

_! 1

1

!

1

1

1

- ^

\

\

\

1

1

1

! 1 1 H 1 1

1

1

/

/ 1

1

1

1

1

1

1

1

/ // / I

/ground

Aday-night

/ LINE -

^

, 1 , 1 , i , 1 , 1 ~

00 04 08 12 16 20 24

foFi - JUNE, 1958

Figure 3.23. Maps of /qFu

(After R. W. Knecht, unpublished.)
142 SYNOPTIC STUDIES OF THE IONOSPHERE

3.3.5.4. The F2 Layer

The F2 layer is by far the most important layer from the point of

view of HF radio communications and it is also the most variable. Unlike the E and Fi layers, the F2 does not follow a cos x law either diurnally or seasonally. This is illustrated in the / plots of figure 3.11 for Adak.

Although during January the sun is at a low elevation (cos x = 0.291)

compared with June (cos x = 0.877), the January noon/oF2 is more than

twice the summer value. This implies a peak electron density ratio of more than four to one. Notice that this "winter anomaly" occurs in the

daytime only. In summer the /0F2 shows remarkably little diurnal variation. Note also the presence of a consistent Fi layer during the summer

day and its complete absence in the winter day.

foF2 AT RASSH 50 JUNE 1200 HOURS GMT

60° 120° 180' 120° 60° 0° EAST I WEST WEST I EASl LONGITUDE Figure 3.24a. World map of /0F2, June.

(After D. H. Zacharisen, 1959, World maps of F2 critical frequencies and maximum usable frequency

factors, NBS Tech. Note 2 (Apr. 1959), and NBS Tech. Note 2/2 (Oct. 1960).
CRITICAL FREQUENCY VARIATIONS 143 The geographical distribution of /0F2 is characterized by marked

geomagnetic control which is revealed by the worldwide maps shown in figures 3.24a and b [25]. These maps are constructed from data for many years which are reduced to a mean sunspot number of 50. The

most distinctive features on these maps are the two regions of high /0F2

lying around =b20° dip latitude. These "highs" lag behind the subsolar

point but move around with the sun. Because of the geomagnetic control,

the critical frequencies of the F2 layer exhibit a marked longitudinal effect. The '"highs" move not only from east to west but also vary in latitude,

tending to remain at constant dip angles.

Turning to the solar cycle variation of/0F2, in figure 3.25 are plotted

the 12 -month running average values of noon /0F2 at Fort Belvoir, Va.,

as a function of the 12 -month running average R of R (Ziirich relative

sunspot number). (Note that the 12 -month running average for a given

Figure 3.24b. World map of /0F2, January.

(After D. H. Zacharisen, 1959, World maps of F2 critical frequencies and maximum usable frequency

factors. NBS Tech. Note 2 (Apr. 1959), and NBS Tech. Note 2/2 (Oct. I960).)
144 SYNOPTIC STUDIES OF THE IONOSPHERE

month is the mean for the preceding 6 months and the succeeding 6

months.) The corresponding data for foE and for/oFi are shown for completeness. If a straightedge is ahned along the plotted data, it can be seen

that, for sunspot numbers between 0 and about 150, the relationship

between /0F2 and R is approximately linear. For values of R greater than

about 150 there appears to be a certain amount of "flattening" of the curve which has to be taken into account when using sunspot numbers

to predict critical frequencies.

3.3.6. Variations in Ionospheric Absorption

3.3.6.1. introductory Remarks

To a first approximation the variations in the ionospheric absorption

of radio waves represent the variations of electron density in the D region.

13

'2

II

109

8 Mc/s 7

6

54

3

1 1 1 1 1 1 1 -:IISS}cVCLE,iuUL 44-

1 1 APRII F,A)

i

_ i!lia?cfcf'IJ!'l CYCLE ,9 (APRIL 54-

APR L 61)

<->*

t »*

*

J

..•

*

1 1

1

1

1 1 1 1 1 1 0 20 40 60 80 100 120 140 160 180 200 SUNSPOT NO.

Figure 3.25. Variation of noon critical frequencies (foE, foFi, and

foFi) with sunspot number at Fort Belvoir.

(After R. W. Knecht, unpublished.)
VARIATIONS IN IONOSPHERIC ABSORPTION 145 This is particularly the case for waves reflected obliquely from the F2

layer for which the absorption near the top of the trajectory is small. For waves reflected from the E layer with essentially vertical propagation,

the absorption near the level of reflection may be comparable with that

suffered lower down.

The most extensive series of absorption measurements in existence

are those made at the Radio Research Station, Slough, England, and

which have been discussed by Appleton and Piggott [4]. These particular

measurements were made using the pulse technique with normal in- cidence. Absorption measurements using the CW technique have been

made at CRPL [26]. In the analyses of these data attempts have been

made to separate out the non-deviative and the deviative types of absorption, or the D- and £^-region absorptions, with only limited success. The results discussed below are based on the assumption that the absorption is of the non-deviative type.

3.3.6.2. Frequency Dependence of Absorption

It was shown earlier (sec. 2.3.3.4) that the non-deviative absorption

L taking place in a region where v'^<K<ji'^ is given

where the + and — signs refer to the ordinary and extraordinary waves

respectively, Jh is the gyrofrequency, and ^ is a constant depending,

however, on the electron density and collision frequency in the D region.

Hence a plot of versus frequency should result in a straight line with slope and intercept —Jh on the frequency axis. This law has

been verified, under certain specific conditions, by Appleton and Piggott

[4], but the law does not appear to hold under all conditions [27] because

of the influence of deviative absorption and absorption at levels where v and CO are comparable.

The variation of ordinary wave absorption with frequency is shown

in figure 3.26. From this we see the overall decrease of L with frequency.

Superimposed on the general trend are two departures due to increased

deviative absorption in the neighborhood of the critical frequencies of the

E and Fi layers. When the frequency of the exploring wave is near a

critical frequency, the wave spends a relatively long time near the level where /x is small and, consequently, is heavily absorbed. In order to study
146 SYNOPTIC STUDIES OF THE IONOSPHERE

T lo

c_Q.

fD^ 0-8

1 0-6

f

0-2

o

o

o

0 ^

o V

t

X £S ^ 1 ECHO TYPE:-

1

1

X )

-1

f-\ O I 2 3 4 5 6 Mc/s

(THEORETICAL) FREOUENCY

JULY II, 1950

Figure 3.26. Variation of absorption with wave frequency (vertical propagation.)

(From E. V. Appleton and W. R. Piggott, 1954, Ionospheric absorption measurements during a sunspot

cycle, J. Atmospheric and Terrest. Phys. 5, 141.)

ol III \ \ 1 I i \ I I \ U

1935 3^ 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Figure 3.27. Noon absorption on 4 Mc/s (Slough). vFrom E. V. Appleton and W. R. Piggott, 1954, Ionospheric absorption measurements during a sunspot

cycle, J. Atmospheric and Terrest. Phys. 5, 141.)
VARIATIONS IN IONOSPHERIC ABSORPTION 147 the D-region absorption, it is necessary first to remove from the total absorption that due to the upper layers. To a first approximation this can be done by taking a parabolic model of electron density as the E

layer and an exponential height variation of collision frequency [28].

The total ordinary wave absorption is expressed in the form

^ = 77^^+^*(/»^//)' (3.34)

where 0 represents some function of the ratio (/qjB//), and fz is the

longitudinal gyrofrequency.

The quantity A is the D-region absorption on an "effective" fre- quency f+fh' With oblique propagation the refractive index never falls to near zero (Snell's law) and the last term in 3.34 is then generally small.

3.3.6.3. Solar Cycle Control

The ionospheric absorption, on 4 Mc/s, measured at Slough over the

period 1935 to 1952 (fig. 3.27) exhibits a marked 11-yr solar cycle variation. The values plotted in figure 3.27 indicate a factor of about 2 between

sunspot minimum and maximum. The dependence of absorption on sunspot number is roughly linear, that is, of the form

L = a{\+hR). (3.35)

Although the value of h appears to vary from one location to another,

the best experimental value seems to be about 0.004.

3.3.6.4. Diurnal Variations

For transmission through a Chapman-type layer which is situated

at a level of low pressure, so that v~ is very much less than (oozbcox)", the

dependence of absorption L on solar zenith angle x is given by

L=C cos3/2^, (3.36)

where C depends on the wave frequency, the peak electron density, and

the collision frequency (see (3.16)).

Although (3.36) has been verified by Best and Ratcliffe [29] in

I
148 SYNOPTIC STUDIES OF THE IONOSPHERE

middle latitudes, a much better fit to the experimental data is given by

L=C cos' (3.37)

where C depends on season, magnetic disturbance, etc., and where in middle latitudes the exponent n lies between 0.7 and 1.0. For large values

of x(>80° say) the cosine function should be replaced by the inverse of

the Chapman function Ch{x, x) —see (1.42) —but for most practical

purposes this is unimportant. From (3.37) we have

log L = log C+n log cos x- (3.38)

The slope and intercept of this line give the values of n and log C

respectively. In table 3.1 are listed some mean values of n for various locations.

It will be seen that n falls sharply in high latitudes. While there is some

evidence for a decrease in n in low latitudes, this cannot be considered

conclusive.

Although (3.37) holds reasonably well around midday, it often

breaks down near sunrise and sunset and so an alternative expression was

developed at the CRPL, namely.

L = A-\-B cos Xi (3.39)

which represents the diurnal variation somewhat more closely than (3.37)

.

Some theoretical justification for including the term A is provided by

photodetachment processes (see fig. 1.4, 2 = 4). At first sight it might

Table 3.1. Solar control of ionospheric absorption L = C cos"x

Location Geographic

latitude" lbadan (Nigeria)

Ahmedabad (India) Delhi (India)

Sydney (Australia)

Tokyo (Japan)

Washington, D.C. (U.S.A.)

Genoa (Italy) Freiburg (Germany)

Slough (England)

Prince Rupert (Canada)

Churchill (Canada)

Baker Lake (Canada)

Resolute Bay (Canada)

7 2328 -34

35

39

4548

5254

5964

75

0.63

0.73

0.62 0.83

0.87

0.83 0.97

0.63 0.75

0.50

0.27

0.18

0.07
VARIATIONS IN IONOSPHERIC ABSORPTION 149

60

40-

L= 21 + 24 COSX

CHURCHILL

JUNE 1956

I 'I 'I I

I I I I 1 I

40 COS^'x

L

= 30 + 13 COS X -—

0/ \ 0

> / 0 1

1

1

1 1 1 1 1

BAKER LAKE

JULY 1957

1 1 1 1 1 1 1 1 1 1 1 1 1 1 24 00 90° IHT

24

Figure 3.28. Comparison between observed absorption and the formulas L = C cos"x cind L =A-\-B COSX.

appear that (3.37) and (3.39) would give very different variations but,

as illustrated in figure 3.28, the differences are, generally, smaller than

the scatter in the data. The sensitivity to solar control is determined by

the value of B which falls off in high latitudes [30]. The empirical factor K used at the CRPL is iC= 0.142 +0.858 cos x- (3.40)

To get the total absorption, K has to be multiplied by other factors representing the seasonal, sunspot, and geometrical (path) variations.

3.3.6.5. Seasonal Variations

If monthly mean noon values of L are plotted against cos % it is found that whereas the summer (and equinox) values tend to obey a

linear law, the winter months exhibit unexpectedly high absorption,

which is known as the "winter anomaly." The increased absorption does not occur uniformly over all days, but appears in the form of high absorption on certain groups of days. It appears primarily to be a middle

latitude effect since it vanishes in polar regions where, in winter, the D

region is in prolonged periods of darkness [30]. From a comparison

between Europe and America, or America and Western Russia, Thomas
150 SYNOPTIC STUDIES OF THE IONOSPHERE

[31] has shown that days of enhanced anomalous absorption in one sector correspond to days of reduced anomalous absorption in the other. Days

of anomalous absorption are also associated with reflections from the D

region [32]. Fortunately, the winter anomaly is not a serious factor from

the point of view of radio communications because the critical frequencies

of the F2 layer are also higher in winter than in summer, so that higher

frequencies can be used. The decrease of absorption due to the use of the

higher frequency more than compensates for the higher absorption on a

fixed frequency so that, in general, radio communications are better on

winter days than on summer days.

3.3.7. Sporadic E

In addition to the regular layers of the ionosphere there are several of transient or irregular nature. The most important of these is the

6poradic-£^ layer, often designated as Eg. Some examples of sporadic-E

reflections on standard ionograms are shown in figure 3.29. It will be seen that the maximum frequency returned from the layer can be much

greater than that from the normal E layer and, indeed, from any of the

normal layers. Sometimes the Eg traces show retardation near the maximum frequency, indicating a relatively thick layer with a well-defined

maximum of electron density. Under other conditions the echoes exhibit no retardation, suggesting that the layer is extremely thin or else due to a sharp change in electron density gradient. On some occasions the Es

layer is opaque and blankets the upper layers; on other occasions the

upper layers can be seen through the Eg, which suggests that the Eg is patchy and that the radio waves are penetrating through the gaps. Sometimes magneto-ionic splitting is evident; at other times there is none.

Sporadic--E echoes can occur over a range of heights from about 90

to 120 km or more, and evidence has been advanced by Helliwell for preferred heights [33]. There is some evidence also for believing that one

type of Eg is due to ionization by meteors. It is almost certain that several

different physical phenomena are lumped together under the general

heading of sporadic E. For the scaling of Eg characteristics see reference

[1].

Because of its variable nature, sporadic E has been studied largely

by statistical means [34], usually by computing the fraction of time that

the maximum frequency fEg exceeds some reference value. Some results obtained in this way are shown in figure 3.30. Close to the equator. Eg is essentially a daytime phenomenon with little seasonal variation. On the
SPORADIC E 151

^ 'I ^mm i.iuriMHni£iBfiii mm

ir^ if'^ - r If * ' tmmtf Hiiittiiifiyyin m m ia «»iP'^niiii:ig{iD9iH

ill ' 111! --mm ffliWiHMiiiHiii^i'ii iiiini

if \ m mmmmmwimmmm mm

lit l»i3iH«iK«S^'riHlllll'lili iini

ij

;

' i mmBmmmm.inm\ m1 1 mm m^^sz^^mmmmmmm

-1 , I 4

' ' '

1 m 1 F —r-t- "'1 .'i^ (c)

^

: -lU

1 -I 1 I—

1

i 1 ] III

Figure 3.29. Examples of sporadic E echoes.

(a) Equatorial—Huancayo, 1457 LST, May 20, 1961. (b) Middle latitude—White Sands, 1604 LST, May 8, 1961. (c) High latitude, night—South Pole, 2055 UT, Aug. 1, 1960.
152 SYNOPTIC STUDIES OF THE IONOSPHERE

AURORAL ZONE

WASHINGTON, 0.C

GEOfcWe. LMT.-XrN

JFMAMJJASONDJFMAHJJASOND

1951 1952HUANCAYO, PERU

GEOMAG. LAT = 1° S Figure 3.30. Fraction of time fEs>5 Mc/s.

(After E. K. Smith, 1957, Worldwide occurrence of sporadic E, NBS Giro. 582.)
SPREAD F 153

other hand, in the auroral zone, Es is most prevalent during the night

hours but again there is little seasonal variation. In middle latitudes fEs is less than elsewhere and the occurrence is subject to diurnal and seasonal variations. In general, Es is more frequent

in local summer than in winter and by day more than by night. Data on

the occurrence of J^s are published monthly in the CRPL F Series, Part A.

3.3.8. Spread F

3.3.8.1. Description of Spread F

It is often observed that the echo pulse reflected from the F2 layer

has a much longer (10 times) duration than the transmitted pulse and

this phenomenon is called spread F. Undoubtedly, spread F is caused by

the scattering of the signal from irregularities embedded in the ionosphere

both in depth and away from the zenith. Some examples of ionograms

with spread- F echoes are presented in figure 3.31 from which it is seen that the phenomenon occurs in high and low latitudes. A survey of the

existing knowledge of spread F has been compiled by Glover p5]. The

rules for scaling spread F are discussed in references [1], [2], and [36].

It should be noted that spread F is generally defined in terms of the ap- pearance of an ionogram rather than in terms of the physical mechanism

operative.

Several classifications for types of spread F have been suggested,

such as high-, medium-, and low-latitude spread F [15], but this method

is not entirely satisfactory. An alternative division into "range type"

and "frequency type" has been suggested [37]. Frequency type spread

refers to diffuseness near the critical frequency of the F2 layer, whereas

the range type refers to diffuseness near the horizontal part of the trace. Some ionograms, such as that shown in figure 3.32a, exhibit spread

only on the multiple echoes. This type is believed to be due to ground

scatter, as illustrated in figure 3.32b.

3.3.8.2. Diurnal Variations

Spread F occurrence is essentially a statistical phenomenon, and

maps have been prepared showing the probability of occurrence [38]. It

is essentially an evening and nighttime phenomenon. In low geomagnetic

latitudes the most likely time of occurrence is between about 2100 local
154 SYNOPTIC STUDIES OF THE IONOSPHERE

time and about 0100, being earlier at sunspot maximum. In middle lati- tudes, there is a tendency for spread F to occur most frequently after midnight.

3.3.8.3. Seasonal Variations

In low latitudes the occurrence of spread F is greater during local summer than during local winter. In higher magnetic latitudes the occur- rence is more frequent in winter than in summer. However, a number of

high -latitude stations exhibit the equational seasonal variations [39].

156 SYNOPTIC STUDIES OF THE IONOSPHERE

T R Figure 3.32b. Spread F due to ground scatter—path.

3.3.8.4. Solar Cycle Variations

In geomagnetic latitudes above about 60° the occurrence probability

of spread F increases with sunspot number, whereas in low latitudes the

dependence is inverse [40].

3.3.8.5. Correlation with Magnetic Activity

One of the more interesting features of spread F is its dependence on magnetic activity. In equatorial regions it occurs on magnetically

quiet days and disappears with the onset of a magnetic storm [41, 42]. In middle latitudes the occurrence is essentially a storm phenomenon.

In magnetic latitudes above 60° the correlation again becomes negative

(magnetic storm—no spread). This may be more apparent than real,

however, as in such latitudes magnetic storms are associated with high

absorption which prevent F echoes being observed.

Spread F occurrence seems to depend on other parameters. It is greater when the virtual height is larger and is smaller when the critical frequency is greater; it is associated also with the scintillations of radio

signals from radio stars.

REFERENCES

[1] Piggott, W. R., and K. Rawer (1961), URSI Handbook of lonogram Interpretation and Reduction (Elsevier Publ. Co).

[2] Wright, J. W., R. W. Knecht, and K. Davies (1957), Annals of the IGY, Vol. Ill, Part I (Pergamon Press).

[3] Piggott, W. R., W. J. G. Beynon, G. M. Brown, and C. G. Little (1957), The

measurement of ionospheric absorption. Annals of the IGY, Vol. Ill, Part II (Pergamon Press).
REFERENCES

[4] Appleton, E. V., and W. R. Piggott (1954), Ionospheric absorption measurements

during a sunspot cycle, J, Atmospheric and Terrest. Phys. 5, 141.

[5] Findlay, J. W. (1951), The phase and group paths of radio waves returned from

region E of the ionosphere, J. Atmospheric and Terrest. Phys. 1, 353.

[6] Ogawa, T. (1958), Frequency variations in short wave propagation, Proc. IRE

46, 1934.

[7] Femvick, R. C, and O. G. Villard (1960), Continuous recordings of the frequency

variation of the WWV-20 signal after propagation over a 400 km path, J. Geophys. Res. 65, 3249.

[8] Watts, J. M., and K. Davies (1960), Rapid frequency analysis of fading radio

signals, J. Geophys. Res. 65, 2295.

[9] Selected papers from J. Res. NBS 65D (Radio Prop.), 197-311 (1961).

[10] Seddon, J. C. (1953), Propagation measurements in the ionosphere wdth the aid of

rockets, J. Geophys. Res. 58, 323.

[11] Knecht, R. W., T. E. VanZandt, and S. RusseU (1961), First pubUshed radio soundings of the topside of the ionosphere, J. Geophys. Res. 66, 3078.

[12] Warren, E. S. (1963), Some preliminary results of sounding of the topside of the ionosphere by radio pulses from a satellite. Nature 197, 636.

[13] Watts, J. M., and J. N. Brown (1954), Some results of sweep frequency investigations in the low-frequency band, J. Geophys. Res. 59, 71.

[14] Watts, J. M. (1952), A note on the polarization of low-frequency ionospheric

echoes, J. Geophys. Res. 57, 287; (1958), The interpretation of nighttime low- frequency ionograms, ibid. 63, 19; and (1959), J. Atmospheric and Terrest. Phys. 15, 73.

[15] Wright, J. W. and R. W. Knecht (1957), IGY Atlas of Ionograms.

[16] NBS CRPL F Series, Part A, pubHshed monthly.

[17] Budden, K. G. (1955), A method for determining the variation of electron density with height from curves of equivalent height against frequency, Proc. Cambridge Conf. on the Physics of the Ionosphere, Phys. Soc, 332.

[18] King, G. A. M. (1960), Use of logarithmic frequency spacing in ionogram analysis,

J. Res. NBS 64D (Radio Prop.), 501.

[19] Titheridge, J. E. (1959), The use of the extraordinary ray in the analysis of ionospheric records, J. Atmospheric and Terrest. Phys. 17, 110.

[20] Davies, K., and A. K. Saha (1962), Study of the "valley problem" with a ray

tracing program. Electron Density Profiles, p. 162 (Pergamon Press).

[21] Storey, L. R. O. (1960), The joint use of the ordinary and extraordinary virtual height curves in determining ionospheric layer profiles, J. Res. NBS 64D, (Radio

Prop.), 111.

[22] Thomas, J. O. (1959), The distribution of electrons in the ionosphere, Proc. IRE

47, 162.

[23] Knecht, R. W. (1959), Observations of the ionosphere over the south geographic

pole, J. Geophys. Res. 64, 1243.

[24] Mean electron density variations of the quiet ionosphere (quarterly), NBS Tech. Notes 40-1, -2, -3, etc.

[25] Zacharisen, D. H. (1959), World maps of F2 critical frequencies and maximum

usable frequency factors (Apr. 1959), NBS Tech. Note 2, and (Oct. 1960) NBS

Tech. Note 2-2.

[26] Taylor, E. W. (1948), Absorption of radio waves reflected at vertical incidence as a function of the sun's zenith angle, J. Res. NBS 41, 575.

[27] Davies, K,, and E. L. Hagg (1955), Ionospheric absorption measurements at Prince Rupert, J. Atmospheric and Terrest. Phys. 6, 18.
158 SYNOPTIC STUDIES OF THE IONOSPHERE

[28] Bibl, K., A. Paul, and K. Rawer (1962), Absorption in the D and E regions and

its time variations. Radio Wave Absorption in the Ionosphere, AGARDograph

53 (Pergamon Press).

[29] Best, J. E., and J. A. Ratcliffe (1938), The diurnal variation of the ionospheric

absorption of wireless waves, Proc. Phys. Soc. 50, 233.

[30] Davies, K. (I960), A study of 2-Mc/s ionospheric absorption measurements at high latitudes, J. Geophys. Res. 65, 2285.

[31] Thomas, L. (1962), The winter anomaly in ionospheric absorption. Radio Wave

Absorption in the Ionosphere (ed. N. C. Gerson) (Pergamon Press).

[32] Dieminger, W. (1952), On the causes of excessive absorption in the ionosphere on

winter days, J. Atmospheric and Terrest. Phys. 2, 340.

[33] Seddon, J. C. (1962), Sporadic E as observed with rockets. Ionospheric Sporadic

E (ed. Smith and Matsushita), p. 78 (Pergamon Press).

[34] Smith, E. K. (1957), Worldwide occurrence of sporadic E, NBS Circ. 582.

[35] Glover, F. N. (1960), A study of spread F, NBS Tech. Note 82.

[36] Hanson, G. H., E. L. Hagg, and D. Fowle (1953), The interpretation of ionospheric

records, DRTE Report R-2, Canada.

[37] McNicol, R. W. E., H. C. Webster, and C. G. Bowman (1956), A study of spread-F

ionospheric echoes at night at Brisbane, I., Australian J. Phys. 9, 247.

[38] Tao, K. (1962), On the theoretical study of F scatter, J. Geomagnetism and Geoelectricity VIX, 71.

[39] Reber, G. (1956), Worldwide spread F, J. Geophys. Res. 61, 157.

[40] Shimazaki, T. (1959), A statistical study of worldwide occurrence probability of spread F, J. Radio Res. Labs. (Tokyo) 6, 669.

[41] Wright, R. W. (1959), The geomorphology of spread F and characteristics of equatorial spread F, J. Geophys. Res. 64, 2203.

[42] Wright, R. W., and N. J. Skinner (1959), Equatorial spread F, J. Atmospheric and

Terrest. Phys. 15, 121.
CHAPTER 4

Oblique Propagation

4.1. CHARACTERISTICS OF HF PROPAGATION

High-frequency (3 to 30 Mc/s) radio waves have been and still are one of the basic vehicles for long-distance transmission of information.

The reasons for this may be summarized as follows:

(a) Low cost of terminal equipment,

(b) Low power requirements,

(c) Adequate bandwidths,

(d) Adequate signal strengths. In contrast with the above, it may be noted that medium wave fre- quencies (300 kc/s to 3 Mc/s) suffer very heavy absorption during the

day, while on lower frequencies there is insufficient bandwidth for more

than a few voice channels. Frequencies much above 30 Mc/s are not,

normally, reflected from the ionosphere. For propagation over long dis- tances the F2 layer is of fundamental importance.

The disadvantages in using high frequencies are:

(1) The variability of propagation conditions which, for optimum

results, requires frequent changes in the operating frequency. Even on

the optimum frequency, communications are often subject to interruption by ionospheric storms.

(2) The large number of possible propagation paths and the re- sulting time dispersion of a single signal.

(3) The large and rapid phase fluctuations.

(4) The high interference.

(5) Wide-band signals suffer from frequency distortion. In the lower part of the high-frequency spectrum, refraction in and

reflection from the E region (particularly Es) contribute to the complexity of the echo structure.

159
160 OBLIQUE PROPAGATION

The range of high frequencies useful for medium and long distance

radio communications is limited, on the upper end, by the height and

maximum electron density in the controlling layer and, on the low-fre- quency end, by absorption in the D region. In this chapter we shall be concerned with methods of calculating

the maximum frequency and with the identification of the structure of

signals both by experiment and by means of ray tracing.

4.2. EQUIVALENCE RELATIONSHIPS

4.2.1. Plane Earth and Plane Ionosphere

4.2.1.1. The "Secant Law"

j In this section we shall consider the relationships that exist between

the frequencies, virtual paths, and absorptions of two waves, one reflected with oblique incidence and the other reflected with normal incidence from

the same true height. For this purpose consider a ray incident on a plane

ionosphere at an angle as shown in figure 4.1, in which the electron

density is increasing with height so that total internal reflection takes

I place.In the absence of both collisions and an imposed magnetic field, the

I refractive index ji for a wave of frequency /, at a level where the plasma

I T = TRANSMITTER REAL PATH

J] R = RECEIVER VIRTUAL PATH

A' A

II B' / B \ ^—\ \ IONOSPHERE

VERTICAL

EARTH

\0BLIQUE

T R' T R

r Figure 4.1. Equivalence theorem for plane earth and plane

ionosphere.
PLANE EARTH AND PLANE IONOSPHERE 161 frequency is /at, is given by (2.78): — (4.1) (f

Application of Snell's law ()u= sin 0o) gives, at the level of reflection,

Jn =/ cos (f)Q. Now iffv is the frequency which is reflected with normal incidence from

the same true height (i.e., same plasma frequency) as the frequency /

with oblique incidence, then fv =Jn. Therefore

/„=/cos</)o, (a) or (4.2)

f=fv sec 00. (b)

The frequency is called the "equivalent vertical -incidence frequency,"

corresponding to /. Equation (4.2b) is the so-called secant law. It shows

that, with oblique incidence, the ionosphere can reflect much higher fre- quencies than with normal incidence.

4.2.1.2. Breitand Tuve's Theorem [1

Another relationship of importance is known as Breit and Tuve's

theorem. It states that the group (or equivalent) path P' (see (2.130)),

for transmission between a transmitter T and a receiver R (fig. 4.1),

is given by the length of the equivalent triangle TA R. That is, P'=TA +AR, (4.3)

which can be proved by the following argument:

P'= \ —= /

; / dx = - =TA-\-AR.

•'tbr M M sin 0 sm 00 J sm 0c Note that the true height of reflection (at B) is always less than the equivalent height at A.

Figures in brackets indicate the literature references on p. 214.
162 OBLIQUE PROPAGATION

It should be remembered that (4.3) appHes only when sender and

receiver are situated outside the ionosphere. If the transmitter and re- ceiver are located within the ionosphere at a level where the refractive

index is /ii, the right-hand side of (4.3) must be divided by jui in order that

is still to mean the group propagation time multiplied by the free space velocity.

4.2.1.3. Martyn's (Equivalent Path) Theorem [2]

If / and fv are equivalent frequencies of waves reflected obliquely

and vertically from the same real height, then the virtual height of re- flection oijv is equal to the height of the equivalent triangular path for the oblique signal.

Consider the refractive indices /Xob and jiv for the oblique and vertical waves, respectively, at the same real height at which the plasma fre- quency is /at; we have

and by Snell's law /Zob sin 0 = sin 0o- Combining these equations we get

(a)

(4.4)

(b)

)Uob COS 4> = fJLv COS 00* (4.5)

Now the group path for the oblique signal is

''TBR Mob •'0 dh 2 r^'^dh 2

h,' = iP' cos (f)o = i{TA-{-AR) cos <t>o = AD.

Hence

p'(f)=h' ( /,) sec 00- (4.6)

This theorem expresses the important relationship that the virtual height

of reflection of an obliquely incident wave is the same as that of the

equivalent vertical wave.
EFFECT OF THE CURVATURE OF THE IONOSPHERE 163

4.2.1.4. Martyn's (Absorption) Theorem [2]

If [Lo]io is the absorption suffered by a wave of frequency / in- cident on the ionosphere at an angle 4>q and [Lv]o is the absorption

suffered by the equivalent vertical wave, then

[Lo]^o = cos 0oCL,]{ (4.7)

This may be proved as follows: From (2.100) we have that

Lq= [ — ( Mob) ds= f

( Mob) 7 . -'tBR \Mob / •'O \Mob / COS 0

Where K is the height of reflection together with (4.5) we have

^0 C \jJLv cos 00/ COS 00 •'o Cily \ J / = cos 00 / — ( ~ ) dh = cos 00 / - I y.v]dh = Lv COS 00.

It is interesting to note that Martyn's equivalent path theorem applies even when collisions are present, provided that co^ is very much

greater than v^. In this case the angular frequency equivalence is given by

ccl^+v'={c^l-]-v') Bec'^cf>o (4.8)

and (4.5) is still valid. The above theorems do not apply in the presence of the earth's magnetic field or in a curved ionosphere.

4.2.2. Effect of the Curvature of the Ionosphere

In a curved ionosphere Snell's law takes the form

Mr sin i = Moro sin io? (4.9)
164 OBLIQUE PROPAGATION

0 Figure 4.2. Ray geometry with oblique incidence.

where r is the length of the radius vector from the center of the earth

to the level where the refractive index is /i and the angle between the

radius vector and the ray is i, as shown in figure 4.2.; /zo, ro, and io are ar- bitrary reference values. Let us take ground level as reference so that

iUo=l, ro = a, and io = (7r/2)— A where A is the angle of elevation. Then

/xr sin i = a cos A. (4.10)

The relationship between a frequency / and the equivalent vertical fre- quency fv which is reflected from the same real height hr is given by substituting (4.1) into (4.10) and replacing /isr by /„. This gives

Now let (f)r be the angle between the continuation of the unrefracted ray

and the radius vector at the level K as shown in figure 4.2. From the ge-
PLANE IONOSPHERE 165 ometry we have that

(a -\-hr) sin 4)r = a cos A. (4.12)

Hence

/.=/cos0,. (4.13)

From (4.11) and (4.13) it will be seen that the equivalent frequency

depends not only on A but also on the height of reflection hr. Instead of defining in terms of the height of reflection, it can be

defined in terms of (4.6) or (4.7) but, unlike the plane ionosphere case, the values of will depend on the definition.

4.3. CALCULATION OF MAXIMUM FREQUENCIES

4.3.1. Plane Ionosphere

The theorems of Breit and Tuve and of Martyn stated above show

that, for a plane ionosphere, the reflection process is equivalent to mirrortype reflection at a height equal to the virtual height h' of reflection of

the equivalent vertical frequency. The variation of the latter with fre- quency can be determined experimentally by means of a conventional

sounder.

The relationship between oblique and equivalent-vertical frequencies,

in the case of a plane reflector at an equivalent height h\ for transmission over a distance D, is given by

/ob=/. sec <^o=/. >/l +^^,y. (4.14)

In the case of a curved earth and a plane ionosphere 4>o is given by

sin / . -. ^ X l-\-{h /a) — cos ^6 where a is the earth's radius (6370 km) and 6 is the angle at the center

of the earth subtended by the transmission path.

To obtain /ob for a given value offv we need to know h' as a function

of —from an ionogram—and the relationship between sec </)o and h'
166 OBLIQUE PROPAGATION

800

700

600

E 500

I-X

X 400

_i<H 300 >

200

100

0

I 2 3 4 5 6 7 8 9 10 II 12 13

f, Mc/s

Figure 4.3. Family of transmission curves parametric in frequency for a fixed distance of 2000 km superimposed on an h'f curve. A flat earth and flat ionosphere are assumed.

which, when presented graphically, is called a transmission curve, which was introduced by Newbern Smith [3]. The application of a transmission curve to an /i'/ curve is, essentially, a graphical solution of these two equations. A family of such transmission curves for a distance of 2000 km is shown in figure 4.3 and is plotted on the same h'-f grid as a conventional

hj curve. The intersections of a transmission curve, for a given (oblique)

frequency/, with the vertical h'(fy) curve give the virtual heights of re- flection of the transmitted waves. In figure 4.3 the three sections of the

h'(fy) curve would correspond to reflections from the E, Fi, and F2

layers. A frequency of 14 Mc/s, for example, propagating over a distance

of 2000 km could travel by several different paths, two of which would be

reflected from the F2 layer at heights corresponding to the intersections

marked a and a' on the h'{fy) curve with the transmission curve marked

14 Mc/s. The same transmission curve also intersects the Fi section in two places and the E section in one place.

The corresponding ray paths are shown in figure 4.4; the path cor- responding to the lower virtual height of each pair is called the low-angle

ray, whereas the path corresponding to the higher virtual height is known
PLANE IONOSPHERE 167

F2 LAYER

F| LAYER

HIGH-ANGLE F,

HIGH-ANGLE Fg LOW-ANGLE F2

LOW-ANGLE F

T R Figure 4.4. Ray paths corresponding to intersections of trans- mission curves and ionograms.

as the high-angle or Pedersen ray. There would be five different ray paths

for a 14 Mc/s wave. The 18 Mc/s transmission curve intersects the F2

and E layers, but misses the Fi section; thus no reflection from the Fi

layer is possible on this frequency.

As the frequency / of the parametric curves increases, the points of

intersection {hh' ) come closer together, merging in a tangent contact at one point c. At this point only one ray path would be possible, and 20

Mc/s is the highest frequency which could propagate over 2000 km under

these ionospheric conditions. The frequency of the tangent curve is called the maximum usable frequency (MUF). At this point, where the high

and low waves merge, focusing takes place and the received signal will be enhanced.

For values of / above 20 Mc/s there is no value of /„ sec </)o that will satisfy (4.14) and hence no level of reflection. Therefore, the signal is said to skip at the distance concerned (2000 km). The distance for which

a given frequency is the maximum frequency is called the "skip" distance

for that frequency. Within this distance no signals are received from the

ionosphere by the regular process of ionospheric refraction. In figure 4.5 are shown the paths for various frequencies in the case

of a single (F2) layer. Note that, as the operating frequency is increased,

the real height of reflection of the low-angle ray increases, whereas the

height of the high-angle ray decreases until they coalesce at the maximum

frequency. In figure 4.6 we see what happens to the ray path (on a given fre- quency) as the angle of elevation (takeoff) slowly increases. For low

angles the propagation path 1 is long. As the elevation increases, the

ground range (path 2) decreases until the skip is reached (path 3), after which the range increases rapidly as shown by paths 4 and 5. Eventually
168 OBLIQUE PROPAGATION

TO THE MUF. SINGLE WAVE AT THE MUF(20Mc/s).

OCCURRENCE OF SKIP AT A FREQUENCY(22McMAB0VE THE MUF. Figure 4.5. Ray paths for fixed distance, for different frequencies.

Tl ^

) SKIP ZONE Figure 4.6. Ray paths for fixed frequency, with varying elevation.

penetration occurs as shown by path 6. Paths 1 and 2 are the low-ray

paths and 4 and 5 are the high-ray paths. The variation of ground range

D with angle of incidence 0o for a parabolic layer is sketched in figure 4.7
CURVED IONOSPHERE 169

D

Figure 4.7. Variation of range D with angle of incidence <po for a

plane parabolic layer.

for various ratios of the operating frequency to the penetration frequency.

Note that for a given distance there are two values of one corresponding to the low-angle path and the other to the high-angle path. The

minimum distance is the skip distance. Note that the high-angle ray is very sensitive to changes in 00-

4.3.2. Curved Ionosphere

The breakdown of the equivalence theorems in the case of a curved

layer requires a modification of (4.15) for obtaining sec 0o. The complete

modification is very complicated due to the fact that it depends on the

electron density profile and, therefore, differs from one set of ionospheric

conditions to another. For many practical purposes it is sufficiently ac- curate to amend the Secant law to

The correction factor k depends upon the distance and has values ranging

from 1.0 to about 1.2 for most practical purposes. The quantity k sec </)o is often referred to as "sec 0o corrected."

The value of A: is a function of the distance and real height of re- flection and is very difficult to calculate. For a given virtual height, it

is possible to calculate this factor for the limiting case of two different

foh = kfv sec 00. (4.16)
170 OBLIQUE PROPAGATION

I 200

0 1000 2000 3000 4000

DISTANCE (km)

Figure 4.8. Variation of correction factor k with distance.

(After B. Wieder, 1955, Some results of a sweep-frequency propagation experiment over

a 1100 km east-west path, J. Geophys. Res. 60, 395.) types of electron density profile, one for which the ray path penetrates

deep into the layer, the other for which the wave is reflected from the

lower boundary [3]. From a curve drawn between these two limiting

values it is possible to obtain a reasonably good empirical correction factor. The variation of this correction factor with distance is shown in figure 4.8. The primary purpose of transmission curves is the determination of

maximum frequencies for a given radio circuit. For this purpose it is possible to construct a type of transmission curve whereby a single curve

suffices for each distance and a family of curves parametric in distance can be drawn on a single transparent overlay for use with standard

ionograms. This is done by making the frequency scale logarithmic, and

requires that the frequency scale of the vertical ionogram be logarithmic

also.
CURVED IONOSPHERE 171

SECANT <^o (CORRECTED)

Figure 4.9. Logarithmic transmission curves for curved ionosphere.

A family of such standard curves is shown in figure 4.9, in which

the factor k sec 00 is plotted on the same logarithmic scale as the ionogram

but with the numbers increasing in the opposite direction to the fre- quency of the ionogram. The virtual height h' is the same as that on the

ionogram. These curves are plotted on a transparent overlay and placed over the ionogram so that the height scales coincide and the curves will, in general, intersect in two places. Opposite the abscissa 1.0 will appear

the values of product kf^ sec 0o or foh- As the overlay slides along the

horizontal axis, different values offob will be obtained. Note that because

of the logarithmic frequency scale, the same number, except for the deci- mal point, will appear on the transparency opposite the 1.0 index on the

logarithmic ionogram scale. The transmission curve for a given distance can be slid along the abscissa until it is just tangent to the hj curve. The product, as then read at the 1.0 index, is the value of the maximum

frequency.

For many purposes, the maximum-usable-frequency factor (M factor)

is desired, that is, the ratio of the maximum frequency to the critical frequency of the layer. This may be found directly from the logarithmic

scale on the transparency opposite the critical frequency cusp when the

transparency is set to read the maximum frequency (i.e., tangent condition) . The transmission curves given in figure 4.9 are most accurate for F2 layer heights because the factor k is based on typical F2 layer profiles.

Over short distances they will be accurate for any layer because, as the
172 OBLIQUE PROPAGATION

distance approaches zero, k approaches the value 1.0. The effects of the

earth's magnetic field have been neglected in constructing the transmission

curves. The errors introduced because of this procedure will be discussed

below.

4.3.3. The Parabolic-Layer Method

Instead of calculating maximum frequencies by the use of a vertical

hj curve and a transmission slider, it is possible to fit a parabolic model

to the nose of the F2 layer and, from this, to calculate the maximum fre- quencies on the basis of analytical formulas [4]. The height ho of the

bottom of the parabola and its semi-thickness (see sec. 3.3.4.2) are de- termined from the ionogram. The ground range D cannot be determined

for the parabolic layer, but by neglecting small terms [4] it is given by

a . 1—A:2[j^/(a+/io)] sin^ 00+^ cos 00 a+«o l—x^lj^/{a-\-ho)j sm^ (po—x cos 0o +2a cot 0o-2aVcot2 0o- (2/io/a), (4.17)

where x =f/fc and 0o is the angle of incidence.

The maximum frequency and the skip distance can be evaluated

from the condition that dD/d4>Q = 0. Hence families of curves can be constructed showing the variation of :*:(M factor) with distance for a range

of values of the height of maximum electron density /im(=^o+Jm) and

for different values of the ratio ym/ho as depicted in figure 4.10. If these

X

1

' 1

' 1

' --^^=200

SKIP DISTANCE '- ^^^<^^Z' -

^=0,4

^^^^^^ ho

0 1000 2000 3000 4000 5000 6000 TOOO km

Figure 4.10 M factors for a parabolic layer.

(After E. V. Appleton and W. J. G. Beynon, 1940, The application of ionosptieric data to radio communication problems, Proc. Phys. Soc. 52, Pt. I, 518; 1947, Proc. Phys. Soc. 59, Pt. II, 58.)
EXPERIMENTAL TECHNIQUE 173 parameters are known, together with it is possible to determine the

maximum frequency by interpolation between curves. To get the most

reliable estimate of the factor at any time, it is desirable that ho and jm

should be determined directly from ionograms at the midpoint of the

path. Such a course is, however, rarely practicable, and it is necessary

to predict the most probable values oi ym and /^o from past history. From

the network of ionospheric sounding stations the diurnal, seasonal, and

sunspot cycle variations of these parameters are known over most of the

world. Comparisons have shown that the results obtained by the parabolic method and by Smith's transmission curves are essentially the same. For two-hop propagation it is necessary to calculate the factor for half

the distance.

The transmission theory presented above applies to the case of a

spherically stratified ionosphere only. Now, over long transmission paths,

the ionospheric parameters may vary appreciably and so the various hops

will be of unequal length. The parabolic layer theory has been extended

by Kift [5] to include such variations and will be considered later.

4.4. OBLIQUE IONOGRAMS

4.4.1. Experimental Technique

The most convenient way of determining the echo structure of signals

transmitted obliquely is by the ionosonde technique but with transmitter

and receiver at different ends of the path. From the technical point of

view this introduces two problems:

(a) The repetition frequencies at the sender and at the receiver must

be very nearly the same; otherwise the received pulse will "drift" along

the time base of the display oscilloscope.

(b) The frequency of the receiver, as a function of time, must be

kept in tune with the sender. Pulse synchronization (a) is achieved by employing signals from in- dependent stable crystal oscillators. The frequencies of such oscillators are normally in the range 100 kc/s to 5 Mc/s, and electronic frequency

dividers are used to obtain the desired repetition frequency. The oscilla- tors can be adjusted (in frequency) either independently with reference to an external standard (e.g., WWV), or else the oscillator at the receiver can be adjusted periodically until the drift of the pulses from the sender

is reduced to a minimum. Other synchronization methods used have in-
174 OBLIQUE PROPAGATION

volved fixed-frequency pulses transmitted from the sender to receiver

via a cable [^6] and also by the transponder technique in which the re- ceived pulses are used to trigger the display time base. Neither of the

latter methods has been particularly successful. The tuning of the transmitter and receiver can be accomplished in several ways. The two most commonly used are

(1) the accurate shaping of the cams which determine the frequency

sweep [7];

(2) the synthesis of the frequency from a set of crystal oscillators [8],

With this technique studies of oblique transmission via the ionosphere

have been carried out in Canada p, 10], Germany [11], Great Britain

[5, 12], Japan [6], and the United States [13].

4.4.2. Conversion from Vertical to Oblique Incidence

This process is illustrated in figures 4.11a and b. Consider points

A, C, D, E, and F on the vertical ionogram. For a plane ionosphere

and a given distance of transmission we can calculate sec </)o corresponding

to the various virtual heights. From this we can obtain fob =fv sec 4>o and

so plot the oblique ionogram shown in figure 4.11b. Note that the vertical

scale in figure 4.11b can be related to the equivalent oblique path by the

fc = CRITICAL FREQUENCY

fm = MUF

{a)VERTICAL ( b)OBLIQUE

Figure 4.11. Corresponding vertical and oblique ionograms.
EXPERIMENTAL RECORDS 175 transformation P' = 2h' sec 4>q. As we increase the frequency from A to B to C, etc., the virtual height is increasing whereas sec 0o is decreasing.

Between A and C the increase in fv predominates so that foh increases,

but from C to F the sec 0o factor predominates and so foh decreases. The

obhque trace A'B'C represents the low ray, whereas that marked D'E'F'

represents the high ray. Notice that the maximum frequency is not re- flected from the height of maximum electron density but at a lower height

which decreases with increasing obliquity.

4.4.3. Experimental Records

4.4.3.1. Medium Distances

Figure 4.12 shows a sample oblique ionogram taken during magnetically quiet conditions in middle latitudes [14]. The traces are clear,

and the maximum frequency of the one-hop F2 trace is well defined (about

13.5 Mc/s) . The high-angle trace (marked H) can be seen for the one-hop

trace.In the description of oblique ionograms it is desirable to eliminate

the term maximum usable frequency because of the ambiguity in the

meaning of "usable." The following terms will be used:^

P ^

2

3F

; i

^FJF.;. hIOF

100 kmi *- 1 \

F

F

srrr-

JF mm p|wmmm MOF - III 1

I 5 I 10 15 20 25

I

I

I

I MC/S

LOF FLLOF

Figure 4.12. Ionogram Boulder-Sterling, Sept. 1, 1954, 2012 {90°WMT).

2 Recommendationa of the Lindau Meeting held in May 1963.
176 OBLIQUE PROPAGATION

(1) Maximum observed frequency, MOF, means the highest fre- quency on which the sounder transmitter signals are observed on the

ionogram, regardless of the propagation path involved.

(2) Lowest observed frequency, LOF, means the lowest frequency on which the sounder transmitter signals are observed on the ionogram,

regardless of the propagation path involved.

(3) These terms (MOF and LOF) may be used also to describe

identifiable modes. For example, 2F2 LOF means the lowest frequency,

observed on the ionograms, which is propagated by two reflections at the

F2 layer with an intermediate ground reflection. Similarly, 2F2 MOF

means the highest observed frequency of the two-hop F2 trace.

(4) The lowest observed frequency of the high-angle ray may be

distinguished from that of the low-angle ray by the letters H and L,

respectively. Thus F2 HLOF is the lowest frequency of the high-angle

signal which is propagated via the one-hop F2 path. Likewise, F2 LLOF

is the lowest observed frequency of the corresponding low-angle signal.

(5) When it is required to distinguish between the ordinary and

extraordinary raypaths, an "o" or "x" may follow in parentheses. Thus

the F2 MOF(x) is the maximum observed frequency of the extraordinary wave which is reflected once at the F2 layer.

(6) The frequency at which the high- and low-angle rays join will be called the "junction frequency" and will be denoted by JF. Note that

this frequency has been called the "classical MUF."

Note that capital letters are used in oblique work in contrast to the

small letters agreed upon in vertical soundings.

2

ICQ km

Figure 4.13i Ionogram Boulder-Sterling, Nov. 29, 1954, 1321 (90° WMT) showing

difference between JF and MOF.
EXPERIMENTAL RECORDS 177 The above terminology is illustrated in figure 4.12 in which the F2 JF

and F2 MOF are identical. Notice also that LOFs of the multi-hop signals are lower than that of the one-hop. Figure 4.13 shows a case where the

MOF is appreciably larger than the junction frequency. This difference

is thought to be due to some scattering process in the ionosphere. It ap0800 1200 90° WMT

2400

Figure 4.14. Diurnal variation of percent difference between JF

and MOF {Boulder-Sterling). TRIPOLI - ACCRA

3300 km

OCTOBER 3, 1961, 1425 UT

;ll!ISB.

1 14 17 20 23 26 29 52 35 38 41 44 Mc/S JF^ DIFFERENCE BETWEEN MUF AND MOF

I 47 49

OCTOBER 7, 1961, I325 UT

14 17 20 23 26 29 32 35 38 41 T 44 47 49 MC/S JF, MOF IDENTICAL MUF AND MOF

FiGXJRE 4.15. lonograms, Tripoli-Accra.
178 OBLIQUE PROPAGATION

TRIPOLI -ACCRA

OCTOBER 3, 1961 2255 UT

1000 km iLOF ..^._.^.__TM_^„^ ^ ^

J J ^ 1 2 8 14 20 26 32 38 44 49 Mc/s

Figure 4.16. lonogram, Tripoli-Accra, showing spread F echoes.

pears to be essentially a winter daytime phenomenon in these latitudes. The diurnal variation of the difference (MOF—JF) for the BoulderSterling path is shown in figure 4.14. The two ionograms of figure 4.15

also illustrate that in low latitudes the MOF may be the same as or differ from the junction frequency. The greatest difference between the MOF

and the junction frequency occurs during certain equinox evenings on

circuits near the magnetic equator. This is illustrated in figure 4.16. The

junction, which is obscured by the spread echo, is around 25 Mc/s,

whereas the MOF is nearly twice th's value.

It should be realized that the maximum observed frequency and the

minimum observed frequency will depend, to some extent, on equipment

characteristics.

4.4.3.2. Long Distances

As the transmission distance increases, the complexity of the echo

structure tends to increase. Furthermore, signals which may be relatively

unimportant over short distances may become determining factors over

long distances. An example of this, which has been demonstrated by

Canadian workers [15], is the importance of the Pederson ray in deter- mining the maximum frequency. One of their records, reproduced in figure 4.17, shows the one-hop high ray which extends over the approximate frequency range from 42 Mc/s to 48 Mc/s. The occurrence of the

Pedersen ray tends to peak near noon at the midpoint when horizontal

gradients of electron density along the path are at a minimum.

Some further samples of long-path ionograms are shown in figures 4.18 and 4.19 for the respective paths Delhi-Slough (6730 km) and Ascension Island-Slough (6750 km). The latter illustrates the complexity of

the echo structure with long transequatorial paths. See section 4.7 for further discussion of these difficulties.
DEFINITIONS OF MUF 179

17 23 27 35 41 47 Mc/s

Figure 4.17. Ottawa-Slough ionogram, Nov. 14, 1957, 1556 UT.

(By permission of the Chief Superintendent DRTE.)

5F2 4F2 3F2 2F2

Frequency (Mc/s) Figure 4.18. Delhi-Slough ionogram, Nov. 7, 1961, 1015 UT.

(Reproduction is by permission of the Controller of Her Brittannic Majesty's Stationery

Office and is by arrangement with the Director of Radio Research.)

Mc/s 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Figure 4.19. Ascension Island-Slough ionogram. Mar. 27, 1961, 2118 UT.

(Reproduction is by permission of the Controller of Her Brittannic Majesty's Stationery

Office and is by arrangement with the Director of Radio Research.) 4.5. DEFINITIONS OF MUF

In the early days of ionospheric communications, the term "maximum usable frequency" (MUF) was used without regard to the meaning

of "usable." In practice, the maximum frequency usable for a given

purpose over a given distance may or may not correspond to the maximum

frequency deduced from a vertical ionogram taken at the midpoint of the

path. In most cases the practical upper frequency limit is higher than that

obtained by the methods described in section 4.3, even when allowance

is made for the effect of the magnetic field. The reasons for this involve

a number of additional propagation factors, among which are sporadic-J^

propagation, ionospheric irregularities (large and small), and ground
180 OBLIQUE PROPAGATION

irregularities in the case of multi-hop propagation over long distances.

Such factors also mean that signals may be usable within the nominal

skip zone. In order to clarify and standardize the various meanings of MUF,

the International Radio Consultive Committee (CCIR) of the Inter- national Telecommunications Union (ITU) adopted the following recom- mendation (Recommendation No. 318, "Meaning of MUF")

1. That the term "classical MUF" should be used to designate the highest frequency

transmitted by ionospheric refraction alone. For the approximation of this value obtained by application of a standard transmission curve or a distance factor, the term "standard MUF" may be used. (For the results of theoretical calculations the term "theoretical MUF" seems to be adequate, and similarly the term "experimental

MUF" might be used for the results of special experiments.) If used without reference to a particular mode of propagation, the term "classical MUF" should imply the

highest of the classical MUFs of the individual modes.

2. That the term "operational MUF" should denote the highest frequency permitting

operation at a given time between points under specified working conditions. The

operational MUF may be higher than the classical MUF as a result of effects such as ionospheric and/or ground scatter. If known, the modes of propagation involved, in- cluding those involving ionospheric and/or ground scatter, should be specified.

4.6. ACCURACY OF MUF CALCULATIONS

4.6.1. Effect of the Earth's Magnetic Field

The sample ionograms in figure 4.20 show clearly the decomposition

of the signal into ordinary and extraordinary waves. The wave having

the higher junction frequency is the extraordinary wave and the wave It A [- -A

i-i

"HLOF(c

[ j FHLOLF(x) —

-1 •- —

4-

\

- — -

100 km 0 — F MOF

' j: —

5 1 10 15 20 LOF MC/S

Figure 4.20. Oblique ionogram (Sterling-St. Louis, 1150 km,

' March 6, 1952, 0901 75° WMT) showing o-x separation of high-angle trace.
EFFECT OF THE EARTH'S MAGNETIC FIELD 181 with the lower junction frequency is the ordinary wave. Now the trans- mission curve theory described in section 4.3 ignores the effect of the

earth's magnetic field, and the consequence of this is that there is a tendency to underestimate the maximum frequency of the ordinary wave [16]. Of course in the case of east-west propagation along the

magnetic equator, where the propagation is transverse, there should be no error in the maximum frequency of the ordinary wave. For quasi- transverse propagation, the frequency separation at the maximum decreases with increase of distance of propagation [3]. The variation of this frequency separation with distance for east -west propagation in the

United States is shown in figure 4.21, from which we see that the o-x separation falls from 0.8 Mc/s for zero distance to less than 0.2 Mc/s

at 3000 km. It must be remembered that this is a statistical result and

that the o-x separation depends on the junction frequency itself, the

electron density profile, etc. If the propagation is quasi-longitudinal, as

in north-south propagation across the magnetic equator, the o-x separation at the junction is independent of distance and is always equal to the

gyrofrequency fn- It is important to remember that the transmission curve should not be apphed to the extraordinary trace on the vertical ionogram in order to obtain the maximum frequency of the x wave.

1.0

0.8

° 0.6

—} if)

IT 0.4

0.2

0 0 1000 2000 3000

km Figure 4.21. JF(x)-JF(o) as a function of distance for east-west propagation in the United States.
182 OBLIQUE PROPAGATION

4.6.2. MUF Extension

It was mentioned in section 4.4.3.1 that for east-west propagation

in the United States, and for approximately north-south propagation in Africa, the junction frequency is often ill-defined due to an extension

of the trace to higher frequencies. This is sometimes called the MUF

extension, and it makes scaling of junction frequencies very uncertain.

One way of getting around this difficulty is to define the "junction fre- quency" as that at which the high- and low-angle traces merge (extrapolated if necessary) . Even when this is done it is found that, on the average, measured maximum frequencies defined in this way are about 4

percent higher than the values calculated from midpoint ionograms

(standard MUF) for east -west propagation on winter days in the United

States. It is of interest to note that the MUFs observed on the BoulderSterling path are about 7 percent higher than the calculated values. In summer the difference is about 1 or 2 percent, and this smaller value may

be attributed partly due to the absence of the MUF extension on the F2

trace in summer. The difference (between the junction frequency and

the standard MUF) is partly due to errors in the correction factor k

(4.16), which is only an average correction over a variety of ionospheric

profiles. Still, even this error may not be important in comparison with

other factors such as sporadic E, ionospheric and ground scatter, ionospheric distortion (tilts), and so on.

4.6.3. Sporadic E

Figure 4.22 shows that Es reflections can play a dominant role in determining the maximum frequency. With vertical propagation, reFiGURE 4.22. lonogram showing Eg reflections.
SPORADIC E 183

flections from Eg appear to be essentially specular, in the sense that little or no gradual bending takes place within the layer; this is in contrast to the gradual refraction process involved in reflection from the regular E

and F layers. Reflections from Es are often observed to be only partial,

and the reflection mechanism is still in some doubt [17]. From a practical

point of view, however, it has been shown that the relationship /max

(oblique) =fEs sec (po holds over distances of the order of 1000 km [18].

Over long distances, however, the role of Es in determining maximum

frequencies is not known in detail. Indeed the propagation mechanisms

possibly vary with the type of sporadic E. It is relatively rare for Eg

to extend over a sufficiently large area of the world to be the sole reflect- ing layer. It does appear to play a decisive role in modifying the propagation paths involving the regular layers as is illustrated in figures 4.23a

and b. For example, the M path involves a reflection at the topside of a sporadic E patch near the midpoint and may be particularly important

in high latitudes during periods of high absorption since it avoids a double

traverse of the intensely absorbing D region. The occurrence and strength

of Es echoes cannot be predicted with certainty, except near the magnetic equator, so that its value in the design of communications problems

is still in an unsatisfactory state.

Figure 4.23a. M-type reflections.

Figure 4.23b. N-type reflections.
184 OBLIQUE PROPAGATION

4.6.4. Ionospheric Scatter

This can play an important part in radio wave transmission. In

particular, the presence of spread F raises questions of where, among

the confusion of a spread F trace on an ionogram (see sec. 3.3.8.), should

a transmission curve be placed in order to give the observed maximum

frequency. In middle latitudes the oblique traces are frequently much

less spread than those on the corresponding vertical ionogram [13]. This

source of error may be much more important than inaccuracies in the

transmission curves. Near the magnetic equator, spread F occurs frequently after sunset and its onset is associated with marked flutter fading on transequatorial

circuits. On these occasions the oblique ionograms are characterized by

broad traces extending to frequencies much higher than those predicted

from vertical ionograms. These traces move in range from one ionogram

to the next and are thought to be due to magnetic field-alined irregularities

moving from west to east near the magnetic equator [19].

It may also be noted here that ionospheric scatter in the D region,

by meteoric ionization and turbulent mixing, plays an important part in the ionospheric transmission of very high frequency waves (30 to 300

Mc/s). (See ch. 8.)

4.6.5. Ground Scatter

Consider the situation illustrated in figure 4.24, in which part of an east-west path is in darkness so that the ionosphere is unable to reflect waves along the path TAR. Because of the higher critical frequencies

in the sunlit hemisphere, propagation along the path TCS is possible

followed by ground scatter at S. Scattered energy may now be propagated

DARK PENETRATES

LIGHT

IONOSPHERE

GROUND

SCATTERING Figure 4.24. Importance of ground scatter.
GROUND SCATTER 185

POSSIBLE PROPAGATION PATHS, GREENVILLE-MUNICH

Figure 4.25. Transmission from Europe to the United States via side-scatter over Africa.

(After H. Leighton, unpublished.) along the path SBR because, although B may be on the dark side of the

sunrise line, the angle of incidence (and hence sec 0o) is larger than for the path TAR. Alternatively, the signal from T may arrive at R after two reflections in regions off the great circle path where /0F2 is higher

than along the direct path. This side scatter is illustrated in figure 4.25,

which shows how communications can be established between Europe and

North America via side scatter in Africa. Such a path gives not only

higher maximum frequencies (than the direct path) , but also may avoid

auroral disturbance effects [20].

Ground backscatter can give rise to ionogram records of the type

shown in figure 3.32. The signals are reflected from the ionosphere

(obliquely), are scattered at the ground, and retrace the same path back

to the receiver [21]. The backscatter trace starts off at the vertical- incidence trace of the two-hop extraordinary wave, and it would be ex- pected that the lower edge of the trace gives the maximum frequency

corresponding to the equivalent path showTi on the ordinate scale, which

is related to the skip distance. Such backscatter ionograms provide a convenient means of determining the maximum frequency, over a wide geo-
186 OBLIQUE PROPAGATION

graphical area, from a single ionosonde. The fact that the echoes can be

seen only over a narrow path range is probably due to focusing near the

edge of the skip zone.

4.6.6. Ionospheric Tilts

From figure 3.18 we see that the assumption of spherical stratifica- tion of the F2 layer can, under certain circumstances, be invalid. Such

distortion of the ionosphere occurs near sunrise and sunset and near the

magnetic equator. Clearly, under such conditions, the use of the trans- mission curves presented above can lead to erroneous conclusions since

the ray paths are, in general, asymmetric. In such cases the propagation

paths have to be plotted point by point through the ionosphere [22].

When this is done for north-south transmission across the magnetic

equator in the 75° west geographic meridian, a path such as that shown in

figure 4.26 may be obtained. Some features of this path are:

(1) There are two ionospheric reflections without an intermediate

ground reflection. (2) The signal is propagated to long distances with only two transits

of the absorbing region, thus giving high signal strength.

(3) Because the angles of incidence are greater than in the case of

a spherically stratified layer the maximum frequencies will be greater.

(4) There is a marked asymmetry in the path so that the angle of

departure (0°) differs from the angle of arrival (about 10 ). A complete plot of ground range (D) versus angle of takeoff (A) is shown

in figure 4.27. This is much more irregular than the single layer plot in

figure 4.7 and reveals additional phenomena. For example, owing to a decrease in maximum electron density or to a modification of the angle

of incidence, a multi-hop signal may penetrate the ionosphere on one of

its hops. Furthermore, when a downcoming ray is just tangent to the

earth, a slight increase in takeoff angle may cause the ray to miss the earth

and return, after another reflection, at a much greater range. This type of

distorted ionosphere gives rise to marked focusing and defocusing of the

signals. An instance of focusing can be seen in the two-hop signal between

angles of about 13° and 24°. All the energy radiated between elevation

angles of about 13° and about 23° is concentrated in a range of a few

hundred kilometers.

188 OBLIQUE PROPAGATION

PLOT OF RANGE VERSUS TAKEOFF ANGLE

FOR RAYS THROUGH IRREGULAR IONOSPHERE

AAA 7 HOP

0 5 10 15 20 25 30 35 40 45 50 55 60 TAKEOFF ANGLE (A) IN DEGREES Figure 4.27. Range versus elevation plots for transequatorial propagation. March 1958, 1900, 75° WMT, 15 Mc/s

4.7. SOME PROBLEMS IN LONG-DISTANCE TRANSMISSION

4.7.1. Path Identification

When the distance of transmission is much greater than 4000 km,

considerable difficulties arise in the identification of the propagation

paths. We have already seen in figure 4.17 that, for a distance of 5300

km, the high-angle one-hop F2 path can be important. Also sporadic E

may play a vital role in reflecting waves, sometimes to the advantage of

the communicator and at other times to his disadvantage since it may cut

off a usable signal. It is useful to identify paths by the number of hops

and the layers from which the reflection takes place.

The following terminology is suggested for the description of such

paths.^ ~ ! 3 Recommendations of the Lindau Meeting, May 1963.
PATH IDENTIFICATION 189

(1) For propagation paths involving reflections by different layers,

the reflections (or hops) should be specified in order of their position with

respect to the transmitter.

(2) A dash will be used to represent a ground reflection. The absence

of a dash will then show up Mtype reflections (fig. 4.23a) and supermodes

(fig. 4.26). Thus figure 4.23a and 4.23b, respectively, would be described

as F2ESF2 and J^2-Es. Figure 4.26 is described by F2F2 and figure 4.28 by FEsF-Es-F. Note that 2F2 means a two-hop F2 path and 3E means

a three-hop E path with intermediate ground reflections.

Figure 4.28. Long-distance paths involving F and Eg reflections.

Assuming thick parabolic F2 layers, the parameters of which are allowed to vary from one hop to another, and a thin Es layer, Kift [5]

has shown how the paths can be deduced from measurements of angle

of arrival and of the time delay in excess of that which would be required

for the signal to travel around the earth's surface between sender and

receiver. Kift plots angles of elevation and excess time against ground

range and obtains mode plots, an example of which is shown in figure 4.29 for the path Ascension Island to Slough, distance 6750 km. At this range one sees that the composite signal received at Slough may have

traveled along the following paths: 2Es-F2, M-F2, G-F2, G-2F2, F2-Fs-3F2,

F2-2Fs-3F2, 5F2 with a possible high angle 5F2, where a G (guided) path

is one involving reflections between E and F. It is easy to see that, in general, the composite signal has a very complex structure, and simple

inspection of an oblique ionogram is usually insufficient to reveal the

actual paths. Even with ray tracing there may be ambiguity because of

the close time spacing of the various echoes and takeoff angles. A similar

identification can be made with figure 4.26 if equivalent path is plotted

against elevation angle.
190 OBLIQUE PROPAGATION

T GREAT-CIRCLE DISTANCE, Km R O \ 2 3 4 5 6 i 7xtOFiGURE 4.29. 19.87 Mc/s mode plots: Ascension Island-Slough, April 11, 1956, 0930-1030 UT.

(After F. Kift, 1960, The propagation of high frequency radio waves to long distance, Proc. lEE 107B,

127.) (a) X plot, hmF2 fairly constant at 340 to 360 km. (b) Mode-delay plot, (c) Mode-angle plot.

4.7.2. E-Layer Cutoff Frequencies for F2 Propagation

The ray path of a signal reflected from the F2 layer penetrates the

E layer at one or more points; hence, in order for the signal to traverse the entire path, the frequency must be sufficiently high to penetrate the

E layer at each of these points. The lowest such frequency is called the

E cutoff frequency.

Referring to figure 4.30, a wave traveling up to the F layer inter- sects the E layer at P. If the frequency is below the E layer penetration

frequency; the wave is reflected and returns to earth at B. This conconstitutes a one-hop E path for the range TB, the radiation angle of
E-LAYER CUTOFF FREQUENCIES FOR F2 PROPAGATION 191

Q -7%""

/ \

Figure 4.30. E layer cutoff.

jp20 y 40 go ao 100 eoo soo 400 eoo sootooo

GROUND

8000 3000 4000

10 90 40 60 60 100 200 300 400 600 800 OOO PATH LENGTH, km

2000 3000 4000 Figure 4.31. Radiation angle wrsus path length, based on virtual reflection heights. E layer—105 km; F2 layer—320 km.
192 OBLIQUE PROPAGATION

which is the same as that for the F2 path. The penetration frequency at the point P is, therefore, equal to the E maximum frequency for the

range TB.

To determine the range TB, we need to know the angle of elevation

A as a function of distance. This is given in figure 4.31 for assumed heights

of 105 km (E) and 320 km (F2). From the location of the point P, we

determine the appropriate E critical frequency and, hence, the corre- sponding E layer maximum frequency. When this is done at each E layer

penetration point, the highest frequency is the E layer cutoff frequency

for the particular path.

4.7.3. Optimum Working Frequency

In designing a communications circuit involving F2 layer trans- mission, it is desirable to use as high a frequency as possible in order to reduce the ionospheric absorption (which decreases as the square of the

operating frequency). The monthly median maximum frequency is unsuitable because it would be reflected 50 percent of the time only. Hence,

to allow for day-to-day changes in critical frequency, it is customary to use 0.85 of the monthly median, and it is called the optimum working

frequency—FOT from the French initials. It is not necessarily the fre- quency of maximum signal or minimum time dispersion. It is based on a

statistical result that it lies below the maximum frequency 90 percent

of the time. That this definition of "optimum" may be misleading in individual cases is illustrated by the oblique ionogram in figure 4.17. The maximum frequency is close to 48 Mc/s so that the 85 percent fre- quency is 40.8 Mc/s. Thus the "optimum" frequency would fall in the

middle of the "dead" space between the maximum frequency of the twohop F signal and the minimum frequency of the one-hop Pedersen ray.

4.8. MULTIPATH PROPAGATION TIMES

The oblique ionograms above show that, as the maximum frequency

is approached, the time dispersion of the signal decreases. This time dis- persion can be of considerable importance in the transmission of information at high speeds because the maximum rate (in binary units per second)

is roughly equal to the reciprocal of the range of multipath propagation

times ATm, where AT^ is a function of frequency, path length and location, local time and season.
MULTIPATH PROPAGATION TIMES 193 The muldpath reduction factor (MRF) is defined as the lowest per- cent of the MUF for which the range of multipath propagation times is less than a specified value [23]. The MRF thus defines a frequency above

which a specified minimum protection against multipath is provided.

From experimental data (oblique ionograms) for a number of paths

in different geographic locations, MRF curves have been deduced, statistically, and are presented in figure 4.32. It can be seen, in the ionograms

shoAVTL above, that the multipath spread approaches zero at the maximum

frequency. It can be seen also that the spread may be significantly re- duced when operating on lower frequencies using such signals as the highangle ray in figure 4.17 or on the Es ray in figure 4.22. It is conceivable

that the rate of transmission of information could be increased by a factor of 100 over normal values by a judicious choice of operating frequency.

To illustrate the use of the MRF curves, consider a path length of 2500 km. When operating on a frequency between 1.0 and 0.85 of the

maximum, the multipath spread should be less than 500 /xsec. On fre- quencies between 0.65 and 0.85 of the maximum, the spread will be less than 1 msec, and in the range 0.43 to 0.65 of the maximum, the spread will be between 1 and 2 msec. There is a frequency on which the spread is a maximum. This frequency is given by figure 4.32, and the value of the

maximum multipath spread is shown in figure 4.33. For a 2500-km path,

the maximum time dispersion is about 3 msec. For a 1000-km path, the

maximum dispersion is about 5 msec, and occurs at a value of MRF;=^56

percent.

1

"""^

1

1

\

s \

msec -

PATH DISTANCE, km Figure 4.32. Multipath reduction factor.
194 OBLIQUE PROPAGATION

10^ 10^ lO'* 10' PATH DISTANCE, km

Figure 4.33. Maximum expected time delay difference.

4.9. RAY PATHS

4.9.1. Without Magnetic Field

It is sometimes necessary to know the path of energy flow between

a transmitter and a receiver. This is particularly important in the analysis of complex pulse-echo patterns observed on oblique ionograms. Ray

tracing is often necessary to establish the feasibility of transmission of

energy from one point to another, and to predict the extent to which

focusing (or defocusing) modifies the distribution (over the ground) of

the reflected energy. A knowledge of the ray path is necessary for the

calculation of time of flight, signal strength, phase, and polarization of

the reflected wave.

It is convenient to think of the ray path as the trajectory of a packet

of waves limited in both frequency and in space. Consider the case of

such a wave packet having a takeoff angle (at the earth's surface) A and

incident on a spherically stratified ionosphere in which the refractive

index is varying slowly with height as illustrated in figure 4.34. Let x

be the range, along the ground, corresponding to a point on the ray path
WITHOUT MAGNETIC FIELD 195

ds\>j<r dh

"^f^ —-(a +h) d0

/ \ r

,a + h + dh

Figure 4.34. /?ay path geometry for a spherically stratified ionosphere.

at a height h above ground, and let x subtend an angle 0 at the center of

the earth. From figure 4.34

{a-\-h) dQ = tan i'dh, (4.18)

together with Snell's law (see 4.9)

/z(a+/i) sin i = a cos A, (4.19)

this gives a cos A dh e = /

"^"^^^^

. (4.20)

One solution to the problem of ray tracing is to approximate the electron

density profile by a suitable model in order to evaluate, analytically.
196 OBLIQUE PROPAGATION

the integral for 0. This is relatively simple to do in the case of a plane

earth and plane ionosphere when the ground range x is given by

cos A dh

\//a2 — COS^ A

(4.21)

The solutions of (4.21) for some of the more commonly used models are given by Budden [24, ch. 11].

When the curvature of the ionosphere is taken into account, the

problem is more difficult. Appleton and Beynon [4] assumed a layer shape

which is derived from a parabola by neglecting small terms, and they obtained (4.17) for the ground range. In general, however, it is not possible to find suitable analytic functions which represent adequately the electron

density profiles [25, 26]. Under such circumstances the ray path has to be computed by dividing the profile into a number of laminae and postulating an analytic N{h) function within each lamina. As the number

of laminae used is increased, the result becomes less and less dependent

upon the form of the assumed distribution within each segment.

An interesting graphical method has been developed by Chvojkova

[27] which is illustrated in figure 4.35 where, for clarity, the refracting

shells are separated by infinitesimal non-refracting shells. From Snell's law {{ir sin i = a constant) we see that, outside the ionosphere, the ray

direction must always be tangent to the surface of a sphere of radius

r sin io; and at any point inside the ionosphere at which the refractive

index is /x, the ray is tangential to a sphere of radius (r/fx) sin io.

r Figure 4.35. Chvojkova's construction.
WITH MAGNETIC FIELD (WAVES AND RAYS) 197 4.9.2. With Magnetic Field (Waves and Rays)

From the point of view of ray tracing, the main effects of the magnetic field are

(1) Ordinary and extraordinary waves are produced;

(2) The direction of energy flow (ray direction) differs, in general,

from the phase normal;

(3) The refractive index depends upon the angle of refraction, so that

it is not possible to solve Snell's law directly.

The angle a between the directions of phase propagation and energy

propagation is given by (2.123), namely

\ dv 1 d^x tana= — —= - — . (4.22)

vdd fi dd

Substituting the expression for /x(2.77) in (4.22) we obtain

The + and — signs refer to the ordinary and to the extraordinary rays

respectively. Note that a is of opposite sign for the ordinary and extra- ordinary waves except when the refractive index of one of the rays is greater than unity. Furthermore, the sign of tan a changes as 6 goes through 90°. Bremmer [28] has summarized the ray behavior as follows:

(a) The wave normal is parallel to the plane of incidence and satisfies Snell's law.

(b) The ray is situated in the plane through the wave normal and

the earth's magnetic field. (c) The angle a measured from the wave normal to the ray, is given

by (4.23).

Before considering some actual ray paths, it is of interest to consider

the implications of these rules. First they imply that, as a wave packet

penetrates into the ionosphere, it "slips" sideways in a direction parallel to the magnetic meridian. For upgoing waves the extraordinary ray is (for ju<l) deflected towards the magnetic equator, whereas the ordinary

ray is deflected away from the magnetic equator. Second, let us consider

(4.23) in the case of waves propagating vertically. We see that tan a is
198 OBLIQUE PROPAGATION

zero under the following conditions:

Y= 0, no magnetic field ^ = 0°, 180° propagation at the magnetic poles

^ = 90° propagation at the magnetic equator

^2 = 1. At the levels of reflection, n = 0 and X=l for the ordinary wave and

X = l± y for the extraordinary waves. This gives

tanao=— cot^, (4.24)

sin 6 cos d smd cos 6 tan ax = y . = . (4.25) V^in^T-HcoP^ 1+COS2 0

^

^

Hence, at reflection, the ordinary ray is perpendicular to the earth's magnetic field. Note that ax depends on the direction, but not on the

magnitude, of the earth's magnetic field.

4.9.3. Some Sample Ray Paths

4.9.3.1. Vertical Propagation

Applying Snell's law in a plane stratified ionosphere, we find that

the wave normal is always vertical. The lateral deviation Z) at a height

h is given by

D= f

tan a dh. (4.26)

In the general case this expression is too complicated to solve analytically, but D can be found by dividing the electron density profile into a number of slabs and determining the mean value of tan a (tan a say) for each slab, then summing, i.e., i>=Xt^ir^A/ii, (4.27)

i where Ahi is the thickness of the ith slab. Ray paths over Boulder, Colo., which have been calculated by this method, are shown in figures 4.36 and 4.37. Consider first the paths on

frequencies greater than the gyrofrequency ( = 1.5 Mc/s approx.). The
Figure 4.36. Some ray paths ivith normal incidence over Boulder on frequencies above the gyrofrequency.
200 OBLIQUE PROPAGATION

Figure 4.37. Some ray paths with normal incidence over Boulder on frequencies less than

the gyrofrequency.
SAMPLE RAY PATHS 201

following features are of interest:

(1) The ray paths lie entirely in the magnetic meridian.

(2) On a given frequency, less than the penetration frequency, the

deviation (to the north) of the o ray at reflection is always greater than

that (to the south) of the extraordinary ray at its level of reflection. (3) On a given frequency and for the same real height, the deviation

of the extraordinary ray is greater than that of the ordinary ray.

(4) Most of the deviation of the ordinary ray takes place relatively

close to the reflection level. On a frequency less than the gyrofrequency, the situation is a little different. The ordinary wave behaves much the same as before, but

the behavior of the extraordinary (z) wave is different. In figure 2.9 we

see that, for 0<X<1, the refractive index of the extraordinary wave is greater than unity so that in this range /jl^—I is positive and the ray is deflected to the north. For values of X between 1 and 1+ Y (reflection),

ju is less than unity and the ray veers to the south. Whether the point of

reflection lies to the north or the south of the point of entry will depend

on the frequency and on the profile. The path of the downcoming wave is identical with that of the upgoing wave. Owing to electron collisions, these

paths will be modified slightly, the modification becoming more pro- nounced as the wave frequency approaches the gyrofrequency.

On a frequency close to the penetration frequency of the F2 layer,

the ordinary ray may be deviated by 50 or 60 km; however, the deviation

within the layer falls off rapidly as the frequency increases above /oi^2. For example, with /oi^2= 10 Mc/s the deviation, with a complete passage

through a Chapman layer on a frequency of 40 Mc/s, is of the order of

0.1 km.

Because of the lateral deviations, the ordinary and extraordinary

rays, in practice, sample slightly different electron density profiles.

4.9.3.2. Oblique Paths

For fairly short distances of transmission, the plane containing the

emergent ray is parallel to, but not necessarily coincident with, the great

circle plane containing the incident ray. The incident and emergent

planes are coincident for exactly east-west propagation in all latitudes

and for north-south propagation in a magnetic meridian. Some ray paths

have been calculated in the case of approximately east-west propagation

in the United States with a parabolic distribution of electron density with

height and the dipole approximation (earth centered) to the earth's
202 OBLIQUE PROPAGATION

DIPOLE FIELD,

ho = 200 km, Vm = 100 km

ELEVATION = 26.717°

f = 14.142 MC/S TRANS:

39° LAT. -75° LONG.

LATERAL DEVIATION (METERS)

40° LAT.

-105° LONG.

400 • EXTRAORDINARY^,

EXIT ^

ENTRY

200

-200 - 600 1 550 ^n500 450 ^.--'^OO 350 RANGE

-400 - EXIT -^ORDINARY NORTH

Figure 4.38. Horizontal projection of ray paths in a parabolic layer for geographically

east-west propagation in the United States.

magnetic field. The projections of the paths on to a horizontal plane are shown in figure 4.38. The paths are twisted, veering first in one direction

and then in the other. The maximum deviations are about 0.3 km, and

the net deviations, at the point of exit from the ionosphere, are only about

100 m. Furthermore, the ordinary and extraordinary rays are, roughly,

mirror images of each other. The deviation tends to increase with operating

frequency because of the increase in depth of penetration of the ray into

the layer; however, the deviations with oblique propagation are much less than with vertical propagation.

With propagation in the magnetic meridian (north-south) there is no

lateral displacement of the ray, but the point of energy reflection is, in general, displaced from the center of the path. The point of reflection of the ordinary wave is displaced to a higher magnetic latitude than the

midpoint and vice versa for the extraordinary wave.

Ionospheric ray paths can be calculated in a variety of ways.

Those more commonly used are the Booker quartic [29], the iterative method [30], Haselgrove's equations [31], Titheridge's approximate

method [32], and Poeverlein's graphical construction [33].

Poeverlein's method is of interest because it illustrates the existence

of the ""spitze." It is a graphical method and depends on the fact that,

for a refractive index surface,"* the radius vector gives the wave normal

* The refractive index surface is the locus of end points of a vector whose magnitude is the refractive index and whose direction is the direction of phase propagation.
SAMPLE RAY PATHS 203

direction and the normal to the surface is the ray direction, as shown in figure 4.39. The wave normal direction is known from Snell's law, so the ray direction can be obtaiued from the construction shown in figure

4.39. From this direction the next point on the ray is determined and the

procedure is repeated. Note that the condition for energy reflection is given by a point such as A where the normal to the /x surface is horizontal,

but where the wave normal is not, in general, horizontal.

DIRECTION OF EARTH'S MAGNETIC FIELD /

Figure 4.39. Illustrating Poeverlein's construction

Direction in which the ray R is normal to the refractive index surface. N, the wave normal, is given by the direction of the radius vector. Curves not drawn to scale.

Using this construction, with oblique propagation in the magnetic

meridian, Poeverlein showed that, for angles of incidence less than a

certain critical value 0^ (where sin 0,. = \/ [ Y/ ( 1 + Y) ] cos/, /=dip),

the path of the ordinary ray never becomes horizontal, but has a cusp at the level X=l. This phenomenon, called the ^^spitze," is illustrated by

the ray paths in figure 4.40. An excellent description of the behavior of rays for many special cases is given by Budden [24, ch. 13] where he

shows that on frequencies greater than the gyrofrequency the spitze is not exhibited by the extraordinary ray.
204 OBLIQUE PROPAGATION

DIRECTION OF MAGNETIC FIELD

/

/

T EARTH Figure 4.40. Sample ordinary ray paths for oblique propagation in magnetic meridian, showing the Spitze. Not drawn to scale.

4.9.3.3. Topside Soundings

With the advent of artificial earth satelUtes it is necessary to consider reflections from the topside of the ionosphere and transmission between satelhtes and ground.

Some ray paths for waves having the vertical direction of phase

propagation are shown in figure 4.41 for various heights above the peak

of a Chapman layer in the northern hemisphere. Note that the ordinary

ray is deviated to the south and the extraordinary ray is deviated to the

north. As the height of the satellite decreases, i.e., as the surrounding

electron density increases, first the extraordinary wave and second the

ordinary wave get "imprisoned" in the satellite because the plasma is overdense to waves of that frequency (e.g., 5 Mc/s). When the satellite

is near its reflection level, the ordinary wave energy slides almost side- ways. An additional path (the z path) is possible, which may be understood by reference to figure 2.9. For Y<1 it will be seen that there is a branch of the extraordinary curve lying in the range

l_y2

<x<n-y.

Normally this wave cannot originate except from a source embedded in
SAMPLE RAY PATHS 205

Penetration frequency (o wave)=10 Mc/s

fH=0.75 Mc/s

Dip=72.9°.
Figure 4.42. Some z ray paths from a topside sounder located at a height of 1000 km in a Chapman layer.

Penetration frequency (o wave)=10 Mc/s

/jy=0.75 Mc/s

Dip=72.9°

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 Mc/s

Figure 4.43. Topside ionogram, Singapore, Nov. 19, 1962, 0810 UT.

(Reproduction is by permission of the Controller of Her Brittannic Majesty's Stationery

Office and is by arrangement with the Director of Radio Research.)
SAMPLE RAY PATHS 207

the plasma. To get some idea of what the ray paths may look like we notice

that /z^>l near X= {I— Y^) / (I— YD and /z drops below 1 as it ap- proaches reflection. The quantity (/i^— 1) and, hence a, will change sign.

The ray path veers first to one side and then to the other, as illustrated

in figure 4.42. The existence of the z-wave has been confirmed in recent soundings of the topside—see figure 4.43.

4.9.3.4. Satellite-to-Ground Paths

To a first approximation on very high frequencies, the effective ionosphere exists only within a definite range of heights, and we shall assume (for the sake of discussion only) that the refractive index is unity

both above and below this range. Consider a wave of frequency considerably greater than the critical frequency; at very oblique incidence the rays

are reflected (see fig. 4.44) but within a cone of semiangle 0o = sin~^ Hm all rays will penetrate the ionosphere. The refractive index = V^l — (/c//)^]

is the value at the height of maximum electron density in the absence

of the earth's magnetic field and collisions. This blocking effect of the

ionosphere for zenith angles greater than a critical value is sometimes

called the ''iris" effect.

0

Figure 4,44. The iris effect (plane ionosphere).
208 OBLIQUE PROPAGATION

Figure 4.45. Effect of ionosphere curvature on angular error. With angles less than 00, the ray is bent in the layer and so the angle

of elevation at the ground is increased by an amount /3 as seen in figure

4.44. The angle (3 is called the "angular error at the observer" and, in

this case, it is equal to —/3', the "angular error at the source." The effects mentioned above for a plane-stratified ionosphere are modified slightly by the curvature of the ionosphere. The geometry is shown in figure 4.45 and shows that the total bending (i.e., the difference

in direction of the ray at the source and at the observer), r = /5+/5', is no

longer zero. Thus the total bending which occurs in a ray passing through

the ionosphere is a second-order effect, since the bending of the ray on

entering the ionosphere (from above) is compensated for (actually, over- compensated for) by the bending on leaving the ionosphere. With the

exception of the special case of radio astronomy, where the source-observer

distance is essentially infinity, the angular error at the observer generally

differs from, and may be greater or less than, the total bending.

It can be seen that the overall effect of the refracting iris is to focus rays from a large section of the sky into a relatively narrow cone. From

the point of view of signals received at the earth from a satellite, this means a smaller signal/noise ratio (see ref. [28], ch. X, sec. 8).

The effect of the earth's magnetic field is to produce two images of

the satellite—ordinary and extraordinary. In the general case of propagation making an angle (non-zero) with a magnetic meridian, the two

rays are deviated in opposite direction from the plane of incidence but

the lateral deviation is much smaller than the refractive effects in the

plane of incidence. Thus we get a good approximation to the actual ray
SAMPLE RAY PATHS 209

1324 MST, SEPT. 17, 1958 AZIMUTH = 350°

foF2 = 9 MC/S

hMAx = 382 km

1200

S 900

LlI 600

300

5.9

„ 0.4km

5.76°

S BOULDER N Figure 4.46. Ray paths (o and x) from satellite to ground near Boulder, Colo. (By permission of R. S. Lawrence and D. J. Posakony, 1962, A digital ray-tracing program for ionospheric

research. Space Research II, Proc. 2d Intern. Space Sci. Symp., Florence, North Holland Publ. Co.) path if we project the ray on to the vertical plane of incidence. In figure

4.46 is an example, projected on a vertical plane (not to scale) , of ray

paths from a 20 Mc/s satellite -borne transmitter near Boulder, Colo.

The total bending along the extraordinary ray always exceeds the total bending along the ordinary ray. In figure 4.46, for example, the total bending of the extraordinary wave is 2°. 73 while that of the ordinary wave is only 2°. 61. Notice that this relationship does not necessarily mean that

the angular errors at the observer are similarly related. Several methods

are available for estimating the angular error at the observer in the

absence of the earth's magnetic field [34, 35].

The above treatment assumes a spherically stratified ionosphere so that horizontal gradients in electron content are ignored. The treatment

of refraction in the presence of ionospheric distortion is a complicated

process, except in cases of simple models. One such model is that of a "wedge" of electrons. For angles of incidence near the zenith the relation- ship between the wedge refraction r and the horizontal gradient of total electron content is given by [36]

(4.28)
210 OBLIQUE PROPAGATION

Data on ionospheric irregularities can be obtained from measurements

on radio-star signals [37, 38], and on satellite radio signals [38].

4.9.4. Propagation Effects Associated With Ray Paths

(a) Phase path P is given by

P=jl^ cos a ds. (4.29)

(b) Group path P' is given by

P' = j fi' cos ads. (4.30)

(c) Total absorption L is given by

L = y^ K cos a ds, (4.31)

where fi and fx' are the phase and group refractive indices respectively and

K (kappa) is the absorption per unit length of path.

It is of interest to note that, when the magnetic field is absent, the

relationship between /x, /x', and L is given by

L = ^{P'-P) (4.32)

2c

provided that v (the collision frequency) is independent of height.

4.9.5. Faraday Rotation

4.9.5.1. Rotation of the Plane of Polarization

A linearly polarized wave can be considered as the resultant of two

vectors, of equal amplitude, rotating in opposite senses with the same

angular speed. In the case of quasi-longitudinal propagation in the absence of absorption, the two characteristic waves (ordinary and extra-
FARADAY ROTATION 211 -COMPONENT

REFERENCE PLANE

RESULTANT

^+ COMPONENT

Figure 4.47. Faraday rotation. (Propagation is perpendicular to the plane of the paper.) ordinary) are essentially circularly polarized. These waves, being characteristic waves, suffer no change of polarization as they propagate

through the medium but, because they have different phase velocities,

the plane of polarization of the resultant linearly polarized wave rotates gradually. This phenomenon is known as Faraday rotation and its magnitude can be computed as follows. Consider an element of path length ds in which the rotation of the

electric vectors of the o and x waves are dK^ respectively (see

sec. 2.5.3.). Figure 4.47 shows the relationship between c?K+, dK^ and

the angle through which the plane of polarization rotates in the dis- tance ds. From this figure we have

d^ = i{dK+-dKJ),

(4.33)

12 = i(i^-f-i^-),

where

27r „ 27r , K+ = — P+ = —ds,

Xo X+

(4.34)

and

(4.35)

where the P's are the phase paths, X's are the wavelengths within the

ionosphere, and Xo is the free space wavelength. Note that we have im-
212 OBLIQUE PROPAGATION

plicitly set cos a = 1, which restricts the discussion to frequencies well

above the plasma frequency.

From (4.33), (4.34), and (4.35) we obtain

fi = f f

(/x+-M_) ds. (4.36)

In the case of quasi-longitudinal propagation we have (sec. 2.3.3.2)

On very high frequencies m=1 and, on expanding this expression, neglecting the high order terms, and reducing, we get

iu+ -M-^X Yl=XY cos d. (4.38) In terms of the mks units, (4.36) now becomes

12 = ^^ ( NBo cos dds, (4.39)

where ^ = 2.97X10-2.

It is important to remember that several approximations have been

made in deriving this expression and its validity becomes questionable

as 6 increases and it breaks down completely when quasi-longitudinal

propagation gives way to the quasi-transverse type. Nevertheless it has

proven very valuable in the interpretation of 12 measurements in terms of

the total electron content JN ds. Measurements of Faraday rotation 12 have been made on signals from

artificial satellites [39] and from radar reflections from the moon [40]. In moon echo experiments the frequencies are usually high enough

(several hundred megacycles per second) so that (4.39) is accurate. To

find the total electron content in a unit vertical column of the ionosphere

it is possible to replace the path element ds by dh sec i where i is the local zenith angle (between the ray and the vertical) and dh is an element of

height. In this case (4.39) becomes

12 = ^ I NMdh, (a)

(4.40)
FARADAY ROTATION 213 where

M=Bo cos 6 sec (p. (b)

It must be remembered that (4.40) apphes to one passage through the

ionosphere.

Although further restricting the generahty of the expression, it is convenient to take M as the constant in that part of the ionosphere

(0 to 1000 km, say) in which the bulk of the rotation occurs, and to

write

^/ NdK (4.41)

for one-half the total rotation of a moon echo. M is a weighted average

of M [41]. In the case of frequencies below about 40 Mc/s, such as those often

used for satelhte beacon measurements, (4.39) is only approximate and

ray tracing methods are required to determine the electron content by

a trial and error process.

4.9.5.2. Some Results of Faraday-Rotation Experiments

These measurements have given information about the electron

density profile above the height of maximum density of the Fi layer /imax (the so-caUed topside).

When combined with electron density profile data for the bottom

side, they provide a determination of the ratio of total electron content

to the content below /imax- This ratio appears to vary between about 3 2% I ,

Figure 4.48. Irregularities in electron content 0834, 105° WMT, Sept. 4, 1958.

(After C. G. Little and R. S. Lawrence, 1960, the use of polarization fading of satellite signals to study

the electron content and irregularities in the ionosphere, J. Res. NBS 64D (Radio Prop.), 335.)
214 OBLIQUE PROPAGATION

and about 5 from day to night. The daytime peak in electron content is six to eight times greater than the nighttime minimum. Furthermore,

the noontime content seems to be somewhat higher in winter than in summer. During magnetically disturbed conditions the total electron content appears to decrease.

Because of the high sensitivity inherent in this method, it is possible to observe the irregular structure in the electron content of the F2 layer

as shown in figure 4.48.

REFERENCES

[I] Breit, G,, and M. A. Tuve (1926), A test of the existence of the conducting layer, Phys. Rev. 28, 554.

[2] Martyn, D. F. (1935), The propagation of medium radio waves in the ionosphere,

Proc. Phys. Soc. 47, 323.

[3] Smith, N. (1939), The relation of radio sky wave transmission to ionosphere

measurements, Proc. IRE 27, 332.

[4] Appleton, E. V., and W. J. G. Beynon (1940), The application of ionospheric data

to radio communications problems, Proc. Phys. Soc. 52, Pt. I, 518; (1947), Proc. Phys. Soc. 59, Pt. II, 58.

[5] Kift, F. (1960), The propagation of high frequency radio waves to long distances, Proc. lEE 107B, 127.

[6] Aono, Y. (1962), Study of radio wave propagation in sweep-frequency pulse transmission tests in Japan, J. Radio Res. Lab. 9, 127.

[7] Sulzer, P. G. (1955), Sweep-frequency pulse-transmission measurements over a 2400 km path, J. Geophys. Res. 60, 411.

[8] Hatton, W. L. (1961), Oblique sounding and H.F. radio communication, IRE

Trans. Commun. Syst. CS-9, 275.

[9] Cox, J. W., and K. Davies (1955), Oblique incidence pulse transmission. Wireless Eng. 32, 35.

[10] Sandoz, O. A., E. E. Stevens, and E. S. Warren (1959), The development of radio

traffic frequency prediction techniques for use at high latitudes, Proc. IRE 47,

681.

[II] Moller, H. G. (1958), Further results of sweep frequency oblique-incidence measurements, J. Atmospheric Terrest. Phys. 13, 173.

[12] Wilkins, A. F., and F. Kift (1957), Characteristics of H.F. signals. Electronic and

Radio Eng. 34, 1. [13] Agy, v., and K. Davies (1959), Ionospheric investigations using the sweepfrequency pulse technique at oblique incidence, J. Res. NBS 63D (Radio

Prop.), 151.

[14] Agy, v., K. Davies, and R. Salaman (1959), An atlas of oblique-incidence iono- grams, NBS Tech. Note 31.

[15] Warren, E., and E. L. Hagg (1958), Single hop propagation of radio waves to a

distance of 5300 km. Nature 181, 34.

[16] Davies^, K. (1959), The effect of the earth's magnetic field on m.u.f. calculations,

J. Atmospheric Terrest. Phys, 16, 187.

[17] Thomas, J. A., and E. K. Smith (1959), A survey of the present knowledge of sporadic E ionization, J. Atmospheric Terrest. Phys. 13, 295.
REFERENCES 215

[18] Wright, J. W., and T. N. Gautier (1960), Note on a test of the equivalence theorem

for sporadic E propagation, J. Res. NBS 64D (Radio Prop.), 347.

[19] Calvert, W., K. Davies, E. Stiltner, and J. T. Brown (1963), Equatorial spread-F

motions, Proc. Intern. Conf. Ionosphere, p. 316 (The Institute of Physics and

the Physical Society, London).

[20] Hagg, E. L., and W. Rolf (1963), A study of transatlantic radio propagation modes

at 41.5 Mc/s, Can. J. Phys. 41, 220.

[21] Silberstein, R. (1954), Sweep-frequency backscatter—some observations and

deductions, IRE Trans. Ant. Prop. AP-2, 56.

[22] Villard, O. G., S. Stein, and K. C. Yeh (1957), Studies of transequatorial ionospheric propagation by the scatter-sounding method, J. Geophys. Res. 62, 399.

[23] Bailey, D. K. (1959), The effect of multipath distortion on the choice of operating

frequencies for high-frequency communications circuits, IRE Trans. Ant. Prop.

AP-7, 398.

[24] Budden, K. G. (1961), Radio Waves in the Ionosphere (Cambridge Univ. Press).

[25] De Voogt, A. H. (1960), Ionospheric models as an aid for the calculation of ionospheric propagation quantities, Proc. IRE 48, 341.

[26] Muldrew, D. R. (1959), An ionospheric ray -tracing technique and its application

to a problem in long distance radio propagation, IRE Trans. Ant. Prop. AP-7,

3939.

[27] Chvojkova (Woyk), E. (1959), The refraction of radio waves by a spherical ionized

layer, J. Atmospheric Terrest. Phys. 16, 124.

[28] Bremmer, H. (1949), Terrestrial Radio Waves, Ch. XI (Elsevier Publ. Co.).

[29] Booker, H. G. (1949), Application of magnetoionic theory to radio waves incident obliquely upon a horizontally stratified ionosphere, J. Geophys. Res. 54, 243.

[30] Lawrence, R. S., and D. J. Posakony (1962), A digital ray-tracing program for ionospheric research. Space Research II, Proc. 2d Intern. Space. Sci. Symp.,

Florence (North Holland Publ. Co.).

[31] Haselgrove, J. (1955), Ray-theory and a new method for ray-tracing. Report on

Conf. on Phys. of the Ionosphere, 355, Phys. Soc, London.

[32] Titheridge, J. E. (1959), Ray-paths in the ionosphere, J. Atmospheric Terrest. Phys. 14, 50.

[33] Poeverlein, H. (1949), Strahlweze von Radiowellen in der lonosphare, Z. angen

Phys. 1, 517.

[34] Lawrence, R. S., C. G. Little, and H. J. A. Chivers (1964), A survey of ionospheric

effects upon earth-space radio propagation, Proc. IEEE 52, No. 1, P. 4. [35] Weisbrod, S., and L. J. Anderson (1959), Simple methods for computing tropospheric and ionospheric refraction effects on radio waves, Proc. IRE 47, 1770.

[36] Smith, F. G. (1952), Ionospheric refraction of 81.5 Mc/s radio waves from radio

stars, J. Atmospheric Terrest. Phys. 2, 350.

[37] Komesaroff, M. M. (1960), Ionospheric refraction in radio astronomy. I. Theory, Austrahan J. Phys. 13, 153.

[38] Lawrence, R. S., and J. L. Jespersen (1961), Refraction effects of large scale iono- spheric irregularities observed at Boulder, Colo., Space Research II, Proc. 2d

Intern. Space. Sci. Symp., 277 (North Holland Publ. Co.).

[39] Little, C. G., and R. S. Lawrence (1960), The use of polarization fading of satellite signals to study the electron content and irregularities in the ionosphere, J. Res. NBS 64D (Radio Prop.), 335.

[40] Evans, J. V. (1957), The electron content of the ionosphere, J. Atmospheric

Terrest. Phys. 11, 259.

[41] Yeh, K. C, and V. H. Gonzales (1960), Note on the geometry of the earth magnetic field useful to Faraday effect experiments, J. Geophys. Res. 65, 3209.

CHAPTER 5

Signal Strength

5.1. MEANING OF SIGNAL STRENGTH

The instantaneous value of a sine wave function at a point is defined

by the peak ampUtude and the instantaneous phase at the point. The

ampUtude of a composite wave signal is given by the vector sum of its components; thus, if the components are in phase, the resultant amplitude

will be the algebraic sum of the individual waves. If the phases of the

separate components are varying randomly with respect to each other,

the resultant signal power, averaged over many fading cycles, is given

by the sum of the powers in the component waves. In this chapter the

term "signal strength" will be used in a broad sense to mean either the

amplitude (field strength) or the power received by an antenna. The signal strength at any time depends upon absorption along the

path, path focusing, polarization, and phase of the waves. In this chapter we shall discuss some aspects of these phenomena.

We shall discuss first the factors affecting the average power received

(system loss) and then the factors which produce variations about the

average (i.e., fading)

.

5.2. FACTORS AFFECTING SIGNAL STRENGTH

Consider a radio communications system which consists of a transmitter, a transmission line, a transmitting antenna, the propagation

medium, a receiving antenna, a receiver transmission line, and, finally a

receiver. It is possible to consider the entire circuit between transmitter

output terminals and the receiver input terminals as a "black box" as shown in figure 5.1. If pt is the power fed into the terminals of the feeder

line from the transmitter and if pr is the signal power available from the

terminals of the line from the receiving antenna, then the total system

217
218 SIGNAL STRENGTH

TRANSMITTER

TERMINALS oPt

ANTENNAS

TRANSMISSION LINES AND

MEDIUM

RECEIVER o TERMINALS

•Pr

Figure 5.1. Block diagram to illustrate the power loss between transmitter terminals and receiver terminals. power loss [1]^ Ls, expressed in decibels, is given by

L. = 10.og(g)=-10.og(|-;). (5.1)

Thus, for a given transmitter output power, as the loss L increases, the

received power pr decreases. Let us represent the powers by small letters and the logarithms by

capital letters so that

P^ = 101ogp, (a)

and (5.2)

P.= 101ogp.. (b)

Then (5.1) can be written in the form

Ls = Pt-Pr (in decibels). (5.3)

Let us now consider the losses incurred by the signal as it travels between the transmitter terminals and the receiver terminals, as shown

schematically in figure 5.2. First of all there are the ohmic losses in the

feeder line and in the transmitting antenna due to the resistance of the

wire and to the finite conductivity of the environment (induced earth

currents, etc.). The rest of the power is radiated into space, mostly from

the antenna, but a small amount from the transmission line. The radiation efficiency of the antenna is given by the ratio of the power radiated

to the power absorbed from the source. For high frequencies the efficiency

of most antennas is relatively high (e.g., the efficiency of a half wave dipole

is generally greater than 90 percent)

For an isotropic radiator the power is radiated equally in all direc- tions and the power radiated in any direction can be taken as a reference. All actual antennas have radiation patterns such that the power flux

1 Figures in brackets indicate the literature references on p. 255.
FACTORS AFFECTING SIGNAL STRENGTH 219

EFFECTIVE TRANSMITTING ANTENNA GAIN (OR LOSS)

ANTENNA

(GAIN OR LOSS)

1 -4

OHHIC LOSS

IN TRANSMISSION

LINE AND ANTENNA

TRANSMITTER

PATH LOSSES

-

SPATIAL LOSS

ABSORPTION LOSS

FOCUSING (LOSS OR GAIN) SCATTERING NET LOSS

EFFECTIVE RECEIVING ANTENNA GAIN (OR LOSSf

1 ANTENNA

MISMATCH

GAIN OR LOSS

ANTENNA

GAIN OR LOSS

»>

OHM 10 LOSS

IN TRANSMISSION

LINE AND ANTENNA

RECEIVER Figure 5.2. Block diagram showing the various sources of power loss as a signal travels from a transmitter to a receiver.

is maximized in certain preferred directions. Of course, when the total power radiated is the same for both the hypothetical and actual antennas,

then if there is a power gain in some directions, this must be exactly

balanced by a loss in other directions. After the signal has left the antenna it loses energy density by

several processes, such as:

(1) The spatial spreading of the energy (inverse distance squared

dependence)

.

(2) Polarization matching (or mismatching). We have seen in chapter 2 that, within the ionosphere, two progressive waves can exist (ordinary and extraordinary). On entry into the ionosphere a wave with

arbitrary polarization will excite ordinary and extraordinary waves by

different amounts depending on the propagation angle at the bottom

of the ionosphere. Thus, from the point of view of a single magneto-ionic wave, there is a loss of power, in general, on entry into the ionosphere.

(3) Absorption of energy will occur in the D and lower E regions due

to electronic collisions, as explained in section 2.3.3.3. The energy in the wave is in fact converted into heat.

(4) Due to curvature of the ionosphere and/or due to the change of

ground range with angle of elevation, the power flux at any point on the

earth may be enhanced by focusing or diminished by defocusing. Energy

may also be scattered in or out of the main path by ionospheric irregularities, but this problem is too difficult to be considered here.
220 SIGNAL STRENGTH

(5) On leaving the ionosphere the polarization for a particular

magneto-ionic wave will have a certain configuration depending on the

angle between the wave normal and the earth's magnetic field at the

bottom of the ionosphere. Since the angle between the magnetic field and the emergent wave differs from the angle between the magnetic

field and the incident wave, the polarization of the emergent wave will, in general, be different from the polarization of the incident wave. Further- more, the polarization of the wave will not in general match that of the

reqeiving antenna and there will therefore be a loss of received signal due

to polarization mismatch. For certain directions there may be a gain due

to the antenna pattern; in other directions there will be a loss. Finally, there are ohmic losses in the receiving antenna and in its transmission line. The polarization mismatch losses can be included with the antenna

gain to give an "effective antenna gain" for the particular angle of takeoff

and wave polarization. Our main concern, in this book, is with propagation in the medium between the antennas. The power losses along the

propagation path, and which are not associated in any way with the

antennas, will be called the "path loss."^ In what follows it will be assumed that the polarizations of the hypothetical isotropic radiators are perfectly matched to the polarizations of the

characteristic waves excited in the ionosphere.

Consider a single propagation path, with a given characteristic wave,

between a transmitter and a receiver. With an actual antenna, let Lta = the ohmic loss in the transmitting antenna and its transmission

line, in decibels,

Ltp = the polarization mismatch loss of the transmitting antenna,

G< = the gain of the transmitting antenna in the desired direction,

Lp = the path loss in decibels,

Lrp = the polarization mismatch loss of the receiving antenna,

Gr = the gain of the receiving antenna in the desired direction, and

Lra = the ohmic loss in the receiving antenna and its transmission line. Then the system loss is given by

Ls= Lta-\-Ltp—Gt-\-Lp-]-Lrp—Gr-\-Lra' (5.4)

Of course, it sould be remembered that the antenna gains Gt and Gr may

be positive or negative depending on the direction of radiation.

2 CCIR Recommendation No. 241 defines a quantity called "basic transmission loss" and states that

it is sometimes called path loss. It is important to note that our definition of path loss is not the same as that of basic transmission loss.
FACTORS AFFECTING SIGNAL STRENGTH 221 In practice, the total signal arriving at a receiver, after reflection at the ionosphere, is composed of individual signals which have traversed

different paths and which have differing characteristic polarizations. To

draw an electrical analogy, we can think of the component paths as a

set of resistances in parallel. The presence of additional paths, although

they involve losses, actually increases the received power and, therefore,

diminishes the effective loss of the system. The ohmic losses in the an- tennas and their transmission lines (see fig. 5.2) are the same for all paths.

However, the effective antenna gain will depend on the particular propagation path. Hence, the additional paths must be considered as parallel

channels across the terminals A and B in figure 5.2. Let Li represent, for channel 1, the sum of the losses (in decibels)

given by (5.4), with the exclusion of the ohmic losses; that is, Li= Ltpi — Gti-\-Lpi-{-Lrpi — Gru (5.5)

and, similarly, for L2, L3, etc. To determine the manner in which the net

loss between A and which we may call Labi is related to Li, L2, L3,

etc., it is necessary to deal with the fraction / of the power which is lost along each path. That is, Li=10 log /i, etc. (5.6)

Invoking the analogy of parallel resistances, it will be seen that the net

loss Iab is given by —1111 = -+T+-+etc.,

Iab n h h

and Lab by

Lab = 10 log Iab = — 10 log

1 1 1 -+-+-+etc.

h h h

(5.7)

To take a simple example, consider three possible paths for which the

losses between A and B are Li = 50 dB, L2=50 dB, and L3=100 dB.

The corresponding values of the /'s are: /i=10^, /2=10% and /3=10^°, so that the net loss /^5 = 5X10^ and L^b = 47 dB. This shows that the contribution to the total signal from path 3 is negligible, and that the contributions from paths 1 and 2 give a net loss which is 3 dB less than that for either path 1 or path 2. Consider the case where Li = 50 dB, L2 = 60 dB,

and L3 = 70 dB, which gives h = 10^, = 10\ and h = 10^ The net loss Ub =
222 SIGNAL STRENGTH

9X10^ which gives Lab = ^9.S dB. As would be expected, the contributions to the total signal from paths 2 and 3 amount to only 0.5 dB.

5.3.1. Components of Path Loss

In high-frequency propagation via the ionosphere, the received signal

usually consists of a number of component waves which have traveled over different paths. The relative phases of individual waves vary rapidly

and randomly so that the total received power, averaged over a period

(e.g., several minutes) long compared to the fading cycles, is essentially

the sum of the powers in the individual waves. It is important to realize that when we talk of path loss we imply an average power loss. The components of path loss (for a single path) have been enumerated above (in sec. 5.2) and are

(1) The simple inverse distance or dispersion of the energy in space; we shall denote this loss, in decibels, by Ld.

(2) Absorption in the ionosphere. La.

5.3. PATH LOSS

Figure 5.3. Illustrating the focusing and defocusing of iono- spherically reflected radio beams.

(a) Convergence of rays (focusing), (b) Divergence of rays (defocusing).
FOCUSING 223

(3) Focusing or defocusing of power, L/. Note that L/ will be positive for defocusing and negative for focusing.

The path loss, Lp, in decibels, is given by the sum of its components,

namely,

Lp=Ld+La+Lf. (5.8)

Let us now discuss these losses in more detail.

5.3.2. Spatial Loss

As a wave travels out from a small source, the power flux falls off inversely as the square of the distance s from the source, therefore,

Ld = 201ogs. (5.9)

5.3.3. Focusing

5.3.3.1. EfFective Path Length

Focusing is the result of the convergence or divergence (defocusing)

of originally neighboring rays (in addition to the divergence responsible

for Ld) as illustrated in figure 5.3, for example. In practice it is very

difficult to take into account the focusing of ionospherically reflected radio signals. In fact, it is necessary to have a detailed knowledge of the

ionosphere along the ray path together with an elaborate ray-tracing

program, as already discussed in section 4.6.6. Nevertheless, it is possible to consider the effect of focusing in terms of an effective path length Se. The physical meaning of this effective path length can be seen from the

following argument. In the absence of all other forms of energy loss the

power flux at a distance Sg from an isotropic radiator, which radiates a

total power pta^ is given by

Now let the energy radiated into the same cone by the antenna be de- focused as shown in figure 5.4. Let s be the distance from the antenna

at which the area covered by the defocused rays is the same as that for
224 SIGNAL STRENGTH

Figure 5.4. Illustration of the concept of effective path length which takes into account thefocusing and defocusing of radio beams.

IONOSPHERE

Figure 5.5. The divergence of a radio beam for a curved earth.

the original case, so that the power flux is the same for both. Thus the

defocusing can be taken into account by replacing the true distance s of the receiver by an effective distance Sg. In this way the spatial loss and

the focusing losses can be combined in the expression

Ld+L/=20 log Se. (5.11)
FOCUSING 225 Note that Se is greater than s for defocusing and less than s for focusing.

By using this effective distance we see that is equal to the ratio of

the cross section of the effective cone (fig. 5.4), which is equal to that

of the actual defocused cone, to the cross section at unit distance from

the source.^ This is illustrated in figure 5.5 in which a rectangular beam of

vertical angular width dA, of horizontal angular width drj, and elevation

A is reflected from the ionosphere. In this figure the ionosphere is assumed

to be spherically stratified so that angles of arrival and departure are

equal, though this is not always the case in practice. Let 6 be the angle

subtended at the center of the earth by the path. From the enlargement

shown in figure 5.6 we see that the cross section of the beam at unit dis- tance from the transmitter is dA{dr] cos A). Referring to figure 5.5, we

see that the cross section of the beam at the receiver is given by RQ • R S

sin A. Now RQ= a dd, where a is the radius of the earth. The distance

RS can be obtained by the construction shown in figure 5.7 in which

SP and RP are perpendicular to TO. SP= RP= a sin 6 and, hence,

SR = a sin d dr). The cross section of the beam at R is given by (add)

Figure 5.6. Enlarged view of the beam (of fig. 5.5) near the transmitter.

» Provided there is no focusing within a unit distance.
226 SIGNAL STRENGTH

Figure 5.7. Spreading of the beam in the horizontal direction.

(a sin 6 drj) sin A = a^ sind sin A dd drj and, hence, Se is given by

si = a- sin d tan A (dd/dA) (a)

(5.12) = a sin (9 tan A (dD/dA) (b)

where D is the ground range. For a given value of A, d and dD/dA can be calculated either analytically, in the case of certain model layers, or by means of ray-tracing

programs such as those discussed in section 4.9.

5.3.3.2. Skip Distance Focusing

In figure 4.7 we see the variation of ground range D with in the

case of a parabolic layer. It can be seen that, near the edge of the skip zone (minimum D), dD/dipQ{ = —dD/dA) tends to zero as also does Sg, implying a large signal strength. In fact the above theory breaks down,

in detail, near the skip distance, and a more elaborate treatment is neces- sary to establish the degree of focusing. Bremmer [2, ch. 10] and Budden

[3, ch. 11] have shown that, in the vicinity of the skip distance, the rays form a caustic surface in much the same way as when parallel light rays

are reflected from a spherical mirror. The resulting variation of signal
FOCUSING 227

strength with distance is shown in figure 5.8. This shows that within the

shadow the signal falls off rapidly but not sharply. In the illuminated zone

oscillations are produced by the interference between high and low rays. A somewhat similar variation of signal strength with frequency is obtained near the MUF for a fixed distance and it is then called MUF

focusing. Because of the bandwidths involved, the focusing of short

pulses at the skip distance would be less than that of long pulses or continuous waves because the higher sidebands will penetrate the ionosphere. In any case the effect is appreciable only within about 5 km of the skip

distance, or within a few kilocycles of the MUF.

Most experimental evidence indicates that the focusing factor is on the order of 6 to 9 dB. An example of such focusing is shown in figure

5.9 in which the transmitted frequency is fixed but the maximum fre- quency changes with time.
228 SIGNAL STRENGTH
FOCUSING 229

5.3.3.3. Antipodal Focusing

If the earth and ionosphere were perfectly smooth and concentric,

energy could reach the antipode by all possible great circle paths [2].

However, because of the great geographic variations in ionospheric conditions, such focusing does not appear to be of great practical importance.

5.3.3.4. Horizon Focusing

Putting A = 0 in (5.12) we see that si goes to zero. This type of fo- cusing is called "horizon" focusing.

It is interesting to note that in multi-hop propagation, if the successive hops are all alike, the degree of focusing in the vertical plane is the same as for the first hop. This can be proved as follows: Let Sa be the

effective distance taking account of spreading in the vertical plane only

(see fig. 5.5). Then

SA = asm A{dd/dA). (5.13)

The degree of focusing in the vertical plane may be denoted by the ratio

of Sa to the actual length of the ray path. If S' denotes the actual length

of the ray path for the first hop, the actual ray path length for n hops is n S'. The value of Sau for the n hops is

^A = asmA —

;—= /iSa, (5.14)

dA

where Sa' is the value of Sa for the first hop. The degree of focusing for the n hops is thus nSA'/nS' = Sa'/ S', which is the degree of focusing for the first hop.

5.3.3.5. Ionospheric Distortion

Focusing (or defocusing) due to ionospheric distortion can be very

important, as was seen in section 4.6.6, where ionospheric curvature

simulates convex or concave mirrors. This phenomenon is particularly

important in transequatorial propagation during the afternoon and early

evening because of the existence of a relatively stable deformation. Part

of the long-period fading (half to one hour) of high-frequency skywaves
230 SIGNAL STRENGTH

is the result of focusing by transient deformations of the ionospheric

layers. In particular, such distortions in the F layer can produce focusing

and defocusing of the reflected radio signal amountiag to between 5 and

10 dB variation in the path loss.

5.3.3.6. Defocusing Due to Underlying Ionization

Consider an electron density profile, such as shown in figure 5.10a,

in which a block of electrons (simulating an E layer) is located below a sharply bounded reflecting F layer. Because of refraction in the lower

layer the ray path (for fo^l.S fE) will be as shown in figure 5.10b. The

effective path Se to the same range will, therefore, be greater than it would

be in the absence of the underlying ionization and, as a result, the path

loss is increased.

km

400

300

200

100

0

(a)

(b)

Figure 5.10. Defocusing due to underlying model E layer in which

' the electron density is constant over the height range 100 to 300 km.

(a) Profile and ionogram. (b) Ray path for /=1.5 fE
ABSORPTION 231 5.3.4. Absorption

5.3.4.1. The Absorption Coefficient

The absorption term La which appears in (5.5) is given by

La =10 log ^' = 20 log p. (5.15)

Pu

where pr is the actual power received and pu is the power which would

have been received in the absence of absorption and where p is the effective

amplitude reflection coefficient as defined in section 3.2.2.1 (see (3.4)).

From (3.3) and (3.4) we find that the relationship between La and the

absorption coefficient k (see (2.96)) is given by

where the integration is carried out over the ray path. In (5.15) we have

neglected any differences between the direction of phase propagation and

the ray path. In most problems of radio transmission involving high frequencies

or very high frequencies it is sufficiently accurate to use (2.103) for the

determination of k for non-deviative conditions. The higher the wave

frequency the better is the QL approximation for a given 6, or the

larger is the range of 6 for a given degree of accuracy. For deviative absorption (fjL small) it is preferable to use (2.100) to obtain k but in oblique

propagation fj, never gets very small and in the case of F-layer propagation absorption near the top of the trajectory can be ignored.

During some polar cap absorption events and certain solar flares, the

variation with frequency of the absorption does not follow (2.103) be- cause electrons are produced at very low heights (50 to 60 km) in the

atmosphere. At these levels it is necessary to use (2.101) to determine

K. However, under such conditions, absorption may be taking place over a range of heights and the exact determination of k may be a complicated process. The geographical and temporal variations in Jk ds may be found in section 3.3.6.

(5.16)
232 SIGNAL STRENGTH

5.3.4.2. Martyn's Absorption Theorem

By analogy with (4.7) the absorption L, for a wave incident at an

angle 0 on a plane ionosphere, is related to the absorption of the equivalent vertical wave, as defined in section 4.2.1, by the formula

L = Lv cos (j). (5.17)

This relation is not exact for the actual ionosphere with the earth's magnetic field, but it is a useful guide. An easy way to remember this theorem

is to notice that the oblique path length is sec <f) times the vertical but

that the equivalent vertical wave (of frequency / cos <^) suffers sec^ 0 more absorption because the absorption varies inversely as the square

of the frequency, (2.99)

.

5.3.4.3. Variation of Absorption with Distance

Daytime absorption on high frequencies takes place mainly in the

D region, between 80 and 100 km. The amount of absorption suffered by

a high-frequency wave passing through this region is proportional to the

length of the path in the region. Since the thickness of the region is very

small compared to its radius of curvature (distance to the center of the

earth) , the length of the path in the region is very nearly equal to the

secant of the angle of incidence 0d at the mean height of the region multiplied by the thickness of the region.

On frequencies sufficiently far above the £'-layer critical frequency,

the ray path may be reasonably well represented by an equivalent tri- angle like that depicted in figure 5.11. The variation of sec 0d with dis- tance for such a path is shown in figure 5.12 for four combinations of ho

the mean height of the D region, and h' the height of the apex of the

equivalent triangle. The two values of ho are 80 and 100 km, and the two

values of h' are 250 and 500 km.

Beyond about 1000 km, these curves can be approximated by the

straight dashed lines drawn through the origin, at least to the degree of

accuracy normally attained in transmission loss determinations. All four curves bend over at the top, but the departure from the straight lines is not serious until the distance is greater than about 2600 km for the

h' = 2S0 km curves (departure angle o^S°) and about 3800 km for the

ft' = 400 km curves (departure angle ^^3°).
ABSORPTION 233

Figure 5.11. Angle of incidence in the D region.

7 —

0 500 1000 1500 2000 2500 3000 3500 4000 4500 PATH LENGTH IN km

Figure 5.12. Variation of sec <t>D with ground rangefor the model shown in figure 5.10.

(After T. N. Gautier, unpublished.)
234 SIGNAL STRENGTH

During daytime when there is an appreciable E layer present the

ray paths will be modified as sketched in figure 5.10b. In general, the deviation in the E layer will decrease with increase of frequency for a given

angle of elevation. It will decrease with increase in elevation on a given

frequency.

5.3.4.4. Deviative Absorption

The calculation of deviative absorption is a difficult process depending on the details of ray path, electron density profile, and collision fre- quency profile. In fact it is impossible, in practice, to determine just what

is deviative and what is non-deviative since these terms are defined in terms of limiting conditions. Because the collision frequency v decreases

rapidly with height, absorption tends to be concentrated in the lower

regions of the ionosphere. Thus for waves reflected from the F region,

deviative absorption tends to be greatest not near reflection but in the

f/fE^X^-f

Figure 5.13. Variation of deviative absorption vjith frequency for various ground- ranges {in km) and the electron density profile shown in figure 5.10. XE={fE/f)\ (After T. N. Gautier, unpublished.)
ABSORPTION 235 lower part of the E region except, possibly, at night. To determine the

deviative absorption it is necessary either to choose suitable ionospheric

models of N{h) and v(h) so that the integral ^2k ds can be evaluated

analytically, or to compute the absorption step by step in an actual N{h)

profile with a computer (ray-tracing) program.

With an N{h) profile of the type shown in figure 5.10a and a v{h)

profile given by

f h-im

1^ = 6X104 exp , (5.18)

the variation of absorption with wave frequency for different distances

is sketched in figure 5.13. At the right-hand side of the figure (large f/fE)

where the curves are flat, the absorption is non-deviative. Deviative

absorption is manifested by the upward bending of the curves to the left. The distance 3128 km corresponds to ^1^ = 0, that is, when a ray incident

vertically on the 100 km level is refracted so as to be tangential. Under

such conditions the absorption would be large. The 3836 km distance is the maximum one-hop distance achieved with no E layer refraction

(i.e., ^iE = l).

5.3.4.5. Geographic Considerations

Middle latitudes. The variations of non-deviative absorption in middle latitudes are fairly well-behaved and may be approximated by

a formula given by Rawer [4]:

La = 430(l+0.0035i?) cos^-^^ x sec 0z)(/=b/L)-^ (5.19)

in decibels per hop. Here R is the sunspot number, x is the solar zenith

angle, and / and Jl are in megacycles per second. The numerical values in

this formula are based on analyses of vertical incidence measurements at Slough, England.

The formula does not take account of the mnter anomaly—section

3.3.6.5. To get an estimate of the absorption for the winter months, the

values given by (5.19) should be multiplied by the factors in table 5.1. These numbers may be used in dipole latitudes of 40° to 70° north and

south. It should be kept in mind that these are average values. On in- dividual days the factor may vary from less than 1 to around 2.0. The value of the factor depends somewhat on the degree of geomagnetic

activity [5].
236 SIGNAL STRENGTH

Table 5.1. Absorption factors for winter months in northern and southern hemispheres Month

Factor Northern Southern

hemisphere hemisphere

November

December

January

February

May

June

July

August

1.2 1.5

1.5

1.2

High latitudes. In high latitudes the most important consideration

in radio communications is the onset of radio blackouts rather than the

average absorption. This subject will be dealt with in chapter 6. Low latitudes. These latitudes have been discussed by Piggott [6],

who has listed the following characteristic features of low-latitude propagation:

1. The relatively great importance of E-layer trajectories.

2. The variability of the F-layer profile. This seriously limits the

practical value of F-layer propagation at short ranges and makes the

angle of elevation and path loss for F reflections at a given range exceptionally variable.

3. The absorption of the ordinary wave on a given frequency and

trajectory is usually greater than at higher latitudes because/^ is smaller,

other factors being the same.

4. Interference fading between modes having equal amplitudes is relatively more common since the differential absorption between the

ordinary and extraordinary waves is smaller than in higher latitudes.

5.3.5. Polarization Mismatch Factors

When a wave propagates in the ionosphere it is polarized in a manner

which depends primarily on the electron density, wave frequency, and di- rection of propagation relative to the magnetic field. The polarization

at the bottom of the ionosphere (where the electron density N=0) is called the limiting polarization.

To illustrate the effect of polarization mismatch on a wave, consider a ray incident at an angle of 45° on a plane ionosphere in the magnetic

meridian as shown in figure 5.14a. Let the magnetic dip angle be 45°

and the polarization of the transmitting antenna be such that the in-
POLARIZATION MISMATCH FACTORS 237

RECEIVING .ANTENNA

RECEIVING ANTENNA

Figure 5.14. Path losses due to polarization mismatch.

(a) Transmitted wave linearly polarized, (b) Transmitted wave circularly polarized. cident wave is linearly polarized with the electric vector parallel to the

magnetic field. On entry into the ionosphere at the point all the in- cident power is used in exciting the ordinary wave. Thus, for the ordinary wave, the loss oLtp is zero, whereas for the extraordinary wave ^Ltp is infinite. Now as the ordinary wave travels through the ionosphere, the

propagation angle 6 varies continuously so that the wave polarization

changes from linear to elliptical until it reaches at which point the

polarization is circular, because ^ = 0°. If the receiving antenna is linearly

polarized it will pick up half the incident power, so that oLrp is 6 dB.

Next, consider the case in which the transmitting antenna radiates a circularly polarized wave (see fig. 5.14b) such that, on entry into the

ionosphere at A, all the power is used in exciting the ordinary wave. Once

again oLtpis zero for the ordinary wave and ^Ltpis infinite for the extra- ordinary wave. Within the ionosphere the wave polarization becomes

elUptical until at B it is linearly polarized with the electric vector parallel to the magnetic field Bq. Now if the receiving antenna is linearly polarized to pick up the ordinary wave oLrp is zero, whereas if it is polarized per- pendicular to this direction the loss is infinite. If (p is the angle between

the direction of the magnetic field and the direction of linear polarization

of the receiving antenna the loss for the ordinary wave is given by 10

log cos^ (p = 20 log cos <p. Of course if the transmitting antenna emits

circularly polarized waves with the opposite sense of rotation, then the
238 SIGNAL STRENGTH

EXTRAORDINARY WAVE ELLIPSE

io (EARTHS MAGNETIC FIELD)

\ ^

/

/ /

4 1—

_

\ \ * \

1 1 \ \ V \ —^ r

/ /

ORDINARY WAVE ELLIPSE ^

Figure 5.15. Limiting polarization ellipses produced by a horizontally polarized wave

incident on the ionosphere in the magnetic meridian.

losses for the ordinary and extraordinary waves are reversed. If the in- cident radiation, in the case of figure 5.14b, is linearly polarized, then the

incident power is divided equally between the ordinary and extraordinary waves so that oLtp = TiLtp = () dB. Of course the total power in the composite wave may still be the same. We now have an extra wave to take

into account. To illustrate further what happens when a radio wave enters the

ionosphere, consider radiation from a horizontally polarized antenna in- cident on the ionosphere in the magnetic meridian. On entering the ionosphere the wave is split up into two characteristic waves (see sec. 2.3.3.2)

which are, in general, elliptically polarized with opposite senses of rotation. Since the incident wave is horizontally polarized the vertical axes

of the two polarization ellipses must just cancel, and so the ellipses must

be as shown in figure 5.15. The shapes of the ellipses are given (approxiimately) by the formula X=0 in (2.74)

R= ^~1 Yl±Vn+^l]. (5.20)

Now

( E^) 0 = i?+ ( E2) 0,
POLARIZATION MISMATCH FACTORS 239 and

hence

{E^),=

Substituting from (2.90) we obtain

{E,), = Rl{E,) (a) or (5.21)

(E^),= R^{E^),. (b)

Equation (5.21) enables us to determine the way in which energy in the

incident wave is distributed between the ordinary and extraordinary

components. From then on the two components travel essentially in- dependently until they emerge from the ionosphere. However, since the

absorptions suffered by the two waves are unequal the emergent waves

will not cancel out in the vertical plane and the resultant wave will, therefore, be elliptically polarized.

Substitution of numerical values of y(0.1, say) and ^(45°, say) in (5.20) shows that i?^—1 so that, except for nearly transverse propagation, the energy is divided almost equally between the two magneto-ionic

components. On lower frequencies, however, this is not the case as can

be seen by substituting Y= \ and ^ = 45° in (5.20). This gives {Ez)o =

When the propagation is nearly transverse, ^^90°, so that R-P^

{Yl/Y"^) —>0 and R+^ ( Yj/ Y^) —> . Hence the ellipses are very narrow.

In the absence of collisions the major axis of the ordinary wave ellipse is parallel to the magnetic field, whereas that for the extraordinary wave

ellipse is perpendicular to the magnetic field. In intermediate and high

latitudes the ordinary wave ellipse has its major axis nearly vertical and the extraordinary wave ellipse has its major axis nearly horizontal.

Except when 6 is within about 15° of the normal to the magnetic field the ellipses are so nearly circular that the differences between ordinary

and extraordinary wave ellipses are unimportant on frequencies well above the gyrofrequency.

For east-west propagation along the magnetic equator, antennas

should be horizontally polarized so as to excite the ordinary wave, whereas

in high latitudes the ordinary wave is excited by a vertically polarized

2(E3)..
240 SIGNAL STRENGTH

AZIMUTH Cp Figure 5.16. Directions for which 6 {the propagation angle) =90° for different angles of magnetic dip e. The azimuth </) is measured from the magnetic meridian. (After W. R. Piggott, 1959, Radio Research

Special Report No. 27, Her Majesty's Stationery Office, London.) wave. The necessary conditions for polarization to be important are (a)

that the propagation be quasi-transverse at the point of entry into or

exit from the ionosphere (or both), and (b) that the differential absorption between the magneto-ionic waves be large. Polarization effects are, therefore, most important on frequencies in the vicinity of the gyro- frequency that is in the frequency band from 0.3 Mc/s to 3 Mc/s.

For the calculation of path loss it is necessary to know Ltp (5.4)

and this can be determined by the use of equations such as (5.21) and

a knowledge of the polarization of the transmitted wave. Similarly Lrp can be determined from a knowledge of the emergent polarization and the

antenna polarization, the angles of elevation and azimuth at which the

polarization may become important can be seen in figure 5.16, which gives

the angles of elevation and azimuth as a function of the dip angle near the

transmitter or receiver as appropriate. The critical range of angles falls in the middle of the most important range of angles for practical communications in temperate latitudes. Vertical polarization is preferable to horizontal whenever polarization is important in these latitudes.
ANTENNA GAIN 241 For short-range transmissions on the lower frequencies it is often

convenient to use polarization as a method of discriminating against noise. Very considerable gains in signal/noise ratio are possible in the daytime

by using antennas which are insensitive to vertical polarization on the

frequencies where most of the interference is propagated via the ionosphere. In multi-hop transmission, depolarization of a characteristic wave may occur after a ground reflection, especially if the magnetic dip is different for the two hops so that a downcoming ordinary wave may,

after a ground reflection, give rise to ordinary and extraordinary waves.

5.3.6. Antenna Gain

A detailed discussion of antennas is beyond the scope of this book

and so a few simple ideas will suffice for our present purposes.

It has become customary to specify the gain of an antenna in a given

direction as the ratio of the power radiated in that direction to the power

which would be radiated in the same direction by a standard reference antenna. Standard antennas used for this purpose are (1) an isotropic

radiator, (2) a half-wave dipole (this has a power gain of 1.64 [2.15 dB]

relative to an isotropic radiator), and (3) a short electric dipole which

has a maximum power gain of 1.5 (1.76 dB) over an isotropic radiator.

If Pq is the power radiated in kilowatts, the power pA radiated per

unit solid angle at an elevation A is given by

PA=pogA (5.22)

where g^ is the free space gain of the antenna at an elevation A over an

isotropic radiator. The value of gA can be calculated from the geometry of

the antenna. Note that po is the actual power radiated (current squared

times radiation resistance) and not the power output of the transmitter

or the power input to the antenna. For a short dipole (less than 0.1 wavelength), gA = 1.5 sin^ A, where

A is measured from the axis of the dipole. For a short vertical wire, one end of which is on a perfectly conducting ground, the gain is given by

gA = 3 cos^ A. Part of the field intensity near the ground (A;^0°) is due

to the surface wave, which is negligible when the wave reaches the ionosphere. Consequently, the vertical directional pattern of an antenna,

for skywave calculations, may be considerably different from the pattern

measured near the antenna.
242 SIGNAL STRENGTH

5.4. FADING

5.4.1. General Characteristics

In the above discussions of path loss we concerned ourselves with the

average power received. Now the instantaneous field strength may

fluctuate widely about the mean value and amplitude variations of the

order of 10 to 1 can occur in the course of a few seconds. Fading may be

caused by several different ionospheric phenomena, e.g., movements of

the ionosphere causing interference fading, rotation of the axes of the

polarization ellipses, time variations in ionospheric absorption, focusing,

and skipping of the signal due to MUF failure. In the case of signals trans- mitted from a moving source—e.g., a satellite—fading will result from the

motion of the source relative to ionospheric irregularities. Fading of cos- mic radio noise is often referred to as "scintillation."

The period of a fading cycle depends largely on the cause of the

fading. Thus the fading period of interference and polarization fading may

vary from a fraction of a second to a few seconds, absorption fading may

have a period of the order of an hour or longer, whereas focusing may

be of the order of 15 to 30 min. Signals can fade in or fade out if the fre- quency of the signal is near the maximum frequency and the critical frequency is changing with time (see fig. 5.9). It is, therefore, highly

irregular as far as period is concerned and may occur only in the early

morning and late afternoon (fade in and fade out)

.

In general, fading is faster on high frequencies than on low frequencies

because a given movement in the ionosphere produces a greater phase

shift on the shorter wavelengths. The fact that fading is frequencydependent means that different sidebands in a modulated wave fade

differently. This gives rise to a distortion of the modulation envelope

which is called selective fading.

5.4.2. Interference Fading

A beam of radio waves incident on the ionosphere is not reflected from a point but from an extended region. Small irregularities in electron

density near the level of reflection give rise to individual reflected wavelets

and the received signal is the vector sum of the individual signals at the

receiving antenna. Movements of ionospheric irregularities give rise to

variations in the relative phases of the individual wavelets and thus
INTERFERENCE FADING 243 produce interference fading. It is not uncommon for a received highfrequency signal to consist of a mixture of high- and low-angle rays, each

having extraordinary and ordinary components; each such set may be

combined with other sets corresponding to rays having different numbers

of hops.

The resultant amplitude can vary over wide limits, the maximum

value being when all the individual components are in phase. The root mean square value of the fluctuating signal is equal to the steady value of

the field that would have existed had the ionosphere not broken it up into

many components. Because it is impossible to determine the resultant

amplitude at any given moment, the subject has to be treated on a statistical basis. Such phenomena are said to be ^^stochastic." The distribution of amplitude approximates the Rayleigh law when

the various components are of approximately the same amplitude and the

relative phases are varying randomly. For the Rayleigh distribution, the

percentage of time p{A) that the amplitude exceeds the value A is p(^)=exp i-A^Al), (5.23)

where A% is the mean square value of A (i.e., proportional to the mean

power). Ionospheric signals are, often, better described by a Rice dis- tribution 1^7] in which a wave of steady amplitude (specular component)

is added to the randomly varying signals. If As is the steady amplitude

the distribution function is given by

pM)=-^/;^e.p[-^]/„f-^').., (5.24)

where Iq is the Bessel function of zero order and imaginary argument.

For As/Ar<KI, the Rice distribution approaches the Rayleigh law.

For As/Ar^I it approaches a normal distribution with mean As and

standard deviation 0.101 Ar.

The amplitude distribution of a continuous wave, and of trains of

long pulses, involving several paths, is usually close to Rayleigh. In- dividual modes resolved by short pulses often have shallower (and slower)

fading corresponding to a substantial specular component, As/Ar = 2

or more. With a Rayleigh distribution, the median amplitude is equal to 0.832 times the rms value. For such a distribution the lower decile value,

or the amplitude exceeded 90 percent of the time, is 0.39 of the median

value. The upper decile value, that is the value exceeded 10 percent of

the time, is 1.8 times the mean value.
244 SIGNAL STRENGTH
FADING POWER SPECTRUM 245 Some examples of (a) random, (b) periodic, and (c) double periodic

fading of WWV-20 as received in Boulder, Colo., are shown in figure

5.17. The periodic fading in figure 5.16b, that is sharp minima and blunt

maxima, is the resultant of two sine waves of almost equal amplitude

whose phase difference is changing at a constant rate. In figure 5.17c

the short -period fading could be due to high and low rays and the longperiod fading could be due to beating between ordinary and extraordinary waves.Very bad interference fading is experienced in cases where the skygroundwave and skywave amplitudes are comparable. This combination

produces much more severe fading than is usually experienced with sky- waves alone. A somewhat related type of interference fading is experienced primarily on low frequencies, where radio transmission is relatively

stable. Near sunrise and sunset the heights of the reflecting D layer

change rather rapidly, and the skywaves arrive alternatively in and out

of phase with the groundwaves. This produces fading with a relatively

long period.

Flutter fading is experienced near the auroral zone during disturbed

periods and often, during normal conditions, in transequatorial propagation. It is also experienced in certain types of scatter transmission. The

fading rate is usually in the range of 10 to 100 c/s; indeed it is so fast that

normal pen recorders cannot always follow the fluctuations. With such

equipment, the fading depth appears to decrease.

5.4.3. The Fading Power Spectrum

The speed of fading can be described in terms of the time autocorrelation function of the amplitude or, equivalently, in terms of the

fading frequency power spectrum which is the Fourier transform of the

autocorrelation function. If A{t) represents the amplitude as a function

of time, such that the average value is constant over the interval t to

t-\-T, the autocorrelation function p(r) is defined by

A(t)A(t+T) dt. (5.25)

If V represents the fading frequency and if F{v) is the Fourier transform
246 SIGNAL STRENGTH

of A (t) , that is F{v)=~- / A(t) exp i-ivt) dt, (5.26)

the power spectrum P{v) of the fading is P{v) = | F{v) P which is proportional to /p(t) exp { — ivr) dr: the Fourier transform of p(r).

No matter how irregular the ionosphere the amplitude of the signal at a fixed receiver would be steady if there were no time variations in the

ionosphere. The width of the power spectrum (the speed of fading) is in

fact related to changes in the ionosphere and/or to changes in the position of the receiver (for a fixed transmitter).

A convenient method of depicting the fading spectrum is that described in section 3.2.3.2, in which the fading frequency is multiplied

so as to produce an audio tone which is then analyzed by conventional

audio techniques. Some examples of the variations in the spectra, on

quiet and disturbed days, are shown in figures 5.18a and b respectively.

The frequency spectrum of flutter fading signals transmitted near the

magnetic equator is shown in figure 5.19. When the fading speed is high,

the spectrum is broad, and vice versa. ^

HIGH^ ^Li^^J4_._/^° ^^^^

low NOMc/s

-^-r-r-T^,

08 10 12 14

0812 lANUARY 31, 1433 FLARE AND SWF

1961

(a)

lywW^ N^.'W* 'M^'rn^ m,fmmm u^^ >

%\ 08 10 12 14 16 18 20 0605 SC NOVEMBER 15, 1960

(b)

Figure 5.18. Frequency spectra of WWV {10 Mc/s and 20 Mc/s) as observed at Boulder,

Colo. (2370 km).

r (a) Magnetically quiet conditions, (b) Magnetically disturbed conditions.
FADING POWER SPECTRUM 247

I

i

{

f

I

I

1

I

J

li

i

IP

J

• - I

I

I

I

I

I

f

e

i

f

,/

I

i

n

•1

I

m

•4 e .1.1

0, ^1

i ^

! o ^ ^ I

S u >1

n

li

I

\ 1 I

\

1 I

\ 1 (SNOisiAia s/og) ijiHS aBiddoa

I

\

1
248 SIGNAL STRENGTH

5.4.4. Scintillations^

This refers to the amplitude and phase variations of high-frequency

signals transmitted through the ionosphere from outside the earth. The

two common sources are cosmic noise from outer space and signals from

artificial satellites. When a radio wave travels through an irregular ionosphere the latter behaves as a diffraction grating so that there is a re- distribution in the amplitude of the wave with position which results in fading due to ionospheric movement. There are also irregular fluctuations

in the apparent position of a radio source viewed through the ionosphere.

These two processes are usually described as amplitude and angular scintillations, respectively [8].

The phenomenon can best be treated by reference to a thin phase

changing screen [9, 10]. Let us consider a plane wave incident upon the

ionosphere such that no absorption of the wave takes place. Immediately

below the region containing such irregularities the surface of constant phase in the emergent wave will be corrugated in an irregular way. The

amplitude distribution will, however, still be uniform since no energy is extracted from the wave.

In order to investigate the process by which amplitude variations are

built up from the pure phase-modulated wave, it is convenient to consider the angular spectrum of the wave. The angular spectrum of a phase

changing screen is analogous to the frequency spectrum of a phasemodulated carrier wave, the deviation in angle of a particular component

being equivalent to the shift in frequency of a particular side band with

respect to the carrier wave. For the case of a phase-modulated carrier wave it is well known that the side bands occur not only at all the fre- quencies in the Fourier analyis of the phase-modulation but also at sums

and differences and multiples of these frequencies, and the relative magnitude of these side bands depends on the phase deviation. By analogy

it can be shown for the case of diffraction, without specifying the screen

in any detail, that the total spread of the angular spectrum depends on

the phase deviation as well as on the lateral scale of the phase variations.

Now the phase relationship between the components of the angular

spectrum is such as to produce a pure phase modulation at the screen

itself. As the wavefront leaves the screen, however, the relative phases

will be changed owing to the different directions of propagation within

the angular spectrum; and, in this way, amplitude variations will be

* Taken, from a lecture by Dr. H. J. A. Chivers.
SCINTILLATIONS 249 introduced into the diffraction pattern. The amplitude variations will grow in magnitude as the distance from the screen is increased until the

initial phase relationship is entirely destroyed. The more deeply modulated the screen, the wider will be the angular spectrum, and the finer the

structure in the diffraction pattern.

As long as the average phase changes introduced by the diffracting screen are less than about 1 rad (radian), then the scale size of the ir- regularities observed on the ground is the same as the scale of the irregularities in the ionosphere. If the average phase changes are greater than

1 rad, then the scale of the pattern observed at a distant plane is smaller

than the scale size in the ionosphere by a factor equal in magnitude to the average phase change in radians.

Hence, in cases where the average phase changes are less than 1 rad, the scale of the irregular structure of the emergent radio wave is the same in all planes below the screen. In this case it has been shown

[11] that the amplitude variations become fully developed at a distance

where an average irregularity in the ionosphere occupies about the size of the first Fresnel zone radius. For a screen viewed from a distance R,

observing at a wavelength X, the Fresnel zone radius is given by V^X.

In the case of a transmitting earth satellite, the radio wave incident on the ionosphere will have a spherical wavefront if the satellite is at a low

altitude. Therefore, in the satellite case, we must consider the distance

from the satellite to the irregular layer as well as the layer-to-earth dis- tance. When the satellite is located at the bottom of the layer of irregularities, then the Fresnel zone radius is only half the radio wavelength;

and, to observe strong scintillations at the ground, there must be substantial phase changes over this order of distance in the ionosphere. Such

a situation is unlikely, so scintillations will not be observed. As the dis- tance from transmitter to the screen increases, the Fresnel zone radius

increases so that, when the satellite-to-ionosphere and ionosphere-to

ground distances are equal (say i?), then the Fresnel zone radius is \/R\/2. Hence for a given receiving station, the Fresnel zone distance

is smaller for satellite observations than for radio star observations. Since

the proportion of fluctuation in the observed signal depends on the average

phase changes over distances comparable to the Fresnel zone distance,

there will be proportionally smaller fluctuation in a satellite signal than

in a radio star signal viewed through the same part of the ionosphere.

The average voltage amplitude of the scintillations depends on the square

of the average phase changes over the Fresnel zone distance [12]; therefore, the above calculation indicates that, when transmitter and receiver

are equidistant from the ionosphere, the amount of scintillation is about
250 SIGNAL STRENGTH

one-half of that to be expected from a radio star observed at the same

time and in the same direction. In order to estimate the magnitude of the irregular component in electron density which is necessary to produce scintillations, we must

first compute the total change in phase path length which is imposed on

a radio wave in traversing the ionosphere, then consider the fractional

variation in this path which will result in phase differences of about one

radian in waves emerging at places separated by approximately the

Fresnel zone radius.

The total phase path length P from source to receiver is given by

ju ds,

where ju is the refractive index and s the source distance. Hence, the dif- ference in phase path length introduced by the ionization is j ds- j fjLds = AP.

Now, when the wave frequency is high compared with the plasma

frequency (/at) we have, from (2.78),

and hence

(5.27)

(5.28)

Taking the typical value 10^^ electrons/m^ column for {Nds and

assuming a radio wave frequency of 40 Mc/s (4X10^ c/s), we get AP^

2500 m. This corresponds to about 2000 rad at 40 Mc/s. Now, if we take

as a typical value for the distance to the irregularities 400 km, then the

Fresnel zone radius \/R\, for 40 Mc/s observations, is approximately

2000 m.

Since for strong scintillations we require changes in phase of about

1 rad over the Fresnel zone distance, the calculations show that on 40

Mc/s th^re must be differences in electron density of about 1 part in 2000 over distances of about 2000 m. Such variations can be expected
SCINTILLATIONS 251

to be quite common, indicating that scintillations on 40 Mc/s would be

observed very frequently. This is, in fact, the case. A similar calculation for a radio frequency of 400 Mc/s shows that

electron density variations of 1 part in 200 are required over distances

of about 500 m. Since this distance is of the same order as the mean free path for electrons in the ionosphere, it is unlikely that there would be

sufficiently rapid density variations to cause scintillations at 400 Mc/s.

Experimental observations support this conclusion; strong scintillations at 400 Mc/s are normally observed only during auroral disturbances or at the magnetic equator, where the horizontal field inhibits vertical diffusion. Using the above approach, some idea can be obtained of the expected

variation of scintillation activity with the elevation angle at which observations are made. With decreasing elevation angles, the effective thick- ness of the ionosphere increases. In addition, the radius of the first Fresnel zone increases as the square root of the slant range. The two facts combined mean that smaller fractional deviations in electron content oc- curring over greater distances can cause scintillations at low elevations

compared with variations necessary at high elevations. Thus it can be ex- pected that, at low elevations, scintillations will be more common and more intense than at high elevations. Again this is supported by experimental evidence.

Scintillations are apparent in both the amplitude and phase variations

of the received signal. Amplitude variations are the more simple to observe and have consequently received the greater attention. In radio

star work a moderately directional antenna system is required for straightforward observations of the brightest radio sources. The output of the

second detector of a sensitive superheterodyne receiver is amplified and

displayed on a pen recorder, and scintillations are revealed as a marked

fluctuation of the recorded trace in excess of the smoothed noise fluctu- ations normally seen at the output. Samples of the output of such a re- ceiving system are shown in figure 5.20. The top trace (a) shows the re- corded noise level in the absence of scintillations, the middle trace (b)

shows moderate scintillations, while the lower trace (c) indicates very

intense scintillations. The records were made using a radio frequency of

80 Mc/s by observing the intense radio source in Cassiopeia (231N5A).

In the case of satellite observations, the signal-to-noise ratio is usually

higher than that from a radio star; hence a very simple antenna will

suffice to give good records. A simple antenna has the advantage of ex- tensive sky coverage, thus avoiding the necessity of steering the antenna

to follow the satellite. Simple amplitude experiments are usually confined to routine observations to investigate the diurnal, seasonal, and other time changes in
252 SIGNAL STRENGTH

2100 (a) NOV. 16, 1958 J200 2300

%

t .i : i.'

1

;

1 »

5 040 3 (b) AUG. 20,^ 3 0500 0600

Figure 5.20. Amplitude recordings on 80 Mc/s of Cassiopeia-A

showing (a) no scintillations, (b) moderate scintillations, and (c) strong scintillations.

(After H. J. A. Chivers, 1960, J. Atmospheric Terrest. Phys. 19, 54.) the phenomena. Similar observations at two or more independent sites can be used to assess the size and shape of the electron density irregularities which cause the scintillations, and to indicate their apparent movement.

Phase scintillations can most easily be observed by measuring the

irregular variations in the times of lobe crossing in the output from a system using two antennas as an interferometer. Such a system is the

analog of the Michelson interferometer in optics. When used in its simplest

form, it suffers from the disadvantage that the relative motion of a radio

star through the lobes gives a very slow rate of information. For both the

radio star and satellite cases, it is common practice to sweep the lobe structure across the sky in order to increase the rate at which phasescintillation measurements can be made.

The depth of fading falls off with increasing frequency. This is measured by a fluctuation index which is the mean variation in received
RECIPROCITY 253 power relative to the average power. For normal scintillations, this index

varies from about unity at 30 Mc/s to a small value at 300 Mc/s. Scintil- lations have been reported on frequencies as high as 900 Mc/s, but tropospheric effects cannot be ruled out on this frequency.

The rate of scintillation, in the case of radio stars, varies from about

0.1 per minute to around 10 per minute. The scintillation rate appears to be independent of wave frequency down to about 30 Mc/s. When satellites are used as sources, the scintillation rate depends mainly on the

height and speed of the satellite and on the height of the irregularities.

Sample values are around 10 fades per second.

The variation in angular position of a radio star is usually a few

minutes of arc on 36 Mc/s with an observed upper limit of about 0.5°. The diurnal variation of scintillations in temperate latitudes at low

sunspot numbers shows a peak of occurrence at night but little by day. In high latitudes and during high solar activity the distinction between

day and night disappears. The seasonal variation is characterized by

peaks during the equinoctial months. It is fairly closely correlated with

the occurrence of spread F.

5.4.5. Fading Correlation Bandwidth

Because phase path differences in multipath propagation are a function of the wavelength, the fading on adjacent frequencies tends to be

different. As the frequency difference 5co increases the correlation between fading on frequencies of wo and ooo-\-8w will decrease and, at a sufficiently large difference, the fading on the two channels will be unrelated.

This selective fading can produce distortion in an amplitude modulated wave (double sideband) if the carrier fades to a level below that of the

sidebands. This gives an effect similar to overmodulation. On high fre- quencies, for a CW signal, the bandwidth of correlation is found to be

around 3 kc/s and even less under severely disturbed conditions on arctic paths. Single pulse signals without overlapping time may have a correlation bandwidth of 40 kc/s or so.

5.4.6. Reciprocity

A radio signal of given frequency traveling from A to B may be

expected to exhibit the same fading as a similar signal received at A

from B. Although this is true as far as paths and amplitudes are concerned.
254 SIGNAL STRENGTH

0 60 120 180 240 300 360 J\Ml (sec) Figure 5.21. Nonreciprocal (polarization) fading over the 960-km path Ottawa-Halifax

Canada.

11.45 Mc/s F layer low-angie ray (o+x), 18:15:20-18:21:20 UT, March 28, 1962. (After G. W. Jul! and

G. W. E. Pettersen, unpublished.) Budden [13] has shown that the phases at the opposite terminals can be

reversed. This impHes a degree of nonreciprocal fading the existence of

which has been confirmed by a number of workers [14, 15]. The most

important source of nonreciprocal fading appears to be polarization fading.

Now reciprocity in polarization fading can be expected only for special

orientations of linear antennas at each end of a (magnetically) northsouth path. For transmissions along an ionospheric path entirely within

either hemisphere, one condition for reciprocal polarization fading is that the antennas at the terminals must take equal and opposite angles

with the direction of the earth's magnetic field. Thus for any arbitrary

path orientation nonreciprocal polarization fading can be expected [16].

Observations by G. W. JuU (private communication) on signals trans-
DIVERSITY 255 mitted over the east -west path Ottawa, Ontario, to HaUfax, Nova Scotia

(960 km) have shown that time displacements in polarization fading

maxima can occur. Time displacements of up to one-half a fading cycle were observed (see fig. 5.21).

5.4.7. Diversity [17]

To minimize the effect of fading on quality of reception, use can be

made of the fact that fading is correlated only over relatively small dis- tances, and frequency bandwidths. Also signals from antennas having

different polarizations may fade differently.

Space diversity is obtained by mixing signals from antennas separated

by distances greater than the correlation distance. This is the distance

beyond which the correlation coefficient of the fading falls to some specified value (e~^ say).

Frequency diversity is obtained by transmitting and receiving on

frequencies separated by more than the correlation bandwidth. This

method is not recommended as it is wasteful of the usable frequency

spectrum.

Polarization diversity is useful when there are two magneto-ionic waves present with essentially equal amplitudes. As discussed in section

4.9.5.1, the resultant of such waves is, approximately, a linearly polarized wave which rotates steadily so that sinusoidal (Faraday) fading would be

observed with a linearly polarized antenna. Deep fading can be avoided

by the use of two orthogonal antennas. There is little point in using polarization diversity when only one magneto-ionic component is likely to be present.

REFERENCES

[1] Norton, K. A. (1959), System loss in radio wave propagation, J. Res. NBS 63D

(Radio Prop.), No. 1, 53.

[2] Bremmer, H. (1949), Terrestrial Radio Waves (Elsevier Publ. Co.).

[3] Budden, K. G. (1961), Radio Waves in the Ionosphere (Cambridge Univ. Press).

[4] Rawer, K. (1952), Calculation of sky-wave field strength. Wireless Engineer 29,

287.

[5] Thomas, L. (1962), The winter anomaly in ionospheric absorption. Radio waves

absorption in the ionosphere, AGARDograph No. 53 (ed. N. C. Gerson)

(Pergamon Press).

[6] Piggott, W. R. (1959), The calculation of the median sky wave field strength in
256 SIGNAL STRENGTH

tropical regions. Radio Research Special Report No. 27, Department of Scientific and Industrial Research.

[7] Rice, S. O. (1944), Mathematical analysis of random noise. Bell Syst. Tech.

J. 23, 282; (1945) 24, 46.

[8] Little, C. G., and A. C. B. Lovell (1951), The origin of the fluctuations in the

intensity of radio waves from the galactic sources, Phil. Mag. 42, 267.

[9] Booker, H. G., J. A. Ratcliffe, and D. H. Shinn (1950), Diffraction from an ir- regular screen with applications to ionospheric problems, Phil. Trans. Roy. Soc. (London) A242, 579.

[10] Bowhill, S. A. (1961), The scattering of radio waves by an extended randomly

refracting medium, J, Atmospheric Terrest. Phys. 20, 9. [11] Hewish, A. (1951), The diffraction of radio waves in passing through a phase

changing ionosphere, Proc. Roy. Soc. (London) A209A, 81.

[12] Booker, H. G. (1958), The use of radio stars to study irregular refraction of radio waves in the ionosphere, Proc. IRE 46, 298.

[13] Budden, K. G. (1954), A reciprocity theorem on the propagation of radio waves

via the ionosphere, Proc. Cambridge Phil. Soc. 50, Part IV, 604.

[14] Meadows, R. W. (1956), An experiment to test the reciprocal radio transmission

conditions over an ionospheric path of 740 km, Proc. lEE (London) 103B, 224.

[15] Balser, M., W. B. Smith, and E. Warren (1958), On the reciprocity of HF iono- spheric transmission, J. Geophys. Res. 63, 859.

[16] Budden, K. G. and G.W. Jull (1964), Reciprocity and non-reciprocity with magnetoionic rays. Can. J. Phys. 42, 113.

[17] Baghdady, E. (1961), Lectures in communications systems theory, McGraw-Hill,

New York.
CHAPTER 6

Ionospheric Disturbances

6.1. TYPES OF DISTURBANCE

The term "ionospheric disturbance" is used to cover a wide variety

of ionospheric conditions that show some departure from the usual state. Thus shght perturbations in the electron configuration that move with

time are called traveling disturbances. These are usually localized in space. From the point of view of radio transmission, these traveling dis- turbances are not nearly so important as the more (geographically)

extensive disturbances which are all associated, in some way or another,

with a flare on the sun (see section 1,7.6).

These solar flare associated effects may be classified as follows:

(1) Sudden ionospheric disturbances,

(2) ionospheric storms,

(3) polar cap absorption events (PCAs).

The reason these disturbances are important from the point; of view

of radio communications is that they often result in interruption of communications. The absorption in the D region is enhanced so much that

intelligible radio communications may be impossible for periods lasting

from a few minutes to several days. Furthermore, the critical frequencies

of the F2 layer are sometimes depressed (ionospheric storms) , resulting

in loss of signal due to MUF failure. It is a very difficult matter to predict the onset of an ionospheric disturbance and since the ionospheric

conditions can change rapidly from very quiet to highly disturbed, tlie idea of "average" conditions (e.g., path loss, maximum frequency, etc.) tends to have only limited value. The purpose of this chapter is to outline the effects of these disturbances on radio signals and to discuss some

ways of dealing with the problems.

Before discussing these various phenomena in detail, however, it is useful to consider the general pattern a little further. Although all the

regular layers (D, E, and F) are affected, the E layer is not strongly

affected except for the occurrence of sporadic E in certain ionospheric

257
258 IONOSPHERIC DISTURBANCES

storms. The D and F layers are subject to much stronger effects. The

D region effects often occur simultaneously with the appearance of an

optical solar flare, whereas the F region effects are often delayed by a day or more. These simultaneous and delayed effects are illustrated in figure 6.1. We have seen (sec. 1.7.6) that the occurrence of a solar flare may be

accompanied by the emission of radio waves, ultraviolet, and x rays,

all of which arrive simultaneously at the earth because they travel with

the free space velocity of light (essentially) . Solar cosmic rays are also emitted with relativistic velocities and these may take 15 min to several

hours to reach the earth, where they produce polar cap absorption. Slower

particles, which have transit times of from 20 to 40 hr, result in ionospheric storms, magnetic storms, and visible displays of the aurora borealis.

It should be remembered, of course, that not all the effects shown in figure 6.1 are associated with every flare.

6.2. SUDDEN IONOSPHERIC DISTURBANCES

6.2.1. D-Region Absorption

At times, communications on high frequencies by skywave propagation over the daylight hemisphere of the earth are '^^blacked out" by abnormally high absorption in the D region. The association between these

shortwave fadeouls (SWF) and solar flares was discovered by Dellinger

[1].^ The condition of high absorption may last from a few minutes to

several hours. Onset of this absorption is usually, but not always, very

sudden (hence the name "sudden ionospheric disturbance," SID) ; it

is followed by a relatively slow recovery, as shown in figure 6.2. Short- wave fadeouts (SWFs) are sometimes accompanied by transient vari- ations in the earth's magnetic field (fig. 6.2) indicating the existence of

electric currents in the D region. Not all shortwave fadeouts are sudden

and, at the National Bureau of Standards, SWFs are described as sudden,

slow, or gradual, depending on the time variation of the recorded signal.

Information on the occurrence of ionospheric effects of solar flares is given in CRPL F Series, B, Solar Geophysical Data, issued monthly by

the National Bureau of Standards. The production of ionization in the

D region gives rise to associated phenomena such as the sudden absorption of cosmic noise (SCNA) received on frequencies above the F2 layer

Figures in brackets indicate the literature references on p. 287.
D REGION ABSORPTION 259

4

II
260 IONOSPHERIC DISTURBANCES

5000

tOOO

500

H

3

CLZ 200

- -T -

1 9570 kc/S,WlXK»MlLLIS, MASS.,

600 Kilometers from

Jl

1 WASHINGTON.D.C.

1 I

1 nun

if) 100

-Jo

O 50

cru

20

5

0

1400

I hilil' .111 llniJIii

1500 1600

f

pi

1700 GMT 1800

1400 1500 1600 (700 GMT 1800

TERRESTRIAL MAGNETIC RECORD.

Cheltenham, Mo.

Figure 6.2. Example of a shortwave fadeout and magnetic disturbance on November

26, 1936.

(After J. H. Bellinger, 1937, Sudden disturbances of the ionosphere, J. Res. NBS 19; Proc. IRE 25, 1253; and Terr. Mag. and Atmos. Elec. 42, 49-53).
D-REGION ABSORPTION 261

critical frequency, the sudden phase anomaly on very low frequencies

(SPA), and the sudden enhancement of atmospherics on very low fre- quencies (SEA). From the point of view of interruption of radio communications, shortwave fadeouts are not too serious, but they do constitute a nuisance. The following data on SWFs observed at Washington,

D.C., give an idea of this nuisance value. During the sunspot maximum

year of 1937, SWTs were observed on 84 days. On 66 of these the fade- out was classified as intense. On 39 days there was more than one SWF

and on 33 days the fadeout lasted for more than 1 hr. On the other hand,

in the sunspot minimum year of 1944, the corresponding numbers were

only 5, 3, 0, and 2. In the sunspot maximum vear of 1947 they were again

high: 121, 104, 54, and 33. The height in the atmosphere at which the additional electrons are produced during a solar flare is of importance because it determines the

dependence of the absorption on wave frequency. Figure 6.3 shows the

time variation of absorption of 10 Mc/s cosmic noise at College, Alaska

during a large solar flare on July 11, 1961. From the ratio of the absorption of the ordinary and extraordinary waves it is found that the fre- quency dependence is given by (/dz/x)"^, from which we infer (using

2.103) that the absorption is taking place at a level where (cozLcol) ^^j'^.

Or

2

4-

5-

8 O 10 IQ_

IP o

m 14 <

16

1806

f = 10 MC/S ^ORDINARY WAVE

/

r

EXTRAORDINARY WAVE

07 08 09 10 ALASKA STANDARD TIME

Figure 6.3. Solar flare absorption on 10 Mc/s, College, Alaska, June 11, 1961.

(After R. S. Lawrence, C. G. Little, and H. J. A. Chivers, 1964, A survey of ionospheric

effects upon earth-space radio propagation, Proc. lEE 52, No. 1, p. 4.)
262 IONOSPHERIC DISTURBANCES

On the other hand, there is evidence which indicates that absorption can

occur at low levels such that (wdrcoL) is comparable with v. It is of interest to note that during the flare of July 11, 1961, the absorption in the D

region increased by a factor of the order of 10. The vast majority of radio fadeouts is associated with solar flares. Therefore, they exhibit the same 11 -yr occurrence cycle as do flares and sunspots. In general, the magnitude of the SID depends on the solar zenith angle.

Shortwave fadeouts have been studied using measurements of the

minimum frequencies observed on ionograms [3] (see sec. 3.2.2.4.) to

give a synoptic picture of the worldwide distribution. It has been found

that /min varies as cos^-^^ x? where x is the solar zenith angle.

6.2.2. Sudden Phase Anomalies

The increase of ionization in the D region produces an effect on the

phase and amplitude of long and very long waves—usually a phase ad- vance due to a lowering of the effective level of reflection. Changes in the

effective height of reflection of from 0.9 to 15 km have been reported |^4].

There appeared to be a threshold value of this height change of about 6

km, above which SPAs were accompanied by SWFs.

6.2.3. Sudden Frequency Deviations

During a solar flare, it is found that the frequency of a very stable radio signal, observed after reflection from the ionosphere, undergoes

certain characteristic changes of a few cycles per second. The technique

has already been described in section 2.5.3. An increase in the electron content of the ionosphere usually brings

about a decrease in the phase path of ionospherically reflected signals

because of one or both of the following reasons:

(1) A lowering of the height of reflection, or

(2) A lowering of the refractive index along the path below the level of reflection.

It is possible to separate these two types of changes under the follow- ing extreme conditions:

(a) When the height of the reflecting layer changes without change

of layer shape, and/or the refractive index

''(=Vi-'=75)
SUDDEN FREQUENCY DEVIATIONS 263

is approximately equal to

(b) When the electron content increases in a layer, below the re- flection level, in which the refractive index is approximately unity, i.e., non-deviative.

Under condition (a) the phase path P is independent of wave frequency

/. Under condition (b) the refractive index

n=Vl-k (N/f) ^1 - ik (N/f) , where N is the electron density and A: is a constant (see 2.78). Substitution of these conditions into (2.128) shows that the change A/ in frequency

is related to the carrier frequency by the formulas:

A/cc/, (a)

(6.1)

(b)

If the effect of the earth's magnetic field is included and the propagation

conditions are quasi-longitudinal, (6.1a) remains unchanged but (6.1b)

is modified as follows: A/oc-^, (6.2)

where the + and — signs refer to the ordinary and extraordinary waves,

respectively.

An example of the effect of a solar flare on the reception of WWV-10

is shown in figure 6.4. The frequency increases to a peak, then drops

rapidly, overshoots, and recovers slowly. The total change in phase path

Figure 6.4. Effect of solar flare on received frequency of WWV, September 4, 1961.
264 IONOSPHERIC DISTURBANCES

AP can be determined from the area under the curve, i.e., AP=-Xoj Afdu (6.3)

where Xo is the free space wavelength. With the use of suitable models

to represent the electron density profile, it is possible to convert the phase

path changes into changes in total electron content or changes in height

of reflection. It is of interest to note that the following equivalence exists between

frequency shifts on oblique and vertical paths [19]. A/„5 = A/„, (6.4)

where Afoh is the frequency shift on a wave transmitted over an oblique

path and A/^ is the frequency shift on the equivalent vertical wave

(see 4.2). In the case of changes below the level of reflection, it is possible to estimate the height at which the extra electrons are produced from simultaneous measurements of the changes in absorption AA of the signal and

in phase path AP. It can be shown (using (2.100) and the definition of

phase path, P= ffi ds) that for a thin layer, in which the ray path length

is s, that

A = KS =

2c

and P=txs.

Hence A^ = — — ( —+1 jA/zs;^

Afxs

AP=Ams.

This gives —-= — . \0.d)

AP c Knowing the variation with height of the collision frequency v, it is possible to estimate an average height of electron production. Application

of this theory to experimental data shows that, while no two flares pro- duce identical results, most of the observed frequency changes are due

to enhanced ionization in the E region [5].

Flares that produce shortwave fadeouts are not necessarily those

that produce the large frequency changes. Indeed some flares, which have
ASSOCIATION WITH MAGNETIC STORMS 265 produced large absorption by the creation of a relatively small number of

electrons at levels where the collision frequency is high, produce little frequency change.

6.2.4. Effects on Very High Frequencies

Very high frequency waves (50 Mc/s) are propagated via the D

region by scattering from ionospheric irregularities. During shortwave

fadeouts it has been found that these signals are enhanced by as much as 9 dB and there is little evidence of any weakening of the signal (on 50

Mc/s) during an HF blackout [6]. However, on 27.7 Mc/s it was found

that the signal enhancement lasted for a few minutes only and was fol- lowed by marked attenuation [7J. From these observations it would be

concluded that the scattering occurred in the absorbing region and that

the increased absorption was compensated for by increased scattering on the higher frequency but not on the lower frequency.

6.3. IONOSPHERIC STORMS

6.3.1. Association with Magnetic Storms

The term ^'ionospheric storm" is used to describe the conditions which

may prevail for several days and which are accompanied by magnetic

disturbances of the type referred to in section 1.5.3. It is, therefore, of

interest to consider briefly the characteristics of magnetic storms. Magnetic storms are disturbances of the earth's magnetic field lasting from a few hours to several days during which time the various

components of the earth's field fluctuates over much wider limits (several

percent of the total field in middle latitudes) than they do under normal

conditions (a few tenths of one percent). In spite of the irregularity of

the field the overall pattern can generally be classified into certain types.

One such type is that which begins with a sudden commencement

(SC) which is essentially simultaneous all over the world. During the

first few hours (the initial phase) the horizontal component remains

above normal; then it drops rapidly to well below normal (the main or negative phase) . After this a slow recovery takes place over several days

and this is called the post -perturbation phase. Magnetic disturbance is usually most intense in the vicinity of the auroral zones. Large magnetic storms with either sudden or gradual commencement are accompanied by one or more of certain ionospheric phenomena
266 IONOSPHERIC DISTURBANCES

such as: a depression of the daytime critical frequencies of the F2 layer,

radio blackout, enhanced spread F, and sporadic E. These ionospheric

effects may last from 2 to 5 or more days. During sunspot maximum years

there is a tendency for the effects to be shorter (2 to 3 days) and more

severe while during sunspot minimum they tend to last longer (4 to 5 days) and are rather less intense.

6.3.2. Depression of F2 Critical Frequencies

The most prominent features of ionospheric storms are the reduction

in the F2 critical frequencies and the increase in D region absorption.

The practical consequence of this lowering of the maximum usable fre- quency and increase in the lowest usable frequency is a narrowing of the

usable frequency spectrum. The effects of a magnetic storm on foF2 at a given location depend, in an involved way, upon the local time, season, magnetic latitude, and the storm time (that is, time measured from the

onset of the storm)

Figure 6.5 shows the effect, on critical frequencies, of a storm in middle latitudes. The associated magnetic storm had the following time

sequence:

Start—about 0400 LT, March 26; Maximum—morning, March 27 (1^=8 +; see section 1.5.4.);

End—late, March 29. On the / plots for the second and third days, /0F2 is well below normal

and the maximum electron density at noon is down by a factor of seven. Note also the appearance of the Fi layer. On the fourth day, the daytime

/0F2S return towards normal, but depressed values and spread F (sohd

vertical lines in / plot) continue during the night hours for several additional days (not shown). In certain latitudes, when the storm starts in the afternoon, the first effect on foFi is an increase rather than a decrease. Later the usual decrease sets in. Some results of a statistical study of the morphology (space and

time variations) of ionospheric storms, by Matsushita [8], are shown in figure 6.6. The world is divided into eight zones of geomagnetic latitude

as follows: zone 1, 60°-55°; zone 2, 55°-50°; zone 3, 50°-45°; zone 4, 45° -40°; zone 5, 40° -29°; zone 6, 29° -20°; zone 7, 20° -9°; and

zone 8, +9° to —9°. The results shown represent the average effects of 51 strong storms and 58 weak storms that occurred in the period 1946

through 1955. It will be seen that the most severe depressions in electron
ABSORPTION 267

density (and hence /0-F2) occur between about 20 and 40 hr storm time

in geomagnetic latitudes of 45° and higher. In intermediate latitudes

onlv a mild depression occurs, and in equatorial regions an actual increase

is observed. Note also, that an initial increase tends to occur during the

first 9 hr or so of the storm in all zones except those with the lowest lati- tudes. Of course, it must be realized that this is the statistical picture

and so an individual storm ^\ill not necessarily foUow this pattern. In addition to the storm time variations there are marked variations

which depend on the local time. Thus the time of maximum depression

of iX^max depends on local time. Some useful factual data are presented

in table 6.1 (after Matsushita), showing how the times (local and storm)

of maximum depression depend on magnetic latitude.

Table 6.1. Variation with geomagnetic latitude of times of peak depression of Nmax

during a storm

(A) (B) (C) (D) Zone Decrease Local Time Storm Time

{Hours) (Hours) 60°-55° 30-50 14-22 17-42

55°-50° 30-45 22-04 10-41

50°-45° 30-45 01-07 10-42

45°-40° 15-25 03-13 19-55

40°-29° 15-20 03-13 20-48

The table should be interpreted as follows: In the zone given in column (A) a maximum decrease

of about the percentage sho%\Ti in (B) will occur at about the local time shown in (C) during the period

after the onset of a strong magnetic storm with a sudden commencement indicated in (D).

The fact that the statistical picture in figure 6.6 can be a little misleading is shown by the seasonal variation of storm pattern in zone 6. The data shoAvn would suggest that there is relatively little storm time

variation in the F2 layer in these latitudes. The results of a seasonal

analysis, however, show that the electron density is depressed during the summer but enhanced in the winter. The overall average is, therefore, not representative of a single storm in either of those seasons.

6.3.3. Absorption

6.3.3.1. Blackout Statistics

During some magnetic storms, the absorption of radio v/aves in the

D region is so intense that no detectable signals are reflected. This is
268 IONOSPHERIC DISTURBANCES

o

a*) iMimi Figure 6.5. Ionospheric storm ejjects in middle latitudes.
ABSORPTION 269

X3

Figure 6.5.—Continued. Ionospheric storm effects in middle latitudes.
270 IONOSPHERIC DISTURBANCES

%

20

10 ZONE I O

-10 -20 -30

10 ZONE 2 0

-10 -20

-30

10 ZONE 3 0

-10 -20 -30

10 ZONE 4 0

-10

: A,

ZONE 5 0

-10

10 ZONE 6 0

-10

ZONE 7 0

10 ZONE 8 0

-10

STRONG STORMS WEAK STORMS

i

0 12 24 36 48 60 72 0 12 24 36 48 60 72 STORM TIME Figure 6.6. Storm time variations of maximum electron densities {F2) in different latitudes.

(After S. Matsushita, 1959, A study of the incrphology of ionospheric storms, J. Geophys Res. 64, 305.)
ABSORPTION 271

particularly true near the auroral zones and the absorption is often re- ferred to as auroral absorption or auroral blackout. These blackouts have

been studied statistically by several workers [9, 10, 11] to determine

the geographic and time distributions in their occurrence. The procedure

has been to count the occurrences of the no-echo condition on conventional ionograms. This condition is denoted by the letter B on the hourly

data sheets of ionospheric characteristics. Alternatively, a measure of

absorption can be obtained from the minimum frequency /min observed on ionograms (see sec. 3.2.2.4). The occurrence of high absorption can

be determined from the occasions when /min exceeds a certain frequency.

6.3.3.2. Time of Maximum Occurrence

The most probable time of occurrence of blackout is in the morning

and the least probable in the evening. Furthermore, the most probable

time is later as the latitude increases; for instance, it varies from about

0700 at Winnipeg to about 1300 at Resolute Bay. The geographical vari- ation of the local time of maximum occurrence of blackout during the

International Geophysical Year is shown in figure 6.7 for the northern

120° 90° E 60°

120° 90° W 60° Figure 6.7. Local mean time of maximum frequency of occurrence of blackout, northern hemisphere-IGY.

(After V. Agy, unpublished.)
272 IONOSPHERIC DISTURBANCES

120" 90" E 60°

120° 90° W 60° Figure 6.8. Universal time of maximumfrequency of occurrence

of blackout, northern hemisphere-IGY.

(After V. Agy, unpublished.)

hemisphere. Note that the Hnes of given time are not concentric with

geographic latitude but are, roughly, circles centered on the geomagnetic

pole. When plotted in universal time, the above circles are transformed

into a series of arcs as shown in figure 6.8. These arcs have been called

spirals by analogy with the Stormer-Birkeland spirals for the precipitation of ions in a dipole magnetic field, but this analogy may be quite

misleading [12, 18].

6.3.3.3. Total Time of Occurrence

The amount of blackout as a fraction of the total time is shown in figure 6.9 for the various seasons during the International Geophysical

Year 1957-58. It can be seen that the summer and winter patterns are very similar with two regions of high occurrence (8 percent), one over northern Scandinavia and the other over Alaska. During the equinox

there appears to be a westward shift of the Alaska high and an increase

of occurrence to around 10 percent. Because of the uncertain nature of the
ABSORPTION 273
274 IONOSPHERIC DISTURBANCES

data on which these maps are based, too much attention should not be

paid to small variations. The average diurnal path of the blackout pattern

for the equinox months is shown in figure 6.10. Notice that the blackout

pattern moves around with the sun (shaded region represents darkness)

and that the peak percentages vary with longitude. In all three seasons the maximum contour leads the sun by some 6 hr or so and the motion

of the contours is relatively uniform except over Canada (;^90° west).

6.3.3.4. Latitude Variation

Maps such as those shown in figures 6.9 and 6.10 show that the maximum occurrence of blackout takes place in a ring similar to, but not

necessarily identical with, the visual auroral zone. North of this zone

there is a polar region in which the incidence of blackout is relatively low.

The width of the absorption zone has not yet been established with

certainty but appears to lie between about 6° [13] and about 15° [14].

This difference may be brought about by an increase in both the radius

of the ring (southward motion) and a broadening with increasing sunspot

numbers.

Within the auroral ring the average incidence of blackout is of the

order of 5 percent [15], although at a small number of abnormally sensi- tive stations in the ring the average may rise to 15 percent.

6.3.3.5. Magnetic Correlation

In relatively low latitudes, outside the absorption ring, there is a high correlation with the Kp index. In higher latitudes, however, the magnetic correlation is obscured by the presence of polar cap absorption [14].

There is also a marked 27-day recurrence tendency in the occurrence of

auroral absorption similar to that in magnetic activity [14].

6.3.3.6. Sunspot Variation

There appears to be a strong association between the 11-yr sunspot

cycle and the long-term cycle of auroral blackout occurrence [14]. The

peak phases of the two cycles are displaced by 2 to 3 yr. The peak in blackout occurrence over Canada took place around 1950-51, whereas

the sunspot numbers peaked in 1947 and reached a minimum in 1954

[14]. This behavior is similar to that of moderate geomagnetic dis- turbances, which also fail to show a clear decrease at sunspot minimum.
ABSORPTION 275
276 IONOSPHERIC DISTURBANCES

6.3.4. Sporadic £

Certain types of Eg, those associated with magnetic activity, may

be called storm Eg [16]. This type of Es occurs frequently near the auroral

ring during storms [17] and particularly during the nighttime. As in the

case of blackout, statistical analyses show that the universal times of

maximum occurrence of Es lie on arcs [18] but the curvature of the arcs

is in the opposite direction as shown in figure 6.11. This implies that

the peak time occurs earlier in higher latitudes.

I80"

Figure 6.11. Time of maximum occurrence of storm Ei. Mean percent time of IGY "auroral zone" blackout occurrence, northern hemisphere. (After L. Thomas,

1960, The temporal distribution of storm-type sporadic E in the northern hemisphere. Some Ionospheric Results—International Geophysical Year (ed. W. J. G. Beynon), Elsevier Publ. Co., 172.)
DURATION

6.4. POLAR CAP ABSORPTION

277

6.4.1. Duration

The majority of auroral blackouts is relatively short lived, lasting

up to a maximum of 5 or 6 hr. The duration of long-lasting blackouts

usually increases with latitude, as illustrated in figure 6.12. This type of

disturbance is evidently associated with the polar regions and not with

the auroral ring. Furthermore, it is not closely correlated with magnetic

disturbance except, possibly, in its later stages. Polar cap absorption is believed to be due primarily to the ionizing effects of high-energy solar protons down to altitudes of the order of 50 km.

120" 100" 80" 60" Figure 6.12. Average duration of eight long-lasting blackouts, 1949-52.

(After v. Agy, 1954, Geographic and temporal distribution of polar blackouts, J. Geophys. Res. 59, 499.)

Useful techniques for studying polar cap absorption are the riometer

(sec. 3.2.2.3), VHF forward scatter [20], and partial reflections [21, 22].

Together with ionogram blackout data, these techniques have resulted

in the determination of the geographic, temporal, and sunspot cycle

variations of PCAs.

Some major characteristics of PCA events are as follows [23]:

(1) They are almost always preceded by a major solar flare on the

visible hemisphere of the sun. The time interval between the appearance
278 IONOSPHERIC DISTURBANCES

of the flare and start of the PCA is from a fraction of an hour to several

hours.

(2) The duration is usually about 3 days but may be as short as

1 day; the longest may be about 10 days.

(3) They are not usually accompanied by noticeable increases in either geomagnetic or auroral activity, except in the later stages when an

auroral zone storm may set in. Although there is a paucity of data for the south polar cap it is believed that PCA events occur simultaneously in both hemispheres.

6.4.2. Temporal Variations

Within a few hours after the solar flare, strong absorption occurs over the polar cap in geomagnetic latitudes greater than about 64°. The

absorption attains its maximum within a few more hours and, thereafter,

begins to decay. During the decay period, the radio wave absorption

Figure 6.13. Cosmic noise absorption at Churchill and blackout pattern for northern

stations, 22-25 August 1959.

(After C. Collins, D. H. Jelly, and A. G. Matthews, 1961, High-frequency radio-wave blackouts at medium

and high latitudes during a solar cycle. Can. J. Phys. 39, 35.)
TEMPORAL VARIATIONS 279

exhibits a pronounced diurnal variation. The daytime value is about four

times greater (in decibels) than at night. An example of a PCA event

is shown in figure 6.13. The absorption (c) was that measured at Churchill

[24]. lonogram blackout data show clearly the long duration in high

latitudes. Notice that the absorption has occurred for about 32 hr

before the onset of the magnetic storm. The long-term variation in the occurrence of PCA events is shown

in figure 6.14 together with the annual mean sunspot numbers. Clearly

the events are closely associated with the general level of solar activity,

as would be expected from their association with major flares.

20 .

18 -

16 -

49 51 53 55 57 59 61 Figure 6.14. Distribution of polar cap absorption events 1949-1961.

(After D. H. Jelly, unpublished).
280 IONOSPHERIC DISTURBANCES

6.4.3. Geographical Extent

A sequence of events in the development of a PCA is shown in

figure 6.15. This is based on/min data [25]. The time of a sudden com- mencement is indicated by the appearance of the geomagnetic coordinates.

Notice that the PCA starts in a small area in relatively low latitudes and

spreads until it engulfs the polar cap. The PCA finally breaks up into

smaller regions which may be over the polar cap or in the auroral ring.

This particular event should not be construed to be typical of all PCA

events.

1700. 10-20

SID

0600. iO-21

PCA BEGINS

2140. 10-21

MAGNETIC

1900. 10-22 2200, 10-22

1000. 10-21

PCA BEGINS

1700. 10-21

PCA

"COMPLETE" SUDDEN IMPULSE UNDERWAY

0400. 10-22

"BREAKUP"

0100, 10-23

(UT)

1400, 10-21

PCA DEVELOPING

1000. 10-22

"BREAKUP"

CONTINUES

EVENT OVER

BY

0400. 10-23

Figure 6.15. Geographical development of a PCA, Oct. 20-23, 1957.

(After v. Agy, unpublished.)
GENERAL CONSIDERATIONS 281

6.4.4. Frequency Dependence of the Absorption

If the absorption takes place high in the D region, where i^<<Cco, we

should expect the absorption to obey (2.99) , whereas if it occurs very low

down, where v^co, we should expect (2.101) to hold. The frequency dependence can, therefore, be used to determine (at least roughly) the al- titude at which the absorption takes place. This approach has been used

by Little and Silberstein [26] in an analysis of continuous wave trans- missions between Barrow and Kenai, Alaska, on 5, 10, and 15 Mc/s

along with riometer measurements on 50 Mc/s made by aiming the

riometer antennas along the probable oblique HF paths at both ends. It was concluded that the inverse square law was inoperative on the lower

frequencies and, therefore, that the absorption takes place at levels from

50 to 70 km.

6.5. EFFECTS ON RADIO COMMUNICATIONS IN HIGH

LATITUDES

6.5.1. Some General Considerations

The effect of shortwave fadeouts on radio communications is so

insignificant, especially in high latitudes where the solar zenith angle

is large, that it will not be considered further. On the other hand, the

effects brought about by storms and polar cap events are often catastrophic.

A lowering of the maximum frequency (due to depression of the

critical frequency) and an increase in the lowest frequency (due to absorption) can occur separately or simultaneously. In all cases the effect

is a narrowing of the usable frequency spectrum. The former often happens

in middle latitudes and the latter has been observed near the auroral ring.

Ionospheric storms are frequently accompanied by spread F constituting a breaking up of the reflecting layer. This in turn brings about

rapid fading called "auroral flutter." This flutter is disastrous to voice

communication . The combination of these effects makes HF communications via the

auroral regions rather unreliable. Also, the southward extension of the

auroral ring during storms disrupts communications between North

America and Europe and relaying of the traffic through low-latitude

stations is necessary. Thus, although ionospheric disturbance may last only 5 percent of the time, high-frequency communications cannot be

used when 100 percent reliability is essential.
282 IONOSPHERIC DISTURBANCES

6.5.2. WWV Monitoring

Some information on the reliability of HF communications for paths

into the Arctic from outside can be obtained from a monitoring of WWV

carried out for many years in Canada. These data are published by the

Defence Research Telecommunications Establishment, Ottawa, and

consist of aural estimates of the strength of WWV, on frequencies of 2.5,

5.0, 10.0, 15.0, and 20.0 Mc/s using a range of 0 to 9. 0 denotes no signal

and 9 denotes the strongest signals. This rather subjective approach has

shown that one or others of the above frequencies is received over 90 per

cent of the time at Resolute Bay, Baker Lake, and Churchill, During

1953-54 the percentage reception times were Churchill, about 90 percent;

Baker Lake, 98 percent; Resolute Bay, 95 percent. The corresponding

figures for 1957-58 were Churchill, 98 percent; Baker Lake, 98 percent;

Resolute Bay, 95 percent. The relatively low value at Churchill for 1953-54 is due to MUF limitation (F2) at low sunspot numbers.

These results might be interpreted as indicating that, with a free choice of frequencies (2.5 to 20 Mc/s), it would be possible to communicate between arctic and non-arctic stations over 95 percent of the time.

However, this figure depends on the type of modulation used and the

information rate required.

6.5.3. Some Path-Loss Data

From what has been said above, it will be realized that the most

important factor in high-latitude radio propagation is the variability of

ionospheric conditions rather than the average state. Thus propagation

near the auroral ring is, for long periods, as good as elsewhere and at other

times communications are entirely disrupted. To describe the conditions we need, in addition to an average value of some characteristic, a measure

of the variability from hour to hour and from day to day.

Very little information of this sort is available; however, an experiment was carried out by the CRPL during the International Geophysical

Year, using transmissions on 8 Mc/s over paths from Bismarck, North

Dakota, to College, Alaska, and Anchorage, Alaska, and from Maui,

Hawaii, to the same receiving locations (fig. 6.16) . For the 9-month period

April to December 1958, it was found that path loss (relative to that over

the Maui-Anchorage path) over the four paths could be compared for the nighttime hours. The results are shown in table 6.2, from which we

see the marked increase in path loss for those circuits nearest the auroral
PATH-LOSS DATA 283

1 80° 120! 60°

Figure 6.16. Transmission circuits near the auroral ring. CO—College, AN—Anchorage, BI—Bismark, MA—Maui.

(After V. Agy, unpublished.) Table 6.2. Path loss relative to Maui-Anchorage (dB)

(2200-2400 150° WMT; April-December, 1958)

Receiver Transmitter Anchorage College Maui 0 7 Bismarck 12 22

(These values have been corrected for the difference in path and transmitter power).

ring. It must be borne in mind that these data are for (a) specific paths,

(2) nighttime, (3) monthly mean conditions averaged over 9 months,

and (4) the peak of the sunspot cycle.

The dispersion of the night -to-night data is shown in table 6.3 for the same 9 -month period. The values given are interdecile ranges; that

is, the range between the lower decile (exceeded 90 percent of the time)

and the upper decile (exceeded 10 percent of the time) . These values in- dicate that the paths with higher path losses are those with greater variability. It has been found that, for non-auroral paths, the decile separation is about 13 dB.
284 IONOSPHERIC DISTURBANCES

Table 6.3. Dispersion of daily values

(2200-2400 150° WMT; April-December, 1958)

Inter-decile ranges (dB)

Receiver Transmitter Anchorage College Maui 13 19 Bismarck 26 30

6.5.4. Remedial Measures

The WWV monitoring results suggest that one remedy is a relatively

large selection of operating frequencies. Owing to the overcrowding of

the spectrum and the methods of allocating frequencies, this method is not particularly practical except in special cases (e.g., WWV).

The use of oblique ionosondes to determine the optimum frequency

is another possibility. This may be particularly valuable in certain phases

of ionospheric storms because of the enhancement of Es, which may ex- tend to sufficiently high frequencies at which ionospheric absorption is low enough to yield a usable signal. This method also requires a free choice of frequencies.

Given a free choice of frequencies, it is possible to put a signal of

usable strength into the polar regions over 90 percent of the time—if the

period of trial is long enough. The quality of the signal, however, is un- known on a percentage-of-time basis. For voice circuits the rapid "flutter" fading is probably the worst of the difficulties to be overcome. Although

suggestions have been made for combating its effects [27], no serious

attempt has yet been made to carry them out.

I One remedy which has been used, to some extent, is the relaying of

messages around the disturbed area. This is feasible where the blackouts

are most frequent along the auroral ring and are usually (though not

always) limited in time to a few hours, and in extent to a few hundreds

of kilometers. Furthermore, owing to their local time dependence, it is possible to forecast their occurrence to some extent, and hence take re- medial action. Such action is, however, of only limited value in polar cap

absorption events which cover very large areas and the occurrence of

which cannot be predicted. Even in PCAs there have been reports of radio contact in high latitudes. These signals may have been propagated by

paths which avoid the absorbing region either because of tilts (sec. 4.6.6) or side scatter (sec. 4.6.5). An alternative possibility is that the ionization
RADIO PROPAGATION FORECASTING 285

is created very low down in the D region; under these conditions the absorption would not increase on the lower frequencies (see (2.101)) as much as it would if the absorption occurred at higher altitudes. Other alternatives are the use of very low frequencies, very high

frequencies (forward scatter, meteor scatter, etc.), and tropospheric

scatter.

6.6. RADIO PROPAGATION FORECASTING

Forecasting of the probable occurrence of an ionospheric storm can

be very useful from several points of view. For example, a communications operator is warned to transmit his essential messages before his

circuit is blacked out; alternatively he may start up various relay links, or change his operating frequency.

The two radio forecasting centers of the Central Radio Propagation

Laboratory regularly issue three types of forecasts of radio propagation

conditions. These forecasts apply to skywave propagation (usually

within the frequency range 2 to 30 Mc/s) over certain particularly important radio paths. The North Atlantic Radio Warning Service is con- cerned primarily with transmission over paths such as New York-London

or Washington-Paris; their forecasts will apply to a lesser extent on nearby

paths like Boston-North Africa, Maine-Greenland, etc. The North Pacific Radio Warning Service forecasts are designed for paths like AnchorageSeattle, San Francisco-Fairbanks, or Tokyo-Anchorage; they can be

given special interpretation, however, for others, such as short intra

Alaska circuits, but again with less reliabihty.

Average quality is forecast for a specified 6-, 12-, or 24-hr period. All times are Universal Time (UT or GCT). The CRPL radio quality scale

is used in all instances:

1—Useless 6—Fair-to-good

2—Very poor 7—Good

3—Poor 8—Very good

4—Poor-to -fair 9—Excellent.

5—Fair

The average quality in the 2 hr preceding the issue time is expressed

in the following letter code:

I W—disturbed (1 to 4)

U—unsettled (5)

N—normal (6 to 9)
286 IONOSPHERIC DISTURBANCES

The forecasts must be interpreted in the Ught of the user's own ex- perience. A forecast of "3" means that the conditions experienced should

be relatively poor, but the operator must interpret this in terms of the

expected performance of his circuit. If the forecast is correct, no more than

5 or 10 percent of all days should be so poor. There may be, however, a systematic difference between the word-descriptions used by the operator

and by the forecaster, and the operator must take this into account in interpreting the forecast. For instance, he may be used to calling conditions "very poor" when the forecaster calls them "poor," or the operator

of another, perhaps easier, circuit may never see conditions as worse than

"fair." The forecasts are expressed on a scale which corresponds to the

average experience reported on a typical circuit. The estimate of present conditions (the letter) is made available to

aid the user in interpreting the forecast (the number) . For example, if an "N-5" is issued, and the operator is already at the time of the forecast experiencing what he would call unsettled (quality 5) conditions, then

he would expect conditions to become even worse. The statement N-5

indicates that the forecaster looks for a deterioration of at least one grade

during the forecast period. The value of this scheme rests on the fact that

the operator is concerned with expected changes in conditions and so is given information to tie in with his current experience. If the "5" had

been issued without the "N," the user would not have been prepared for a drop in quality since he was already experiencing what he called quality

"5" conditions, although the concensus available to the forecaster rated

Conditions "normal."

A third forecast, the 24-hr forecast, is also available daily by telephone

and teletype from the two forecasting centers. Separate quality estimates

are issued for nighttime and daytime of the ensuing 24-hr period. The

range of frequencies on which the predicted quality should be realized

is also included.

Additional information concerning the radio forecasting services may

be obtained from:

For the North Atlantic area: North Atlantic Radio Warning Service (or NARWS)

National Bureau of Standards, Box 178, Fort Belvoir, Va.

(Telephone—Washington, D.C., 780-1436 or 780-1444)

For the North Pacific and Alaskan area: North Pacific Radio Warning Service (or NPRWS)

National Bureau of Standards, Box 1119, Anchorage, Alaska

(Telephon^753-2211 or 753-7210)
REFERENCES 287 Past CRPL forecasts together with the actual conditions which developed

are included in the CRPL F series, B, Solar Geophysical Data.

REFERENCES

[1] Bellinger, J. H. (1937), Sudden ionospheric disturbances, Terr. Mag. and Atmos.

Elec. 42, 49.

[2] Ratcliffe, J. A. (1960), S.I.D.'s during the IGY, Some Ionospheric Results

International Geophysical Year (ed. W.J.G. Beynon), p. 124 (Elsevier Publ. Co.)

[3] Kasuya, I., Y. Hakura, and H. Hojo, (1959), On the SWF phenomenon (Bellinger

effect) and/min in the world-wide distribution, J. Radio Res. Labs, (Tokyo) 6, 1.

[4] Bracewell, R. N., and T. W. Straker (1949), The study of solar flares by very long waves. Monthly Not. Roy. Astron. Soc. 109, 28.

[5] Bavies, K. (1963), Boppler studies of the ionospheric effects of solar flares, Proc.

Int. Conf. on the Ionosphere, Inst. Phys. and Phys. Soc, 76.

[6] Bailey, B. K., R. Bateman, L. V. Berkner, H. G. Booker, G. F. Montgomery, E. M. Purcell, and W. W. Salisbury (1952), A new kind of radio propagation at very high frequencies observed over long distances, Phys. Rev. 86, 141.

[7] Bailey, B. K., R. Bateman, and R. C. Kirby (1955), Radio transmission at VHF

by scattering and other processes in the lower ionosphere, Proc. IRE 43, 1181.

[8] Matsushita, S. (1959), A study of the morphology of ionospheric storms, J. Geophys. Res. 64, 305.

[9] Agy, V. (1954), Geographic and temporal distribution of polar blackouts, J. Geophys. Res. 59, 499.

[10] Cox, J. W., and K. Bavies (1954), Statistical studies of polar radio blackouts. Can.

J. Phys. 32, 743.

[11] Thomas, L., and W. R. Piggott (1960), Some aspects of the incidence of polar blackout during the IGY, Some Ionospheric Results—International Geophysical Year (ed. W. J. G. Beynon) (Elsevier Publ. Co.), 61.

[12] Agy, V. (1960), Spiral patterns in geophysics, J. Atmospheric and Terrest. Phys.

19, 136.

[13] Agy, V. (1954), The location of the auroral absorption zone, J. Geophys. Res. 59,

267.

[14] Collins, C, B. H. Jelly, and A. G. Matthews (1961), High-frequency radiowave

blackouts at medium and high latitudes during a solar cycle. Can. J. Phys. 39,

35.

[15] Piggott, W. R., and L. Thomas (1960), Variations in the incidence of polar black- out with magnetic activity, Some Ionospheric Results—International Geophysical Year (ed. W. J. G. Beynon) (Elsevier Publ. Co.), 72.

[16] Thomas, L. (1960), The temporal distribution of storm-type sporadic E in the northern hemisphere. Some Ionospheric Results—International Geophysical Year (ed. W. J. G. Beynon) (Elsevier Publ. Co.), 172.

[17] Hill, G. E. (1960), Ionospheric disturbances following a solar flare, J. Geophys.

Res. 65, 3183.

[18] Hagg, E. L., B. Muldrew, and E. Warren (1959), Spiral occurrence of sporadic

J. Atmospheric Terrest. Phys. 14, 345.
288 IONOSPHERIC DISTURBANCES

[19] Agy, v., D. M. Baker, and R. M. Jones (1965), Studies of solar flare effects and

other ionospheric disturbances with a high-frequency Doppler technique, NBS

Tech. Note No. 306.

[20] Bailey, D. K. (1959), Abnormal ionization in the lower ionosphere associated with

cosmic-ray flux enhancements, Proc. IRE 47, 255.

[21] Gregory, J. B. (1963), Particle influx at high latitudes, 1. Temporal and latitude

variations, J. Geophys. Res. 68, 3087.

[22] Gregory, J. B. (1963), Particle influx at high latitudes, 2. Solar protons, J. Geophys. Res. 68, 3097.

[23] Leinbach, H., and G. C. Reid (1960), VHF radio wave absorption in northern

latitudes and solar particle emissions. Some Ionospheric Results—International Geophysical Year (ed. W. J. G. Beynon) (Elsevier Publ. Co.), 281.

[24] Jelly, D. H., A. G. Matthews, and C. Collins (1962), Study of polar cap and auroral absorption at HF and VHF frequencies. Radio Wave Absorption in the Ionosphere (ed. N. C. Gerson), AGARDograph No. 53 (Pergamon Press), 206.

[25] Agy, v., and K. Davies (1962), Worldwide patterns of ionospheric blackout

occurrence. Radio Wave Absorption in the Ionosphere (ed. N. C. Gerson),

AGARDograph No. 53 (Pergamon Press), 202.

[26] Little, C. G., and R. Silberstein (1961), A comparison of arctic HF transmission

loss and VHF riometer data (private communication).

[27] Villard, O. G., and K. C. Yeh (1960), A proposed technique for improving the

intelligibility of voice radio transmissions in the presence of auroral flutter fading, J. Res. NBS 64D (Radio Prop.), 79.
CHAPTER 7

Ionospheric Propagation Predictions

7.1. AIM OF THE CHAPTER

The aim of this chapter is to give the reader a brief idea of the way

in which ionospheric data are apphed to the problems of high-frequency

communications via the ionosphere. The problems concerned with the

prediction of optimum working frequencies (see sec. 4.7.3) and system

loss are more adequately dealt with in another publication [1 J of the

Central Radio Propagation Laboratory, and the reader of this chapter is urged to consult that work. Data on the world wide distribution of

noise levels, which are required for the determination of required trans- mitter power, are given in CCIR Report 322 [2]. These two documents

will be extensively referenced in this chapter.

An outline will be given of the procedures used at CRPL in preparing predictions, and the application of the data to practical problems will be illustrated by some simple numerical examples.

7.2. PURPOSES OF PREDICTIONS

Because the ionosphere varies from hour to hour and from day to day, etc., it is necessary to have a knowledge of this variability in order

to select the optimum frequency, required transmitter power, antenna

configuration, and so on. Broadly speaking there are two types of predictions required.

(1) Relatively short-term frequency predictions are required by the

circuit operator in order that he may be able to anticipate MUF failure and thus increase the circuit reliability.

(2) The long-term predictions are required for the planning of

terminal installations. This involves both the circuit planner and the

^ Figures in brackets indicate the literature references on p. 341. 289
290 IONOSPHERIC PROPAGATION PREDICTIONS

frequency allocator. The sort of questions they are faced with are: What

will be the range of usable frequencies over the next sunspot cycle? What

is the minimum power necessary to fulfill the requirements of the circuit? What elevation angles must be used in antenna design?

It might be noted here that yet another type of prediction, if it may

be called a prediction, is the short-term information obtainable from

oblique ionosondes (sec. 4.4.) or backscatter observations. This type

is of importance primarily to traffic control centers and those concerned

with circuit operation.

For the first type of prediction, the most accurate method is to predict median values of the required parameters month by month. Such

monthly predictions are issued usually about 3 months in advance and

include observed ionospheric data up to 1 year before the prediction is made. The solar cycle information required is usually based on even more

recent data. Predictions of type (2) are needed over a complete sunspot

cycle and normally include data over the solar cycle prior to that in which

the prediction is made. The behavior of the E and Fi layers of the ionosphere is so regular that permanent nomograms can be used for deter- mining the required characteristics. On the other hand, the F2 layer is very irregular, and since it is the most important from the point of view

of high-frequency communications, maps have been prepared giving

the variation of /0F2 and the M factor (sec. 4.3.2), etc., as a function of

time of day, season, and sunspot number.

The purpose of the present chapter is to show how a prediction system

can be used to give information about a specific circuit. The essential

phenomena concerning the ionosphere and the underlying theory have

already been discussed and will be considered only briefly below.

7.3. PREDICTABLE CHARACTERISTICS'

7.3.1. Sunspot Number

The long-term variation of ionospheric parameters is tied closely to the sunspot cycle, and although no completely satisfactory measure of

solar activity is available, the 12 -month running average sunspot number

is most widely used (see sec. 3.3.5.4). Normally, the most practical way

for circuit operations and planners to determine the sunspot number is to use the predictions of others p]. When predictions of future cycles are required, an average minimum of 10 and an average maximum of 130

Most of the figures in this section are from a lecture by G. W. Haydon.
MAXIMUM FREQUENCIES 291

are recommended as a rule of thumb. New indices, based upon other pa- rameters (e.g., ionospheric and solar noise), are being investigated [4, 5].

7.3.2. Maximum Frequencies

The predictions of /0F2 are based on the diurnal, seasonal, and geographical variations and/or sunspot number dependence established from

previous data (see sec. 3.3.5.4). No attempt is made, in these long-term

predictions, to estimate the day-to-day fluctuations in critical frequency

since these are rather localized in both space and time. Furthermore, no

account is taken of ionospheric disturbances, such as those discussed in chapter 6, as these constitute a relatively small percentage of the total time.

The basic ionospheric data used in predictions are the Fi, and F2

layer ordinary -wave critical frequencies and the M(3000) F2 (sec. 4.3.2) —

that is, the M factor for a distance of 3000 km.

The behavior of the E and Fi layers is such that the critical fre- quencies can be predicted, fairly accurately, in terms of solar zenith

angle x and sunspot number R by means of (3.31) and (3.32) respectively. Furthermore, the higher critical frequency and the lower M factor

for the Fi layer are such that the product gives roughly the same maximum frequency as do the corresponding values for the E layer. The

E layer is usually the controlling layer for distances up to about 2000

km and the Fi layer for distances between 2000 km and 3000 km. Thus,

from a knowledge of x and i5, nomograms can be constructed to give foE. The use of these nomograms will be discussed below.

The behavior of the F2 layer is more complicated than that of the

E and Fi layers and cannot be represented analytically. In the preparation of F2 predictions, the first step is to obtain the line of best fit of the

monthly median values of /0F2 to the 12 -month running average sunspot

number. This is done for each hour (or each alternate hour) of the day

and for all stations. The slopes and intercepts of these lines are then used

to construct worldwide maps from which, with a knowledge of it is possible to calculate /cF2. Sometimes, the value of /0F2 at some specific

-R( = 50, for example) is given instead of the intercept or together with

it to give the slope. The predictions of the M(3000)F2 are prepared in a

similar manner. In those prediction methods (which are published

monthly) the sunspot, seasonal, and diurnal variations are automatically

taken into account [3]. Given the F2 zero distance maximum frequency,

MUF, (ZERO) F2(=/xF2) and the 4000 km maximum frequency, it is
292 IONOSPHERIC PROPAGATION PREDICTIONS

o o o

Figure 7.1. Nomogram for transforming F2(ZER0)MUF and F2{4000)MUF to equivalent maximum usable frequencies for intermediate transmission distances.

Also conversion scale for obtaining optimum working frequency (FOT). The nomogram can be used to find the skip distance for a given frequency from the MUF(ZER0)F2 and MUF(4000)^2.
RADIATION ANGLE 293

possible to interpolate for intermediate distances by means of figure 7.1. Note that the M(4000)F2 is obtained by multiplying M(3000)F2 by 1.1.

7.3.3. Radiation Angle

This depends on the height of reflection (assumed specular) of the

waves. In the case of the E layer, it is sufficiently accurate to take the

angles of elevation given in figure 4.31. This figure can also be used to

give rough values in the case of F2 layer propagation but, in general,

it is more accurate, if the height of reflection is known, to determine the

elevation angle from figure 7.2. The monthly median heights of the F2

layer are given on a worldwide basis in reference [1].

IONOSPHERE LAYER HEIGHT- Hj^- KILOMETERS

100 200 300 400 500

5i)0 4.00 3.50 3.00 2.50 2.30 M-4000 FACTOR Figure 7.2. Radiation angle as a function of great circle distance and ionospheric layer

height.
294 IONOSPHERIC PROPAGATION PREDICTIONS

7.3.4. System Loss

7.3.4.1. The Elements of System Loss

The concepts of system loss and path loss have already been dis- cussed in sections 5.2 and 5.3, respectively. In this section we shall consider the various losses that occur between the transmitting and the re- ceiving terminals.

We shall need to consider the following path losses:

(1) Ground loss which occurs on reflection in multi-hop propagation, Lg;

(2) Distance loss due to spatial spreading of the wave. Lap;

(3) Ionospheric absorption. La;

(4) Fading and polarization factors;

(5) Antenna gain, G.

7.3.4.2. Ground Loss

This depends on the conductivity of the ground and on the angle of

elevation of the incident radiation. The losses for a good conducting

surface (e.g., sea water) are less than for a poorly conducting surface

such as bare rock or desert. For two types of surface the value of Lg

(in decibels) can be obtained, with a knowledge of the wave frequency

and the radiation angle A, from figures 7.3a and 7.3b.

7.3.4.3. Distance Loss

In general, it is too complicated to take into account the detailed

effects of focusing, etc., so that the effective distance Se (see (5.8)) is essentially the geometrical distance of the path which depends upon the

ground range and height of reflection. For long distance transmission,

involving single or multiple hops, the effective distance is, essentially,

linearly related to the ground range. This is incorporated into the nomo- gram of figure 7.4 in which the distance attenuation has been combined

with the frequency characteristics of an isotropic radiator for which the

plane wave capture area in free space is given by (P-I^-Kp^ where c is the

free space velocity of height.
SYSTEM LOSS 295

3 5 10 15 20 25 30 MC/S

Figure 7.3. Power loss at reflection.

(a) Poor earth, €=4, (T=10"» mho/m. (b) Sea water, e=80, <r=5 mho/m.
296 IONOSPHERIC PROPAGATION PREDICTIONS

REFERENCE

km

40000

30000 -i

20000 4.

10000 8000 -I 6000 -i 5000

4000

3000 -i

2000 4

1000 -z 800

600 -I 500 ^

400 -| 300 ^

200

100

dB

I- 180

170

I— 160

150

140

(4)-

(2)

130 y

/- 120 - 110

100

90

80

I- 70

"

Mc/S

100 -

70 H

5040 -

30 -

20/

y

y

10

7

5

4 -

3 -

2

0.7

0.3 (1)

0.2 -z - 60 ^ 50

0.1

A**

- 80

75

70

h 65

60

55

50

0.5 45

0.4 F 40

35

30 F 20

10 0

Figure 7.4. Nomogram for the determination of transmission loss due to distance attenuation with an isotropic radiator. Example. (1) For a great circle distance of 1200 km and A=8°, draw a straight line which gives reference point (2). With reference point (2) and the wave frequency (in Mc/s) draw line (3). The intersection of line (3) with the dB axis gives the spatial loss (4).
SYSTEM LOSS 297

7.3.4.4. Ionospheric Absorption

The ionospheric absorption, La, depends on several parameters,

namely: sunspot number, solar zenith angle, season, operating frequency.

Figure 7.5. Nomogram for the determination of absorption index I from the solar zenith angle (x) and the mean sunspot number R.

Example: With x=40° and i2=100, draw a straight line. The intersection of this line with the absorption

index lines gives 7=1.06.
298 IONOSPHERIC PROPAGATION PREDICTIONS

gyrofrequency, and radiation angle. The dependence on solar zenith

angle x and sunspot number R can be expressed, to a sufficient degree

of accuracy, in terms of an absorption index / by the formula (see sec. 3.3.6.2 and sec. 3.3.6.3)

/= (1+0.0037jR) (cos 0.88Ix)i (7.1)

This equation is incorporated into the nomogram shown in figure 7.5, whence / can be obtained for given values of x and R. The seasonal dependence on cos x has to be corrected for the winter

anomaly (sec. 5.2.5.5). The corrected / (/c, say) is obtained by multiplying the value obtained from figure 7.5 by the factors in table 5.1. The next step is to incorporate the frequency dependence (sec. 3.3.6.2) and the path length in the medium. These are incorporated in

figure 7.6 in which the corrected absorption index, Ic, should be used where

(f+f^) Mc/s Figure 7.6. Nomogram for obtaining the ionospheric absorption per hop from the absorption index /, the effective wave frequency f-\-fn-i ond the angle of elevation A.

Example: (U Enter with the absorption index I (1 = 1.09) and the elevation angle A (=8°). (2) Mark the

reference point of intersection with the center line. (3) With reference point and effective frequency

f-\-fu (=22.4) draw a straight line as far as the curve marked absorption per hop (=6 dB).
SYSTEM LOSS 299

appropriate. The gyrofrequency,/^, can be obtained for any geographical

location from figure 7.7. Note that the use of Jh instead of Jl introduces some error into the calculated absorption of the ordinary wave, but this

is relatively small except for strictly east-west propagation when it is probably better to drop the magnetic term altogether. The nomogram

3aniiivn Figure 7.7. World map of gyrofrequency for a height of 100 km.
300 IONOSPHERIC PROPAGATION PREDICTIONS

should be used as follows: With the corrected absorption index and radiation angle draw a line interesecting the center line. The intersection gives a reference point. With the reference point and the effective frequency

extrapolation gives the absorption per hop (in decibels)

.

7.3.4.5. Allowance for Fading, Polarization, Etc.

The above considerations of transmission loss are all based on median

values; that is, they refer to nonfluctuating signals. Owing to short-term

variations in electron content along the ray path, the signal will, in general, fade so that for a certain fraction of the time the signal level

will drop well below the median value. In order to ensure that the signal

exceeds a minimum level for a certain percentage of the total time, an

allowance must be added to the path loss. By this means, the matching

polarization terms Ltp and Lrp (see (5.5)) are automatically taken into account. Tables giving the necessary allowances for various types of

service are given by the CCIR [6].

Figure 7.8. Space-wave radiation of a half-wave horizontal antenna 20 m above poor earth, e = 4, o- = 10~3 mho/m.

Numbers on curves are decibels above an isotropic radiator in free space.
MONTHLY PREDICTIONS 301

7.3.4.6. Antenna Gain

In order to determine the system loss, it is essential to know the gains

of the transmitting and receiving antennas at the appropriate radiation

angles. Of course, this information can only be obtained from the ge- ometry of the antemias. An example of the type of information required,

for the case of a half-wave horizontal antenna, is shown in figure 7.8.

7.4. FREQUENCY PREDICTION SYSTEMS

7.4.1. Monthly Predictions^

A variety of ionospheric predictions is issued monthly by laboratories in a number of different countries, usually three months or so in advance. Many of them are for localized areas, but several attempt worldwide predictions [3, 7]. While all prediction services use essentially the same ionospheric data and established physical relationships, there is considerable variation in the form of presentation and in the approximations used in applying the various predictions to propagation problems.

The CRPL prediction system, based on a method of numerical mapping

of ionospheric characteristics developed by Gallet and Jones [8, 9, 10],

using electronic computers, will be described briefly.

The term ^^numerical map" is used to denote a function, r(X, 0, t), of the three variables: latitude (X), longitude (^), and time (t) . The function r(X, 6, t) is obtained by fitting certain polynomial series of functions

of the three variables to the basic ionospheric data. The general form of

r(X, ^, t) is the Fourier time series H

r(X, t) ±ao(X, e)+Y. [j^ii^ ^) cos jt+hj{\ e) sin jt], (7.2)

where H denotes the number of harmonics retained to represent the

diurnal variation. The Fourier coefficients, ay(X, d) and 6y(X, ^), which

vary with the geographic coordinates, are represented by series of the form

i^DskG.iX.d) (7.3)

A:=0 "where the (X, 6) are given in table 7.1. The index s denotes which Fourier

This section was written by Mr. S. M. Ostrow.
302 IONOSPHERIC PROPAGATION PREDICTIONS

Table 7.1. Geographic functions Gk(\, 6)

Main latitudinal Mixed latitudinal and longitudinal variation

variation

First order in longitude Second order in longitude

k Gk{\ 6) k Gk(\, 6) k Gk(\, 6) 0

12

1 sin X

sin^X

ko +l /co+2

/co+3

cosX cosd cosX sind sinX cosX cosd

sinX cosX sind h+2

fei+3 fei+4

cos^X cos 20

cos^X sin 2d

sinX cos^X cos 20

sinX cos^X sin 2d

ko sin«oX

sin^iX cosX cosd

sin^iX cosX sind K-l

K

sin^zx cos^X cos 29

sin32X cos^X sin 2d

coefficient is represented, in the order given by

s = 2j\ foray(X, ^),y=0, 1, .-sH, (a)

(7.4)

s = 2y-l, for6,(X, ^),y=l, 2, - ".H. (b)

A numerical map, r(X, 6, t), is completely defined by a relatively small

table of coefficients, Dsk- An important advantage of the numerical mapping method is that, as new data become available, the coefficients can be easily revised by

the use of an electronic computer. Also, as additional physical relation- ships are established, they can be incorporated readily into the mapping

program. The value of the parameter mapped can be derived for any

location, and graphical maps may be prepared by computations using the

table of coefficients. The numerical map is particularly useful when large numbers of propagation path computations are required. The use of a computer

permits rapid and economical inclusion of all required propagation vari- ables in routine computation. Tables of predicted coefficients may be obtained in the form of tested sets of punched cards from the Prediction

Services Section, CRPL. Users who do not have access to a computer, or whose requirements are not large enough to justify their own computer

facility, may arrange to have ionospheric propagation calculations per- formed at a reasonable cost by the Frequency Utilization Section, CRPL.

For those who do not have access to a computer, or require a manual

solution to an ionospheric propagation problem for some other reason, the CRPL also issues a monthly pubhcation. Ionospheric Predictions [3j.

This bulletin contains the basic tables of predicted coefficients of /0F2
PERMANENT PREDICTIONS 303 and M(3000)F2 three months in advance, in addition to world maps of

predicted MUF(ZER0)F2 and MUF(4000) F2 for every even hour of

Universal Time. The predicted maps are calculated from the tables of

predicted coefficients using the approximations:

MUF ( ZERO) F2 =foF2 +////2 =/,F2, (7.5)

MUF(4000) F2 =/oF2 X M(3000) F2 X 1.1. ( 7.6)

Instructions for the use of these maps may be found in the National

Bureau of Standards Handbook 90 [11]. Tables 7.2 and 7.3 give examples

of tables of predicted coefficients Dsk defining the function F ( X, 6, t) for monthly median /0F2 and M(3000)F2 for June 1963. Figures 7.9a and

7.9b show examples of world maps of MUF(ZERO) F2 and MUF(4000) F2

for the hour 1800 Universal Time, predicted for June 1963. These maps

were derived from the predicted coefficients of tables 7.2 and 7.3.

7.4.2. Permanent Predictions

In contrast to the monthly prediction systems, permanent predictions systems describe the variation of the ionosphere over a complete

solar cycle. They are particularly useful for long-term frequency planning

and communications equipment specification. Such systems have been

issued by the CRPL, the United States [12]; the Radio Research Station,

England [13]; The Defence Research Telecommunications Laboratory,

Canada [14]; and the Radio Research Laboratories of Japan [15]. These

are usually issued in the form of a set of maps for solar cycle minimum and

maximum conditions, but may also be in the form of a set of maps for a specific level of solar activity accompanied by a set of maps showing the

world variation of the dependence on solar activity. Permanent predictions

in the form of numerical maps for solar cycle minimum and maximum are

available from CRPL and are part of the current CRPL prediction system.

By applying a suitable index of solar activity to a permanent prediction system, ionospheric characteristics may be obtained for any level of solar activity. They may be used as monthly predictions by using a pre- dicted monthly index. The Ziirich sunspot number has been the most

commonly used index of solar activity. An index based on past ionospheric

data, such as /(F2) of the Radio Research Station, is also sometimes used.
304 IONOSPHERIC PROPAGATION PREDICTIONS

3aniiiv"i

Figure 7.9a. Predicted median F2 layer parameters for 0800 UT for June 1963, MUF{ZER0)F2.

(From CRPL Ionospheric Predictions.)
MONTHLY PREDICTIONS 305

3aniiivn Figure 7.9b. Predicted median Fz layer parameters for 1800 UT for June 1963, MUF(4000)F2.

(From CRPL Ionospheric Predictions.)
IONOSPHERIC PROPAGATION PREDICTIONS

to mmm

,^,^g-^^,-._O-^O--l.-lO^r^(^J^0'-lfMO0-l->f^Jl^] oooooooooooooooooooooooooo mmmmimuimim

r- S3ggS8S8333o3 3S33g3gg3gg33g33S§g3S3gg3S

iiiiiiiiiili

333§§§3333S§§

mmmm

33§§§333S333§

ifiiafi

33 3333ggg§3g3g3§333§gg3§3'3

(0

lO

Hi^^^^^^^?S^HH2^^g«H^i^

iiiiiiiiiiaii

S3333ggg3g3g3333gg33g33gSS

iH^H^^i3^°H^HH3sH^H

s:<^s:v^5L^si3.5iHi?r35:-rsL^

<r 3g§§33S33§3§S

Hfiiiiliiii T 7 ^ V T " 7 7 7 ^

ro ooooooooooooo iiiiii

333§§3§3 333 33 33333 3333g3S3

liiliiHIliiii

sss5:?S3;ss?;;;?r--«sg3S2SS:?:ss

CVJ §§33SS3333333

mmmm

33ogg3goo3goo33o333o333ooo

mmmmrBmtMrmi

§3§333SSSSS33

mmm

333g3833g33 33 3333333333333

EWmrmrfBwmmti

mmmmmmm

o O §3g333SS3S3S3 S33gggg33 333 33 3 333 333333 3S

u

§

E X

X a

NOiivmvA ivo.iHdvaooao
MONTHLY PREDICTIONS
IONOSPHERIC PROPAGATION PREDICTIONS

(T

UJ

Nl MrNI -< -i -i-iOO-<'-i OO-H ^ O-i o oooooooo o

1 OOOOOOOOOOOOOOOOO

Ij

1 1 1 t 1 1 1 1 IjJ llJ _lJ UJ :JJ :lj LJ -L) \±i

1 1 1 1 1 1 1 II II 1 jJ U .J U uJ U UJ uJ UJ uJ oJ UJ 'JJ UJ UJ jJ UJ

•H r- X3 a 7^ O vO ^0^J^~-r^OOC0-0C^^^C7>0•.^r>7^0^

OJ>r^ -Or^^ c^'Of-Hrrir-HON'NJvOCOr^vO

(0 a =0 'NJ ^0 n r-1 ^ —1 fNj Q^ GO CO -H r^r-^oxij-o-to^o-l-M-i-n-o—lo

to ^ rH rH ,-( r-l o -1 m <-l AJ J- .-1 -1 -H ^ ^ rH ,-1 O IN H -1 O oooooooo o OOOOOOOOOOOOOOOOO 1 1 1 1 1 II

UJ jJ jJ UJ UJ iJ jJ UJ

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 O -n o -M <r O O C^'OO-d-O-na-'Irri^rO-rir^^'NJco

in ojoOtTirHro^to r^jvr~-xi-a-^vO-nr-o^7D-oo~oaoco

coco4-a30in(Njx> OOr<i-a-'\JOrNirNiOrNjcor-rNir^~trr)(M o O-£)Or^-0O<J-s0 -0 om-tr~-n-HMr--^-t^<t-ONr-fNjo o s\ on:NO(^o-j--aa3o<j--a-r--coi--r^

r-i ^ojoOOO-t-H ~n Aj NJ rH ,-i ,-i —1 o o -H o o —1 -< o o

o

1 oooooooo II II o OOOOOOOOOOOOOOOOO

UJ jJ jJ UJ JJ UJ iJ

1 1 1 1 1 1 1 II II

jJ Jj -U Jj uJ U 'Jj UJ UJ 'JJ 'iJ UJ '-U UJ jJ iU UJ

J3 OO.-nr-rNjXNO-t-OC'lfM'-lOsOO^l-O

csj ^ sj" 7% Psj iH rsj

r>- or~-jo oov iriO-4 in Lnr— ^J-0'^a^oo'7^^-lr-^•^^c»1(^J_(-ll^^ -^OsOlOO^J-OvO •n O^r^ OtNivOOfNiJ- Ococooor^ O.^rn

r^rr^Tt OiX^ 0i"0^

Ln»i"'Nj oj^iA^co

1 II ^AJ^O-IO-IO -NJ orNJNjrNI-i-(-H-('-ir-<o-~<'-i-<^-<Nj o oooooooo III 1

1 o OOOOOOOOOOOOOOOOO

LU Uj JJUJUJUJUJUJUJ UJ uJUJ;iJUJUJUJ'uJujuJujuJujuJuJuJuJjJ O v0-(0 O^O'NJMO^OO.-O O -O O

ro

-0 (N ^-c^N c^^ooooo- j-ct-ia^vOoovOOr^Ai

c^ rvjc<>0cx30r^0r\l in O^Oi'ncnvOao—iOc<NrNjoocooa3aoa3iri o mcocoj-M'MXio m '^ao-o^OfNJ^^.na^m^"^-dco^^l—(GOvOr^ tMOvO^f^JOtMOO -t ornrNiunco-Hoon ovornr-in-ox)

rHC^'-tO'^J OfNJO moD—ioOrH>£)r--.-iir\ or-aDr--a^-t(7> II II 1 '7^ CO-—^CNjr^icOrOc^^r-HsijrNJ'—<r*rn^ It 1 1 1 1 III

-( -IOOOOOOO fM rvj^^H^^^OOOrNj OOO-IOOO o

1 OOOOOOOO 1 O OOOOOOOOOOOOOOOOO

UJ UJ 'Jj UJ IjJ UJ LU UJ UJ

1 1 1 1 1 1 1 1 UJUJUJUJUJUJIjJUJUJUJUJUJUJLlJUJUJUJ

,OvOav-j-r-ONXiT3r-.oc7vc>ro^o-^)'Njin

C^C^-3•r\la^a^(M^^ oa>r<~ico<J-^OcOOcOrNJrHa3(MvOO-00

la—*r^f\lLr\'HOO

(NJ cotNiir\Lnp~r~-f\jt\i r^o~to^^vOvOi^rfia^<j-inLnr-Hr-Lno

-O O^^O.d^rlO^^OlAC^ o CO in m .-1 o in'm inotMC^oor^^rorNj

CM (\Jr-(rHrHrHrNJ^fNJ (NJ fNj(Nj.HrH^rNj-HOOrNJOOOfNJOOO O OOOOOOOO O OOOOOOOOOOOOOOOOO

UJ UJUJUJUJUJUJUJUJ

1 1 1 1 1 1 1 1 1 OmtNjO'-<^00>rTia>c<NrNjrH<}-oaorNJ

cj»coc7^o;?^cor^Lnintr\fNjr-(vOco-j'rO'—

)

- rvjc^^o^f—(co»—*^ cDOr^a3roi(M^sO.-i^inom-tunr~-dO(M<ri0N-Hr-ia0in i-ir^(NjKOLno-*coininvOLnfNj^o~t(Nj'H

i- in r-HOor^^c^(>in<7»0["^rNivOLnr* 4-fNj (\jr^vO<t"f^f^Of*^ CO o^r-(<icnr-i^o(*^Ln-tooor--4-ooa>—

1

CO ^0'H>00(?>-H0<3- f—tr^r*-oOfNjiA(Ni-HOvO^>^r^or^fNj

1 III fNi(Nj--^fNjr~^a>r-i-d-'-ir-icNjr~-co.-ir-i<)-

1 1 1 1 1 1 1 1

o -HO^O-iO-iO 'M Og-H^rNlt-^^O-H^OOO-HrHOi-l^

o oooooooo O OOOOOOOOOOOOOOOOO

lL

1 1 1 1 1 1 II II II

~t^O^-S-Ot»~lfM.-( OvOin'-iaooNcor~^sOf<>r--ooo^c<~iOin

<J- aDr^vj-oOf<~if^m cor*Of*^(Mir»rNj-^>^-inc^inOcMr^r^<j- o o o r^-OOJ-rHma^COrrviDinrHfNI^J-OOrri

vO rHfNJCO-J-lTlfNJCOr-ICDvOfNJO^Or-rHCOin

<(• sOD c^O LTi^OOcO rNjmCTvu-icOvOao>£irNj>Or-(inLna>.-it\jr^

c*>r^ vOfNjrn f^^r-4co^f^iAfNj^r^ ^o^o OX-J-r-iOvODr^ <ffNJO4'r-(\jmr<^TnrNJOOv0O-0v0r1 II 1 iNj^rNj<trNji^,-irH<|-^(NjrHrN4vO'-iOiri

U) /

_o o o^(Niro<j'tr(vl}f^coc7^0'—irN]f<^>:fir»v£) 'co /

^

EoX

NOIlVmVA nV0IHdVH9039
MONTHLY PREDICTIONS

J LU jJ LU -U "oJ LU > .A -A 33 rJ3 (M A ro r-l r~ >0

-ri O -I -M r- -o -J- O P~

<}• O J> TO O J3 M vO r- -I -H sO

J> XI M -O X) J- ^ OOOOOOOOO

O ^ M OS -I cn > r<-i aO'MC0NO>r--A

l^fT^O rHOn^ Of^LA A^^--o-<r~sD^<JTs-O-f-TTsO—lOr^-

X\-t7sLAMCDOr~.-<-i

lArNj-ri-i^-l-i n-l

O O O O

U LU lU LU a t\i n a\

sO «o ^ o

o (Nj m ro

CO f\i ro rvj f\j ^

Ni O OS -J- sO lA lA

r\j

JJ LU -U LU LU LU LU

Js -I OS » O ~sl

-1- A -M O

rO ^ w r- "vj ,<-, sO <! O OS rsj O »

CO uA O -A ^ r-

-I O -O 7- o

lA ^ O O r- o J-> XI > (M -A

O O O O O O O

<t O O r\l O ^ ^

(sg r\j 00 O Os O- ro ^ —I fo lA yO rsj rsj OS OS O r~- ro ro (M

fsj lA lA O fNJ CO ^

r-i r-- (O vO r\J lA o

ro 00 -I J- lA vO

OS r\i

CO OS -H

fsj r- CO

CO f\/ ro <t sO -O OS O O <) O ro

ro -M -o M 0 o o o

1 1 1

1

CSJ

-SI OS N ^ ^ ^ -sj lA O O

lA r- 'SJ M

r\| CO X5 -< r~ sO OS

-A r- OS o

sO —1 —

CD

-0 ro o O O O O

-

1 1 t 1 ^ r-l D

C> lA lA ^

JD X) rsj X) P~ ~0 ^ XI CO CO CO CO -0 r\l N -M -(

1 1

\J -\J ,sj o o o o

1 1 1 1 U U LU -U

X) XJ rM sD O O O

OS OS o a-\ OS OS O cA

<>J 0> OS

-1 N r~ <Jin

,-xJ rO CM 0 o o o

1 1 1 1 r- .£1 -( <f

<} o- <r CO

-o <f- ro uO

ro la r- o

<J- sO OS CO

O- <t r~ J-

<t -A .0 lA

X) ro ro rr

^ ^ (sj :\l o o o o

CD

LU LU LU '-U X) o r~ o

00 XI OS ^ rsi o lA

CO o X! lA rsj rvj <J- O rsj 00 lA

r\l .-1 -(

1 1

oj rsj rM CNJ O O O O

CO Os C7> O O rsi 00 XI 00 lA Os '-A

fs- <> O rsj OS CO rsj

o CO /

O ^ fNJ CO /

^

Horn

NOIiVmVA

nVDIHdVa9039

r\] <3- iTt nO

. C

1=1 •£ i i O O)

5 ^

Q

LU

f-O

Q

UJ

q:

CL
310 IONOSPHERIC PROPAGATION PREDICTIONS

7.5. RADIO NOISE PREDICTIONS

7.5.1. Importance of Noise

In every communications system (radio or otherwise) noise is the

limiting factor which determines whether or not the signal is usable for the transmission of information. In principle, if all noise could be elimi- nated from a system then only an infinitesimal transmitted power would

be required and the amplification in the receiver could be unlimited. In the presence of noise, there is a limit to the amount of useful amplification because both signal and noise are amplified to the same extent. Thus, in choosing a receiving site, it is very important to have a knowledge

of the ambient noise with which the desired signal must compete so that

sufficient power may be transmitted in order to override the noise. Radio noise arises from a number of noise sources such as resistors,

radio tubes, etc. (thermal noise), galactic noise (thermal) from outer

space, atmospheric noise from lightning discharges (thermal and/or

impulsive in nature), and from electrical machinery (impulsive or spikey) [16].

Noise internal to the receiving system is usually the dominant noise

in systems operating on frequencies above about 300 Mc/s. In the highfrequency band (3 to 30 Mc/s), atmospheric and galactic noise usually

determines the noise level at sites well removed from civilization. It is with these types of noise that we shall be concerned in this chapter.

Measurements of atmospheric noise levels have been made for many

years by the Radio Noise Section of the Central Radio Propagation Laboratory and the reader is referred to their publications [17, 18, 19] for details on the method of noise measurement and the applications to the

design of communications systems. These details need not concern us

here; it will suffice to know that experience has shown that the noise

power is generally the most significant single parameter in relating the

interference effect of the noise to system performance.

The noise power is measured in terms of quantity. Fa, which is de- fined as the external noise power available from a lossless antenna, ex- pressed in decibels above A: To, where k is Boltzmann's constant and To =

288.39 °K is a reference temperature, which is the noise generated in a unit bandwidth by a thermal source at a temperature To. On the as- sumption that noise power is proportional to the bandwidth b (in cycles

per second) we have that the the total power (P„ in decibels above one

watt) available at the terminals of a lossless antenna is given by
PRESENTATION OF NOISE DATA 311 Pn=Fa+B-20i dB/W {1.1)

where B = 10 log 6 and 10 log A: To = —204. Notice that this is based on

the assumption that the noise is incident on the antenna uniformly in all directions.

7.5.2. Presentation of Noise Data

7.5.2.1. Long-Term Characteristics

The noise power at any point on the earth's surface depends on the

following:

(1) Geographic location;

(2) Time of day;

(3) Season of year;

(4) Operating radio frequency;

(5) Bandwidth of the receiving system.

Hourly noise data have been collected at a number of locations on a

routine basis over several years. Any long-term variation appears, at

present, to be small. The diurnal and seasonal variations of the noise

parameters are represented by dividing the year into the following four

seasons:

Seasons Months

Northern hemisphere Southern hemisphere

December, January, February

March, April, May

June, July, August

September, October, November

Winter

Spring

Summer

Autumn

Summer

Autumn

Winter

Spring

The noise levels are presented as median values Fam of Fa for each of the

following 4-hr periods of local time at the receiver: 00-04, 04-08, 08-12,

12-16, 16-20, and 20-24. The statistical distribution of the individual

values Fa about the median Fam is given by the upper decile ratio £>„

( = Fau — Fam) whcrc Fau is thc valuc of Fa exceeded 10 percent of the time.

When plotted on a normal probability graph (level in decibels), the amplitude distribution of the deviations, D, above the median can be repre-
312 IONOSPHERIC PROPAGATION PREDICTIONS

Figure 7.10. Worldwide radio noise data, winter season, 0800-1200 local time.

(a) Expected values of Fam, in decibels above kToB, on 1 Mc/s.

314 IONOSPHERIC PROPAGATION PREDICTIONS

sented with reasonable accuracy by a straight line through the median

and upper decile value. A corresponding line through the median and

lower decile value Di can be used to represent the deviations below the

median. The lower decile is of little practical importance and will not be

considered here. The values of Fam presented in the maps are deduced from values

taken at several geographical locations and on a number of frequencies.

From the frequency dependence of Fam a reference value on an effective frequency of 1 Mc/s is obtained and this is plotted on the sample noise

map in figure 7.10a. Of course, the data presented are smoothed values

and the measurements on a specific frequency at a particular location

will, in general, differ from the value deduced from the curves. A measure

of the error introduced by the smoothing procedure is, therefore, given

by the standard deviation of these differences o-Fam- ^ similar way, the

standard deviations of aou-, are measures of the difference to be ex- pected between the values of Du obtained from the curves and the actual

measured values. The variations with frequency of the above noise pa- rameters are given in figures 7.10b and 7.10c. A complete set of these

maps can be found in the CCIR Report 322.

7.5.2.2. Short-Term Characteristics

The parameters discussed above represent the fluctuations in the

long-term character of the noise, that is, from one time block to the next and from season to season. To evaluate the effect of the noise on a communications system, we need also some knowledge of the short-term character of the noise. This subject is dealt with fully in the publications of

W. Q. Crichlow and his coworkers [17, 18, 19] and the interested reader

should consult those references. For many purposes, and particularly

those involving subjective factors, the simplest procedure is to take the

short-term effects into account by using the CCIR tables of signal/noise

ratio [6].

7.5.2.3. Application of Noise Data

To understand how the information presented in figure 7.10 is applied

to an actual problem, let us consider the following example.

Determine the noise level at Washington, D.C., on a frequency of 13 Mc/s in a 6 kc/s channel at 1400 UT in December 1963.
DISTANCES LESS THAN 4000 KM 315 From an atlas or some other source we determine the geographic

coordinates of Washington, D.C.—39°North, 77°West and, hence, the

local time is approximately 1400 — 0500 = 0900 hours. From the noise

grade map of figure 7.10a we find that Fam on 1 Mc/s is about 32 dB. In

order to determine the value of Fam on 13 Mc/s we locate the 32 dB

point on the 1 Mc/s line in figure 7.10b and move up in frequency (keeping just above the 30 dB line). On 13 Mc/s, we have Fam^32 dB. To

take into account the uncertainty in the value of Fam due to the spread

of the data we add a correction apam obtained from figure 7.10c. On 13

Mc/s we find that aFam^^ dB. Hence the noise power on 13 Mc/s in an

effective bandwidth of 1 c/s is 32+6 = 38 dB above the reference value

of A; To. On the assumption that noise power is proportional to bandwidth we

find that the noise power in a 6 kc/s channel is 38 +10 log 6000 = 38 +

37.8 = 75.8 dB above kTo. Substitution in (7.7) gives Pn= -128.2 dB

above 1 W.

7.6. CALCULATION PROCEDURES FOR DISTANCES

LESS THAN 4000 km

7.6.1. Introduction

The average height of the F2 layer (320 km) corresponds to a maximum one-hop distance of about 4000 km. Hence, this distance gives a convenient dividing line between long distance and intermediate distance

transmission. In this section we shall discuss, by example, the procedure

to be followed for transmission distances of less than 4000 km.

7.6.2. Problem 1

Part 1. Determine the optimum working frequency around noon

in June 1963 for a transmitter in Boulder, Colo., and a receiver in Washington, D.C.

Part 2. Find the transmitter power required to ensure the following

performance of an A3 telephony double sideband system with a bandwidth of 6 kc/s. The required grade of service is marginally commercial

for 90 percent of the hour and the antennas are half-wave horizontal

dipoles at heights of 20 meters.
316 IONOSPHERIC PROPAGATION PREDICTIONS

g fe s s? s ! Him h. Hinos s ^ h s k h s. -4

[ —

/

s \

' r—

!

? (

4

4

I

r \

f:

;V

•ai-"

•A I* .\

L V

\ 1

1 1 i .— , 'T, f

[

1 p

'—I1

<?

UJ S Q

CD ~

g S e S 55 S & =; sHiUONS^HinOSs S S S 5? 3aniiiv"i s s s

Figure 7.11. World map used for determining latitude and longitude of end points^

midpoint, control points, and great circle path.
DETERMINATION OF OPTIMUM FREQUENCY 317 Path Length, Location of Midpoint, and Solar Angle

First we find the geographic coordinates of the end points, from a

To find the path length and midpoint we lay a sheet of transparent paper

over the world map (fig. 7.11) and proceed as follows: Step 1: Draw on it the equator and the 0° and 180° meridians.

Step 2: Locate and mark the geographic coordinates of the transmitter

and receiver. Step 3: Transfer the transparency to the great circle chart (fig. 7.12)

and, with the equators coincident, slide the transparency along

the equator until the terminals lie on the same great circle (solid

lines) or a proportionate distance between adjacent great circles. Step 4: Estimate the great circle distance from the broken lines—this gives about 2400 km.

Step 5: Estimate the midpoint location from the broken lines—approximately 40.4°N 91°W—and mark on the transparency.

Step 6: Transfer the transparency to figure 7.13 and read the dipole

latitude at the path midpoint—about 51°. Step 7: Determine the appropriate universal time at the path midpoint.

1200 (90° WMT) corresponds to 1800 UT.

Step 8: Determine the sun's zenith angle x as follows. Place the trans- parency over the chart in figure 7.14. Keeping the equators co- incident make the zero meridian coincide with the universal

time (1800) obtained in step 7. Then read off, by interpolation

if necessary, the value of x at the midpoint of the path—about

18°. A complete set of maps of x is given in reference 1.

7.6.3. Determination of Optimum Frequency

Step 9: From figure 7.9a and b, respectively, we obtain

map (figure 7.11) or elsewhere:

Boulder 40°N

Washington 38.9 °N

105°W

77°W

MUF( ZERO) F2 = 6.0 Mc/s

MUF(4000)F2=17.0 Mc/s.

Step 10: From the data obtained in step 9, we find, from figure 7.1, by
318 IONOSPHERIC PROPAGATION PREDICTIONS

Figure 7.12. Great circle chart centered on the geographic equator for use with figure 7.11. The solid lines represent great circles. The numbered dot-dash lines indicate distance in thousands of kilometers.
DETERMINATION OF OPTIMUM FREQUENCY 319

EAST WEST WEST EAST

LONGITUDE Figure 7.13. World map of magnetic dipole latitude.

interpolation, that the MUF and FOT for 2400 km are respectively 13.8 Mc/s and 11.7 Mc/s. The FOT is 0.85 MUF (see

sec. 4.7.3.). It is now necessary to determine the effect of the E layer. Here there

are three possibilities.

(1) The normal E layer will determine the MUF.

(2) The sporadic E layer will determine the MUF.

(3) That E layer cutoff will occur (sec. 4.7.2.).

Step 11: Determine the radiation angle for one-hop E propagation for a distance of 2400 km. From figure 4.31 we find that this is less than zero and so this possibility is eliminated.

Step 12: The angle of elevation A(F2) for one-hop Fi propagation is found by first determining the height of the F layer from figure 7.15 as follows: Place the transparency over the appropriate

chart and, keeping the equators coincident and with zero degree

meridian coincident with the universal time (1800), read off the F2-layer height at the midpoint of the path. We find the

height to be about 400 km. From figure 7.2 we obtain A(F2) =

13°. A complete set of maps for obtaining the F2-layer height

is given in reference \_\~\. Step 13: To see whether the MUF for the two-hop E mode dominates we proceed as follows for a distance of 1200 km (half the path
320 IONOSPHERIC PROPAGATION PREDICTIONS

S33a93a 'Baniiivi oiHdvaooao

S33a93a '3anillV1 3IHdVd9039

Figure 7.14. Solar zenith angle for June.
DETERMINATION OF OPTIMUM FREQUENCY 321

00 02 04 06 08 10 12 14 16 18 20 22 00 LOCAL TIME

Figure 7.15. World map of layer heights for June.

length). Knowing the zenith angle (18°) and the average sunspot number (25) we find the MUF(2000)E from figure 7.16. MUF(2000)£=17.6 Mc/s

Using figure 7.17 we find

MUF(1200)£;=14.5 Mc/s

which is also equal to the combined E-Fi optimum working

frequency because the day-to-day variation in this quantity

is negligible. The reason for combining the E and Fi layers is that the greater value of /oFi (as compared with JqE) is almost

exactly balanced by the greater obliquity of the E layer path

giving the same fv sec 0o (see sec. 4.2) as for the Fi path.

We see now that the MUF for E layer propagation exceeds

that for F2 layer propagation.
322 IONOSPHERIC PROPAGATION PREDICTIONS

Figure 7.16. Nomogram for obtaining MUF(2000)E from the 12-month moving average sunspot number R and solar zenith angle xr Example: With x=15° and R=25°, the MUF(2000)£^ is 17.6 Mc/s.
DETERMINATION OF OPTIMUM FREQUENCY 323

MUF{2000)E, Mc/S

50 -3

45 -|

40 A

35

30

25

20 -

109 H

8

T

6 -I

5

4 —

3 -

MUF, Mc/S

50 -tq 40

30

20

15.

iO -

3

2.52

DISTANCE, km

2500-4000

2000 — 1500 - 1000 - 800

700 600 - 500 - 400 - 300 - 200 - 100

0

Figure 7.17. Nomogram for transforming MUF(2000) E to equivalent maximum

frequencies and optimum working frequencies due to combined effect of the E

layer and the Fi layer for other distances.

Also from the MUF (2000) £" it is possible to find the skip distance corresponding to a given frequency. Example: With AIUF(2(X)0)£ of 17.6 Mc/s, the MUF(1200)£ is 14.2 Mc/s.

Step 14: To see whether the sporadic E layer controls the maximum

frequency we use figure 7.18. This gives the median fEs contours

for the month of June. A set of 12 such maps (one for each

month of the year) is given in reference [1]. Note that the

solar cycle variation of Eg has not been definitely established

and so, for the time being, these charts may be considered as permanent. Furthermore, it will be seen that dipole latitudes
324 IONOSPHERIC PROPAGATION PREDICTIONS

NORTH GEOMAGNETIC LATITUDE south oooooooooo oooooooob

Figure 7.18. Worldwide distribution of /Eg for June.
DETERMINATION OF OPTIMUM FREQUENCY 325

are used to simplify the longitudinal presentation of the data. From the dipole latitude, obtained in Step 6 ( = 51°N), we find the median fEs to be 5 Mc/s. The corresponding median value

of MUF(2000) is given by multiplying by 5, i.e., MUF(2000)E. = 25 Mc/s.

Because of the variability of the fEs an allowailce must be

made as a safety margin to insure communications 90 percent

of the days. As a working rule, it is suggested that the optimum

working frequency for 2000 km be obtained by subtracting 4

Mc/s from the MUF(2000)E,. This gives OWF(2000)

21 Mc/s. With the aid of figure 7.17 we obtain OWF(1200) Es^

17 Mc/s. Clearly, propagation via the Es layer will determine

the optimum working frequency.

Step 15: To determine the E (or Es) layer cutoff frequency we proceed

as follows: Step 12 gives A(F2) =13° and, by using figure 4.31, we find that the corresponding E distance is approximately 800

km. Knowing the MUF(2000) =25 Mc/s), from figure 7.17 we find that the MUF(800) Es^lS.3 Mc/s. Thus the OWF

(17 Mc/s) will penetrate the E layer (for A = 13°). However,

since this frequency is well above the MUF(2400)^2 it will not normally be reflected from the higher (F2) layer.

We now conclude that the dominant path for propagation

is the two-hop Eg path and that the optimum working frequency

is 17 Mc/s.

Path loss

Step 16: The absorption loss is determined as follows. The index / is obtained (for x = 18°, = 25) from figure 7.5. This gives /= 1.04. From figure 7.7 we find that the appropriate value of fn

is 1.5 Mc/s. Therefore, /+/// = 17 +1.5= 18.5 Mc/s. The radi- ation angle for two-hop Es (from fig. 4.31) is A(2 Es)=8°.

Using figure 7.6 we obtain

absorption per hop = 8.5 dB

total absorption =17 dB.

Step 17: Distance loss. With an isotropic radiator, this is obtained

from figure 7.4:
326 IONOSPHERIC PROPAGATION PREDICTIONS

distance loss per hop = 120 dB

total distance loss = 120+6 = 126 dB.

Step 18: Ground reflection loss. From figure 7.3b we obtain, for A = 8°

a ground reflection loss = 3 dB.

Total path loss Lpath= 17+126+3 = 146 dB.

System Loss

Step 19: Antenna gain. From figure 7.8, with A = 8°, the gain per antenna

is 6 dB. Therefore, the antenna loss Lo= —12 dB. For information on other types of antennas the reader may consult reference

[20] and follow up the references cited therein.

Step 20: Total system loss Ls is given by

Ls = Z/path +La = 146-12 = 134 dB.

Step 21: Required carrier/noise ratio. From the CCIR tables [6] we

find that the required value of peak RF signal/noise ratio under

steady (nonfading) conditions for the specified performance

is 27 dB. On the assumption of 100 percent depth of modulation

this requires a median carrier/noise ratio of 21 dB. To allow

for the random (Rayleigh) fading of the signal we must add

8 dB, i.e., the ratio of the value P exceeded 90 percent of the

time to the median Pm. This is obtained from the formula

T= exp {-0.693P/P^} (7.8)

where T is the fraction of time that the instantaneous value

exceeds P. For the upper decile value, 10 log P/Pm^S dB.

The required carrier/noise is, therefore, 21+8 = 29 dB.

Step 22: Noise power. Following the procedure outlined in sec. 7.5.2.3, we obtain from figure 7.19a

PamOnlMc/s = 70 dB.
DETERMINATION OF OPTIMUM FREQUENCY 327 Together with figure 7.19b this gives

Fam on 17 Mc/s^33 dB.

This value of Fam, being a median, gives the noise level exceeded

50 percent of the days. In order to find the level exceeded 10 per- cent we require the upper decile value Faw This is obtained

from Du( = Fau — Fam) which is given, as a function of frequency,

in figure 7.19c. On 17 Mc/s, D^,^8 dB, therefore Fau=Fam+

Du = 33+8 = 41 dB. Because of the spread in the data, from

which Fam and Du are derived, there are inherent inaccuracies

in the median values. These inaccuracies can be partially taken

into account by the standard deviations ap^^ and cfd^ respectively which are given in figure 7.19c. From this figure we obtain

(jPam'^'^ dB; (tdJ^^ dB. The total uncertainty cr^ is deduced

on the basis that the errors are uncorrelated, i.e., cr\' = o'^ma'^

o-|)y, hence 0-^=5 dB. The effective upper decile is, therefore,

Feff= FawH-o-y = 46 dB. When circuit operation is required for some percentage of the time other than 90 percent, Fau and

Fam can be plotted on probability paper and the appropriate

value of Fa obtained by linear interpolation (or extrapolation).

A more complete account of this procedure is to be found in CCIR Report 322 [2]. Furthermore, further corrections need

to be made to obtain the true total uncertainty err but these

are negligible and will not be considered here. The interested

reader should consult CCIR Report 322 for a more detailed treatment. The effective noise level for a 6 kc/s channel is given by

substitution in (7.7).

Pn = Fefi+B -204 = 46+37.8 - 204 = -120.2 dB above 1 W.

Step 23: Required carrier power Pr at receiver. From step 21 we have

Required carrier/noise = Pr — = 29 dB

Pr = 29+Pn = 29-120.2 = -91.2 dB above 1 W.
328 IONOSPHERIC PROPAGATION PREDICTIONS
DETERMINATION OF OPTIMUM FREQUENCY 329

qp

.2= 1^ >3
330 IONOSPHERIC PROPAGATION PREDICTIONS

Step 24: Required transmitter power Pt. Pt=Pr+Ls.

From step 19, Ls = lU dB; and step 23, P,= -91.2 dB.

P< = 42.8 dB above 1 W

;^19,000 W=19 kW.

7.7. CALCULATION PROCEDURES FOR DISTANCES

GREATER THAN 4000 km

7.7.1. Control Points

As the distance of propagation is increased beyond the one-hop F2

limit (around 4000 km) it has been found (empirically) that the propagation is not suddenly cut off. Some physical reasons for this, discussed

in section 4.6, are ionospheric and ground scatter, the high-angle ray, and

ionospheric tilts. Empirically, it has been found that propagation did not appear to fail until the ionosphere failed to support the propagation

at two "control points" on the great circle path at 2000 km from each

end. This was apparently true, within limits, over wide ranges of path

lengths, geographical locations, and time. In the practical solution of determining the MUF for F2-layer propagation, the control points 2000 km from each end are chosen. The MUF

for the path is the lower of the two MUFs, for a distance of 4000 km, for each control point as the midpoint of the 4000-km path.

When it is desired to apply the procedure to the E, £"5, and Fi layers, an additional pair of control points 1000 km from each end may be used. However, there is less justification for this course than is the case with

F2 propagation.

7.7.2. Statement of Problem 2

Determine the transmitter power requirements of the following

circuit:

^ Transmitter location London 51.5°N 0°W

Receiver location Washington 38.9°N 77°W
FREQUENCY CALCULATIONS 331 Month—December 1963 Time—1400 UT

Sunspot number 17 (CRPL Predictions)

Frequency 13 Mc/s

Antennas—half-wave horizontal antennas 20 meters high, A3

telephony—good commercial quality, 90 percent of time

Bandwidth 6 kc/s

7.7.3. Control Points and Midpoint

Mark a sheet of transparent paper, as in problem 1, and determine

the coordinates of the midpoint and the two control points (2000 km

from either end). Following the procedures outlined in problem 1 we

obtain the following information:

Geographic Geomagnetic

Control point ^: 55°N 30°W 62°N 30°W

Control point 5: 50°N 57°W 60°N 57°W

Midpoint: 52°N 42°W

Midpoint gyrofrequency: 1.4 Mc/s

Path length 5900 km

7.7.4. Frequency Calculations

We follow the course outlined in problem 1, bearing in mind that the

use of the control point method implies that the maximum frequency is that appropriate to a distance of 4000 km, i.e., zero angle of radiation.

We obtain the following data.

Step Parameter Source A Midpoint B

(1) Local time 1200 1112 1012

(2) Solar angle x Step (1) and figure 78° 75° 77°

7.21

(3) MUF(ZER0)F2 CRPL Predictions 6.5 6.2 (Mc/s) (fig. 7.20a)

(4) MUF(4000)F2 CRPL Predictions 22.5 21.5 (Mc/s) (fig. 7.20b)

(5) F-z layer height (km) Figure 7.22 225 220 220

(6) Average F2 height Average of step (5) 222 (km)

(7) Absorption index I Figure 7.5 0.28 0.333 0.30

(8) Average I Average of step (7) 0.30

(9) Corrected I Step (8) and table 0.46

(10) OWF(Mc/8)

5.10.85X21.5 18.3
332 IONOSPHERIC PROPAGATION PREDICTIONS

3aniiivi Figure 7.20a. Predicted median F2 layer parameters for December 1963, UT=1400,

MUF(ZER0)F2

334 IONOSPHERIC PROPAGATION PREDICTIONS

S33d93a '3anillVn 3IHdVd9039

S33a93a ' 3aniiivn oiHd\/a9039

Figure 7.21. Solar zenith angle for December.
PATH STRUCTURE 335

00 02 04 06 08 10 12 14 16 18 20 22 00 LOCAL TIME

Figure 7.22. World map of F2 layer heights for December.

Hence (since 18.3 > 13), propagation on 13 Mc/s will be possible for more than 90 percent of the time.

7.7.5. Path Structure

The next step is to determine the dominant propagation paths (see

sec. 4.7.1) . For this we must depend on the stable paths so that although

the Pedersen path (sec. 4.4.3.2), or scatter (sec. 4.6.4), may sometimes

predominate, these paths cannot be relied upon for stable propagation.

First we find the ground ranges corresponding to a single leg of the multihop path, e.g., 2F, 3F, etc. We then find the maximum elevation

angle for reflection from the E layer and the minimum F layer A that can penetrate the E layer. In this way forbidden paths can easily be
336 IONOSPHERIC PROPAGATION PREDICTIONS

INDEX,

I

r-

'-"^ - 1.4

1.0 H 0.8

0.7

0.6 ol"

I- 0.4

0.3

0.2

0.1

0.05

0

E- PENETRATION, Mc/S

20 - 15

109

87

6

5

4

3.5

3

2.5

1.5

0.7

0 -n

10 -

15

20

25 -

30 -

35

40

45

50

70 -

90 -

Figure 7.23. Nomogram for the determination of the E layer penetration frequency for any elevation angle A.
SYSTEM LOSS 337 eliminated as follows:

step Parameter Source 3^ 4iE

Paths2F 3F 4F

(11) Distance per hop Total distance num- 1967 1475 2950 1967 1475

ber of hops

(12) Radiation angle Steps (6) and (11) 1.5° 4° 2° 8° 13^ A°

^ and figs. 7.2 (F) and 4.31 (E)

(13) Maximum A (E Minimum of step (7) <0°

layer) A or B and figure

figure 7.23

(14) Minimum A (F Maximum of step <0° <0° <0''

layer) (7) A or B and

figure 7.23

(15) Minimum F Minimum A or B of 1600 1600 1600

distance (km) step (3) and step

(4) and figure 7.1 (for/=13 Mc/s)

A consideration of these paths shows:

(a) 3E and 4£' are impossible because A exceeds the maximum A ( E)

,

(b) 2F and 3F are possible,

(c) 4F is impossible because the hop distance (1475 km) is less than

the minimum ( 1600 km)

.

7.7.6. System Loss

7.7.6.1. Path Loss

Paths

Step Parameter Source 2F 3F

(16)

(17) Effective frequency

Loss per hop (dB)

/+/h = 13+1.4 = 14.4 Steps (9), (12), (16) and figure 7.6 Step (17) times number of hops

8 6

(18) Total absorption loss (dB)

Ground loss per reflec- tion (dB)

Total ground loss (dB)

Distance loss Path loss Lpath

16 18

(19) (20)

(21)

(22)

Step (12) and figure 7.3a Step (19) times number of re- flections Frequency, distance. A, and

figure 7.4 Step (18) + step (20) + step

(21)

1

1 130

147

0.5

1.0 130

149
338 IONOSPHERIC PROPAGATION PREDICTIONS

7.7.6.2. Antenna Loss We shall assume that the appropriate antennas are perfectly matched

to the transmitter and receiver. From figure 7.8 we obtain the following

antenna gains relative to an isotropic radiator.

Step Parameter Source Paths 2F 3F

(23) Transmitter antenna gain Figure 7.8 and step (12) -5 4

(24) Receiver antenna gain Figure 7.8 and step (12) -5 4

(25) Total antenna loss Lantenna 10 -8

7.7.6.3. Total System Loss

Ls(2F) =147+10 = 157

L,(3F) =149-8=141

Since the loss on the 2F path is very much larger than that on the

3 F path, the latter is the dominant path and it alone needs to be considered further. !

I 7.7.7. Noise Power n

From section 7.5.2.3 we see that, on 13 Mc/s, FaTO = 32 dB and (TFam —

6 dB. To find the effective upper decile value we proceed as follows:

Step Parameter Source 3F Value

(26)

(27)

(28)

(29)

(30)

(31)

(32)

'

Du

Upper decile Fau Total uncertainty

Effective noise level above kTab

Correction for 6 kc/s bandwidth

Correction for fcTo

Figure 7.19c Figure 7.19c (Tt= {<^Fam+<^Z)ul^ Fan +0" T Add 10 log 6000 = +37.8 (see

(7.7) -204

9 dB

3 dB

41 dB

6.7 dB

47.7 dB

85.5 dB

-118.5 dB/W
OPTIMUM WORKING FREQUENCY

7.7.8. Required Carrier Power at the Receiver

339

Step Parameter Source 3F Value

(33) Peak RF signal/ Reference [6] 35 dB

(34) Carrier/noise Step (33) — 6 dB 29 dB

(based on 100%

modulation)

(35) Allowance for Ray- Equation (7.8) 8 dB

lei gh fading

(36) Required carrier/ noise Step (34) + step (35) 37 dB

(37) Required carrier power Pr

Step (32) + step (36) -81.5 dB

7.7.9. Required Transmitter Power Pt Pt=Pr+Ls = -81.5+141 = 59.5 dB/W

= 890 kW.

This rather high value of required power will normally be reduced

by the use of more highly directive antennas.

7.8. CHOICE OF OPERATING FREQUENCY

7.8.1. Optimum Working Frequency

The optimum working frequency (0.85 MUF) can be calculated for each hour of the day by the methods described above. In principle, it would be desirable to change the frequency slowly throughout the day

in order to make use of the optimum conditions. However, in practice,

this is both inconvenient and, in most cases, impossible because of inter- national methods of allocating frequencies. In general, a user is allocated

1 only two or three frequencies for use on a given circuit. A knowledge of

the diurnal variation of the FOT will, however, aid the circuit operator

in anticipating circuit failure due to penetration of the ionosphere by the

signal.
340 IONOSPHERIC PROPAGATION PREDICTIONS

7.8.2. The Lowest Usable Frequency

For a given transmitter output power, as the operating frequency is decreased, the available power at the receiver normally decreases due to increased ionospheric absorption, etc. Furthermore, the noise power in- creases so that the signal-to-noise ratio deteriorates and the circuit re- liability decreases. The minimum frequency below which the reliability

is unacceptable, is called the lowest useful high frequency (LUF). The

LUF depends upon transmitter power, the factors that determine the

path loss (frequency, season, geographical location, etc.), and the

noise level (mainly frequency and receiver location). One of the main

factors is ionospheric absorption and hence, since this normally varies

with solar zenith angle, the LUF peaks around noon. Consequently, in

>- 12 o

I 10 o

I I I I I I I I I

I M

CANARY ISLANDS — LONDON DECEMBER {R-29)

I

I I I I I I I I.

FOT

o o o o

o o

LUF

I I I I I I I I I I I I t I I I I I 12 UT

Example: With 7=0.49 and A=1.5° the E penetration frequency is 13 Mc/s. Figure 7.24. Sample diurnal variation of the optimum working frequency (FOT) and t lowest usable high frequency (LUF) to illustrate the selection of operating frequencies.
REFERENCES 341

selecting a frequency, it is necessary to ascertain whether the LUF ex- ceeds this frequency.

7.8.3. Operating Frequency

The diurnal variations of the FOT and the LUF for a circuit between

the Canary Islands and London in a December when the average sunspot number is 29 are shown in figure 7.24. It will be seen that, during

the night, it is necessary to use a frequency of around 6 Mc/s in order to ensure that the operating frequency does not exceed the FOT by an appreciable amount for too long a time. The use of this frequency band

during the day is impossible because it lies below the LUF. During the

daytime it would be better to use a frequency around 15 Mc/s.

Of course, it should be realized that occasionally the MUF may drop

to an exceptionally low value, as during a magnetic disturbance, or that

increased D region absorption will raise the LUF. Under these circumstances even the FOT may be unusable.

REFERENCES

[1] Haydon, G. W., and D. L. Lucas, Theoretical considerations in the selection of optimum frequencies for high frequency sky-wave communication services (to be published).

[2] CCIR Report 322 (1964), World distributions and characteristics of atmospheric

noise.

[3] CRPL Ionospheric Predictions, issued monthly, 3 months in advance, U.S. Government Printing Office, Washington, D.C. 20402.

[4] Bazzard, G. H. (1960), Short-term differences in the behavior of two daily indices of solar activity during the IGY, J. Atmospheric Terrest. Phys. 18, 290.

[5] Minnis, C. M., and G. H. Bazzard (1960), A monthly ionospheric index of solar activity based on layer ionization at eleven stations, J. Atmospheric Terrest. Phys. 18, 297.

[6] CCIR (1959), Documents of the IX Plenary Assembly, Los Angeles, Recommendation 161, Bandwidths and signal-to-noise ratios in complete systems, also Recommendation 164, Fading allowances for the various classes of service.

[7] Monthly predictions of radio propagation. Institute of Terrestrial Magnetism,

Ionosphere, and Radio Propagation, Russia.

[8] Jones, W. B., and R. M. Gallet (1962), The representation of the diurnal and geo- graphic variations of ionospheric data by numerical methods, J. Res. NBS 66D

(Radio Prop.), 419.

[9] Jones, W. B., and R. M. Gallet (1962), Methods for applying numerical maps of ionospheric characteristics, J. Res. NBS 66D (Radio Prop.), 649.
342 IONOSPHERIC PROPAGATION PREDICTIONS

[10] Jones, W. B., and R. M. Gallet, Representation of diurnal and geographic variations of ionospheric data by numerical methods. Part II, Control of Instability

(private communication).

[11] Ostrow, S. M. (1962), Handbook for CRPL Ionospheric Predictions, Based on

Numerical Methods of Mapping, NBS Handb. 90.

[12] Zacharisen, D. H. (1959), World maps of F2 critical frequencies and maximum

usable frequency factors, (April 1959) NBS Tech. Note 2, and (Oct. 1960) NBS

Tech Note 2-2.

[13] Predictions of radio wave conditions using the index /(F2) and Bulletin A, Radio

Research Laboratories of the Ministry of Posts and Telecommunications (1958).

[14] Prediction of optimum traffic frequencies in northern latitudes. Defence Research Board of Canada, December (1954).

[15] World maps of F2 critical frequencies and maximum usable frequencies for 400 km.

Radio Research Laboratories of the Ministry of Posts and Telecommunications (1958).

[16] Bennett, W. R. (1960), Electrical Noise (McGraw-Hill Book Co., Inc., New York).

[17] Crichlow, W. Q., D. F. Smith, R. N. Morton, and W. R. Corliss (1959), Worldwide radio noise levels expected in the frequency band 10 kilocycles to 100 megacycles, NBS Circ. 557.

[18] Crichlow, W. Q., C. J. Roubique, A. D. Spaulding, and W. M. Beery (1960), Determination of the amplitude-probability distribution of atmospheric radio

noise from statistical moments, J. Res. NBS 64D (Radio Prop.), 49.

[19] Crichlow, W. Q., A. D. Spaulding, C. J. Roubique, and R. T. Disney (1960), Amplitude-probability distributions for atmospheric radio noise, NBS Mono. 23.

[20] Josik, H. (1961), Antenna Engineering Handbook (McGraw-HiU Book Co. Inc., New York).
CHAPTER 8

Scatter Propagation on Very High Frequencies

8.1. SCATTERING FROM IONOSPHERIC IRREGULARITIES

The very high frequency (VHF) band is usually defined as the fre- quency range from 30 Mc/s to 300 Mc/s. Such a definition is of course purely arbitrary. From the point of view of magneto-ionic theory, the

numerical values of Y (2.69) are very small and, in general, are negligible,

except possibly for Faraday rotation effects (see sec. 4.9.5). Further- more, the maximum electron densities in the ionosphere are rarely sufficient to reflect waves on frequencies much above 30 Mc/s except for relatively short periods (e.g., in the equatorial regions near the peak of

the sunspot cycle) . Ionospheric transmission on VHF is, therefore, mainly

the result of scattering of waves by irregularities in the electron density

distribution in the ionosphere rather than by gradual refraction. If sufficiently high transmitter powers are used the net scattering of energy

from the individual electrons (quasi-incoherent scatter) can be detected. The chief sources of irregularities in the ionosphere are:

(1) Irregularities due to turbulent mixing in the D region.

(2) Ionized trails due to the passage of meteors through the at- mosphere.

(3) Spread F irregularities (cause unknown)

.

(4) Sporadic E.

(5) Individual electrons. In this chapter we shall select a few of these topics for discussion.

8.2. CHARACTERISTICS OF PROPAGATION ON VERY

HIGH FREQUENCIES

Ionospheric effects on frequencies above 100 Mc/s are small (but

see sec. 4.9) and not particularly important from the point of view of

343
344 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

radio communications. We shall, therefore, concentrate our attention on

the frequency band from 30 Mc/s to 100 Mc/s.

Ionospheric propagation in the 30 Mc/s to 100 Mc/s range is characterized by the following features:

(a) Regular but weak scattering from the D region which is useful

for continuous single-frequency communication in the 30 Mc/s to 60

Mc/s range over path lengths of the order of 1000 to 2000 km.

(b) Intermittent reflections from ionized meteor tracks which are useful for burst communications in the 40 Mc/s to 80 Mc/s range over path lengths up to 2000 km.

(c) Sporadic and intense reflections on frequencies which may be

useful up to about 50 Mc/s to long distances (greater than 4000 km)

via irregularities in the F region at times of high sunspot number.

(d) Reflections from patches of sporadic E are sometimes important

(especially as a source of interference) up to distances of 2000 km or so and on frequencies as high as 80 Mc/s.

The chief disadvantages of VHF propagation, from the point of view

of radio communications, are:

(1) Low signal strengths, because of the relative ineflftciency of the

scattering mechanism.

(2) Rapid fading.

(3) Limited ground range (2000 km).

(4) Mutual interference between channels normally independent.

8.3. D-REGION SCATTERING^

8.3.1. Scattering From Irregularities in the D Region

Irregularities are produced by the action of turbulence, wind shears,

etc., on the electron distribution in the height range between about 70

km and about 90 km. These irregularities in electron density result in corresponding fluctuations in refractive index. Since turbulence merely

brings about a redistribution of the electrons, these types of irregularities

will exhibit marked solar control as does the overall electron content of

the D region. There is also evidence for stratification in the D region [1^,^

which means that the refractive index changes abruptly with height.

This section is based on a lecture by R. C. Kirby.

Figures in brackets indicate the literature references on p. 390.
SCATTERING FROM IRREGULARITIES IN THE D REGION 345

Figure 8.1. Geometry of forward scatter from the D region.

The effect of these rapid changes, both in time and space, on very- high-frequency waves is to scatter the energy out of the direction of the

incident beam [2]. Since most of the energy is scattered in directions

making small angles with that of the incident beam, the phenomenon is called "forward scatter." The geometry of forward scatter is sketched in figure 8.1 in which a volume V of the ionosphere is illuminated by a transmitter. If is the

power radiated in the direction of K, then the available power pa from a

receiving antenna R is given by

To is the electron radius (2.8X10~^^ m),

/ is the distance from V to R,

b is the thickness of the scattering volume,

is the effective area of the receiving antenna,

7 is the angle through which scattering takes place,

S(K) is the spectrum of turbulent irregularities.

Pa=PtroH-'bAr CSC (t/2)S(K), (8.1)

where

and

sin i7, (8.2)

where X is the wavelength. Equation (8.1) applies when single scattering

is the dominant mechanism (i.e., the amplitude of a twice-scattered wave

is negligible) and for isotropic irregularities.
346 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

The scattering process acts like a narrow band filter on the spectrum,

emphasizing those irregularities of size K~^, where K is given by (8.2).

Notice that the isotropy assumption prevents the application of this theory to magnetic field-alined irregularities. Furthermore, we have

neglected the effect of the polarization of the incident wave. The latter requires the inclusion, in (8.1), or a sin^ x term where x is the angle between the incident electric vector and the scattering direction. Equations

(8.1) and (8.2) emphasize the joint frequency-distance dependence of

received power which is characteristic of scatter propagation, and shows

that the spectrum of irregularities is the basic description of the turbulent

electron density variations which is required in electromagnetic theory. In the case of turbulent mixing it can be shown [2] that

S{K)=K--{dN/dh)\ (8.3)

where dN/dh is the electron density gradient.

From (8.1), (8.2), and (8.3) we find that the relationship of system

loss to the frequency / and geometry of the propagation path is given by

Pt/pa^l'M^inhyY^-\ (8.4)

where ns{ns = n-\-2) is the frequency exponent for an antenna the gain of

which is constant with respect to frequency. The use of Us allows for the

frequency dependence of y4r because the gain of the antenna increases as the square of the frequency.

8.3.2. Height of Scattering

Experimental evidence suggests that the scattering of VHF waves is produced primarily from two layers. During the daytime the predominant

heights are around 70 km; this scattering layer is subject to solar control

and, therefore, is thought to be due to turbulence. During nighttime the

scattering appears to come from the 85 to 90 km region, the ionization in which is thought to be produced by the influx of meteors. Some observations seem to be best explained on the basis of simultaneous scattering

from both layers.
SIGNAL STRENGTHS IN MIDDLE AND HIGH LATITUDES 347 8.3.3. Signal Strengths in Middle and High Latitudes

8.3.3.1. Long-Term Variations

From hourly median values of signal strengths it has been found that,

in the frequency range from 25 to 108 Mc/s, over distances of from 1000

to 2000 km, the system loss ranges from about 140 dB to ab(fut 210 dB.

The loss depends on several factors such as wave frequency, type of antenna, geography, and time.

Median values of system loss indicate that on a frequency of

about 50 Mc/s the diurnal variations of signal strength are as follows: Middle latitudes: A maximum near noon and a minimum near 2000

hr local time with the diurnal curve broader in summer than in winter,

as would be expected from the solar illumination.

High latitudes: The diurnal maximum is broader and tends to be

centered earlier in the day as compared with middle latitudes. The system

loss for a given hour varies considerably from day to day. This variation

is greater in high latitudes than in middle latitudes. In middle and high latitudes the seasonal variation is characterized

by a strong maximum in summer for all hours of the day. No definite long-term (solar cycle) variation has been established.

The above results were obtained over paths of about 1200 km length

and with narrow-beam (6°) rhombic antennas aimed along the great

circle.

8.3.3.2. Frequency Dependence

According to (8.4) the system loss should vary with frequency to the power Ug. Observations with narrow-beam (6°) antennas show that the

values of Ug vary with time but that 90 percent of the observations give

values in the range 7 to 9.5 with an overall median of 8. Daytime values

are generally greater than nighttime by 1 or 2. Furthermore, summer

values tend to be lower than those in other seasons, though winter daytime

values are also lower than equinoctial daytime values. With wide beam

(56°) antennas the values of Us are about J to 1 less than with the narrow beam (6°) antennas. The diurnal and seasonal variations of Ug, and the beamwidth de- pendence, have been interpreted as evidence of the combined effects of

turbulence and meteoric ionization. The lower values of Us are associated
348 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

with dominant meteoric contributions to the received signal, and the

higher values with turbulence.

A limited amount of data indicates that average values for frequency

dependence for arctic paths are about the same as in middle latitudes,

though less data are available. The measurement of frequency dependence

in high latitudes is often complicated by the prevalence of high absorption on the lower frequencies.

The dependence of the intensity of the signal on scattering angle in the plane of the great circle has also been measured directly. Measurements have been carried out in summer daytime, over short paths (500

to 800 km) using pulse transmissions to separate ionospheric and tropospheric returns. Values of n from 4 to 8 (corresponding to values from 6

to 10 for Us) have been obtained. These are not inconsistent with the values

from frequency dependence measurements, but as very few observations

have been made, the statistical significance of the frequency dependence

measurements is much greater.

8.3.3.3. Short-Term Variations

8.3.3.3.1. Amplitude Distribution and Fading Rate Observed amplitude distributions show that, during most of the day,

the envelope is, essentially, distributed in a Rayleigh manner. The dis- tributions are peaked somewhat at the high -signal end during the late night and early morning hours. Fading rates normally lie between 0.2 c/s and 3 c/s, the rate increasing with frequency. Most observations show

that this rate depends on carrier frequency raised to a power between

0.75 and 1.25. One would expect a linear dependence (exponent = 1.0) if the drift speed of the scattering region were dominant compared to the

changing structure of irregularities. This departure from linear dependence

at times favors the idea of a turbulent D region as against meteor-pro- duced ionization.

Fading rates are higher for broad-beam systems, and for off-greatcircle paths, than for great-circle transmission with narrow beams.

8.3.3.3.2. Space Correlation

Correlation of signals received on antennas spaced in the great circle

is much greater than for antennas spaced perpendicular to the path.

Measurements on 50 Mc/s, with narrow-beam transmitting antennas,

show that the correlation coefficient falls to 0.5 at 3.5 wavelengths normal

to the path, while along the path the corresponding distance is about 40
ABNORMAL BEHAVIOR 349 wavelengths. In the analyses of these data, recognizable meteoric signals were excluded.

8.3.3.3.3. Frequency Correlation The extent of correlation of fading across a frequency band affects the modulation bandwidth which may be usefully employed and, hence,

the design of frequency diversity techniques. Using narrow-beam (6°)

antennas on 50 Mc/s, the correlation coefficient has been found to fall to about 0.5 for frequency separations of 6 kc/s during the early morning

hours; and near noon the corresponding (6 kc/s) correlation coefficient

is 0.65, falling to 0.5 for about 7 kc/s separation. This correlation is poorer for broad-band systems and for off-great-circle paths.

8.3.3.4. Geographical Variations

Observations have shown that, except for paths near the equator, the

transmission loss for paths in the arctic, the United States, and Europe

differ by less than ±5 dB from the overall median value. Within these

limits, the signal strengths on the arctic paths are, statistically, higher

than those in middle latitudes. Near the magnetic equator the signal intensities are, on the whole,

much higher than in the United States. The background scatter signal is about the same, but this is obscured for a large portion of the time by

strong enhancements (up to 50 dB) which appear to be reflected from

field-alined ionization in the E region [4]. Rapid fading is often characteristic of these enhancements.

It may be of interest to note here that there is little correlation between VHF transmission loss in temperate latitudes and /qE, or HF at- tenuation. There appears to be little variation of signal intensity with

sunsport number but there is a statistical correlation (positive) with the

magnetic K index [5].

8.3.4. Abnormal Behavior

8.3.4.1. Sudden Ionospheric Disturbances

These have been discussed already in section 6.2.4, but a few more

comments are appropriate as it appears that the behavior of the received

VHF signal varies with frequency. The increased ionization created by
350 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

the flare radiation appears to produce two effects: intensity enhancement

(more efficient scattering) and increased D region absorption. On the

lower frequencies, where the absorption effects are greatest, the net result

is a decrease in signal. On the higher frequencies the overall effect is an

increase in signal. On intermediate frequencies little effect is seen in many

instances, from which it may be concluded that the two processes just

cancel. The effect on the received signals on five frequencies are shown

in figure 8.2 for signals transmitted over a 1295 km path (United States)

employing narrow beam antennas. A definite frequency dependence is evident. On the other hand, with parallel broad-beam systems, increased

attenuation was observed on all frequencies up to 75 Mc/s (the highest

frequency used)

.

8.3.4.2. Correlation With Auroral Phenomena

We have seen already (sec. 6.3.3) that HF propagation in the auroral zone is characterized by periods of high absorption. These periods are

NARROW-BEAM (6°) RHOMBICANTENNAS USED

TRANSMITTING AND RECEIVING VAL UES ARE

ADJUSTED TO 2kW TRANSMITTER POWER

— 210

1000 1130 105° W. TIME

1230

Figure 8.2. Signal behavior on five frequencies during a sudden ionospheric disturbance, March 29, 1958.

(After J. Blair, R. M. Davis, and R. C. Kirby, 1961; J. Res. NBS 65D (Radio Prop.), 417.)
IONIZATION BY METEORS 351

not, in general, periods of high absorption of VHF waves. On the contrary,

high signal intensities, on 50 Mc/s, are usually observed during periods

of enhanced HF absorption and strong geomagnetic activity. It has been

found also that marked increases in signal level often coincide with iso- lated intervals of HF blackout [6].

8.3.4.3. Sputter

An additional effect associated with aurorae is the occurrence of

rapid fading called "sputter," which is due to a multipath signal. There

have been occasions when "sputter" speeds of up to 200-300 c/s have

been observed, i.e., about 100 times the normal fading rate. The effect

is minimized with narrow-beam antennas. It may be observed, to some

degree or other, 100 hr and more per year [3].

8.3.4.4. Polar Cap Absorption Effects Forward scatter signals are affected during PCA events (see sec. 6.4) in high latitudes. If the onset of the proton flux (which gives rise to the PCA) occurs at night, the VHF signals are enhanced (fairly

abruptly) followed by strong absorption during the ensuing daylight. The

fact that the scattered signals are absorbed during the PCA while en- hanced during auroral blackouts indicates that the height at which scatter- ing occurs lies below the region of auroral absorption (90 km) but above

the height at which polar cap absorption occurs (60 km).

Polar cap absorption events are generally confined to paths with midpoints at geomagnetic latitudes greater that about 60°. The onset of this absorption (in the lower latitudes) usually follows the onset of a magnetic

storm and often at the time of a strong (Forbush) decrease in the intensity

of cosmic rays which is, in general, many hours after the commencement

of the PCA itself in higher latitudes.

8.4. METEOR SCATTER^

8.4.1. Ionization by Meteors

Mention has been made above to the fact that in VHF forward scatter strong bursts of signal are frequently superimposed on the background

» This section is based on a paper by G. R. Sugar (1964), Radio Propagation by Reflection from Meteor TraUs, Proc. IEEE 52, No. 2, 116-135.
352 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

signal reflected from turbulent irregularities. These bursts are due to

reflections from ionized "trails" produced by meteors mostly in the height

range 80 to 120 km. Billions of these trails are produced daily; they diffuse

rapidly and usually disappear within a few seconds. During their brief

existence, however, these ionized columns will reflect VHF waves particularly in the frequency range 20 to 110 Mc/s. The lower frequency

limit is set by the need to be above the regular maximum usable frequency

and the upper limit is set by technical limitations, since reflections on

the higher frequencies are relatively weak.

The ionized trail is the result of conversion of the kinetic energy

of the meteor into potential energy of ionization as the meteor is slowed

down by collisions with the neutral molecules. The ionization is distributed

in the form of a long, thin paraboloid of revolution with the particle at the head of it. The electron density per unit length of the trail is proportional to the mass of the particle.

The height distribution of trails varies with particle characteristics. The higher velocity particles (of a given mass) produce trails at the higher

(120 km) heights, with the mean trail height increasing by about 10

km as the velocity increases from less than 15 km/s to greater than 60

km/s [7]. For a given velocity, particles of higher mass produce maximum

trail ionization at lower heights. Over the mass range 10~^ to 10^ g the

height variation is around 44 km. There is also a height variation with

the zenith angle (x) of the trail, larger angles corresponding to greater

heights. A variation of about 13 km corresponds to the range of x from

0 to 90°. The lengths of the trails depend primarily on the mass and zenith

angle. Typical lengths range up to 50 km, the most probable value being

15 km, although this depends on the definition of "length."

The initial radii of the trails are in the range 0 to 1.2 m (with a mean

value of 0.65 m) based on visual studies, while radio observations give a range from 0.55 m to 4.35 m. The 0.55-m-radius is for a height of

81 km.

Let us consider now the dissipation of the ionization. Once the trail

is formed it expands by diffusion at a relatively low rate, thus producing

a radial distribution of material that is approximately Gaussian. After

a time t the radius r is related to initial radius ro by the expression:

r' = rl-^^Dt, (8.5)

where D is the diffusion coefficient of the electrons and varies from one mVsec at 85 km to 140 mVsec at 115 km. Hence, after 1 sec, a trail will have a radius in the range 2 to 20 m.
METEOR DATA 353 The practical lifetime of a trail depends, of course, on the means of detection. Most trails, detected by radio methods, are those resulting from

small particles and last for a fraction of a second only. Larger meteors

produce more densely ionized trails, and trails with durations of the order

of 1 min are observed several times per day. Trails with durations of

the order of an hour or more are extremely rare. The dissipation of trails is complicated further by the action of

winds in the 80 to 120 km region. At the time of formation, trails are quite straight but they are deformed rapidly by winds of the order of

25 m/sec and vertical wind shears with maxima of the order of 100 m/sec

per km. A wind shear of this magnitude can rotate part of a trail through an angle of 5° in 1 sec.

8.4.2. Meteor Data

Before considering the reflection of radio waves from meteor trails,

it will be useful to discuss some of the physical properties of meteors. Nearly all our knowledge in this field comes from visual and radio observations. The term "meteor" will be restricted to those particles enter- ing the earth's atmosphere that are completely burned up by frictional heating.

Particles in the mass range of 10~^ to 10^ g and dimensions in the

range 40 )u to 8 cm are primarily responsible for radio reflections. Before

being swept up by the earth's atmosphere these meteors move in elliptical orbits around the sun and they are thought to be of cometary origin.

Meteors can be divided into two classes: Shower meteors are collections of particles all moving with the same

velocity in fairly well-defined orbits around the sun. These meteors, while

the most spectacular, account for only a small fraction of the total in- cidence of meteors. Sporadic meteors comprise nearly all those of interest to radio work.

These meteors seem to move in random orbits so that, in contrast to the

shower meteors which appear to come from a specific "radiant" point in the sky, sporadic meteors have radiants that appear to be randomly dis- tributed over the sky. It is of interest to note that a meteor shower is often named after the stellar constellation in which the radiant point

lies, e.g., Leonid for Leo. The radiants and times of occurrence of sporadic meteors are random

and of course cannot be cataloged in this manner. Their radiant points

are not, however, uniformly distributed in the sky but are for the most
354 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

part concentrated toward the ecliptic plane (the plane of the earth's

orbit) and move in the same direction around the sun as the earth moves

[8]. The orbits are not uniformly distributed along the earth's orbit but

are concentrated so as to produce a maximum incidence of meteors at the earth in July and a minimum in February. This variation in the space

density of meteors is shown in figure 8.3, which has been adapted from the

data of Hawkins [8].

The rate of incidence of sporadic meteors at the earth is further modified by two factors. The first of these, resulting in a regular diurnal vari- ation in meteor rate, is illustrated in figure 8.4. On the morning side of

3 I 1

0 I \ I \ \ \ I \ \ \ I I I I OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEPT MONTH Figure 8.3. Variation of space density of meteors along the earth's orbit.

(After G. S. Hawkins, 1956, Monthly Notices Roy. Astron. Soc. 116, 103.)

METEORS SWEPT UP

MOTION

OF EARTH AROUND

SUN

METEORS

OVERTAKING EARTH

TO THE SUN Figure 8.4. Diurnal variation of meteor rates. In the evening only meteors overtaking the earth are observed. In the morning meteors with orbital directions opposite to that of the earth and the slower ones with the same orbital direction are observed. (After G. R. Sugar, 1964, Radio propagation by reflection from meteor trails, Proc. IEEE 52, No. 2, 116.)
METEOR DATA 355 the earth, meteors are swept up by the forward motion of the earth in

its motion around the sun. On the evening side the only meteors reaching

the earth are those which overtake it. This results in a maximum oc- currence rate around 6 a.m. and a minimum rate around 6 p.m. The ratio of maximum to minimum depends on the latitude of the observer. A

further minor seasonal variation is introduced because of the tilt of the

earth's axis relative to the ecliptic plane. This variation, also dependent on the latitude of the observer, can change the expected hourly rates by

factors as large as 1.4. The mass distribution of sporadic meteors is such that there are approximately equal total masses of each size of particle. There are, for example, 10 times as many particles of mass 10~^ g as there are particles

of mass 10~^ g. This approximate relation between particle mass and

number is given in table 8.1. The mass distribution of shower meteors

is somewhat similar to that for the sporadic meteors with the important

Table 8.1. Order-of-magnitude estimates of the properties of sporadic meteors

Mass

(grams)

Visual magnitude Radius

Number of this mass

or greater swept up by

the earth each day

Electron

line density

(electrons per meter

of trail length)

Particles pass through the at- 10^ -12.5 8 cm 10 mosphere and fall to the ground

Particles totally disintegrated in 103 -10.0 4 cm 102 102 -7.5 2 cm 103 the upper atmos- 10 -5.0 0.8 cm 10* 1018 phere 1 -2.5 0.4 cm 10^ 1017 10-1 0.0 0.2 cm 10« 1016 10-2 2.5 0.08 cm 10^ 1015 10-3 5.0 0.04 cm 10« 1014 10-4 7.5 0.02 cm 109 1013 10-5 10.0 80 m

1010 1012 Approximate limit io-« 12.5 40 fjL 1011 1011 of radar measure- 10-7 15.0 20 tx 1012 1010 ments—

>

10-8 17.5 8m 9 9 Micrometeorites io-« 20.0 4 M Total for Practically

(Particles float 10-10 22.5 2m this group none down unchanged

by atmospheric

10-11 25.0 0.8 M estimated

10-12 27.5 0.4 M as high as

collisions) 1020 Particles removed

from the solar system by radiation pressure

10-13 30 0.2 M
356 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

difference that there are more large particles relative to the number of

smaller ones than for the sporadic meteors [9].

The velocities of meteors approaching the earth are in the range 11.3 to 72 km/s. The lower limit is the escape velocity for a particle leaving

the earth and is, therefore, the lowest velocity that a particle falling

toward the earth can have. The upper limit is the sum of two components,

a 30 km/s component associated with the velocity of the earth in its orbit around the sun, and a 42 km/s component associated with the meteor

itself. This latter velocity is the escape velocity for a particle leaving

the solar system. Nearly all observations indicate that meteor velocities

fall in the above range, which suggests that meteors are members of the

solar system.

8.4.3. Reflection From a Meteor Trail

8.4.3.1. Important Parameters

The distribution of energy reflected by a meteor trail is a function

of many variables. The ionization density distribution across and along

the trail, the orientation of the trail, the radio wavelength, the polarization of the incident wave relative to the trail, motion of the trail either as part of the process of formation or due to ionospheric winds, and the

straightness of the trail are all significant. In discussing the reflection properties it is convenient to divide the trails into two classes—underdense trails and overdense trails—and to examine the properties of each

class independently. Underdense trails are those wherein the electron

density is low enough so that the incident wave passes through the trail and the trail can be considered as an array of independent scatterers. Overdense trails are those wherein the electron density is high enough to prevent complete penetration of the incident wave and to cause reflection of waves in the same sense that the ordinary ionospheric reflections occur. A rough sorting of trails into these two categories can be done on the basis

of trail lifetime or duration. On long wavelengths (relative to the VHF

band) the underdense trails have durations of less than about 1 sec while

the overdense trails have longer durations. The analysis can be further

divided in terms of the radio wavelength. On long wavelengths the ef- fective duration of a trail is large compared to the time it takes the trail to form, and the trail may be considered to have a cylindrical shape. On

short wavelengths, however, the duration is much shorter and the column

must be considered to be of the paraboloidal form previously indicated.
REFLECTION FROM A METEOR TRAIL 357 The solutions to be considered here are at best useful approximations

to the physical problems. They will apply quite well to some of the trails observed and rather poorly to others. A complete analysis of the reflec- tions from even a relatively simple trail would be far too complex to be

of any practical use or interest. In the following treatment the terms long

wavelength, etc., are used in a relative manner to indicate the lower

frequency end of the VHF band, etc.

8.4.3.2. Long Wavelength Reflections From Low-Density Trails On the assumption that the trail is an infinitely long right circular

cylinder of electrons whose diameter is very small compared to the wavelength, assume also that the trail electron density is low enough that

the incident wave passes through the trail without major modification.

Consider the case of radarlike reflections with transmitter and receiver

at the same location. Figure 8.5a illustrates the reflection geometry and

the trail model. Let R be the length of the perpendicular from the radar

set to the trail. The signal received can be computed by summing the

energy backscattered by each electron in the trail while taking proper

account of the phase relations of these contributions. When this is done

it is found that the principal contribution of energy from a trail is from

its first Fresnel zone, a region of length \/2\R, centered at the point on

the trail where the line from the radar is normal to the trail. For example, on 50 Mc/s a trail 200 km away will have a first Fresnel zone 1.6 km in length. As the trail expands by diffusion, the phase difference of the

contributions from the electrons on opposite sides of the trail increases

so that the received power decreases. The signal amplitude will have

fallen to 1/e of its initial value (€ = 2.718) at the time the radius of the

trail is \/2t. On 50 Mc/s this radius is 1 m.

Figure 8.5. Low-density long-wavelength reflections.

(a) Reflection geometry, (b) Variation of received signal with time. (After V. R. Eshleman, 1960, Meteor

scatter, The Radio Noise Spectrum, ch. 4, Harvard Univ. Press.)
358 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

The transmission equation can be written in terms of the scattering

cross section cj in the following way:

where pt and pr are, respectively, the transmitted and received power,

gi and gr are, respectively, the power gains of the transmitting

and receiving antennas relative to an isotropic radiator in

free space,

X is the wavelength in meters,

R is the distance from transmitter to the trail in meters, and

a is the scattering cross section of the trail in square meters.^

If it is assumed that the trail is initially in the form of a line of electrons (an initial trail radius of zero) , the scattering cross section may be written

as

<j= ( vW2r,g)2 exp (^-^^ 0' (8.7)

where re = )UoeV47rm = 2.8178X10"^^ m, the classical radius of the electron,

where //o is the permeability of free space and e and m are the

charge and mass of the electron, q is the electron line density of the trail in electrons per meter,

D is the diffusion coefficient in square meters per second, and

t is time measured from the formation of the trail, in seconds.

The first of the two factors in (8.7) represents the scattering cross section

of the initial line distribution of electrons, and the second factor repre- sents the attenuation with time as the trail expands and destructive inter- ference begins. The first factor may be interpreted as follows: The effective cross section of the trail is the same as would be obtained for in -phase

addition of scattered fields associated with each electron within one-half

of the first Fresnel zone. Since the power scattered by an electron is pro- portional to then the field is proportional to re. The number of electrons

in half of the first Fresnel zone is q\/RX/2 and the field is, therefore, pro- portional to re\/ R\/2. The total effective cross section is just the square

of this product.

The second factor in (8.7) results from the integration across the

trail. The distribution of electrons across the trail has a Gaussian shape

The scattering cross section is the ratio of the power scattered per unit solid angle to the power

incident per unit area.
REFLECTION FROM A METEOR TRAIL 359 [9] with an effective radius of \/4^Dl Using this with (8.6) and (8.7),

it can be showTi that the signal amphtude will fall to 1/e when the effective radius is X/2t.

If the initial radius is nonzero, the peak amplitude is reduced from

that given by (8.6). The form of the time variation of received power is sketched in figure 8.5b. In the above relation, since it was assumed that trails were of infinite length, every trail had a first Fresnel zone and therefore gave a

reflection. In practice, however, since trails are of finite length, this zone may not lie on the trail but rather on an extension of it. In such a case the signal returned from the trail would be a relatively weak one, and

in practice these returns are of little importance. Thus a radar can '^^see" only a fraction of all the trails incident on the ionosphere within its range

because most trails do not have the proper orientation for the line of

sight to be perpendicular to the trail. The requirement for proper orientation can be restated as requiring that the trail be tangent to a sphere

centered at the radar. When the transmitter and receiver are separated, as in the case of

point-to-point propagation, the reflection requirement is that the incident

ray and reflected ray make equal angles with the trail axis. Geometrically

this is equivalent to a requirement that the trail be tangent to an ellipsoid

with foci at the transmitter and receiver. For this case two important

changes take place because of the oblique geometry. First, the length of the first Fresnel zone increases and, therefore, more electrons contribute

to the received signal. Second, the maximum possible propagation path

difference over the cross section of the trail decreases with increasing

obliquity. This decrease is equivalent to an increase in wavelength and

results in both a larger initial signal and a slower rate of signal decay as the trail expands. In this case it can be shown [10, 11] that the peak received power

varies as X^^^ and the signal duration as X^.

8.4.3.3. Long Wavelength Reflections From High-Density Trails

With high electron densities the assumption that the incident wave

passes through the trail essentially unmodified is no longer valid. For

this case it is assumed that the wave penetrates the trail until reaching

a surface of sufficiently high electron density to be reflected. The model

used is that of an expanding cylindrical reflector of radius Tc, figure 8.6a. After a time the electron density everywhere within the trail falls below
360 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

Figure 8.6. High-density long-ivavelength reflections.

(a) Reflection geometry, (b) Variation of received signal with time. (After V. R. Eshleman, 1960, Meteor

scatter, The Radio Noise Spectrum, ch. 4, Harvard Univ. Press.)

the critical value and the underdense model is once more applicable.

However, by this time the radius is quite large and the signal contribution

is rather small. In the case of backscatter, the transmission equation is based on

reflection from a cylinder and is given by

and this applies until approximately the time when the second factor

becomes zero. This occurs at a time

47r2 D

after this time the relation for underdense trails is applicable [12]. The

form of the time dependence of received power predicted by (10.8) is illustrated in figure 8.6b. For the overdense case the maximum received power varies as in contrast to the variation for the underdense case. The dependence

is the same as for the latter case. The dividing line between low- and high-density trails is commonly

taken to be for q in the range 1 to 2.4X10^^ electrons per meter. If the

transition value is taken at 0.75 XlO^^ electrons per meter, then the peak

signals predicted by (8.8) will be equal; this is sometimes done for con- venience [12].
REFLECTION FROM A METEOR TRAIL 361 The extension of (8.8) to the forward scatter case has been done in a relatively simple manner [12]. The derivation, as in the backscatter

case, is based on a reflecting cylinder and the refractive effects of the

electrons beyond the critical radius of the trail have been ignored. These

refractive effects reduce the validity of the transmission equation [13],

but their significance is uncertain.

The dividing line between low- and high -density trails is again at 9=0.75X10^^ electrons per meter. The effect of the initial radius of the

trail can be computed as in the backscatter case.

8.4.3.4. Short Wavelength Reflections From Low-Density Trails

In the previous two sections it has been assumed that the time of

formation of a meteor trail is quite small compared to the total time that

radio waves are scattered by the trail. The formation of the trail was in effect considered to be a transient state preceding the desired ^'steady state" trail and this transient was neglected. However, as the wavelength

is decreased and the duration of this steady state decreases, the duration

of the transient state tends to remain constant. For sufficiently short

wavelengths only the transient state remains. In this section and the

following one this transient state will be considered [14], first for underdense trails, then for overdense trails. Consider first the problem of estimating the shortest wavelength for which the long wavelength results are applicable. The time of formation

of a trail is essentially the time required for the incoming particle to traverse one-half the first Fresnel zone as defined for the long wavelength

case. A rough estimate of the transition wavelength between long- and

shortwave cases may be obtained by equating the time of formation

for a trail to the duration of a longwave echo and solving for the wavelength. For example, consider backscatter reflections from an underdense

trail. The time to traverse half the first Fresnel zone is {R\/2)^/v, where

V is the meteor velocity, and the nominal echo duration (to the 1/e amplitude) is X'^/lGir'^ D. Equating these and solving for Xr, the transition

wavelength, we obtain

\T={l287r'D'~R/v'')K (8.10)

Using as typical values 7? = 500 km, v=40 km/s, and D= 3 mVsec, a

transition wavelength of 3.3 m is obtained.

Since in practice there can be a wide variation in the values of the

parameters in (8.10) it is necessary to evaluate Xr for each specific case.
362 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

If the practical extremes of all of the variables for both the backscatter

and forward scatter cases are investigated, it is found that the transitional

wavelength can be anywhere in the range 0.1 to 100 m. For a random

sample of meteors the transitional wavelength is likely to be near 2.9 m

for backscatter and in the range 0.5 to 1.6 m for forward scatter. The short wavelength case is treated by considering the effects of

differential diffusion as the trail is being formed. Each part of the trail begins to diffuse as soon as it is formed, and thus the effective radius of

the trail is smaller close to the meteor than farther back along the trail where diffusion has been going on for a longer time. The effective radius

for any part of the trail is taken as r= 4 Dt, the same value previously

used for the whole trail. Now it can be shown that, except near the end

of its path, the velocity of the meteor can be considered to be constant. Therefore position along the trail is proportional to t and the relation

r = \/4 i)^ indicates that the trail will have the form of a paraboloid of

revolution.

The geometry is shown in figure 8.7a and the time variation in re- ceived power is given in figure 8.7b. The time i = 0 is the instant of closest approach of the meteor. In this case the peak power varies as q"^ as was true in the long wavelength underdense trail case. With decreasing wavelength the pov/er falls as is compared with for the long wavelength underdense case. This

rapid variation with wavelength is consistent with the fact that very few

observations of meteor reflections have been made on frequencies above

the VHF range.

(b) Figure 8.7. Low-density short-wavelength reflections.

(a) Reflection geometry, (b) Variation of received signal with time. (After V. R. Eshleman, 1960, Meteor

scatter, The Radio Noise Spectrum, ch. 4, Harvard Univ. Press.)
REFLECTIONS FROM METEOR IONIZATION 363

8.4.3.5. Short Wavelength Reflections From High-Density Trails

This case is of less practical interest than those discussed above

and, consequently, will not be treated here. A brief discussion of this case is given in the paper by Sugar [11], which should be consulted by the

interested reader.

8.4.4. Other Aspects of Reflections From Meteor Ionization

In the previous four sections, reflections from meteor trails have been

considered from a relatively idealized viewpoint and many of the practical

aspects have been ignored. In this section some of these will be discussed

from a qualitative viewpoint. The discussion is directed toward the long

wavelength cases, since relatively few observations on short wavelengths

have been made and analyzed.

8.4.4.1. Long Wavelength Reflections During Trail Formation

The transient state associated with trail formation is of some interest

since it accounts for some of the observed characteristics of trail reflections. As a trail is being formed, but before the meteor reaches the first Fresnel

1.2 -

-5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 RELATIVE POSITION OF HEAD OF TRAIL Figure 8.8. Amplitude variation of received signal as trail length

increases. The limits of the first Fresnel zone are at +1 and —1, (After M. Lowenthal,

1956, MIT Lincoln Laboratory Tech. Rept. 132.)
364 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

zone, a weak reflection is obtained from the incomplete trail. This comes

primarily from the part of the trail corresponding to the shortest trans- mission path at the instant; and, when, as is usually the case, this is the

head of the trail, the reflected signal is shifted in frequency because of the

motion of the effective reflecting point. As the meteor approaches the

first Fresnel zone for the trail this frequency shift approaches zero, and

thus the received frequency decreases with time. The observed frequency

will of course depend on trail orientation, meteor velocity, and observing

wavelength. A maximum shift of the order of 5 kc/s is possible on 50

Mc/s over a 1000 km path.

As the meteor crosses the first Fresnel zone, the specular reflection occurs, accompanied by a large signal enhancement. Then as the particle

continues on, the additional ionization from the lengthening trail creates a minor fluctuation of the signal as shown in figure 8.8. Most trails do

not have the proper orientation to produce a specular reflection and in these cases only the weak Doppler-shifted component is observed.

8.4.4.2. Trail Drift and Distortion

The effects of ionospheric winds are appreciable for trails which

last for the order of a second or more. A Doppler shift of the received

frequency will be associated with the average wind velocity at the trail. For a velocity of 25 m/s this '"body Doppler" can be as large as 18 c/s

for backscatter observations on 50 Mc/s and will be somewhat less for forward scatter observations.

The trail distortion resulting from wind shears can lead to the formation of several local first Fresnel zones for the trail since a distorted trail can have several points where the transmission path length has a local minimum. These local minima, or ^^glints" as they have been called, are strong scatters and the received signal is a composite of their contributions. Since they are moving at different velocities, the signals from each

have different Doppler shifts and the resultant composite signal fades

in an irregular manner. On 50 Mc/s the fading rates observed for forward

scatter are of the order of 1 to 10 c/s. In addition to producing the fading

observed for long-enduring trails, the wind shears can rotate a trail suf- ficiently to produce reflections when the initial orientation was not

suitable. Thus these trails lose their aspect sensitivity as time goes on, and if their life is of the order of 10 sec they will scatter in all directions.
SHORT-TERM STATISTICAL CHARACTERISTICS 365

8.4.4.3. Diversity Effects

As pointed out in section 8.4.3, underdense trails act as small co- herent sources and, therefore, CW signals scattered by them exhibit good

space and frequency correlation. Correspondingly, very little pulse broadening is observed when pulse signals are used. The limited available data

suggest that for a forward scatter path about 1000 km in length, operating near 50 Mc/s, the correlation coefficient observed for single ^derdense

trails will fall to 0.5 for antenna spacings of the order of 150 km along the

path, for antenna spacings of the order of 30 km across the path, and for frequency separations greater than 5 Mc/s. Three-microsecond pulses

show no appreciable broadening under these conditions.

Overdense trails, in contrast to the underdense trails, tend to act

like relatively large sources and, therefore, exhibit much poorer space and

frequency correlation properties. Again, as in the underdense case, specific

data on these properties are not available. Available results [13] suggest

that the correlation observed for single overdense trails will fall to 0.5

for antenna spacings of the order of 50 X. Measurements using short

pulses over a 1000-km path indicate that the received composite signal can have a total time spread as large as 10 /zsec [15].

8.4.5. Short-Term Statistical Characteristics

8.4.5.1. General Remarks

From the viewpoint of radio propagation it is the collective properties

of trail reflections rather than the individual reflections that are of primary interest. These statistical characteristics can be divided into two

classes. First there are the short-term properties, the ones which would

be observed during a single hour or less. These can be thought of as being

associated with a small but statistically significant sample of trails. Second are the long-term statistical characteristics of the reflections. These include the diurnal and seasonal variations, geographical factors,

variations with systems parameters, etc. In the following sections the

effects of the initial radii of the trails are ignored—the initial radii are assumed to be zero. This approach appears to be satisfactory since the

simplified theory accounts satisfactorily for nearly all of the radio propagation properties of meteor trails. Difficulties arise primarily when one

tries to deduce properties of the meteors themselves from the radio observations. For example, when the initial radii are assumed not to be zero,
366 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

different height distributions and mass distributions are obtained than

for the zero radius case. These differences will not be important here since

the older theory is consistent with the observations and thus the initial radius problem can be avoided.

8.4.5.2. Peak Amplitude Distribution

The peak amplitude of the reflection from an underdense trail is proportional to the electron line density q and, hence, proportional to the mass of the meteor [9]. For underdense trails the number Nof signals

observed with peak amplitudes greater than A is given by

A^cc^-i. (8.11)

For overdense trails A is proportional to and so NozA-'. (8.12) In general, it is better to write the relationship in the form

N= CA- (8.13)

where C is a constant of proportionality and where a depends on the

details of the observing system and in practice will be a function of the

detection threshold ^. If a very low threshold is used, then nearly all of the trails detected will be underdense and the exponent observed will be quite near a = l. If a very high threshold is used, nearly all of the

trails detected will be overdense and the exponent will be near a = 4. Between these two conditions there will be a transition region where

contributions from both overdense and underdense trails will be important, and in this region the exponent a will lie between 1 and 4. The

extent of the transition region depends on path geometry, antenna di- rectivity, etc. Observations of shower meteors made using backscatter

with highly directive antennas and, therefore, concerned with trails localized in position and orientation, indicated that the transition was

complete in a 2 to 1 amplitude range [9]. In contrast, forward scatter observations of sporadic meteors, which therefore include a wide variation

of positions and orientations, indicated that the transition extended over

a 10 to 1 amplitude range [16]. Figure 8.9 gives the relation between

threshold and rate computed for one experimental path [16]. The system

parameters were j5/=100 JF, X = 7.5 m, gi = gr = 40; a transmitter-receiver
SHORT-TERM STATISTICAL CHARACTERISTICS 367

COUNTING LEVEL Ac(/iV) Figure 8.9. Theoretical rate-amplitude relation computed for the following parameters: Pt = 100 W,X = 7.5 m, gt = gr = 40.

(After C. O. Hines, 1958, Can. J. Phys. 36, 549.) separation of 1000 km was assumed and a mean trail height of 100 km

was used. The upper and lower dashed lines in the figure have slopes of — 1 and —4 respectively, corresponding to the theoretical distributions

for underdense and overdense trails.

8.4.5.3. Duty Cycle Versus Threshold

Duty cycle is defined as the fraction of time that a received signal

exceeds a prescribed threshold. To a first approximation it is the fraction of time that the reception of messages will occur in a meteor-burst communication system and it is an important parameter in systems work.
368 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

The relationship between duty cycle T and the threshold Ai for propagation by underdense trails is given by

T= (r/a) CAr\ (8.14)

Here r is the time taken for the amplitude to fall to (1/2.78' • •) of its initial value and a and C are defined by (8.13). Note that since this can

be written as T= {T/a)N, the factor r/a is just the average duration of a burst. For underdense bursts a = 1 and since duty cycle P is proportional

to T, then

P{A>Ai) o:Ai-''=Ar\ (8.15) In practice, the presence of overdense trails increases the observed value

-40 -30 -20 -10 0 10 RELATIVE THRESHOLD IN DECIBELS Figure 8.10. Duty cycle versus threshold.

(After G. R. Sugar, 1964, Radio propagation by reflection from meteor trails, Proc. IEEE 52, No. 2, 116.)
SHORT-TERM STATISTICAL CHARACTERISTICS 369

of a. Values commonly observed are in the range 1.1 to 3.5, with the

large values apparently associated with a predominance of overdense

trails. An example of the measured variation of duty cycle with threshold

is shown in figure 8.10. Note that tJie slope of the curve increases at higher

thresholds. The points at duty cycles higher than 10 percent include con- tamination from receiver noise and ionospheric scatter transmission as well as signals from overlapping meteor trails. They should not, therefore,

be expected to fit the distribution law derived here.

8.4.5.4. Apparent Location of Trails

The geometrical conditions required for strong reflections from a

trail, combined with the radiant distribution for sporadic meteors, are such as to favor trails occurring in some parts of the sky and to discrimi- nate against those in other parts of the sky. The result is that the meteors

contributing to propagation over a particular path occur in a relatively

small region of the sky, the so-called "hot spot." For the longer trans0 100 200 300 400 500

X (km) Figure 8.11. Relative signal contributionsfrom various parts of the meteor region computedfor a 1000 km path. The origin of coordinates represents the path midpoint, x and y are respectively displacements along and normal to great circle path. Results in the other quadrants are symmetrical to these. (After C. O. Hines, 1956, Can. J. Phys.

34, 1013.)
370 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

mission paths this region is near but not at the path midpoint. The midpoint itself is a region where very few trails are observed [I?]. Figure

8.11, adapted from Hines and Pugh [18], shows the relative cumulative

signal durations for contributions from various parts of the meteor region.

The data were computed for a 1000 km transmitter-receiver separation, a meteor trail height of 100 km, and an isotropic distribution of incident meteors. In practice the actual distributions will differ from these be- cause the incident meteor flux is in fact nonisotropic. Further data on this point will be presented in the next section.

8.4.6. Long-Term Statistical Characteristics

8.4.6.1. Diurnal Variations

The characteristics to be discussed in this section include variations

observable on an hour-by-hour or month-by-month basis and also variations associated with the characteristics of the observing system and

its location. Nearly all data pertaining to these variations are relatively

poor because of the large, seemingly random, hour-to-hour fluctuations in meteor activity that are observed. This random component of meteor

activity is roughly comparable to a random variation in transmitter power

output over a 10-dB range. It introduces a substantial uncertainty into

many observations.

The diurnal variation in meteor rate results in substantial diurnal

variations in many of the characteristics of meteor propagation. Three

basic factors are significant: the meteor arrival rate varies, meteor velocities vary, and the effective radiants vary throughout the day.

The meteor arrival rate will have a roughly sinusoidal variation

throughout the day with a maximum around 6 a.m. and a minimum

around 6 p.m. The ratio of maximum to minimum averages around 4. The average meteor velocity also has a roughly sinusoidal diurnal

variation, with its maximum around 6 a.m. and minimum around 6 p.m.

The diurnal variation in velocity cannot exceed 60 km/s (twice the or- bital velocity of the earth) and, in practice, averages much less than this. A variation of 10 to 15 km/s above and below a daily mean velocity of

35 to 45 km/s is typical. The velocity variation is not in itself of much

significance in radio work but its consequences are. The velocity variation

leads to a diurnal variation in trail height; and this, in turn, because of

the variation of diffusion coefficient with height, leads to a diurnal vari- ation in the duration of meteor bursts. Observations of the diurnal vari-
LONG-TERM STATISTICAL CHARACTERISTICS 371

0.6

0

' ^ ^ \ 1 12 18 00 06 12 6 NOV 1956 7 NOV 1956 Figure 8.12. Diurnal variation of the 1/e duration of under- dense meteor bursts.

(After T. J. Keary and J. H. Wirth, 1960, Statistical characteristics of forward

scattered radio echoes from meteor trails, Electromagnetic Wave Propagation, Academic Press, p. 277.)

ation of the 1/e duration of underdense bursts are illustrated in figure

8.12, which indicates that the duration varies over a 2-to-l range through

the day [19].

The diurnal variation of meteor radiants can be considered here only

in a qualitative manner because of the general complexity of the problem

and the present uncertainties regarding the actual radiant distributions. Because of the orbital motion of the earth, most meteors appear to have

radiants concentrated in the hemisphere ahead of the earth (the morning

hemisphere) ; and very few radiants appear to be behind the earth. As

the earth rotates, the position of the predominant radiants changes rela- tive to the transmission path, and the location of the "hot spot" moves

around. As a result of this motion, average values of the geometric factors

in the transmission equations will vary, and a diurnal change in received

power will occur. This change is difficult to observe since received power

will also change due to diurnal variations in meteor rate. An indication

of the effects of diurnal variation of radiants can be seen in figure 8.13

(after llines [20]), which depicts the predicted diurnal variation in meteor rates for each side of a north-south and an east -west transmission
372 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

NORTH SIDE OF EAST-WEST PATH

/

/

/•-.

EAST SIDE OF NORTH-SOUTH PATH WEST SIDE OF ^NORTH-SOUTH PATH^ SOUTH SIDE OF EAST-WEST PATH

00 06 LOCAL TIME Figure 8.13. Predicted diurnal variations in meteor rates.

(After C. O. Hines, 1956, Diurnal variations in forward scattered meteor signals, J. Atmospheric Terrest. Phys. 9, 229.) path. The differences in the shapes of the various curves indicate the

effects of radiant changes relative to path orientation. The sum of all four curves would be an approximate indication of the diurnal variation

in the arrival rate of meteors. Given adequate measures of the above three basic diurnal factors,

it should be possible to predict the diurnal characteristics of any trans- mission path; and it has been possible to do this with a reasonable degree

of success in the case of meteor rates. The prediction of duty cycles is more complicated because of the diurnal variation of velocities, and it appears that this prediction has yet to be made.

The combination of the above three basic variations together with

the random components of arrival rates results in rather irregular daily

variations of meteor rates. Figure 8.14 illustrates the rates observed on

49.8 Mc/s over a 1245-km path on two days, a week apart [21]. While

the data for each day show the general characteristics described above,

the detailed variations on the two days are quite different.

8.4.6.2. Monthly Variations

Month-to-month variations in meteor-propagation characteristics are primarily associated with similar variations in meteor characteristics.
LONG-TERM STATISTICAL CHARACTERISTICS 373

Figure 8.14. Observed diurnal variation of meteor burst rates. Cedar Rapids-Sterling on 49.8 Mc/s.

(After G. F. Montgomery and G. R. Sugar, 1957, The utility of meteor bursts for intermittent radio communication, Proc. IRE 45, 1684.) 350

^ 200 -

<

50 -

AQUARIDS

PERSEIDS

GEMINIDS ORIONIDS _^|UR,DS

URSIDS

J L JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC Figure 8.15. Seasonal variation of meteor rates.

(After G. S. Hawkins, 1956, Astron. J. 61, 388.)
374 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

There is little evidence that any of the normal month-to-month variations

in ionospheric characteristics are reflected in meteor propagation characteristics, with the possible exception of D region absorption. The

seasonal variation of meteor rates is illustrated in figure 8.15 (after

Hawkins [8]) . The echo rates shown are for meteor trails with an electron

line density of 2.75X10^^ electrons per meter or greater. The contributions of shower meteors are shown above the histogram for the sporadic meteors. The relative contributions of shower meteors will decrease as the system sensitivity is raised, since the two types have a different mass

distribution.

As yet there is no satisfactory answer to the question of year-to-year

variations in meteor activity. Such variations have been observed but

most workers who have observed them have attributed them to changes

in equipment sensitivity.

8.4.6.3. Geographical Variation

As yet this has not been clearly defined. The geographical variations,

if present, are masked by the random variations.

8.4.6.4. Abnormal Absorption

Since most meteor trails are produced at heights above the absorbing

region, the meteor signals are absorbed in much the same way as HF

signals. On frequencies much greater than 30 Mc/s, the normal D region

absorption is negligible. During periods of high absorption in high lati- tudes, the absorption can increase enormously and affect meteor propagation on frequencies as high as 100 Mc/s and more. During a major dis- turbance the duty cycle on a meteor-burst communications circuit between Goose Bay, Labrador, and Ottawa, Canada dropped by a factor over 10^ implying a signal attenuation of over 30 dB [22]. Disturbances

of this magnitude are relatively uncommon and are not important in terms of the average characteristics of meteor-burst propagation. They

are an indication, however, that this mode of propagation, like most

others, can be disrupted and is, therefore, not the basis of a completely

reliable communication system.
METEOR REFLECTIONS FOR COMMUNICATIONS 375

8.4.7. Use of Meteor Reflections for Intermittent Radio

Communications

8.4.7.1. General Characteristics

Before leaving meteor propagation let us consider an application to communication systems. Meteor-burst communication systems are

basically weak signal systems because the signal loss associated with the

meteor-trail reflection is relatively high. For example, a typical system

[15] operating on 50 Mc/s over a 1300 km path with a transmitter power

of 2 kW was commonly set to transmit messages whenever the signal at the receiver exceeded 2X10~^^ W (2 iiY open-circuit voltage for a 50-12 source). This corresponds to a system loss of 170 dB—under similar

circumstances ionospheric scatter propagation would exhibit a system

loss of the order of 180 dB. Of this total about 90 dB represents the at- tenuation associated with the length of the transmission path and 80

dB the scattering loss. Such a system was shown to be capable of a daily

average teletypewriter transmission rate of 40 words per minute at a character error rate of 0.35 percent.

As is implied in the title of this section, meteor communication

systems operate in an intermittent mode. They transmit messages only

during the brief intervals when meteor propagation is present. Control

of message transmission is achieved by providing for two-way transmission over the propagation path and transmitting only a control signal when

a meteor trail is not present. When a meteor burst occurs, its presence is indicated by reception of the control signal, and message transmission can

begin. These principles are incorporated in the JANET system [23]. In the interval between suitable meteor signals a system accepts messages

and stores them for subsequent transmission. The system is, in essence, one that adapts its operation to the conditions of the transmission medium; it transmits only under favorable conditions. The aim is, of course, to obtain better overall transmission by avoiding the times when trans- mission is poor. Whether or not the intermittent mode of operation re- sults in an overall improvement over continuous operation depends on

the details of the equipment and on the characteristics of the propagation medium.
376 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

8.4.7.2. Channel Capacity

For an intermittent system operated at a fixed transmitter output

and with band-limited Gaussian noise interference, the relation between

channel capacity M and system bandwidth B is given by [21]

M=A:B(i-^«\ (8.16)

where A: is a constant of proportionality.

From (8.16) we see that if a lies in the range 0<a<2 then, for a given

transmitter output power, the channel capacity will increase as the signaling bandwidth is increased. Early measurements indicated that 1.2 was

a typical value for a, thus suggesting that meteor-burst communication

might be feasible. It is likely that this result, more than any other, has

provided the impetus for the development of meteor-burst communication systems.

8.4.8. Concluding Remarks on Meteor Propagation

At the present time there is a large amount of theoretical and observational material available on most aspects of meteor propagation

in the lower VllF range. As has been suggested in the previous sections,

the available information is most complete for long wavelength underdense trails and least complete for the short wavelength overdense trails. Some of the areas where substantial work still remains to be done are

studies of radiant distributions, properties of very small meteors, the

effects of fragmentation, geographic factors, and the long-term fluctua- tions in propagation characteristics. The adequacy of the presently available data can be examined from

the viewpoint of the communication system design and engineering. If this

is done, it appears that the present uncertainty in predicting the trans- mitter power required for a meteor communication circuit is probably

of the order of 10 dB. At present it is not clear whether this number can

be substantially reduced by further work. The whole field of system design

is one where relatively little effort has been expended, and it is likely

that major improvements in systems can still be achieved.
CHARACTERISTICS OF F SCATTER 377

8.5. EQUATORIAL F SCATTER

8.5.1. History

Amateur radio operators had discovered that near the peak of the

sunspot cycle (1947) they could communicate over long distances across the equatorial regions on frequencies (50 Mc/s) well above the maximum frequency to be expected for the distances involved. These radio contacts were most pronounced during nighttime in the equinoctial

months.

During the International Geophysical Year more definite experiments were carried out on this phenomenon in the Far East [24] and in South America [25]. These experiments established that the enhanced

signals were reflected from scattering centers located near the base of the F2 layer.

8.5.2. Characteristics of F Scatter

8.5.2.1. Diurnal Variation

The signal appears usually during the evening and night when the

signal level may rise 30 to 40 dB above the level produced by forward

scatter.

8.5.2.2. Seasonal Variation

F scatter appears to be most prevalent around the autumnal equinox.

8.5.2.3. Geographical Variation

The echoes are aspect sensitive [25], so that the signal level depends on the orientation of the path relative to the earth's magnetic field. This

also determines the direction of arrival of the signal. North-south paths,

with midpoints within ±20° of the dip equator, are affected.
378 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

8.5.2.4. Fading

F scatter signals are characterized by flutter fading with fading rates of 10 c/s and more. The ampUtude distribution is essentially Rayleigh

and the carriers show Doppler shifts equivalent to a west-east motion of

the order of 100 m/s.

8.5.2.5. Geophysical Factors

The occurrence of F scatter is associated with equatorial spread

F [25] (frequency spread type) which is thought to be produced by

patches of irregularities located at or below the bottom of the F layer.

The thickness of these patches is estimated as 50 km. The scattering ir- regularities comprising these patches are elongated along the magnetic

field with longitudinal dimensions of 1000 m or more and transverse di- mensions of the order of 10 m or less. The geographical extension of a given

patch may be as great as 1000 km in the east-west direction.

8.5.3. Flutter Fading

From the point of view of radio communications the most disastrous

aspect of F scatter is the occurrence of flutter fading during the prime

listening hours. The most severe fading sets in shortly after sunset (1800

local time) and lasts for 2 to 3 hr. During this period voice modulation is so "chopped up" it is almost unrecognizable.

Fixed frequency (50 Mc/s) pulse studies In the Far East have shown

that, during the period of intense flutter fading, there is marked broadening of the echo pulses as shown in figure 8.16. Sweep-frequency studies (see

fig. 4.16) in Africa have also shown this marked broadening which can amount to factors of more than 10 compared with the transmitted pulse

width.

The spectra [26] of the F scatter signals (in Africa) was studied by means of the Doppler frequency technique described in section 3.2.3.2,

and some records are shown in figure 5.13. The pre-sunset signals can be

seen on the extreme left of figure 5.13; the spectra are relatively narrow. The post-sunset effect takes place around 1830. The frequency spectrum,

during this period, has been known to broaden by at least 18 c/s. One of

the remarkable features of these records is the striated structure which

slopes downwards to the right. The broad nighttime spectra (and hence
RADIO AURORA 379

Poro P. I. to Onna, Ok^inawa (837 miles) Haage markers are 100 micro- seconds Frequency: h-g.8h Mc/s Pulse length: 50 micro- seconds Power: 2 kw Pulse repetition rate: lOO/second

Antennas: 5 element H yagis Receiver bandwidth: 120 kc/s

September 23, I95S

Okinawa Standard Time (C-MT +9) ^3 g

ft r-j P5 CJ Figure 8.16. Range-time records showing pulse broadening of F-scaUer echoes.

(After R. Bateman, J. W. Finney, E. K. Smith, L. H. Tveten, and J. M. Watts, 1959, IGY observations

of F-layer scatter in the far east, J. Geophys. Res. 64, 403.)

the associated flutter fading) may be attributed to the motion of scatter- ing irregularities.

Since the spread F responsible for flutter fading is limited in space

and in time, there is a possibility that its effects may be minimized by

suitable relaying of radio signals.

8.6. AURORAL SCATTER'

8.6.1. Radio Aurora

Radio aurora can be defined as '^the ionospheric ionization, asso- ciated with auroral disturbances, that gives rise to radio reflection" [27].

While aurora itself may be defined as emitted radiation (visible and in- visible), radio aurora is ionization which reflects radio waves. Thus we

should not expect a one-to-one correlation between the spatial and temporal occurrences of one and th^se of the other. Radio aurora and visible aurora are separate phenomena with the same basic origin; that is, aurora

is a manifestation of atomic excitation and ionization, and radio aurora

5 Based on a lecture by R. Cohen.
380 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

is constituted of the electrons and ions separated during the ionization

process. However, reflections from radio aurora usually depend not only on the presence of ionization but also on the geometry involved. These

aspect-sensitive reflections will not be observed unless the radio aurora

is in the right place with respect to the observer. Thus from a given loca- tion one may see visible aurora but not radio aurora. On the other hand,

radio aurora can be observed during the daytime when visible aurora cannot be seen. A review of radio studies of the aurora has been made by Booker

[28] and this should be consulted by the interested reader.

8.6.2. Bistatic Observations

The term ^^bistatic" is used to contrast a two-station (transmitter

and receiver separated) method of observation with a single -station or monostatic method (radar) . Auroral observations of this kind have always

involved continuous-wave transmissions, so that the measurements of

distances have had to be inferred from information on angles of arrival. The most extensive bistatic studies of radio aurora are those of Collins

and Forsyth [27], who have classified enhancements of the received

signals into five categories:

(1) E events, which are strong reflections probably from sporadic

E patches,

(2) S events, which are enhancements which are not accompanied

by a magnetic disturbance.

The following A events are auroral phenomena closely associated with

magnetic disturbance:

(3) Ai exhibits rapid fading (100 c/s) and is strongly aspect sensitive.(4) A2 exhibits slow fading (1 cycle per 5 sec) and is slightly aspect

sensitive.

(5) As exhibits slow fading and no aspect sensitivity, i.e., the signals

arrive in the great circle. This suggests that the As signals are due to scattering from essentially

isotropic irregularities.

Based on these results and some frequency-dependence measurements, Collins and Forsyth conclude that the Ai and A2 events can be

ascribed to field-ahned irregularities above a height of 100 km, and the

Az events to more isotropic irregularities below that height. They also conclude from their frequency dependence measurements in the 32 to
MONOSTATIC (RADAR) OBSERVATIONS 381 50 Mc/s frequency range that the A2 events can correspond to overdense

irregularities with electron density as great as 3X10^ cm~^, and that the

usual electron density for the Ai events was between 1.3 and 1.9X10^

cm~^, corresponding to a plasma frequency range of about 32 to 39 Mc/s.

8.6.3. Monostotic (Radar) Observations

For localized observations of the radio aurora and the determination

of its aspect sensitivity, radar methods are suitable. Furthermore, this method is useful in the study of movements. Numerous workers have contributed to radar-auroral research in the past 30 years and reviews of

this subject are available [28, 29, 30]. Although the results of the radar

studies are not altogether conclusive, certain facts are generally agreed

upon and these will be summarized below.

The determination of the spatial association between aurora and

radio aurora is complicated by the aspect sensitivity requirements of the

latter. By a comparison of the associated aurora with the radar echoes (at

College, Alaska) Bowles obtained good correspondence as illustrated in

figure 8.17. This figure shows, however, that radar echoes are obtained

from only parts of the visual forms.

A striking demonstration of the aspect sensitivity of radio aurora has

been given by Dyce [31], who operated a radar at Point Barrow, Alaska,

located to the north of the visible aurora. The majority of radar echoes was obtained not from the south, but from the north.

The heights from which auroral radar echoes are reflected range from

75 to 135 km with a mean of about 110 km, which corresponds fairly well to the average height of the lower edge of most visual auroral forms.

Leadabrand et al. [32] also measured the azimuthal distribution

and thence the aspect sensitivity of radar echoes on 398 Mc/s, and found

that they could be obtained up to 10° away from the angle of perpendicularity to the earth's magnetic field. Presnell et al. [33] show that this departure is 12° on 216 Mc/s and 6° on 780 Mc/s. Thus, aspect sensitivity

becomes more stringent as the frequency increases. It has been observed

[32] that echoes from radio aurora at lower heights are confined to a narrower departure from perpendicularity than those from greater heights.

The frequency dependence of radar echoes from radio aurora has not been definitely determined. It is clear that the scattering cross section

diminishes with increasing frequency, and that it is small at all frequencies,

corresponding, for example, to a power reflection coefficient of order 10~^ on 106 Mc/s.
382 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

600 RANGE km 400 800

GEOMAGNETIC AZIMUTH

Figure 8.17. Association between visible aurora and radio aurora.

(After K. L. Bowles, unpublished.)
MONOSTATIC (RADAR) OBSERVATIONS 383

A number of workers have measured the frequency spectrum of

radar echoes from radio aurora. Some of the spectra obtained by Bowles

[34] in Ithaca, N.Y., and in College, Alaska, are shown in figure 8.18.

The Doppler shifts and spreads of these spectra correspond to the motion

of the irregularities in the radio aurora, and range motions observed

simultaneously do not always correlate with them in magnitude or direction. Inasmuch as the range motions are probably spatia^ drifts re- sulting from redirection of the source of ionization, this apparent discrepancy is not surprising.

(After K. L. Bowles, unpublished.)
384 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

8.7. INCOHERENT SCATTER'

8.7.1. Historical Note

It has been known for many years, especially in connection with

x-ray scattering, that an individual electron has a cross section for the

scattering of electromagnetic waves. In 1958, Professor W. E. Gordon

[35] pointed out that with the existing radar sensitivities it should be

feasible to measure ionospheric electron densities by detecting this weak

Thomson scattering. Gordon pointed out that, from the theory, the

Doppler spread (pressure broadening) imparted to the radiofrequency

by the thermal motion of the electrons provided a means of measuring

electron temperatures.

The existence of incoherent scatter was demonstrated in October

1958 by Bowles [36] with a scatter-radar in Long Branch, 111. To obtain

the high sensitivity required he used an antenna with a cross-sectional area of almost 5 acres and a pulse transmitter of about 1 MW peak power

on a frequency near 40 Mc/s. The receiver bandwidth was of the order of

10 kc/s. Much to his surprise Bowles found that the line broadening was

about 10 kc/s rather than the 100 kc/s predicted by Gordon. These results were corroborated, on a frequency of 440 Mc/s, at the Massachusetts

Institute of Technology [37].

8.7.2. Scattering From an Individual Electron

The reason for high equipment sensitivity is, of course, the small

value of the Thomson scattering cross section a for a free electron ( 10"^^ m^). The echo amplitude to be expected from a single free electron can

be calculated as follows: The incident power density is ptg/^^irB? where

pt is the power transmitter, g is the antenna gain, and R is the range. The power absorbed (and re-emitted) is ptgcr/iTR'^ and the received

power pr is {p tga/4cTr R^) (a/iwR'^), where a is the antenna cross section. With a typical radar and scattering from the F region we assume the

following values: pt=W W, g=lO\ a=lO' m\ and R = SXlO' m. This

gives pr = 6XlO~^9 W. For unity signal/noise we need about 10~^^ W

so that the scattering volume must contain something like 10^^ electrons. In the F region N is about 10^^ cubic meter so that the scattering

^ Based on a lecture by K. L. Bowles.
SCATTERING FROM AN INDIVIDUAL ELECTRON 385 volume required must be of the order of 10^^ m^ (i.e., 10 km^). Thus a

limit is set to the smallest volume that can be studied by a given radar

system.

If the electrons are in thermal equilibrium with the ions and neutral

molecules they will have, essentially, a Maxwellian distribution of ve4.0

2 3.0

2.0 -

0.0 LOCAL TIME Figure 8.19. Electron cross sections for incoherent scatter measured at Jicamarca, Peru.

(After K. L. Bowles, G. R. Ochs, and J. L. Green, 1962, J. Res. NBS 66D (Radio Prop.). No. 4, 395.)
386 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

locities and these motions will impose various Doppler shifts on the re- radiated waves. For an average F region temperature of 1500 °K one

expects that the spectrum on 41 Mc/s should be about 100 kc/s wide.

The experimental width turned out to be about one tenth this value and

it was realized that something was wrong with the simple theory. The

reason for this discrepancy has been found to lie in the long-range Coulomb

interactions between the positive ions and the electrons. Because of their

charges and motions, the ions and electrons produce statistical fluctua- tions of charge density which almost cancel in space. If this were not so, strong space charges would develop, tending to restore neutrality. Because of this necessity to maintain electrical neutrality the motions of

the electrons are constrained by those of the heavy ions. The observed

line broadening is, therefore, not that due to the free electrons but rather

to the ions wherein most of the momentum lies [36]. Because of this constraint it has been proposed to call the phenomenon "quasi-incoherent

scatter." The theoretical implications of this idea have been studied by

a number of workers [38, 39, 40].

It turns out that, for thermal equilibrium between ions and electrons,

the scattering cross section per free electron is just about one -half the

classical Thomson cross section. In the more general case, when the elec- tron and ion temperatures ( Te and T^, respectively) differ, the relationship between the measured cross section am and the classical value a is given approximately by

-^IT^- ^'-''^

Measurements of am have been made by Bowles at the Jicamarca

radar near Lima, Peru, and the results are shown in figure 8.19a. It

will be seen that the values are all less than the theoretical value of

5X10~29 m^. It is believed that during the middle of the day the dis- crepancy is due to absorption in the D region (approximately 0.5 dB,

as shown in figure 8.19b.). On the other hand, near sunrise it is thought

that the electrons are in fact hotter than the ions.

8.7.3. Electron Density Profiles

We have seen above that the power received from a given volume in the ionosphere is proportional to the number of electrons present. The

incoherent scatter technique thus provides a means of determining the
ELECTRON DENSITY PROFILES 387

electron density profile above the F2 peak provided that the geometry

of propagation is known. The power pr received from a distance R is given by

Pr =

ptaaCTTTrVVA

87ri?2 (8.18)

where a is the antenna aperture area, a is the cross section per unit volume,

c is the velocity of light, r is the pulse duration in seconds,

7/r, ?7s, and tja are factors to correct the aperture for the effects of

resistive losses, side lobes, and tapered feed, respectively.

The following features of (8.18) are worth noticing:

(1) /)r is proportional to rather than as in the case of a single

scatterer. From the divergence of the beam it can be seen that the scatter- ing volume increases proportional to the square of the range; this removes

a factor of R~^.

(2) The aperture a appears to the first power only. This is because

increased aperture (i.e., increased gain) results in a smaller scattering

volume.

Further corrections have to be made to (8.18), depending on the type

of antenna used. taiMuiiiHi

Figure 8.20. Oscillogram showing echo power versus range made

with scatter radar at Jicamarca^ Peru.

(After K. L. Bowles. 1961, J. Res. NBS 65D (Radio Prop.), No. 1, 1.)
388 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

ELECTRON DENSITY (N/cm') Figure 8.21. Electron-density profile obtained from incoherent scatter measurements.

(After K. L. Bowles, Mar. 1963, NBS Tech. Note 169.) Turning to the experimental results, in figure 8.20 we see an actual

oscilloscope photograph made with the radar. Each spot is the result of

averaging the echo power taken over many radar sweeps and is thus a

plot of power versus range. With a knowledge of the equipment characteristics it is possible to determine the cross section per unit volume a from (10.18) and, hence, the electron concentration averaged over a cer-
ELECTRON DENSITY PROFILES 389

ELECTRON DENSITY N / cm ^

)

Figure 8.22, Sample electron-density profiles obtained from incoherent scatter measurements.

(After K. L. Bowles, 1964, Radio wave scattering in the ionosphere, Advances in Electronics and Electron Physics 19, 55, Academic Press.)
390 SCATTER PROPAGATION ON VERY HIGH PROPAGATION

tain volume and over a given time. A sample profile obtained with this technique is shown in figure 8.21. The curve has to be calibrated at least at one point and this is done at the peak of the F layer. The peak electron

density is determined from the /0F2 as observed with a conventional

ionosonde and substitution in the formula

N= 1.24 X 10^0 (foFy electrons per cubic meter.

Further sample profiles are shown in figure 8.22 from which we see that there are rather large variations in the shape of the profiles with time

of day and from day to day. The daytime results for heights below about

200 km are probably too large by as much as a factor of two, due to the

presence of weak coherent irregularities. At greater heights it has been

verified that the echo power is proportional to electron density. One

feature of particular interest is the abrupt change in electron -density

gradient which often occurs on the topside. This change is probably as- sociated with the changeover in atmospheric composition from one constituent to another (e.g., oxygen to helium or helium to hydrogen).

REFERENCES

[I] EUyett, C, and J. M. Watts (1959), Stratification in the lower ionosphere, J. Res. NBS 63D (Radio Prop.), 117.

[2] Wheelon, A. D. (1960), Relation of turbulence theory to ionospheric forward

scatter propagation experiments, J. Res. NBS 64D (Radio Prop.), 301.

[3] Bailey, D. K., R. Bateman, and R. C. Kirby (1955), Radio transmission at VHF

by scattering and other processes in the lower ionosphere, Proc. IRE 43, 1181.

[4] Bowles, K. L., and R. S. Cohen (1962), A study of radio wave scattering from

sporadic-fJ near the magnetic equator. Ionospheric Sporadic-jE (ed. Smith and

Matsushita) (Pergamon Press), 51.

[5] EUyett, C, and H. Leighton (1958), Solar cycle influence on the lower ionosphere

and on VHF forward scattering, Proc. IRE 46, 711.

[6] Norwegian Defence Research Establishment, Report No. 27 (1958), A study of VHF forward scattering in high latitudes.

[7] Greenhow, J. S., and J. E. Hall (1960), The variation of meteor heights with

velocity and magnitude. Monthly Notices Roy. Astron. Soc. 121, 174.

[8] Hawkins, G. S. (1956), A radio survey of sporadic meteor radiants. Monthly

Notices Roy. Astron. Soc. 116, 92.

[9] Kaiser, T. R. (1953), Radio echo studies of meteor ionization. Advances in Phys.

2, 495.

[10] Manning, L. A., and V. R. Eshleman (1959), Meteors in the ionosphere, Proc. IRE 47, 186.

[II] Sugar, G. R. (1964), Radio propagation by reflection from meteor trails, Proc. IEEE 52, No. 2, 116.
REFERENCES 391

[12] Hines, C. O., and P. A. Forsyth (1957), The forward scattering of radio waves from overdense meteor trails. Can. J. Phys. 35, 1033.

[13] Manning, L. A. (1959), Oblique echoes from overdense meteor trails, J. Atmospheric Terrest. Phys. 14, 82.

[14] Eshleman, V. R. (1960), Meteor scatter. The Radio Noise Spectrum (ch. 4) (Har- vard Univ. Press).

[15] Carpenter, R. J., and G. R. Ochs (1962), High resolution pulse measurements of meteor burst propagation at 41 Mc/s over a 1295 km path, J. Res. NBS 66D

(Radio Prop.), 249.

[16] Hines, C. O. (1958), A theoretical rate-amplitude relation in meteoric forward

scattering. Can. J. Phys. 36, 539.

[17] McKinley, D. W. R., and A. G. McNamara (1956), Meteoric echoes observed

simultaneously by backscatter and forward scatter. Can. J. Phys. 34, 625.

[18] Hines, C. O., and R. E. Pugh (1956), The spatial distribution of signal sources in meteoric forward scattering. Can. J. Phys. 34, 1005.

[19] Keary, T. J., and J. H. Wirth (1960), Statistical characteristics of forward scat- tered radio echoes from meteor trails. Electromagnetic Wave Propagation,

(Academic Press), 277.

[20] Hines, C. O. (1956), Diurnal variations in forward scattered meteor signals, J. Atmospheric Terrest. Phys., 9, 229.

[21] Montgomery, G. F., and G, R. Sugar (1957), The utility of meteor bursts for intermittent radio communication, Proc. IRE 45, 1684.

[22] Maynard, L. A. (1961), Propagation of meteor-burst signals during the polar disturbance of November 12-16, 1960, Can. J. Phys. 39, 628.

[23] Forsyth, P. A., E. L. Vogan, D. R. Hansen, and C. O. Hines (1957), The principles of JANET—A meteor-burst communications system, Proc. IRE 45, 1642.

[24] Bateman, R., J. W. Finney, E. K. Smith, L. H. Tveten, and J. M. Watts (1959), IGY observations of F-layer scatter in the Far East, J. Geophys. Res. 64, 403.

[25] Cohen, R., and K. L. Bowles (1961), On the nature of equatorial spread F, J. Geophys. Res. 66, 1081.

[26] Calvert, W., K. Davies, E. Stiltner, and J. T. Brown (1963), Equatorial spread-F

motions, Proc. Int. Conf. lono., 316, Inst, of Phys. and Phys. Soc.

[27] Collins, C, and P. A. Forsyth (1959), A bistatic radio investigation of auroral

ionization, J. Atmospheric Terrest. Phys. 13, 315.

[28] Booker, H. G. (1960), Radar studies of the aurora. Physics of the Upper Atmosphere (ed. J. A. Ratcliffe) (Academic Press).

[29] Chamberlain, J. R. (1961), Physics of the aurora and airglow (ch. 6), Academic

Press.

[30] Little, C. G., W. M. Rayton, and R. B. Roof (1956), Review of ionospheric effects at VHF and UHF, Proc. IRE 44, 992.

[31] Dyce, R. (1955), More about VHF auroral propagation, J. Geophys. Res. 60, 317.

[32] Leadabrand, R. L., L. Dolphin, and A. M. Peterson (1959), Preliminary results of a 400 Mc radar investigation of auroral echoes at College, Alaska, IRE

Trans. Ant. Prop. AP-7, 127.

[33] PresneU, R. I., R. L. Leadabrand, A. M. Peterson, R. B. Dyce, J. Schlobohm,

and M. R. Berg, VHF and UHF radar observations of the aurora at College,

Alaska, J. Geophys. Res. 64, 1179.

[34] Bowles, K. L. (1954), Doppler shifted radio echoes from aurora, J. Geophys. Res.

59, 553.

[35] Gordon, W. E. (1958), Incoherent scattering of radio waves by free electrons with

applications to space exploration by radar, Proc. IRE 46, 1824.
392 SCATTER PROPAGATION ON VERY HIGH FREQUENCIES

[36] Bowles, K. L. (1961), Incoherent scattering by free electrons as a technique for studying the ionosphere and exosphere: Some observations and theoretical considerations, J. Res. NBS 65D (Radio Prop.), 1. [37] Pineo, V. C, L. G. Kraft, and H. W. Briscoe (1960), Some characteristics of ionospheric backscatter observed at 440 Mc/s, J. Geophys. Res. 65, 2629.

[38] Dougherty, J. P., and D. T. Farley (1960), A theory of incoherent scattering of

radio waves by a plasma, Proc. Roy. Soc. (London) A259, 79.

[39] Fejer, J. A. (1961), Scattering of radio waves by an ionized gas in thermal equili- brium in the presence of a uniform magnetic field. Can. J. Phys. 39, 716.

[40] Salpeter, E. E. (1961), Effect of the magnetic field in ionospheric backscatter, J. Geophys. Res. 66, 982.
CHAPTER 9

Propagation of Low and Very Low Frequency Waves

9.1. PURPOSE

The aim of this chapter is to discuss, briefly, those lower frequency

bands which provide alternatives to the use of high frequencies. It has

been seen, in the previous chapters, that high frequency propagation is characterized by the following undesirable features:

(1) Unreliability during ionospheric disturbances.

(2) Fairly rapid and deep fading.

The chief advantage of high frequencies is the relative simplicity of the

terminal equipment required for long-distance communications.

These defects in high-frequency propagation can be largely overcome by the use of low and very low frequencies (LF and VLF) . These waves,

reflected from the lower boundary of the D layer, are not affected by

ionospheric disturbances to the same degree as the HF waves, and are characterized by relatively slow fading rates. The chief disadvantages

are the limited usable bandwidths and the relatively large, and hence

expensive, transmitter installations which are required.

The VLF spectrum is nominally defined as 3 to 30 kc/s, but the

usable band is confined to the range 10 to 30 kc/s. This is largely due to the difficulty in building efficient transmitting antennas for such wavelengths (10 km<X<30 km). The propagation is characterized by rela- tively low path attenuation which is relatively stable with time. This

feature, coupled with the fact that VLF energy is guided for long dis- tances (5000 to 20,000 km) between the earth and ionosphere, makes the

VLF spectrum attractive for long-distance paths when high reliability

is important. In figure 7.10b we saw that the noise on VLF is very high

and, as a result, large transmitter powers are required. This fact, together

with narrow spectrum available, has resulted in most VLF systems having narrow bandwidths. In addition, the bandwidths of most VLF trans393
394 PROPAGATION OF LF AND VLF FREQUENCY WAVES

mitting antennas are of the order of 20 to 150 c/s and their radiation

efficiency is of the order of 10 to 20 percent only.

The low-frequency (LF) spectrum, 30 to 300 kc/s, is characterized

by higher path attenuation, lower background noise levels, and more

stable propagation time delays relative to VLF. As a result LF systems

are usually used for intermediate ranges (1000 to 5000 km). Terminal

equipment is usually cheaper than in the VLF case and, in addition, the

available bandwidths are greater.

Our primary concern is with the propagation, rather than with the

engineering uses, of low and very low frequencies. We shall first discuss some elementary theory and then consider the observational material.

9.2. THEORETICAL CONSIDERATIONS

9.2.1. Ray Theory

The concepts of geometrical ray theory break down in the case of

low and very low frequencies because the wavelengths are comparable

with the thickness of the D region. However, in some cases, geometrical

ray theory is useful for describing certain phenomena. For example, it is convenient to describe the diurnal change A<^ in phase as due to changes

in the height of a fictitious reflecting layer, the phase shift on reflection being assumed constant. For example, if h is the mean height of this

fictitious layer. Ah the diurnal change in height, 2d the distance between

transmitter and receiver, and X is the wavelength, then

where is in radians.

9.2.2. Waveguide Theory

9.2.2.1. Meaning of Mode

The propagation of VLF waves between the earth and the ionosphere, over large distances, can be likened to the propagation of micro- waves along a waveguide. The "mode theory", as it is called, has been
WAVEGUIDE THEORY 395 considered in detail by Budden [1]^ and Wait [2] and a few simple ideas

based on these works will be discussed here. Let us consider first the meaning of the term "mode." The Inter- national Dictionary of Physics and Mathematics (Van Nostrand) defines mode of propagation as follows: '^'A form of propagation of waves

that is characterized by a particular field pattern in a plane transverse

to the direction of propagation, which field pattern is independent of

position along the axis of the guide." In this section it shall be assumed that the transmitted waves are

vertically polarized, i.e., the electric vectors are vertical. Furthermore, we shall confine attention to /ong-distance propagation where a single

mode predominates (see reference [1], sec. 9.13).

9.2.2.2. Basic Concepts

In the simple model showTi in figure 9.1, the earth and ionosphere are represented by perfectly conducting planes. With respect to a cylindrical

coordinate system (p, 0, 2), the ground is the plane z=0 and the lower

PHASE FRONT

4h ' IMAGE ^

2h ' RAY DIRECTION IMAGE 5=^2h cos/3 IONOSPHERE z h

SOURCE GROUND 1 = 0

IMAGE

Figure 9.1. Ray geometry corresponding to the first mode between

parallel conducting planes.

1 Figures in brackets indicate the literature references on p. 441.
396 PROPAGATION OF LF AND VLF FREQUENCY WAVES

boundary of the ionosphere is the plane z=h, p is the radial coordinate

in a horizontal plane and </> is the azimuthal coordinate. Let the source be a vertical dipole located on the ground, at the origin. The electric

field observed at some other point on the ground is in the vertical direction. To an observer on the ground, the signal would appear to come

from the dipole plus a whole series of images in the ground and in the

ionosphere [2]. The images are located just below the ground and at

z = d=2/i, d=4/i, and so on, as shown in figure 9.1. Consider the wavelets emanating from the images in the ionosphere.

These will reinforce in a direction making an angle /? with the vertical

(see fig. 9.1) such that

where C=cosjS, which is a function of the integer n. Thus for a given

value of n

The ground images will add up at an angle (tt — /3) with the vertical. Thus, for a given value of there are two families of waves which have

the same horizontal component (c/Sn) but which have opposing vertical

components of velocity, where

We can imagine the resultant of these two sets of waves as a single wave

traveling parallel to the 2=0 plane with a phase velocity Vp = c/ Sw

Consider the wave directed broadside (ai = 0). We can imagine this wave to originate in a line source in which the effective uniform current

is la- Let s be the length of the transmitting dipole carrying a current /. Since images occur as pairs of dipoles all of the same strength (because

of the perfect reflectors), and since they are separated by distances of

2h we have

2h cos 13 = 2hC=n\, (9.2)

(9.4)

(9.5)

The field Es produced by such a line current is given by [3]

E, = y,o,IaW^{kp)=y,M-hW^^{kp), (9.6)
WAVEGUIDE THEORY 397

in which Hq^-^ (kp) is the Hankel function of the second kind with argu- ment kp, fjLQ is the permeability of free space, w is the angular frequency,

and k = 27r/\. At very great distances, i.e. when p»X, the Hankel function can be replaced by the first terms of its asymptotic expansion, giving

£:. =

^(^[y ^

(Xp)-^expi^exp i-ikp). (9.7)

Note that this field corresponds to the mode obtained by putting n = 0 in

(9.2). We shall call this, for convenience, the zero-order mode.

Next let us consider the mode produced by the pair of nth images

(that is, those located at distances of 2nh above and below ground).

Because of the obliquity of the rays the equivalent line current is / sin (3 ( = ISn). Also the electric field at a point in the plane of the diagram will be perpendicular to the radius vector from the point to the image so that

to obtain the vertical component of the electric field we must again multiply by Sn, so that, for the nth mode, the field is given by

£.„ = 2^ S^H„<«(tpS„). (9.8)

Note that the factor 2 arises because of the two sets of images. For the

zero-order mode we have only one set. The resultant field is obtained by

summing over all modes for integral values of n from 0 to qo . This gives

E. = ^

J2^nSJW^{kpSn), • (9.9)

wherero=l, rn = 2(n = l, 2, 3, •••)•

For the far field (p^X) this expression reduces to

£:. = ^Q^/5/i-HXp)-exp(^i^) ZrnSiexp (-ikpSn), (9.10)

• where Sn= (l-O* and Cn = n\/2h.

It has been assumed above that the earth and the ionosphere are perfect electrical conductors and that the reflection coefficients of the rays are always +1. In practice, for long-distance propagation the ionosphere behaves more like a perfect magnetic conductor with a reflection coefficient of —1, while the ground still has a reflection of +1. In this case the images are located at z = 2h, ±4/?, and so on, but now they al- ternate in sign. If we write down the resonance condition similar to (9.2)
398 PROPAGATION OF LF AND VLF FREQUENCY WAVES

we must include the reversal of sign of the image which is simply the same

as changing the phase by tt. Thus,

2hCn=(n-i)\, (9.11)

where ?i=+l, +2, etc. This shows that there is no zero-order mode

(n = 0) so that there is no coherent family of waves directed broadside. In this case the corresponding expression for the electric field Eg is

(9.12)

For great distances this reduces to

/s(Xp)-ift-i J2 Si exp i-kpSn). (9.13)

The E field patterns along the direction of propagation are shown in

figure 9.2 for the first- and second-order modes when the earth is a perfect

electrical conductor (/?= +1) and when the ionosphere can be regarded

PERFECT REFLECTOR

[-^GUIDE WAVELENGTH^

IONOSPHERE

R=-i

-^E

FIRST- ORDER (TMo,)MODE

P V

PERFECT REFLECTOR

^R = + 1 ^E — p SECOND-ORDER (TMo2)MODE

Figure 9.2. E field in an idealized earth-ionosphere waveguide.
WAVEGUIDE THEORY 399

as a perfect magnetic conductor (i?=— 1). Since we are dealing with waves polarized in the plane of incidence, the modes are transverse magnetic (TM). When the ionospheric reflection coefficient is —1, the mode

pattern can be obtained from the mode pattern of the same order for perfectly conducting boundaries by placing the ionosphere in the plane

of the first null in the vertical electric field below the upper perfectly

conducting boundary.

We have seen above that the phase velocity Vp in the z-direction is given by

v^=^- (9.14)

On

If we let \g be the wavelength in the z direction we have that

\ = (9.15)

On

where X is the free space wavelength. Combining (9.2) and (9.15) we

obtain

mmThis shows that, for \<2h/n, \g is imaginary and, hence, the mode is evanescent. There is a minimum cutoff frequency /„ below which waves

will not propagate where

The cutoff frequency for n=l is, therefore, /i = c/2/i and, taking

h = lS km for the height of the daytime D layer, we obtain /i?ir^2 kc/s.

For the case of a magnetically conducting ionosphere, (9.11) and

(9.15) give, for the cutoff frequency.

It will be seen that the change of R from +1 to — 1 will change the

cutoff frequency (for n=l) from 2 kc/s to 1 kc/s. To be consistent with

the mode-numbering system for perfectly conducting electrical walls.
400 PROPAGATION OF LF AND VLF FREQUENCY WAVES

the idealized earth -ionosphere modes should be denoted by ti — J rather

than hj n. j

9.2.2.3. Modifications for Imperfect Reflection

^ Equations (9.2) and (9.11) are based on the establishment of a standing wave pattern. This can be interpreted as the condition for a wave

to transverse the wave guide, thus suffering reflection at each boundary,

and suffer a net phase change of 27rn radians, thus permitting the twice

reflecting wave front to interfere constructively with the original wave

front. This condition can be written as R,{C)Ri{C) exp (-i2khC) =exp (-j27rn), (9.19)

in which Rg ( C) and Ri ( C) are the reflection coefficients of the ground and

ionosphere respectively for waves incident at an angle (3 where C=n\/2h.

Note that by putting Rg(C) =Ri{C) = 1 we obtain (9.2) and by putting

Ri{C) = — 1 we obtain (9.11). In the case where Rg and Ri are not unity

it is necessary to solve (9.19) for Cn for each mode and, hence, determine

Sn= (1— C^)^ for substitution in equations like (9.13). Now, in general,

Rg and i?i will be complex so that Cn and Sn will be complex. The wave

fields contain the term exp ( — ikpSn) so that when Sn is complex it implies attenuation (see also sec. 2.3.3.3). The absorption index (k) is given by the imaginary part of S„, the guide wavelength X„ is given by

X. = :iT-v ' (9-20)

Ke o„ and the phase velocity Vp is given by

where Im S„ and Re Sn represent the imaginary and real parts, respectively, of Sn- The numerical solution of the mode (9.19) is complicated when the

reflection coefficients of the earth and of the ionosphere depart from

unity, but some solutions have been given by Wait [4]. When signals are propagated over long distances it must mean that the attenuation

per unit distance is small and, thus, that the reflectivity of the boundaries

must be relatively high. Also the angles of incidence must be large (near
WAVEGUIDE THEORY 401

90°). Under these conditions approximate solutions may be obtained as

follows: The Fresnel reflection coefficient R is given by

where /jl is the refractive index of the reflecting medium. For yLF waves

in the ionosphere, oj<Kv, and thus [2]

2 M^^l-y=l (9.23)

Hence

iL-i)Cn-{GL'-iLy^

{L-i)Cn+{ClD-iLy- R^^Crd = )Ar. :rU ' (9-24)

Similarly for the ground

(XG-^)C„-|G^(K-l)-£G+C|GM* ,„ (KG-i)C„+lGHK-l)-iG+C„V!S '

where G = eoci;/o-, K= €e/eo, where ee and a are the permittivity and conductivity of the ground.

The value of L for very low frequencies is of the order of unity and,

for long distances, C„ is small so that (9.24) reduces to R.(Cn)^-l- '^^.^1. (9.26) Lvc

Note that at great distances it is sufficient to take the first-order mode

only.

When the ground conductivity is large, G<3C1 and (9.25) reduces to R,{Cn)^l- IG^CrT' exp [j (7r/4) ]. (9.27)

Now for low-order modes Cl<KL and, assuming that L is real, (9.19) can be solved, approximately, using (9.26) and (9.27), which gives

Re Sn=>S„+(2V27r[(/i/X)]^.)-T(Cn)^(L^-L-)+G^], (9.28)

Im Sn= - (2v27r[(/i/X)]^.)-^[( C„)2(L* +L-) +G^], (9.29)
402 PROPAGATION OF LF AND VLF FREQUENCY WAVES

where _ i Sn={l-Cn'r' and Cn = ^X. Zn These two equations, together with (9.13), determine (approximately) the phase velocities and rates of attenuation of the modes for the simple case of a flat earth and a flat sharply bounded ionosphere,

when the effect of the earth's magnetic field is neglected. It should be

noted also that finite ground conductivity always affects the phase velocity. The phase velocity is affected also by L except when L = l. The

rate of attenuation is a minimum when L = 1 and it increases with decreasing ground conductivity. It will be seen also that the higher order

modes are more highly attenuated than the first order. The above presentation is intended to illustrate the application of

waveguide theory to VLF ionospheric propagation rather than to develop a quantitatively correct theory. It is defective, as it stands, in two

major aspects:

(1) It neglects earth and ionosphere curvature.

(2) It neglects the earth's magnetic field.

9.2.2.4. Effect of Earth Curvature

The most important influence of the curvature of the earth is that

it prevents the angle of incidence at the ionosphere from becoming

grazing while it can become grazing at the surface of the earth. If the

radius of the earth is a, the height of reflection is h, and 0' and 0 are the

angles of incidence at the ionosphere and at the ground respectively we

have, from (4.9), that a sin 0= (a+h) sin 0'. (9.30)

Both the above effects tend to reduce the magnitude of the reflection

coefficients of the ionosphere and earth. On the other hand, antipodal

focusing (sec. 5.2.4.3) may modify the rate at which the signal amplitude

decreases with distance.

A detailed theory of the modifications introduced by the earth's curvature has been worked out elsewhere [3] and a modified mode equation has been derived namely:

RgiQKiiC) expj^-2i/c^ (^'"^^ S^J (^zj= exp (-i27r/i), (9.31)
WAVEGUIDE THEORY 403

FREQUENCY, kc/s

ol \ \ I \ \ \ \ I I \ \ \

I I I I l 2345 3456| H Figure 9.3. Attenuation factor as a function of height. The upper and right-hand scales are specifically for ^i=70 km, which is a typical daytime height {B=\L/h)

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial magnetic field on VLF

propagation, J. Geophys. Res. 65, 2325.)

where C = cos0, C' = cos</)', and z is height. Since {a-\-h) S' = aS, this reduces to the flat earth equivalent as h/a^O. Actually (9.31) is also an approximation and is strictly only valid if | {ka/2)^C

A higher degree of approximation has been used by Wait and Spies

[5]. Some numerical results of these authors, given in figure 9.3a and

9.3b, indicate that the curvature of the earth can increase the attenuation

by a factor of 3 above that calculated on the basis of a plane-earthplaneionosphere model. Some curves showing the attenuation rate as a function of frequency are given in figure 9.4. The effect of earth curvature on the phase velocity is of interest in that the velocity is reduced to less than c in most cases of interest as shown

in figure 9.5. It will be seen that the effect of the curvature is greatest on the lowest order mode. This is to be expected since the higher order

modes involve rays which are less grazing, and the differences between

the angles of incidence for the flat- and curved-earth cases becomes

smaller as the mode order increases. Another effect of earth-ionosphere curvature is the efficiency with

which a given mode can be launched into the waveguide (see page 221

of reference 2) . For ionosphere heights of the order of 70 km and for fre-
404 PROPAGATION OF LF AND VLF FREQUENCY WAVES

8 12 16 20 24 28 8 12 16 20 24 28 FREQUENCY, kc/s Figure 9.4. Attenuation rate as a function of frequency.

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial magnetic field on VLF

propagation, J. Geophys. Res. 65, 2325.)

quencies less than 16 kc/s, there is Httle difference but, for higher fre- quencies or greater heights, the excitation of the first mode becomes rela- tively weak. However, in a few cases the excitation factor may be greater

than unity, particularly for the higher order modes.

9.2.2.5. Effect of the Earth's Magnetic Field

The chief effect of the earth's magnetic field is to make the ionosphere an anisotropic medium (see ch. 2). A wave polarized in the plane of

incidence (E vector in the vertical plane) gives rise to two reflected waves and two transmitted waves. One of each of these is polarized in the plane

of incidence, while the others are polarized normal to this plane (i.e..
WAVEGUIDE THEORY 405

8 12 16 20 24 28 8 12 16 20 24 28 FREQUENCY, kc/S Figure 9.5. Phase velocity for a perfectly conducting earth and an imperfectly reflecting ionosphere.

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial magnetic field on VLF

propagation, J. Geophys. Res. 65, 2325.)

horizontally) . Thus, a vertically polarized wave incident on the ionosphere

gives rise to a horizontally polarized component which, after a ground

reflection and another ionospheric reflection, gives rise to further vertically

and horizontally polarized waves. This results in polarized modes which

are "coupled." However, the degree of coupling is usually small and will be ignored in this book. In principle, the ray properties of VLF signals in the ionosphere can

be determined from the complex refractive index (2.76). It is much

more convenient, however, to use the quasi-longitudinal and quasi- transverse approximations (sec. 2.3.3.2), retaining the colhsion term. In order to take into account the double refraction in the ionosphere,

it is convenient to use the two reflection coefficients \\R\\ and xR± to- gether with two conversion coefficients \\R.l and j.R\\. The first subscript

denotes whether the electric field of the incident wave is parallel (| |)
406 PROPAGATION OF LF AND VLF FREQUENCY WAVES

to or perpendicular (_L) to the plane of incidence and the second subscript

refers to the same characteristic in the reflected wave. For details of the calculations of these reflection coefficients the

interested reader can start with chapter IX of reference [2] and follow

up the references given therein. It will be sufficient for our present purpose

to note how the attenuation and phase velocity is affected by the inclusion of the earth's magnetic field. Some results for the first-order mode are shown in figures 9.6 and 9.7 for attenuation and phase velocity respectively for a real angle of incidence of 82°, for various dip angles /, and

with different directions of propagation 0a (measured clockwise from the

north) . The attenuation results are presented in terms of the ratio [2]

P= Attenuation with magnetic field Attenuation without magnetic field

Figure 9.6. Ratios of attenuation {with and without the magnetic field) as a function of azimuth.

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial n:iagnetic field on VLF propagation, J. Geophys. Res.

65, 2325.)
WAVEGUIDE THEORY 407 and, in figure 9.6, P is plotted for various dip angles and frequencies of

10 kc/s and 22 kc/s. In all these curves the electron density N is 10^ per

cm^, f = 2Xl07sec-\ and the strength of the earth's field is 0.5 G.

When the azimuth 0^ is 0° (propagation towards the north) or 180°

(to the south) the magnetic field has little effect on the attenuation. For

east-west and west-east propagation P departs significantly from unity.

The effect becomes less noticeable as / approaches 90°. The effect of the

magnetic field on the phase velocities of VLF waves is relatively small. One feature, which is evident in both figures 9.6 and 9.7, is the nonreciprocity in P, and in velocity, for <f>a = 90° and 270°. The difference

in P has been observed experimentally [6, 7] and the physical explanation involves the action of the transverse field component on the motion

of the ionospheric electrons in the plane of incidence [6, 8]. These electron motions should not be confused with those giving rise to the ordinary

Figure 9.6b. Ratios of attenuation (with and without the magnetic field) as a function of azimuth.

(After J. R. Wait and K. Spies, 19G0, Influence of earth curvature and terrestrial magnetic field on VLF propagation, J. Geophys. Res.

65, 2325.)
408 PROPAGATION OF LF AND VLF FREQUENCY WAVES

Figure 9.7a. Differences between phase velocities (with and

without the magnetic field).

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial magnetic field on VLF propagation, J. Geophys. Res.

65, 2325.)

and extraordinary waves which are in the plane transverse to the direction

of propagation. It is important to notice that the results shown in figure 9.7 refer to a particular model and the results may be entirely different

with a different model.

9.2.2.6. Modes and Rays on Very Low Frequencies

The question frequently arises as to (a) the relationship between

mode and ray (or geometrical-optical) theories, and, sometimes, (b)
WAVEGUIDE THEORY 409

N = (IO)^ 1 = 84.3°

Figure 9.7b. Differences between phase velocities {with

and without the magnetic field).

(After J. R. Wait and K. Spies, 1960, Influence of earth curvature and terrestrial magnetic field on VLF propagation, J. Geophys. Res.

65, 2325.)

whether one is more correct than the other.

It has been shown [9] that for the case of propagation between perfectly reflecting parallel planes, the series expansions based on ray and

mode theory are related by a Fourier cosine transform. This suggests that,

provided all modes and aU rays are taken into account with appropriate

corrections for losses, the results from both methods will be the same as has been demonstrated [10]. In fact the derivation of the mode formula

given earlier is based on the ray approach. It is not uncommon, however,

for a ray model of VLF propagation to be used which considers just one

ray, reflected several times between earth and ionosphere, from the trans-
410 PROPAGATION OF LF AND VLF FREQUENCY WAVES

mitter to the receiver. A single ray model is satisfactory only at short

distances.

The appropriate question to ask, then, is which method of calcula- tion is simplest. On VLF, the wavelength and height of the ionosphere

are such that only a few modes are important since the higher-order

modes are attenuated at a much greater rate than that of the lowest mode.

At great distances only one mode need be considered. In this case, however, many rays have to be considered. On the other hand, at short dis- tances all propagating modes are comparable in amplitude and must be

considered. Only a few rays need to be considered, however, since the

higher-order rays are incident at smaller angles of incidence where the

reflection coefficient is decreasing rapidly.

On higher frequencies (in the LF band) and at long distances many

modes may be important, and the attenuation coefficients of many of the

less attenuated modes may be comparable. Thus there is less advantage

in using mode theory. Wait 1^10] has given an account of ray theory for use at LF which takes account of the curvature of the earth, showing

how the rays which are identifiable inside the horizon behave as the hori- zon is passed.

9.2.2.7. Effect of Ionospheric Stratification

It has been assumed that the ionosphere is a sharply bounded, semiinfinite medium. This is only a first approximation because what little evidence we have suggests that the D layer is not sharply bounded. It has

been found [2, 3, 11, 12] that a two-layered model is necessary to explain

the observed attenuation rate in the frequency range from 500 c/s to 1.5 kc/s. For frequencies in the range 8 kc/s to about 20 kc/s, however, the

sharply bounded model is convenient for a simple description of what

must be a complicated reflection process. Extensive justifications for the

idealized model have been given recently by Wait and Walters^ in a

series of four papers dealing with the reflection of VLF waves from in- homogeneous ionospheric models.

2 Wait, J. R.i and L. C. Walters (1963), Reflection of VLF radio waves from an inhomogeneous ionosphere, Parts I, II, III, and IV, J. Res. NBS 67D, and (1964) Radio Science.
IONOSPHERIC COUPLING ON LOW FREQUENCIES 411

9.2.3. Ionospheric Coupling on Low Frequencies

In our discussion of the propagation of waves in a magneto-ionic

medium (ch. 2) we assumed that the ordinary and extraordinary waves

are propagated independently. Wliile this is substantially true on high

frequencies, it is not so on low frequencies. Experimental studies have

shown that the echo structure of low-frequency pulses is more complicated

than that on high frequencies. One of the most interesting effects is known

as coupling [13], which has been studied extensively at the Pennsylvania

State University on a frequency of 150 kc/s at night.

Coupling may be thought of as arising in the following way. In the

case of long waves, propagation in an inhomogeneous medium must be

considered. It is no longer possible to consider a purely progressive wave,

because each point in the medium gives rise to a forward and a backward

wave, and these two waves must be taken into account in describing the

propagation. Furthermore, the component magneto-ionic waves no longer

propagate independently; hence coupling occurs not only between

magneto-ionic components but also between the progressive wave of one component and the backward wave of the other. For a detailed description

of the propagation, a full wave theory is required. It has been shown [13]

that when the level X= 1 occurs near the level where v = Vc = o)b. sin^ 6 /cos 6, strong coupling can occur. This level depends on the strength and di- rection of the magnetic field and on the collision frequency profile v(h).

The sketch in figure 9.8 indicates, schematically, the reflection processes

for long waves, including the possibility of coupling. Above the base of

the ionosphere (where X= 0), the two circularly polarized ordinary and

extraordinary waves travel independently with different speeds. Near the

level where coupling can occur, the upgoing extraordinary wave gives

rise to a backscattered ordinary wave and to a progressive ordinary wave in addition to the progressive extraordinary wave. This progressive

extraordinary wave is known as the "whistler mode." Similarly the upgoing o wave gives rise to a backwards x wave. These backward-moving

waves combine to produce a downcoming coupling echo. The polarization

of the coupling echo should be fairly constant, since the backscattering o and X waves should be in proportion. This is, in fact, observed. The

polarization of the coupling echo is roughly constant and the same as

» This section is taken verbatim from a lecture by Dr. J. S. Belrose.
412 PROPAGATION OF LF AND VLF FREQUENCY WAVES

X

X = l +Y

x = i —

\

coupling" ECHO 0^_^X

main" echo Figure 9.8. Sketch to illustrate the mechanism of reflection of LFwavesfrom the ionosphere.

that transmitted. However the amphtude would depend markedly on how

closely the X=l level approaches the :' = Vc level. A second effect of coupling is concerned with the polarization of

the main echo. The upgoing x wave, in the region of coupling, gives rise to a forward-scattered o wave, which combines with the forward progressive o wave, and proceeds to the level X= 1+ Y, where it is reflected. Now, when this downcoming o wave reaches the coupling level, it generates a forward -scattered x wave which, when combined with the

progressive o wave below this level, alters its polarization. In fact the

resulting polarization ellipse, in the presence of strong coupling, may have

its major axis outside the magnetic north-east south-west quadrants, that

is, in a direction "forbidden" by simple magneto-ionic theory.

If the bottom of the ionosphere is "rippled" and these ripples pass over the level where v = Vc so as to change the X=l level from below to above the "critical coupling" level, we would expect that the polarization

could change rapidly [14]. This phenomenon has been observed by the

Pennsylvania State University workers, who have called it "flip-overs,"

i.e., the polarization of the "main echo" can change from right-handed

to left-handed depending on whether v< or >Vc at the level where X= 1, and in the case of "critical" coupling the polarization of the downcoming wave may be in the pair of "forbidden" quadrants mentioned in the

previous paragraph.

(After J. S. Belrose, 1964, unpublished.)
VLF SIGNALS ASSOCIATED WITH THE EXOSPHERE 413 "Coupling" effects, where studied, namely at Pennsylvania State

University, are strongest on frequencies near 150 kc/s at night. No daytime coupling effects have been observed, but if they were, the effect should be strongest for waves of frequency between 300 and 500 kc/s.

9.3. SOURCES OF VERY LOW FREQUENCY SIGNALS

9.3.1. Atmospherics

The majority of the energy in the VLF band comes from radiation

due to lightning discharges (see sec. 7.2.2.2), which are called atmospherics. A typical discharge radiates about 5X10"* joules [15, 16]. A large

part of this energy is radiated in the VLF band, with peaks near 10

kc/s. The transmitted waves are mostly vertically polarized and the

field strengths produced by these discharges can be as great as several volts/meter at short distances. The energy level, at the receiver, is generally greatest between sunset and midnight and tapers off to a broad

minimum after sunrise.

9.3.2. Manmade Signals

These generally originate in transmitters with Morse code or pulsed

CW carriers, and are spread through the range from 10 to 25 kc/s. Radiated powers vary from a few kilowatts to more than a megawatt, and

the signals are vertically polarized.

Another type of manmade radiation comes from nuclear explosions

in the atmosphere.

9.3.3. VLF Signals Associated with the Exosphere

These signals are generated within or are propagated along paths

in the outer atmosphere. The length of such a path may amount to 30,000

or 50,000 km. Whistlers [17] are generated in Hghtning discharges and

are guided along the earth's magnetic field to conjugate points. VLF

emissions, chorus, hiss, etc., are believed to originate in the exosphere.
414 PROPAGATION OF LF AND VLF FREQUENCY WAVES

9.4. PHASE VARIATIONS ON VERY LOW FREQUENCIES

9.4.1. Method of Observing Phase Changes

This is, essentially, described in section 3.2.3.1. For short distances,

up to about 200 km, the groundwave provides a suitable reference signal

because it can be separated from the skywave signal [19]. For longer dis- tances, the reference signal has to be transmitted by some other means,

e.g. telephone line [20]. Both the above methods have the advantage that

the actual frequency transmitted need not be very stable. This is not the

case when a local reference oscillator is used. The latter is required for distances greater than about 200 km because of the difficulty of separating

the groundwave from the skywave.

9.4.2. Regular Diurnal Changes Over Short Distances

It was pointed out above that an incident wave, polarized in the

plane of incidence, will, after reflection, be elliptically polarized. This

reflected wave can, therefore, be resolved into two components:

(a) the normal component, polarized in the plane of incidence;

(b) the abnormal component, with its electric vector horizontal.

The abnormal component can be observed by the use of a loop an- tenna set with its plane perpendicular to the plane of propagation. The

normal component can be observed by means of a loop in the plane of

propagation. In the latter case, the groundwave signal induced in the

loop has to be cancelled by means of a signal received on a vertical whip

antenna [21, 22]. In studies of the diurnal variations of phase, it has been found con- venient to describe them in terms of changes Ah of height h of a fictitious mirror reflector. If the ground distance is 2c? and the wavelength is X, then

A/. = A0^^, (9.32)

ZTT An where A0 is the diurnal phase change in radians.

The diurnal variation in the phase of WWVL (on 20 kc/s) over a 113

km path near Boulder, Colo., is shown in figure 9.9. The phase curves are dish -shaped with the deepest depression centered near local noon. The
REGULAR DIURNAL CHANGES OVER SHORT DISTANCES 415

(After C. J. Chilton, D. D. Crombie, and A. G. Jean, 1963, Phase variations in VLF propagation, AGARDograph 74, 257, Pergamon Press.)
416 PROPAGATION OF LF AND VLF FREQUENCY WAVES

diurnal phase shifts in May 1961 were approximately 720°, corresponding

to a height change of about 18 km. This result agrees well with similar observations in England [19] over a 90 km path. There, on 16 kc/s, phase

changes varying from 430° in November to 600° in June were observed,

which correspond to height changes of 13 km and 18 km respectively.

The English results showed also that the effective height of reflection h{x) varied in a Chapman-like manner (see (1.29)), namely:

h{x)=Ho+H sec X. (9.33)

provided that x <85°. Here ho is the effective height if the sun were over- head, and H is the scale height of the atmosphere (sec. 1.2) at the height

of reflection. It was found that the mean value of ho was about 69 km and

that the values of H varied from 4 km in June and January to about 7 km

in October and April with a mean value of around 5.5 km.

Observations of the abnormal component over a distance of 540

km [23] showed that the diurnal change starts about 1 hr before ground

sunrise at the path midpoint, whereas at 90 km the change commences

about 10 min after ground sunrise. Over this distance (540 km), the phase

change reaches a maximum value near ground sunrise and then decreases

for about 2 hr thereafter. This phase reversal, together with a much

smaller one occurring during the main phase change (neither being observed over 90 km), are thought to be due to reflections from different

D layers [24]. It is possible, however, that these effects may be due to

interference between multiple rays or modes.

9.4.3. Regular Diurnal Changes Over Long Distances

In these experiments, it is necessary to use a local reference oscillator and allowance must be made for oscillator drift. When this is done, it is found that, on an east -west path, the diurnal variation of phase commences some half hour before sunrise at the eastern terminus and continues smoothly until just before sunrise at the western terminus [25].

The relative phase then remains constant until about a half hour after sunset at the eastern terminus when a smooth transition of nighttime

conditions sets in. This trapezoidal diurnal variation is illustrated in figure 9.10. It must be remembered that this trapezoidal representation

is highly idealized and, in practice, the diurnal pattern undergoes considerable variation from day to day and from season to season. Observations of the phase of the GBR (Rugby, England) signal in New Zealand [26] can be explained in terms of the times at which the
REGULAR DIURNAL CHANGES OVER LONG DISTANCES 417

1500 18 20 2 2 00 0 2 04 06 08 10 12 1500 1500 18 20 22 00 02 04 06 08 10 12 1500 HOURS (UT) Figure 9.10. Diurnal variation of phase of the GBR (Rugby, England, 16 kc/s) signal

received in Boulder, Colo. {7400 km).

(After C. J. Chilton, F. K. Steele, and R. B. Norton, 1963, Very-low-trequency phase observations of solar flare ionization in the D region of the ionosphere, J. Geophys. Res. 68, 5421.)

sunrise or sunset line crossed the nearly north-south path, and the angle

between these lines and the path. It is necessary to assume that the height

changes suddenly from its daytime to its nighttime value at the time of sunset and vice versa at sunrise. The magnitude of the phase change can be explained in terms of a waveguide mode theory provided that the

ionosphere is treated as a magnetic conductor [27]. To a first approximation, it has been shown [27] that the phase velocity Vp in a curved earthionosphere waveguido i^iven by

-i-mr'(-=)-

so that for the first -order mode (n = 1) we have

(9.34)
418 PROPAGATION OF LF AND VLF FREQUENCY WAVES

( 1 |-r~r:+ smaller terms

\ a 32n^

If the height h changes by an amount Ah, the corresponding phase

change A0 is given by

(9.35)

in which d is the great circle distance of the receiver from the transmitter

and h is the mean height of reflection. Using this equation it has been

shown [27] that the diurnal height change (day to night) is about 16

km. Curves showing the phase velocity as a function of reflection height

and wave frequency have been shown in figure 9.5. As a particular path

is crossed by a day/night boundary, the relative phase seen at the receiver

will depend on the relative amounts of the path which are in daylight and

in darkness at the instant concerned. If do and dn are the distances in daylight and darkness, and (3o and are the respective phase changes

per unit length, the total phase lag <f>t between transmitter and receiver

is given by

4>t = dol3Q-}-dnl3n = do{^0-^n) +^nd. (9.36)

For an east-west path this gives the trapezoidal variation noted above

while for a north -south path they may tend to pass quickly from daylight

to night giving a rectangular variation as illustrated in figure 9.11.

9.4.4. Influence of Geographical Location

The diurnal curves shown in figures 9.10 and 9.11 show up the effect on the phase of paths in high latitudes. The GBR-Boulder path lies in much higher latitudes than the NBA (Panama) -Boulder path. If one

considers ground sunset and sunrise, the GBR-Boulder path becomes completely dark during June, but this is not reflected in the June curve. If we consider, however, sunset and sunrise at the level of the D region,

then we see that the path never really becomes dark and, thus, we should not expect the full diurnal variation to develop. Examination of the

diurnal phase changes during the months for which the path does become

completely dark suggests that there is a seasonal change in the diurnal

phase shift. In December and January, the mean phase change is 210°

while in March it is 260°.
INFLUENCE OF GEOGRAPHICAL LOCATION 419

OCT 21 DAYS FEB 8 DAYS

PANAMA - BOULDER

MONTHLY - AVERAGES

18 kc/s 4258 km

MAY 6 DAYS JULY --I3 DAYS

1800 1800 20 22 24 02 04 06 HOURS UT1800

Figure 9.11. Diurnal variation in the phase of NBS (Panama, 18 kc/s) signals as

received in Boulder, Colo.

(After C. J. Chilton, F. K. Steele, and R. B. Norton, 1963, Very-low-frequency phase observations of solar flare ionization in the D region of the ionosphere, J. Geophys. Res. 68, 5421.)

Some observations of the relative phase of GBR as measured in Point Barrow, Alaska (6000 km) are shown in figure 9.12. This is a very

northerly path and, ignoring the effect of flares, etc., it is seen that the

diurnal phase shift (;^30°) is small. When allowance is made for the fact that two-thirds of the path is illuminated, the observed phase change

represents an effective height change of 13 km for that portion of the

path which changes from daylight to dark.

It is useful to note at this point that a phase change A0 is sometimes

measured in terms of a time delay At by the formula

0}

It should be remembered that At is not the change in transmission time

since the latter usually refers to group propagation time (see sec. 2.4.2).
420 PROPAGATION OF LF AND VLF FREQUENCY WAVES

Figure 9.12. Relative phase of GBR (Rugby, England, 16 kc/s) signals at Point Barrow,

Alaska.

(After C. J. Chilton, D. D. Crombie, and A. G. Jean, 1963, Phase variations in VLF propagation, AGARDograph 74, 257, Pergamon Press.) 9.4.5. Determination of Phase Velocity

The measurements, over long distances, of the diurnal variation of

phase do not permit a determination of the actual phase velocity.* The

latter requires the determination of the absolute phase change of a signal as it travels between points separated by a known distance. This in turn

requires an independent link between the two points having a known

phase shift. Wait [28] has examined such experimental results and finds that the

data fit waveguide theory if the reflection height is taken to be 70 km

during the day and 90 km at night. Even better agreement is obtained

when allowance is made for the finite conductivity of the ionosphere.

These data, as given by Wait, show that on 10 kc/s the phase velocity is approximately equal to the free space velocity c during the night, while

* See Steele, F. K., and C. J. Chilton (1964), The measurement of the phase velocity of VLF propagation in the earth-ionosphere waveguide, Radio Sci. J. Res. NBS/USNC-URSI 68D, 1269.
EFFECTS OF MAGNETIC DISTURBANCE 421 during the day it is approximately 0.3 percent higher than c. On 14 kc/s,

the phase velocity is approximately equal to c during the day and about

0.2 percent smaller at night. On 16 kc/s the phase velocity is approximately 0.3 percent and 0.1 percent less than c by night and by day re- spectively.

9.4.6. Effects of Meteors

Effects attributed to meteors have been observed both on VLF [29]

and on LF [30]. On VLF the effect is observed on the GBR-Boulder path

as a delay in the onset of the sunrise advance of phase until the meteor

shower has passed or until the entire path has become sunlit, at which

time the phase returns to the normal daytime value. On low frequencies

the diurnal phase curve is also unsymmetrical during meteor showers.

9.4.7. Effects of Solar Flares

In section 6.2.2, we mentioned the effect on VLF waves of a solar

flare. These sudden phase anomalies build up rapidly (1 to 5 min) and

recover slowly (30 min to 3 hr). The magnitude of the phase shift is related to the increase in the flux of the solar radiation, its angle of in- cidence at the ionosphere and to the length of the circuit over which a lowering of the apparent reflection height occurs. Phase shifts of 30° to 60° are common for flares of importance 2. Certain large flares which produce polar cap absorption events (sec. 6.1) produce also unusually large phase changes. A phase advance of 240°

occurred on the GBR-Boulder circuit on May 4, 1960. Such events are, however, relatively rare; about 10 were observed during 1960, for ex- ample. The larger sudden phase anomalies indicate changes in effective height of the order of 18 km whereas more moderate height changes are

7 km or less. There is no simple relationship between the optical importance of flares and their ionizing effects in the ionosphere.

9.4.8. Effects of Magnetic Disturbance

9.4.8.1. Sudden Commencements

Phase advances have been observed during magnetic sudden com- mencements on paths which traverse a certain range of geomagnetic
422 PROPAGATION OF LF AND VLF FREQUENCY WAVES

o

Figure 9.13. Effect of magnetic disturbance on the phase of GBR received at Boulder, Colo.

(After C. J. Chilton, D. D. Crombie, and A. G. Jean, 1963, Phase variations in VLF propagation, AGARDograph 74, 257, Pergamon Press.)

SR SS

12 06 24 18 12 UT

Figure 9.14. Observations of the phase height of 16 kc/s waves observed at Cambridge

during an ionospheric storm. May 15 is a normal day; May lG-17, the primary storm effects; May 19-20, the aftereffect. The dashed

curve represents the expected variation in the absence of a disturbance. (After J. S. Belrose, The oblique

reflection of low-frequency waves from the ionosphere, AGARDograph 74, 151, Pergamon Press.)
REFLECTION COEFFICIENTS 423

latitudes in the vicinity of 65° north. Such a phase advance is shown in figure 9.13.

9.4.8.2. Magnetic Storm Effects

The great fluctuations in the phase of GBR (fig. 9.13) on October

29, 1961 are typical of the VLF effects which accompany a severe magnetic storm. The effects on VLF waves are predominantly night effects and consist of rapid and deep fading during the main phase of the storm

(primary effect) . The phase of 16 kc/s with steep incidence is particularly

susceptible to storms. This is shown in figure 9.14 for a transmission dis- tance of 90 km. The dotted line indicates the mean diurnal variation of

phase for the month. The storm began about 0400 UT on May 16 and

was, essentially, over by about midday on May 17. Reference to the

figure shows that a disturbance effect was, by and large, not detected

until the night of May 16-17; even though the magnetic field was greatly

disturbed during the day of May 16, no marked effect was observed

until near sunset. Large and rapid variations of phase occurred during the

night of May 16-17. These phenomena constitute the primary storm

effect. The phase returned to near normal on May 17-18 but, beginning on May 19, the diurnal phase pattern took a form very different from

normal. After this day, a gradual recovery set in over three days.

9.5. AMPLITUDE VARIATIONS ON VERY LOW FREQUENCIES

9.5.1. Reflection CoefFlcients

Experimental determinations of the reflection and conversion coefficients (i|i?ii and ||i?j.) have been made in England [19, 21, 22, 23].

The measurements were obtained on a pair of crossed vertical loops in and perpendicular to the plane of incidence. The first loop responds to the sum of the groundwave signal and the component of the electric field parallel to the plane of incidence while the second loop responds to the

horizontal (abnormal) component. On the assumption that the ground- wave is constant, its amplitude and phase can be determined from a

sufficient number of observations. The numerical results are summarized

in table 9.1. These measurements suggest considerable variability of

reflection coefficient with season and with angle of incidence, in addition

to the diurnal variation.
424 PROPAGATION OF LF AND VLF FREQUENCY WAVES

Table 9.1. Measurements of reflection coefficient (16 kc/s)

Ionospheric Observers incidence Refl. Coeff. Season and time

angle type mag

Best et al. [21] Best et al. Budden et al. [22] Budden et al. Bain et al. [23] Bain et al. Straker. [19] Straker.

Straker.

Straker.

(deg) 30

30 36-60

36-60

75

70 30-45

30-45

30-45

30-45

II ^11

II i? J. 11-^11 \\R\\ ||i?X l\Rx

\\Rx

0.25

0.50

0.12

0 Oft 0.27

0.55

0.13 0.26

0.56

0.37

Summer day

Winter night

Autumn day

Autumn day

Summer day

Summer night

Summer day

Winter day

Summer night

Winter night

AUGUST 29-30, 1963 16 kc/S

-1111 1 1 1 1 1 1 1 1 1 1 -

: 1

GBR- f :\

'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -

16 18 20 22 00 02 04 06 08 10 12 14 UT

•JANUARY 2, 1962 19.8 kc/S

1 TIT \ \ \ \ \ \ \

\ TTl \ I \ [1 r

1 1 1

1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 I 1

1111

(b)

1

1 1 1 1 1 1 1 1 1 1 18 16 14 12 10 08 06 04 02 GO 22 HOURS UT Figure 9.15. Diurnal variation of the amplitudes and phases of VLF signals.

(a) Short distances: Rugby, GBR-Frankfurt (840 km). (After A. G.

Jean, unpublished.) (b) Long distances: Hawaii, NPM-Boulder (5374 km). (After D. D. Crombie, unpublished.)
ATTENUATION RATE 425 9.5.2. Amplitude

The resultant amplitude of a VLF signal propagated over short dis- tances is highly variable due to interference between the various components and particularly between the ground wave and the once re- flected signal. For a given distance, the amplitude is very sensitive to the

magnitude and phase of the reflection coefficients, and to the height of

reflection. This sensitivity is seen in the diurnal variation where the night-today ratios are around 6 dB in CW signal strength and as much as 20

dB in the level of broadband sferics. In addition, rapid changes of amplitude occur near sunrise and sunset along the path. The amplitude

usually goes rapidly through a minimum or maximum before reaching

its steady daytime or nighttime level—see figure 9.15. Changes in the usual pattern of the field behavior are introduced by

such factors as a land-sea boundary or changes in ground characteristics. At these boundaries standing wave patterns are set up which modify the

field distribution over distances of several wavelengths.

9.5.3. Attenuation Rate

The variation with distance of the vertical field E of the far field in a waveguide mode is given [31], approximately, by

E=^[-^V|-P (9-38) n La sm a/aj

P is the radiated power (kilowatts), a is the attenuation rate, and the

other symbols have their usual meanings. Expressing (9.38) in decibels we have [31]

20 log E+10 log sin (d/a) =a constant - a </, (9.39)

where a is in decibels per unit distance (usually 1000 km) and all the

other factors are lumped together in the constant. If, therefore, the left hand side of (9.39) is plotted against d the slope of the resulting straight

line will give the value of a. Observations on signals from VLF stations have been made by

Heritage et al. [32] on frequencies of 16.6 kc/s and 18.6 kc/s. An example

is shown in figure 9.16. These data give an attenuation rate of 3.0 dB per thousand kilometers.
426 PROPAGATION OF LF AND VLF FREQUENCY WAVES

d i n M m

Figure 9.16. Experimental data showing attenuation rate over the Pacific.

(After J. L. Heritage, S. Weisbrod, and J. E. Bickel, 1947, A study of signal versus distance data at VLF, VLF Symposium Record 4, 77.)

The value of a over the North Atlantic averages around 3 dB per

1000 km on frequencies near 20 kc/s. The night values are consistently

lower than the day values. A typical land path increases the attenuation

rate by about 3 dB per 1000 km compared to that over sea water. Paths

over the Arabian Sea and the Indian Ocean show rates of about 2 dB

per 1000 km at great distances. The result of daytime measurements

[32] in the Pacific give average rates as 1.7 dB per 1000 km.

Observations on sferics by Taylor show that the best conditions for a signal of frequency between 15 and 20 kc/s occur for west-to-east propagation (sec. 9.2.2.5) over sea at night. The rate under these conditions

is a minimum and is about 1.0 dB per 100 km. The maximum attenuation

for this frequency range occurs for a land path from east to west during

dayhght and is about 3.5 to 4.0 dB per 1000 km.

In general, propagation in the 15 to 20 kc/s frequency range over land adds about 1.0 to 1.5 dB per 1000 km to the sea water value. Daytime propagation adds about 1.0 dB per 1000 km to the nighttime value. The nonreciprocity causes about 1.0 dB per 1000 km more attenuation

for east-west propagation as compared with west-east propagation. There

is some evidence which indicates that attenuation is higher in the auroral zone and over large expanses of ice such as Greenland (A. G. Jean, private

communication)

.
NORIMAL BEHAVIOR OYER LONG DISTANCES 427 9.5.4. Polarization

Over short distances (100 to 300 km) the skywave is essentially

circularly polarized, that is, the ratio wRi'-nRn is approximately unity

wdth a 90° phase shift. At longer distances f500 to 800 km), the polarization is approximately linear ^^'ith \\R\\ being much larger than For

distances over 1000 km. it appears that the polarization is essentially

vertical during the daytime and that this changes to an elongated ellipse

(10:1 axis ratio) at night. The polarization is highly variable during

disturbed conditions for short and medium distances. Little is kno\vTi, in general, about polarization for long distances.

9.6. PHASE VARIATIONS ON LOW FREQUENCIES

9.6.1. Normal Behavior Over Short Distances

Experimental data obtained by Belrose [33] indicates that the

heights of reflections of waves, in the frequency range 70 kc s to 245 kc s, are roughly the same as those of VLF waves. For transmission distances

of the order of 1000 km the heights of reflection change from about 90

km by night to about 72 km by day as sketched in figure 9.17. It will be

seen also that the reflecting layer is closely controlled by the sun. When

these frequencies are transmitted over shorter distances (less than about

300 km) they appear to be reflected at somewhat higher heights, namely

80 to 85 km by day and 90 to 100 km by night.

9.6.2. Normal Behavior Over Long Distances

When LF waves are propagated over distances of 2000 km and

greater, the diurnal variation of phase is quite different from that for distances of around 1000 km and less. This is seen in figure 9.18, where

the trapezoidal shape of the curve is emphasized by the dashed line. The

fact that the phase changes during dayhght are independent of solar zenith angle x has led to the suggestion that the height of reflection (zero

phase) is less than 70 km (probably around 65 km) . Note that the phase

of LF signals appears to be highly variable at night over most paths. It

is important to remember that the deductions about the height of re- flection are made on the assumption that the one-hop signal predominates
428 PROPAGATION OF LF AND VLF FREQUENCY WAVES

90-|

-KALUNDBORG ALTERNATIVE

{BY SHIFTING BY 2 TT )SS

06 09 12 15 18 GMT Figure 9.17. Diurnal variation of the height of reflection of low-frequency waves, February 1955.

(After J. S. Belrose, unpublished.)

at all times. Some doubt has been cast on this assumption by pulse observation on 100 kc/s p4].

9.6.3. Effects of Solar Flares

The effects on LF observed during an SID are similar to those on VLF (sec. 9.4.7), In fact, it is found that the lowering of the apparent
NORMAL BEHAVIOR OVER SHORT DISTANCES 429

0.5-1 1 1 ] 1 \ \ 1 1 1 1 1 1

16 18 20 22 00 02 04 06 08 10 12 14 16 UT

BOULDER- OTTAWA 60 Kc/s AT 2460 km

DEC. I 4- DEC. 2, 1959 Figure 9.18. The diurnal phase variation, on December 1-2, 1959, of 60 kc/s waves

received at Ottawa from Boulder (2400 km).

(After J. S. Belrose, 1963, The oblique reflection of low-frequency radio waves from the ionosphere, AGARDograph 74, Pergamon Press.)

height is much the same for all waves in these bands for both long and

short [35] distances. Large flares (of importance 3) may drop the ap- parent reflection height to 60 km, but no reflections have yet been observed from lower heights.

9.6.4. Polar Cap Disturbances

These disturbances are associated with certain large solar flares and

occur primarily in geomagnetic latitudes greater than about 60°. Along

with polar cap absorption (sec. 6.4.), LF propagation disturbances occur. The latter may last from 5 to 15 days during which the phase height is less than normal, principally at night.

9.7. AMPLITUDE VARIATIONS ON LOW FREQUENCIES

9.7.1. Normal Behavior Over Short Distances

The morning variation of amplitude is illustrated in figure 9.19. It

is characterized by successive maxima and minima. It has been shown
430 PROPAGATION OF LF AND VLF FREQUENCY WAVES

PURPLE

71 Kc/s 860km

BLACK yi 85.4 Kc/s 799 Km

RED

ll3.8Kc/s""fI2'^'^ 648

(GREEN POST^ 5 7 GREEN

128 Kc/s 648 Km

BERLIN

185 Kc/s 9IOKm

MOTALA

191 Kc/s 1173 Km

KALUNDBORG

245 Kc/s 813 Km

357 —

r

SR

1 06 09 12 UT

Figure 9.19. Amplitude variation of an LF signal over a distance less than 1000 km,

Berlin-Cambridge.

(After J. S. Belrose, unpublished.)
REFLECTION COEFFICIENT 431 [33] that, by starting at midday and working back towards sunrise,

these maxima and minima can be explained in terms of the interference

between a single skywave, the amplitude of which decreases with time of

day, and the groundwave. If this analysis is continued earlier than ground

sunrise, the results are no longer consistent and it is necessary to assume

that more than one skywave is present. It appears unlikely that the additional skywave is the two-hop signal because of the small magnitude

of the reflection coefficient.

9.7.2. The Reflection Coefficient

The variation of ||jR|| with the equivalent vertical frequency (/cos <f>, where 0 is the angle of incidence) is sketched in figure 9.20 for the months

of November 1954, March 1955, and June 1955. Except in the case of

H

f cos i Kc/s Figure 9.20. Variation of reflection coefficient \\R\\ with equivalentfrequency.

(After J. S. Belrose, The oblique reflection of low-frequency radio waves from the

ionosphere, AGARDograph 74, 1963.)
432 PROPAGATION OF LF AND VLF FREQUENCY WAVES

June, the variations are essentially linear. It should be noted that, for short distances, since the downcoming wave is approximately circularly

polarized, the reflection coefficient \\R\\ and the conversion coefficient \\R± are essentially equal. On the whole, the data from which figure 9.20 was constructed refer to sunspot minimum years. Detailed studies [36] on waves of frequency 245 kc/s over a distance

of 180 km have shown that the difference in attenuation between sun- spot maximum and sunspot minimum is a function of solar zenith angle.

There is a maximum difference in attenuation of 15 dB at x = 70°. Monthly mean values of log | at constant x are closely related to sunspot number

Figure 9.21. Diurnal variation of | |i?jL for 245 kc/s over a distance of 180 km

for 1954 (solid line) and 1956 (broken line).

(After J. S. Belrose, unpublished.)
NORMAL BEHAVIOR OVER LONG DISTANCES 433 up to a value of 150 above which there is little change. This "saturation"

effect is also evident in the monthly mean curves of figure 9.21 giving

the diurnal variation of \\R± (plotted from data in ref. [37]). In winter

and equinox months there is a difference in attenuation over the whole

of the day. In summer the ionospheric absorption, during a year of high

sunspot number, reaches a maximum soon after sunrise. This maximum

is about the same as the midday value during a sunspot minimum year. There is some evidence that suggests that the sunspot cycle effect on LF waves is opposite to that on VLF waves. Thus 16 kc/s waves are more strongly reflected at sunspot maximum than at sunspot minimum

whereas on 245 kc/s the reverse appears to be true. The magnitude of

the difference depends on the sunspot number and, in part, on the season

(for instance on 245 kc/s a difference is found for equinoctial and winter

months only) and is about 3 to 6 dB. On intermediate frequencies the

effect will be less.

9.7.3. Normal Behavior Over Long Distances

9.7.3.1. Diurnal Variation

The diurnal variation of the amplitude of waves of frequency 97

kc/s propagated between Ottawa and Goose Bay in Canada (1500 km)

is shown in figure 9.22. In summer the diurnal variation of amplitude is very regular and,

to a first order, symmetrical about local noon. In winter the daytime

amplitude is greater, and much less regular and the equinox months are

erratic. Deep fluctuations are present near dawn. In these records the

groundwave is negligible in comparison with the total skywave so that

the fluctuation is due probably to the beating between two waves re- flected from different heights.

9.7.3.2. Seasonal Variation

The seasonal variation of the signal strength on 80 kc/s over the 1910

km path from Ottawa to Churchill is shown in figure 9.23a. This shows

the usual seasonal trend with winter signals stronger than the summer

ones. The seasonal variation of the signal strength in the case of 70.4 kc/s waves over the 1700 km path from Comfort Cove, Newfoundland,

to Ottawa is opposite to that obtained for all other transmissions as can

be seen in figure 9.23b.
434 PROPAGATION OF LF AND VLF FREQUENCY WAVES

1 1 1 1 1 1 1

1 0 3 6 9 12 15 18 21 24

AST

Figure 9.22. Diurnal variation of total field intensity received on a

loop antenna at Goose Bayfor 97.1 kc/s transmissions from Ottawa

{1 kW radiated).

(After J. S. Belrose, unpublished.)

9.7.4. EfFects of Solar Flares

The detailed variation of amplitude during a SID depends on the

conditions prevailing prior to the disturbance and so depends on the

season. On the whole, however, it appears that on LF the amplitude

increases during a flare, whereas on VLF and for steep incidence, the

amplitude decreases as illustrated in figure 9.24.^ It can be seen that the

* Note that with oblique incidence there is only a small amplitude change, and this is usually an increase.
POLAR CAP DISTURBANCES 435

^ j'j'a's'o'n'd' j'f'm'a'm'j'

j'j'a's'o'n'd' j'f'm'a'm' j' Figure 9.23. Seasonal variation of monthly median midday and midnight values of total field intensity.

(a) Ottawa-Churchill (80 kc/s). (b) Comfort Cove—Ottawa (70.384 kc/s). (After J. S. Belrose, unpublished.)

change in height of reflection is essentially the same on both frequencies.

The detailed time sequence usually takes the form of a rapid decrease

of amplitude at the beginning followed by an increase at the time of maximum disturbance and a second decrease before the final recovery—as shown by the 16 kc/s curve in figure 9.24. On some occasions, however,

the ^"subsidiary" peak may be smaller than the initial decrease of amplitude. On the whole it appears, that the magnitude of the subsidiary

peak is such as to result in an overall increase in summer and an overall decrease in winter.

The amplitudes of low- frequency waves in the range 60 kc/s to 80

kc/s transmitted over distances of 1700 to 2400 km (in North America)

always increase during an SID.

9.7.5. Polar Cap Disturbances

The effects of a sudden cosmic ray event (SCR) on the propagation

of LF waves in high latitudes are as follows:
436 PROPAGATION OF LF AND VLF FREQUENCY WAVES

60t -i

1 1 1 1 r r

09 10 II 12 UT

Figure 9.24. Estimated reflection heights and amplitudes observed at Cambridge

(April 9, 1956) during a SID.

(After J. S. Belrose, 1963, The oblique reflection of low-frequency radio waves from the ionosphere, AGARDograph 74, Pergamon Press.)

(1) When the SCR is weak the ionospheric effects can usually be

detected by means of LF waves in high geomagnetic latitudes only. The

disturbance effect is mainly one of weaker than normal signal strengths

at night and nighttime reflection heights which are lower than normal.

(2) When the disturbance is moderate, the diurnal variation of signal

strength is opposite to that normally observed. The diurnal change of ap- parent reflection height is less than normal, and the greater reduction

occurs at night.

(3) When the polar cap disturbance is strong the diurnal variation of

both phase and amplitude disappears almost entirely. The apparent re- flection heights are some 10 to 12 km below the normal daytime values
WINTER ANOMALY 437

(i.e., the waves may be reflected from heights between 50 and 55 km).

The signal strengths are about the same as those on a normal day.

9.7.6. Magnetic Storm Effects

The behavior of LF waves during magnetic storm in middle latitudes

has been summarized by Lauter [38] as follows:

(1) The sudden commencement was not associated with any change

of amplitude;

(2) at night, rapid and deep fading accompanied the main phase

of the storm (primary storm effect)

;

(3) daytime records were not usually disturbed during the main

phase of the storm;

(4) when the storm was intense the signal strength during the night was unduly weak for a period which began about 3 to 4 days after the

start of the storm and continued for several days (the after effect).

9.7.7. Nocturnal Anomalies [33, 38 ] At night it is not uncommon to observe phase and amplitude anomalies lasting for about an hour or so. Both phase and amplitude changes

occur together. The phase anomalies always correspond to a decrease in apparent height. Although they are somewhat similar to sudden phase

anomalies, they frequently start more gradually. The decrease in ap- parent height can be as great as 8 to 10 km, which is the size of a normal

SPA. Furthermore, there is evidence to indicate that these nocturnal

anomalies have spatial extents of at least 600 km.

Nocturnal anomalies are associated sometimes with magnetic variations, but not always. They are found both in middle and high latitudes

and are usually accompanied by other "auroral" type phenomena such

as enhanced forward scatter of VHF signals, IIF absorption, and so on.

9.7.8. The Winter Anomaly

During winter days of high absorption on IIF (sec. 3.3.6.5), lowfrequency waves appear to be reflected from heights lower than normal

and the amplitude of waves transmitted over distances of 1000 to 2000

km is greater than normal. When these waves are propagated over short
438 PROPAGATION OF LF AND VLF FREQUENCY WAVES

distances their amplitudes may be greater or less than normal but, when

the HF absorption is intense, their amplitudes are usually greater than

normal.

9.7.9. Variation of Amplitude With Distance

9.7.9.1. Short Distances

At distances less than 100 km the variation is dominated by inter- ference between the groundwave and the skywave. If the amplitude of

the vertical electric field is measured on the ground, or in an airplane flying at a constant height, and allowance is made for the inverse distance

attenuation, a pattern of the type shown in figure 9.25 is obtained. This

pattern is called the HoUingworth pattern. From the positions and signal

strengths of the turning points it is possible to deduce the characteristics

of the downcoming wave.

9.7.9.2. Long Distances

Some idea of the decrease of amplitude with distance can be obtained

from figure 9.26 which is based on data for 180 kc/s waves over land

300 400 500 600 700 800

Distance from sender, km

Figure 9.25. The HoUingworth interference pattern observed during the midday hours on

85 kc/s on November 3, 1949. The full curve represents the calculated groundwave signal. (After R. N. Bracewell, K. G. Budden, J. A.

Ratcliffe, T. W. Straker, and K. Weeks, 1951, The ionospheric propagation of low-frequency radio waves

over distances less than 1000 km, Proc. lEE 98, Pt. Ill, 221.)
(uu/ATy) AilSN31NI
440 PROPAGATION OF LF AND VLF FREQUENCY WAVES

[43]. The following features are worthy of note:

(1) At the geometrical hmits of the one-hop path (;^2000 km) there

is no sharp drop in signal strength. This is in agreement with waveguide

theory.

(2) The amplitudes fall off approximately exponentially with dis- tance both by day and by night.

(3) The amplitudes are greater by night than by day.

(4) The attenuation rate is somewhat greater by day than by night.

9.8. USE OF VERY LOW FREQUENCIES IN FREQUENCY

COMPARISONS

The relatively high phase stability of VLF signals propagated over

long distances makes it possible to transmit reference frequencies to re- mote parts of the world. For this purpose, the frequency of the trans- mitter must be stabilized by means of a stable crystal oscillator or preferably an atomic standard. Under these conditions the limitation on the

accuracy to which a received frequency can be measured is determined

by

(a) the relatively high atmospheric noise [39] and

(b) the phase fluctuations due to ionospheric changes [40].

Frequency is essentially the time rate of change of phase (i.e., d<t)/dt). It can be shown that if and C are the rms noise and signal

powers respectively, then the standard deviation of phase (7(<j)) is given

by

<r(<f>)=^- (9.40)

If n cycles are observed in a time ( T) the error in n is l/2wa{<f)) and thus

the rms error E in the frequency (/) measurement is

n 2t 2ir CfT

Now the noise power N is proportional to the bandwidth (6) of the re- ceiving system, which can be made small (e.g., 0.01 c/s) by suitable in- strumentation [41]. Using such a system, a precision of 1 part in 10^ has been achieved in an hour's observations over a distance of 19,000
REFERENCES 441 km. From this it will be seen that atmospheric noise will rarely be the

limiting factor. The effect of ionospheric height changes is more serious because

the variations are so slow and, thus, long averaging times are required.

If the phase of a VLF signal relative to that of a local oscillator changes

by an amount 0 in a time T, then the angular frequency difference Aw

is given by

Aa> = ^. (9.42)

If cr(</)) is the standard deviation in the fluctuations of </>, the precision

of the frequency measurement will be

aid)) <tM=^, (9.43)

provided that the phases at the beginning and end of the measurement

are uncorrelated. Thus the precision increases linearly with the time of observation. Pierce gives values of (t{<P) for GBR-Boston (16 kc/s) of 0.28 rad for quiet nights and 0.14 rad by day. For GBR-Boulder the day

value of o-(0) is 0.26 rad. The natural limit of frequency comparison over

a north-Atlantic path is about 2 parts in 10^^ for a 24-hr period [42].

9.9. USES OF VERY LOW AND LOW FREQUENCIES

The main uses of VLF are

(1) Long-distance communications ( on-off keying)

,

(2) Continuous-wave navigation systems,

and of LF,

(3) Broadcasting (e.g., Droitwich, 200 kc/s),

(4) Communications (on-off keying and frequency shift -keying),

(5) Continuous wave navigation systems (e.g., Decca),

(6) Pulse navigation and timing systems (e.g., Loran C, 100 kc/s).

REFERENCES

[1] Budden, K. G. (1961), The Wave-Guide Mode Theory of Wave Propagation

(Logos Press).

[2] Wait, J. R. (1962), Electromagnetic Waves in Stratified Media (Pergamon Press).

[3] Wait, J. R. (1960), Terrestrial propagation of VLF radio waves, J. Res. NBS

64D, (Radio Prop.). 153.
442 PROPAGATION OF LF AND VLF FREQUENCY WAVES

[4] Wait, J. R. (1957), The mode theory of VLF ionospheric propagation for finite ground conductivity, Proc. IRE 45, 760.

[5] Wait,' J. R., and K. Spies (1960), Influence of earth curvature and terrestrial magnetic field on VLF propagation, J. Geophys. Res. 65, 2325,

[6] Crombie, D. D. (1958), Differences between E-W and W-E propagation of VLF

signals over long distances, J. Atmospheric Terrest. Phys. 12, 110.

[7] Taylor, W. L. (1960), Daytime attenuation rates in the VLF band using atmospherics, J. Res. NBS 64D (Radio Prop.), 349.

[8] Barber, N. F., and D. D. Crombie (1959), VLF reflections from the ionospheric

in the presence of a transverse magnetic field, J. Atmospheric Terrest. Phys. 16,

37.

[9] Pekeris, C. L. (1950), Ray theory versus normal mode theory in wave propagation

problems, Proc. Sympl Appl. Math. 2, 61, Am. Math. Soc.

[10] Wait, J. R. (1961), A diffraction theory for LF skywave propagation, J. Geophys.

Res. 66, 1713.

[11] Barron, D. W. (1959), The waveguide mode theory of radio propagation when

the ionosphere is not sharply bounded, Phil. Mag. 45, 1068.

[12] Johler, J. R., and J. D. Harper (1962), Reflection and transmission of radio waves

at a continuously stratified plasma with arbitrary magnetic induction, J. Res. NBS 66D (Radio Prop.), 81.

[13] Parkinson, R. W. (1956), The nightime lower ionosphere as deduced from theoretical and experimental study of coupling phenomena, J. Atmospheric Terrest. Phys. 7, 203; ibid. 8, 158 (1956).

[14] Ratcliffe, J. A. (1959), The Magneto-Ionic Theory and its Application to the Ionosphere (Cambridge Univ. Press).

[15] Taylor, W. L., and A. G. Jean (1959), Very-low-frequency radiation spectra of

lightning discharges, J. Res. NBS 63D (Radio Prop.), 199.

[16] Laby, T. H., J. J. McNeill, F. G. Nicolls, and A. F. B. Nickson (1940), Waveform

energy and reflection by the ionosphere of atmospherics, Proc. Roy. Soc. (London) A174, 145.

[17] Helliwell, R. A., and M. G. Morgan (1959), Atmospheric whistlers, Proc. IRE 47,

200.

[18] Gallet, R. M. (1959), The very low-frequency emissions generated in the earth's exosphere, Proc. IRE 47, 211.

[19] Straker, T. W. (1955), The ionospheric reflection of radio waves of frequency 16

kc/s over short distances, Proc. lEE 102, Pt. C, 396; Proc. lEE Monograph

144 (1955).

[20] Bracewell, R. N. (1952), The ionospheric propagation of radio waves of frequency

16 kc/s over distances of about 200 km, Proc. lEE 99, Pt. IV, 217.

[21] Best, J. E., J. A. Ratcliff^e, and M. V. Wilkes (1936), Experimental investigations

of very long waves reflected from the ionosphere, Proc. Roy. Soc. (London) A156,

614.

[22] Budden, K. G., J. A. Ratcliffe, and M. V. Wilkes (1939), Further investigations of very long waves reflected from the ionosphere, Proc. Roy. Soc. (London) A171,

188.

[23] Bain, W. C, R. N. Bracewefl, T. W. Straker, and C. H. Westcott (1952), The

ionospheric propagation of radio waves of frequency 16 kc/s over distances of about 540 km, Proc. lEE, Monograph 37R.

[24] Bracewell, R. N., and W. C. Bain (1952), An explanation of radio propagation at
REFERENCES 443

16 kc/s in terms of two layers below E layer, J. Atmospheric Terrest. Phys. 2, 216.

[25] Pierce, J. A. (1955), The diurnal carrier phase variations of a 16 kc/s trans-Atlantic

signal, Proc. IRE 43, 584.

[26] Crombie, D. D., A. H. Allen, and N. Newman (1958), Phase variations of 16 kc/s

transmissions from Rugby as received at New Zealand, Proc. ZEE B, 301.

[27] Wait, J. R. (1959), Diurnal change of ionospheric heights deduced from phase

velocity measurements at VLF, Proc. IRE 47, 998.

[28] Wait, J. R. (1961), A comparison between the theoretical and experimental data on phase velocity of VLF radio waves, Proc. IRE 49, 1089.

[29] Chilton, C. J. (1961), VLF phase perturbations associated with meteor shower

ionization, J. Geophys. Res. 66, 379.

[30] Cilliars, W. A. (1960), Changes in fading speed of LF radio waves, J. Atmospheric

Terrest. Phys. 18, 339; also (1960) Irregularities in the lower ionosphere, Ph.D.

Thesis, University of Cambridge.

[31] Wait, J. R. (1958), A study of VLF field strength data: both old and new, Geofisica Pura e Applicata 41, 73.

[32] Heritage, J. L., S. Weisbrod, and J. E. Bickel (1947), A study of signal versus

distance data at VLF, VLF Symposium Record 4, 77.

[33] Belrose, J. S. (1958), Some investigations of the lowest ionosphere, Ph.D. Thesis,

Cambridge University.

[34] Doherty, R. H., G. Hefley, and R. F. Linfield, (1961), Timing potentials of Loran-C, Proc. IRE 49, 1659.

[35] Bracewell, R. N., K. G. Budden, J. A. Ratcliffe, T. W. Straker, and K. Weekes

(1951), The ionospheric propagation of low-frequency and very-low-frequency

radio waves over distances less than 1000 km, Proc. lEE 98, Pt. Ill, 221.

[36] Lauter, E. A., Some results of IGY low frequency absorption measurements. Symposium on ionospheric soundings in the IGY/IGC, Nice, France, December

1961.

[37] Geophysikalische Messreihen des Observatorium fiir lonospharen Forschung

Kuhlungsborn (monthly bulletins published by the Deutschen Demokratischen

Republik Observatorium Kuhlungsborn).

[38] Lauter, E. A., and K. Sprenger (1952), Nocturnal ionospheric disturbances in the lower ionosphere, Z. Met. 6, 161 (translation DSIS/DRB, Canada, Translation T826).

[39] Watt, A. D., and R. W. Plush (1959), Power requirements and choice of an optimum frequency for a worldwide standard frequency broadcasting station, J. Res. NBS 63D (Radio Prop.), 35.

[40] Pierce, J. A. (1957), Intercontinental frequency comparison by very low frequency

radio transmissions, Proc. IRE 45, 798.

[41] Allen, A. H., D. D. Crombie, and W. A. Penton (1956), Frequency variations from

GBR, Rugby, Nature 177, 178.

[42] Pierce, J. A., G. M. R. Winkler, and R. L. Corke (1960), The GBR experiment:

a trans-Atlantic frequency comparison between cesium-controlled oscillators. Nature 187, 914.

[43] Belrose, J. S., W. L. Hatton, C. A. McKerrow, and R. S. Thain (1959), The en- gineering of communications systems for low radio frequencies, Proc. IRE 47,

661.

Index

A

A scan, 104, 108 Abnormal component, 414, 416, 423

Absorption, 81 anomalous, 150 change AA, 112

coefficient, 80, 82, 84, 89, 231

cross section, 8, 10, 13 D-region, 36, 108, 145, 147, 160, 219, 232, 234, 257, 258, 262, 265, 285, 374, 386

deviative, 81, 82, 145, 231, 234, 235

differential, 110, 116, 236, 240

index, 82, 112, 297, 298, 300, 331, 400 measurements, 103, 108, 109, 146, 271

non-deviative, 81, 82, 84, 88, 112, 134, 145, 231, 234, 235

of sun's radiation, 4, 13 polar cap, 43, 82, 231, 257, 258, 274, 277, 278, 279, 280, 281, 284, 351

variations, 112, 144, 147, 149, 232, 235, 261, 297, 374

zone, 274

Aerials (see antennas).

Ampere's circuital theorem, 49

Amplitude:

distribution, 243

of wave, 108, 217, 248

ratio, 108

variations VLF, 244

Angle of: arrival, 114, 186, 189, 225

departure, 186, 225

elevation, 164, 167, 189, 192, 208, 219, 240, 290, 293, 294, 298

incidence, 160, 163, 168, 185, 186, 203, 209, 232, 233, 400, 402, 403, 406, 423, 424, 431

radiation, 190, 191, 292, 293, 294, 298, 300, 301, 331, 336 Angular error, 208, 209

Anisotropic medium, 48, 93, 94, 97, 404

Anistropy, 93 AnomaUes: LF phase, 421, 437

winter, 130, 138, 149, 150, 235, 298, 437

Antennas:

dipole, 241

gain, 220, 221, 241, 294, 301, 338, 346

ionosonde, 104

loss, 218, 220, 221, 338

lossless, 310

radiation, 218

radiation efficiency, 218, 394

radiation pattern, 218 Appleton formula, 71 approximate formulas, 73 Appleton -Hartree formula, 63

Arcs, 272, 276 ARDC Model Atmosphere, 5 Asymmetric raypaths, 186 Asymptotic expansion of Hankel function, 397
446 INDEX

Atmosphere, 8, 11, 413

composition, 5 constituents, 4, 5 density, 5

dissociation, 4

heat conduction, 4

heat loss, 4

ionization, 3, 7, 8, 12

isothermal, 3, 12

layers, 1, 2, 17 mean molecular weight, 3, 5 models, 5 neutral, 1 nomenclature, 1 number density, 38

region, 1, 8

scale height, 3, 5

specific heat, 4 temperature structure, 4, 5 temperature variations, 4, 5 terminology, 1 Atmospherics (see spherics).

Atmospheric noise, 440, 441 Atomic oxygen, 12 Atom-ion exchange, 12 Attachment, coefficient of, 12, 14, 17 Attenuation (see absorption):

rate, 374, 400, 402, 403, 406, 410, 425, 426, 432, 440

Axes, right-handed system, 412

Aurora: frequency of occurrence, 34, 36

luminescence of, 27

origin of, 26, 27, 36 Aurora borealis, 258, 382

Auroral:

absorption, 271, 274, 351

activity, 34, 278

blackouts, 271, 274, 276, 277, 278, 279, 284, 351 movement, 36

ring, 274, 276, 277, 280, 281, 283, 284

zone, 27, 35, 36, 153, 245, 265, 271, 274, 278, 350, 426

B B scan, 106, 107, 108 Back Electromotive force, 48

Backscatter, 185, 290, 357, 360, 361, 362, 364, 366, 441 Bandwidth, III, 159, 227, 253, 310, 331, 349, 393, 394

Barometric equation, 2

Bartel's "musical scales," 33, 35 Beat signal, 92, 113, 114

Bi-refringent medium, 45

Bistatic, 380 Body Doppler, 364

Boltzman's Constant, 3, 310

Breit and Tuve's theorem, 161 C

Cahbration, 104, 190, 110, 111

Capacitor, parallel plate, 48, 52 Carbon dioxide, 5 Carrier/noise ratio, 326, 339

Carrier wave, 248
INDEX 447

Cassiopeia, 251, 252

Caustic surface, 226 CCIR, 101, 180, 289, 290, 314, 326, 327

Centrifugal force, 61 Centripedal force, 61 Chapman, 14, 16 formula, 14

function, 19, 148

layer, 18, 34, 147, 205, 206

formation of, 12 height of maximum production, 18

limitations of, 18

solar control, 18

Characteristic waves, 65, 68, 70, 211, 220, 238

Charge:

density, 47, 48

oscillation, 65

surface, 48

Charges, moving, 36

Chorus, 413 Chromosphere, 37

Circularly polarized components (resolution into), 211, 237 Cold plasma, 63

Collision frequency, 71, 80, 82, 84, 87, 108, 134, 145, 147, 210, 264, 265

critical, 82

effective, 89

profile, 234

statistics, 63, 84

Collisions and group refractive index, 71, 73

Collisions, electronic, 63, 68, 69, 73, 88

Colors, 91 Communications:

high frequency, 159, 160, 281, 289, 290

long distance, 159, 160, 188, 190, 281

radio, 150, 217, 236, 257, 281, 310, 344, 374 Complex group refractive index, 45, 63, 80, 84, 87 Complex Poynting vector, 59 Computers, electronic, 73 Conduction current, 4

Constitutive relations, 64, 68, 69

Continuity equation, 9, 12, 52 Continuous waves (CW), 103, 108, 110, 145, 365, 413, 440

Contour:

charts, 271, 273 maps, 280

Control point, 330, 331

Controlled experiments, 102 Convergence, 222 Conversion coefficients, 405, 423, 432, 441 Conversion of ordinary to extraordinary wave (see coupling), 45

Coordinates:

dipole, 20

geographic, 20 Corona, 37, 43 Cosmic rays, 8, 258, 351 Coupled modes, 405

Coupling, 411, 413

critical, 412

ionospheric, 405, 411, 412

level, 411 LF, 410 CRPL (Central Radio Propagation Laboratory), XIII, 1, 24, 31, 39, 130, 145, 148, 149, 153, 258, 283, 285, 387, 289, 301, 302, 303, 304, 305, 310, 331
448 INDEX

Cross section: absorption, 8

ionization, 8 Crossed vertical loops, 423

Curl equations, 53, 54, 66 Current density, 60

Currents: atmospheric, 26 DP, 27

earth, 26

electrojet, 27

L, 27

ring, 27, 36

Sq, 27 Curvature of earth, 224 Curved earth-ionosphere guide, 163, 165, 169 Cusp, ionogram, 203

Cut-off frequency, 190, 192, 399 D

Declination: magnetic, 23

solar, 19 D-days, 26, 34, 246

Defocusing, 194, 219, 222, 223, 224, 225, 230

Density:

atmosphere, 5

electron, 2, 8, 9, 15, 16, 17, 18, 28, 43, 72, 124, 130, 135, 145, 147, 160, 172, 175, 178,

186, 207, 234, 236, 250, 251, 252, 263, 266, 270, 343, 344, 346, 352, 358, 359, 390

molecular, 18 Departure, angle of, 186, 225

Depression in electron density, 266, 267

Deviation, lateral, 198, 208

Dielectric constant, 48

Dielectric polarization, 48

Diffraction, 248, 249

Diffusion, 8

coefficient, 352

separation, 1 Dip:

angles, 240, 407

poles, 26

Dipole, 116, 218, 241

coordinates, 20

displaced, 26

equator, 20, 21

field, 19, 22

field magnetic, 21

latitude, 20, 21, 36, 235, 319

lines of force, 22

longitude, 20

meridians, 20, 21

poles, 19, 20

vertical, 396

Direction:

of energy flow, 45 - of phase propagation, 45, 97

of propagation, 93, 94

of ray^ 94, 97

of wave normal, 95, 96

Dispersion curves, 72, 73, 74, 80, 82, 83, 89

Dispersive medium, 91
INDEX 449

Displacement, 202

Dissociation, 4, 5 Distance factor, 180, 188, 294

Disturbance, 257

Diurnal phase variations, 18, 291, 347, 414, 416, 417, 419, 420, 423, 424, 427, 428, 429,

432, 433, 436

Divergence, 222, 224

Diversity:

frequency, 255

polarization, 255

space frequency, 255 D layer, 257, 258, 259, 391, 399, 410, 416, 418 Doppler shift, 97, 98, 364, 378, 383, 386 Double refraction, 405 Downcoming pattern, 186 D region, 43, 84, 108, 125, 149, 150, 183, 184, 233, 258, 262, 264, 267, 281, 285, 294, 343 344 348

absorption, 36, 108, 145, 145, 160, 219, 232, 234, 258, 262, 265, 285, 374, 386

ionization, 37

Drift, 8, 43, 173, 364, 416

E Earth's curvature, 224, 402, 403, 410, 417

centered dipole, 19 magnetic field, 19, 20, 21, 22, 23, 27, 45, 134, 163, 179, 180, 181, 201, 203, 377, 402,

404, 406, 407

East-west propagation, 170, 181, 182, 201, 239, 254, 299, 407, 418, 426

Echoes, 151, 186, 189, 212, 213 LF, 412

structure, 159, 173, 178, 410

Effective collision frequency, 147

Efficiency, launching, 403 E layer, 18, 19, 27, 118, 125, 137, 138, 139, 145, 147, 150, 166, 167, 182, 190, 191, 192, 232, 234, 235, 236, 257, 259, 290, 291, 292, 234, 235, 236, 257, 259, 290, 291, 293, 314,

323, 325, 330, 335, 336, 337

X dependence, 138, 291

Electric:

field, 27, 46, 47, 51, 62 moment per unit volume, 48

Electro-jet: auroral, 27

equatorial, 27

Electromagnetic:

induction, 50, 51

units, 50, 56 Electromagnetic unit of charge, 56

Electromotive force (emf), 48, 50

Electron density, 2, 8, 9, 16, 17, 43, 72, 124, 130, 131, 135, 145, 147, 166, 178, 186, 207,

234, 236, 250, 251, 263, 266, 270, 407

profiles, 124. 169, 181, 196, 198, 201, 264, 386, 387, 388, 389 D region, 12, 108, 126, 144 E region, 12, 150, 230 F region, 12, 117, 127, 230, 387

Electron energy, 87, 175, 195

distribution of, 2, 87, 201

Electrons, 38, 259

effective, 63 motion of (see ion), 69 number density, 8, 12, 18, 60, 117, 130, 145, 150, 160, 204, 381

rate of production, 9, 19, 134, 261, 264

recombination, 8, 18

slow, 87
450 INDEX

Electrostatic unit of change, 56

Eleven-year cycle, 262

Ellipses:

extra-ordinary wave, 78, 79, 85, 237, 238, 239

ordinary, 78, 85, 237, 238, 239

tilt of, 78

Emission, 38

radio wave, 43

ultra-violet, 38, 43

, x-ray, 38, 43 Energy:

density, 219

flow, 45, 194

direction of, 94, 194, 197 Equation:

of motion, 59, 61, 69 Equator:

(see dipole)

magnetic, 19, 20, 22, 247 Equinox, 178, 272, 273, 275, 377 month, 149, 253, 274

Equivalent frequency, 161, 162, 164, 165 Equivalent height, 103

in exponential profile, 136

in linear profile, 136

in parabolic profile, 135 Equivalent path, 161, 162, 163, 185 Equivalent vertical frequency, 161, 162, 164, 165 E region, 8, 37, 43, 118, 119, 120, 121, 159, 219, 235, 264

Excitation factor, 404

Exosphere, 12, 413 Extraordinary wave, 45, 73, 75, 76, 77, 78, 79, 83, 84, 85, 93, 110, 117, 118, 121, 125,

145, 176, 180, 185, 197, 198, 199, 201, 202, 203, 204, 205, 408, 411

F Fading, 217, 242, 344, 349

absorption, 242

double periodic, 244, 245

frequency dependent, 245, 246, 281

of HF, 393

periodic, 242, 244, 245 random, 244, 245

rates, 245, 348, 351, 364, 378

rotation, 210

selective, 242, 253

short period, 245

spectrum, 245, 246

Faraday's law, 49, 211, 212

Far-field, 397

Field alined irregularities, 184, 346

Field strength, 110, 217, 241, 242

Finite ground conductivity, 402 Fixed frequency techniques, 103, 108, 174

Flat earth, mode theory, 394 F layer, 125, 130, 182, 190, 230, 231, 236, 254, 257, 258, 259, 319, 343, 355

Flip-overs, 412

Flutter fading, 184, 245, 246, 247, 281, 284, 378, 379

Flux, 13, 15, 50, 59, 218, 223

/min, 112, 262, 271, 280

Focusing, 194, 208, 219, 223, 224, 228, 230, 242

antipodal, 229
INDEX 451

Focusing—Continued

effect, merging of low and high waves, 186

effect on field intensity, 217

horizon, 229

ionospheric, 186, 22, 226 MUF, 227

skip, 186

Force, on electron, 69

Forecasts, 35, 285, 286 Formation of layers, 8 Forward scatter, 285, 344, 345, 361, 362, 366, 412 FOT, 192, 284, 289, 292, 319, 323, 325, 331, 339, 340

Fourier:

analysis, 248

integral, 301 time series, 301

transforms, 245, 246, 409 F plots, 122, 123, 124, 266

Free space, 63, 65, 300

velocity, 162, 258, 294, 420

wavelength, 264, 399 F region, 8, 37, 116, 119, 131, 247, 258, 344, 384, 386

Frequency, band, 393

changes (Doppler) Af, 97, 113, 262, 263

comparison, V LF, 440 dependence of, 145, 261, 346, 347, 348, 350

distortion, 159

diversity, 255

lowest useful, 340

range, 410

Fresnel reflection coefficient, 401

Fresnel zone, 249, 250, 357, 358, 359, 361, 365, 364

Fi-layer, 18, 19, 118, 119, 120, 125, 130, 137, 138, 140, 141, 144, 145, 146, 166, 167, 266, 268 290 291 321 323 325 330

F2-layer, 118, 127, 130, 137, 138, 140, 142, 143, 144, 146, 150, 153, 159, 166, 167, 175, 176, 177, 182, 186, 188, 189, 190, 192, 201, 214, 257, 258, 265, 267, 268, 270, 282, 390,

292, 293, 301, 303, 304, 305, 307, 309, 315, 319, 321, 330, 331, 332, 333, 335, 377 G

Galactic noise, 310 Gamma, 23 Gauss unit, 23 GBR, 416, 418, 419, 420, 421, 422, 423, 424, 441 Geomagnetic:

activity, 278, 351

field, XIII, 20, 23, 27

Glints, 364

Gradient:

electron density, 346, 390

horizontal, 178 Gradual commencement, 265 Grazing incident, 402 Great circle, 116

charts, 318

path, 114, 184, 229, 296, 315, 330, 348, 418 Ground:

backscatter, 185

conductivity, 294, 401, 402

range, 167, 186, 196, 219, 294

scatter, 153, 155, 156, 180, 182, 185, 330

sunset, 418 wave, 414, 423, 431, 438
452 INDEX

Group:

height, 103, 104, 109, 117, 118, 124, 135

path, 96, 98, 161, 162, 210

propagation, 89

propagation time, 162, 419

refractive index, 93, 125, 210

retardation, 124

velocity, 91, 93, 98

Gyrofrequency, 62, 73, 134, 145, 147, 181, 198, 200, 201, 203, 239, 240, 298, 299, 331

Gyro-oscillations, 38 H

Heliosphere, 2 Height:

apparent, 124, 436

equivalent, 161, 165

group, 103, 104, 109, 117, 118, 124, 135 measurement of, 103 minimum virtual, 118, 124

of reflection, 124, 162, 163, 165, 293, 294, 416, 418, 427, 436

phase, 136, 416, 422

real or true, 124, 160, 161, 162, 293, 294, 416, 418, 427, 436

phase, 136, 416, 422

real or true, 124, 160, 161, 162, 165, 166, 171, 174, 175

virtual, (see group height), 103, 107, 124, 136, 137, 156, 162, 165, 166, 171, 174, 175 Helium, 37 High angle ray, 169, 175, 178, 300

Hiss, 413

Hollingsworth pattern, 438

Hot-spot, 369, 371 Hour angle of sun, 18 Hydrogen, 5, 37

I IGY (International Geophysical Year), XIII, 34, 35, 101, 121, 272, 273, 276, 283, 377

Images, ground, 396

Imperfect reflection, 400 Imposed magnetic field, 68, 69, 70, 71, 134, 135

direction, 70 Impulsive noise, 310

Incidence, angle of, 160, 163, 168, 185, 186, 203, 209, 232, 233

Incident beam, 13, 345

Inclination (see dip) Index:

absorption, 297, 298

of refraction, 344

refractive, 55, 63, 64, 67, 68, 71, 72, 73, 76, 77, 80, 81, 84, 87, 90, 92, 96, 135, 147,

160, 162, 164, 194, 196, 197, 201, 202, 203, 207, 210, 250, 262, 263, 294

Infrared radiation, 4 Inhomogeneous medium, 410, 411

Initial phase of magnetic storm, 265

International Astronomical Union, 39, 43

International Geophysical Year (See IGY)

International daily character figure, 30

Inverse distance, 219

loss, 219, 221

Inverse square law, 281

Ion, concentration, 60

motion, 59
INDEX 453

Ionization, 125, 230, 284

coefficient, 17

cross section, 8

efficiency, 8, 10

meteoric, 184, 348, 352, 353, 356

Ionized trails, 343, 344, 352, 353, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 369 lonogram, oblique, 174, 175, 180, 184, 189, 192, 193, 194 IGY atlas of, 121 lonogram, vertical, 117, 118, 119, 121, 124, 125, 150, 170, 181, 184

markers, 104

lonosonde, 103, 104, 105, 106, 107, 112, 117, 125

antenna, 104

blanking of display, 106

C-4, 104

interference, 107

oblique, 284 sweep frequency, 103, 104, 107

Ionosphere, 1, 59

currents, 27

curvature, 163, 169, 196, 208, 219, 229, 403

electron distribution, 262, 343

layers, 230, 291, 293

model, 410 movements, 101, 248

quiet, 38, 117

regions, 2 storms, 101, 140, 159, 257, 258, 259, 265, 268, 269, 270, 285, 281, 422

Ions, 19, 61

Iris effect, 207, 208

Isochasms, 36

Isoionic contours, 130

Isosurface, 22

Isotropic radiator, 358

Isotropy, 346 IQSY, XIII

J JANET system, 375

Junction frequency (JF), 176, 177, 178, 180, 181, 182 K

k factor, 40, 56, 68, 169, 170, 171, 172, 182

Kinetic energy of electrons, 352

L Land-sea boundary, 425

Latitude:

dip, 143

dipole, 20, 319

geographic, 19, 20

geomagnetic, 20

magnetic, 20 Layer formation, 17 by attachment, 9 by recombination, 9 Layer model, 1, 226

shape, 196, 262

Levels of reflection, 76 Leyden jar, 51
454 INDEX

Light, 90, 93 Lightning discharges, 310, 413

Linear:

polarization, 210, 237, 238, 255

profile, 136 Line density, 366

Lines of force (earth magnetic), 27

Local reference oscillator, 414 LOF (lowest observed frequency), 176, 177

Log-periodic antenna, 104

Longitude:

dipole, 20

magnetic, 20

Longitudinal component:

of imposed magnetic field, 69

of Y, 70 Loran C, 441 Lorentz polarization term, 63

Loss:absorption (La), 218, 222, 294, 297, 325

antenna, 218, 220, 221, 338

distance, 296

distance (Lsp), 294 ground (Lg), 294, 327

inverse square of distance, 219, 221, 281

ohmic, 218, 220, 231

path, 218, 219, 220, 221, 222, 223, 230, 237, 240, 281, 282, 283, 294, 337, 340

power, 218, 294

spatial, 218, 224 Low (angle) ray, 166, 169, 254 Lowest observable frequency, 266 Low frequency:

spectrum, XIII, 394, 410

broadcasting, 441 phase change diurnal, 428

pulse observations, 141 Low latitude, 236 LUF (lowest usable frequency), 281, 340 Lunar daily magnetic variation, 26 Lyman a radiation, 37 Lyman /3 radiation, 37 M

Magnetic:

activity, 30, 31, 156, 274

conductor, 397, 399, 417

declination, 23

dip, 21, 25, 118, 236, 240

dipole field, 19, 20, 22, 75, 77, 272, 319

dip pole, 25, 118, 236, 240

disturbances, 26, 27, 30, 35, 148, 214, 260, 277, 421, 422

equator, 27, 130, 172, 178, 181, 183, 184, 186, 197, 198, 239, 246, 247, 265, 349

field of earth, 19, 20, 23, 36, 45, 47, 59, 134, 163, 179, 180, 181, 197, 198, 201, 203,

208, 209, 220, 236, 254, 263, 377

of sunspots, 40

field of wave, 58, 96, 197

inclination, 21

indices, 30, 31, 32, 33

daily figure, 30, 34

international daily character figure, 30

local, 30

local K index, 30, 31, 349
INDEX 455

Magnetic-—Continued

indices—Continued

planetary, 31, 32

world, 30, 31

induction, 23

intensity, 22

intrinsic elements, 23

isosurface, 22

latitudes, 30, 31, 75, 202, 266, 267

lines of force, 27 maps, 24, 25

meridian, 197, 201, 202, 203, 204, 208, 236, 238

poles, 19, 20, 26, 198

potentials, 26

properties, 65

relative elements, 346

spherical harmonic analysis of, 26

storms, 27, 28, 29, 36, 43, 156, 258, 259, 265, 267, 279, 351, 423

after effects, 265, 437 main phase, 265, 437 sudden commencements, 437

units, 23

variations, 26, 437 Magnetogram, 27, 28, 29 Magneto-ionic medium, 45, 69, 71, 410, 411 Magneto-ionic splitting, 150, 239

Magneto-ionic theory, XIII, 59, 412 Main phase, 265 Maps, 24, 25, 301, 302, 316, 321, 335 Maximum frequencies, 160, 165, 170, 171, 172, 175, 184, 242, 281, 331 monthly median, 192 Maximum observed frequency (MOF), 176, 177, 178 Maximum usable frequency (see MUF)

Maxwellian velocity distribution, 87, 385

Maxwell's equations, 45, 52, 53 Medium:

anisotropic, 48, 65, 93, 94, 97, 98

birefringent, 45

isotropic, 53, 56, 94

neutral, 53, 63 non conductive, 53, 56 non dispersive, 92 Meridian:

dipole (see dipole).

Mesopause, 2, 4 Mesosphere, 1, 2, 4 Mesopeak, 3 Meteor, 354, 355, 366, 372

activity, 150, 374

bursts, 367, 368, 370, 371, 373, 374, 375, 376 mass distribution, 335

radiants, 371

showers, 353, 421

trails, 343, 344, 352, 353, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 369, 370 VLF effects, 421 Middle latitude, 149, 235, 266, 347, 348 MKS units, 212 Mode, 180, 189, 401, 402, 409, 416

zero order, 297

higher order, 410 number, 395

theory, 394, 408, 410
456 INDEX

Model:

ionospheric, 102, 195

sharply bounded, 410 Modulation envelope, 91, 92, 242 Molecular oxygen, 12 Momentum, transfer, 87 Monostatic (radar), 380, 381 Motions of electrons, 61 MUF, 143, 167, 175, 176, 177, 179, 180, 182, 227, 242, 257, 266, 282, 289, 292, 319, 321,

322, 325, 331, 332, 339

classical, 176, 180

definitions, 167, 175

experimental, 180 4000 km, 292, 293, 317, 330, 331

operational, 180

standard, 180, 182

theoretical, 180 M(2000) E, 321, 322, 323 M(2000) Es, 325 M(ZERO) F2, 291, 293, 303, 309 M(4000) F2, 292, 293, 303, 305, 317

Multipath reduction factor, 193

spread, 193

transmission, radio waves, 186, 193, 253 Musa, 114, 116 N

N(h) profiles, 125, 128, 130, 134, 196, 235

National Bureau of Standards, XIII, 258, 303 Navigation systems, 441 Negative phase, 265

Neutral molecules, 8, 9, 12 number density, 8 No-echo conditions, 271

Noise:atmospheric, XIII, 291, 310

carrier/noise ratio, 241, 326

data presentation, 311, 312, 313

distribution, 311

electrical, 310

extraterrestrial, 110, 112

galactic, 110, 248, 278, 310

importance, 310

impulse, 310

ionosphere, 241

level, 327 maps, 311, 312, 314

power, 110, 112, 310, 311, 326, 340

radio, 39, 110, 111, 242

resistor, 310

solar, 259, 261

source, 310

thermal, 310 Non-conducting medium, 65 Non-deviative absorption (see absorption), 81, 82, 84

Non-reciprocity:

in attenuation, 426

in fading, 254 Normal component, 414 Normal incidence, 72, 75, 76, 116, 145, 160, 161 Northern hemisphere, 236, 272, 276
INDEX 457

North-south, 417, 418

propagation, 181, 201, 202

transmission, 182, 186 Numerical mapping, 301, 302 O

Oblique:

incidence, 160, 161, 162, 164, 207, 397, 434

paths, 201

sounder, 176

Off-great -circle-paths, 185 One-hop:

path, 175, 178, 190, 294, 440

signal, 235, 427

Operating frequency, 159, 167, 169, 192, 202, 284, 297

Operational MUF, 180

Optical:

depth, 13

flares, 421 Optimum working frequency (FOT), 192, 284, 289, 292, 319, 323, 325, 331, 339, 340

Oscillations, 38

gyro, 38 plasma, 38

Oscillator:

drift, 416

fixed frequency, 104

variable frequency, 104 OWF (optimum working frequency) (see FOT).

Oxygen, 5, 8, 12 Ozone, 4, 5 P

Parabolic: ionosphere, 135, 226

profile, 173 Parabohc ray path, 168, 189 Parametric curve, 167

Partial reflections, Es, 277

Path:

effective length, 191, 223, 224, 330, 344

great circle, 348

group, 96, 97, 98, 161, 162

long, 178

loss, 218, 219, 220, 221, 222, 223, 230, 237, 240, 281, 282, 283, 294, 337, 340

phase, 96, 97, 250

virtual (see group path) Pause, 1 PCA (polar cap absorption), 43, 82, 231, 257, 258, 274, 277, 278, 279, 280, 281, 284, 351, 421

Pederson:

path, 335

ray, 167, 178

Penetration frequency, 192, 336, 340

Perfect gas law, 3 Permanent Service of Geomagnetic Indices, 30, 31

Permeability, 297

Permittivity, 401

Permittivity of free space, 46

Phase:

advances, 421
458 INDEX

Phase—Continued

constant, 96, 394

difference, 245, 414 measurements, 103, 112, 414

normal, 197

relative changes, 414 Phase height, 135, 136

fluctuations, 159, 419, 440 Phase path, 96, 97, 210, 211, 250, 263

changes AP, 113, 264 measurements, 113

stability, 440 Phase propagation direction (see direction), 45, 93, 94, 95, 98, 134, 197 Phase velocity, determination, 89, 90, 94, 95, 399, 400, 401, 402, 408, 409 Photodetachment, 19, 148, 406

Photoionization, 8, 10, 16 Photosphere, 37, 40

Plage, 41

Plane-earth, plane ionosphere model, 160, 165, 196 Plane polarized wave, 45, 210, 211

Planes of incidence, 197, 208, 209, 399, 404, 406, 414, 423 Plane waves, 55 Plasma, 89, 103

cold, 63

frequency, 43, 61, 135, 136, 160, 162, 211, 250

oscillations, 38

overdense, 204

Polar cap absorption (see PCA). Polar caps, 27, 36, 43, 280, 429, 435, 436

Polarization, 76, 217, 413, 414, 427

circular, 211, 411, 412, 427, 432

dielectric, 48

ellipse, 84, 85, 237, 238, 239, 242

equation, 70

linear, 78, 237, 238

very low frequency, 427 wave, 27, 76, 79, 211, 217, 220, 237, 346, 399, 405, 411

Polarized medium, 48

Polar region, 421 Post perturbation phase (magnetic), 265

Potential difference, 46, 47 Poynting vector, 59

Precision, time of observation, 441

Prediction:

of long term frequencies, 289, 291, 301

of short term frequency, 289, 301

of solar cycle, 290, 303 optimum working frequency OWF, 289

problems, 289, 301

procedures, 289, 301, 302

Pressure, 2, 3

Profile: electron density (see electron density profile), monotonic, 1, 2, 5 Propagation:

constant, 56

direction of, 407

group, 89

multi-hop, 189, 226, 294

of radio waves, 45, 394

of great distances, 159, 410

Proton, influx, 38, 259, 351
INDEX 459

Pulse:

distortion, 91

drift, 173

reflection method, 108

techniques, 103, 145

transmitter, 104

Pulse navigation systems, 441

Pulse synchronization, 173 Q

Q davs. 26, 34, 127, 132, 246 QL condition, 75, 76, 77, 82, 84, 134, 181, 310, 211, 212, 263 QT condition, 75, 77, 82, 84, 181, 212, 240

Quasi-incoherent scatter, 343, 386

R Radar, 103, 212, 357, 380, 381, 383, 384, 385, 387, 388 Radiant point, 353

Radiation:

absorption, 13

angle, 190, 191, 292, 294, 298, 300, 331, 336

corpuscular, 38

efficiency, 218, 394

trapped, 27 wave, 38

Radiator, isotropic, 218, 358 Radio astronomy, 208, 259

Radio:

aurora, 36

star, 156, 210, 249, 251, 252, 253 Ray:

direction, 94, 95, 196, 197, 203

velocitv, 95

versus 'mode theory, 408, 409, 410 Ray group velocitv, 98 Rayleigh distribution. 243, 348 Rav path, 166, 167. 168, 186, 187, 190, 194, 195, 197, 198, 199, 200, 201, 202, 203, 208, 210, 223, 232, 234, 264

in magnetic meridian plane, 201

topside, 204, 207

with oblique propagation, 164 with vertical propagation, 208 Ray tracing, 160, 189, 194, 195, 197, 213, 223, 226, 235

Reactions, 8, 12 Receiving set noise. 111, 112

Reciprocity, 253, 254 Recombination, 8, 9 Recombination coefficient, 8, 10, 12

effective, 12, 19

Reflection at vertical (or normal) incidence, 72, 73, 75, 78, 161, 162

Reflection coefficient, 108

of the ground, 109, 400

of the ionosphere, 400, 423, 424

Reflection conditions, 72

Reflection height, LF, 161, 164, 191, 412

Reflection level, 167, 183, 201, 262, 293

Refraction, 159, 180, 183, 197, 209, 343

Refractive index. 55, 63, 64, 67, 68, 71, 72, 73, 76, 77, 80, 81, 84, 87, 90, 92, 96, 135, 147,

160, 162, 164, 194, 196, 197, 201, 202, 203, 207, 210, 250, 262, 263, 394

complex, 45, 63, 80, 84, 87 group (see Group refractive index),

surface, 203
460 INDEX

Relativity, 90, 258

Relaying, 284

Repetition frequency (pulse), 173 Resonance- condition, 397

Riometer, 110, 111, 112, 277, 281 Rippled ionosphere, 412

Rotation, sense of, 210

S

Satellite, 208, 210, 212, 213, 248, 249, 251, 252, 253

topside sounder, 116, 204, 207

Scale height, 3, 4, 5, 6, 13 i Scatter, 153, 156, 184, 245

ground, 153, 155, 156, 180, 182, 185, 330

side, 185

Scattering, 265

forward, 285

incoherent, 384 SCNA (sudden cosmic noise absorption), 258, 261 SEA (sudden enhancement of atmospherics), 259, 261

Seasonal variation: of absorption, 149, 235, 297

of LF amplitude, 433

Secant law, 160, 161, 169 Second International Polar Year, 34

Sec (j)o corrected, 169 (see k factor) SEE (solar flare effect), 30, 259

Short wave fadeout, 258, 259, 260, 261, 262, 264, 281 SID (sudden ionospheric disturbance), 257, 258, 259, 280, 349

Side scatter, 185, 284

Signal strength, 110, 159, 186, 194, 217, 226, 227, 344, 347, 349, 439, 440

Simple harmonic motion, 61

Single frequency communications, 344

Skip distance, 167, 172, 185, 226, 227 Sky wave, 414, 427, 431, 433, 438

Snell's law, 72, 147, 161, 162, 163, 195, 196, 197, 198, 203

Solar, 40

activity, 253, 279, 290, 303

control, 148, 149, 344, 346

cosmic rays, 258

daily magnetic variation, 26

flare, 41, 43, 82, 108, 114, 115, 231, 257, 258, 259, 261, 262, 263, 264, 277, 278, 421, 434

flux, 8, 10

protons, 277

radiation, 8, 12, 13, 32

radio emmission, 43

rotation, 35, 41 wind, 38

zenith angle, 12, 13, 18, 128, 138, 147, 235, 262, 281, 291, 297, 317, 320, 322, 334, 340 427 432

Solar flare'disturbances, 41, 257, 258, 261, 262, 263, 278

Sounders, 165

topside, 116, 204, 205, 206, 207

vertical, 19 Sounding stations distribution of, 19, 101, 102, 173 SPA (sudden phase anomoly), 259, 261, 262, 437 Space charge, 63 Space diversity, 255

Specular reflection, 183, 293

Spherical stratified ionosphere, 186, 194, 195, 209, 225
INDEX 461

Spherics, 261, 413, 426

Spitze, 202, 203, 204

Sporadic E, 36, 118, 150, 151, 152, 153, 159, 179, 182, 183, 188, 189, 257, 266, 284, 324,

325, 330

Spread:

F, 153, 155, 156, 184, 247, 253, 266, 269, 281, 343, 378, 379

echo, 153, 178

Sputter, 351

Stable crystal oscillator, 113, 173

Static field, 46

Statistics collision, 84 Steady state solution, 63 Storm:

Es, 276

geomagnetic, 156, 274, 281

ionosphere, 4, 284

noise, 43

time, 266, 270, 271

Subflare, 41 Subsidiary peak, 435 Sudden commencement, 114, 261, 265, 267 Sudden frequencies deviations, 262

Sun:

declination of, 19 hour angle of, 19 Sunspot, 40, 42, 130, 262

cycle, 40, 41, 43, 130, 138, 146, 262, 274, 277, 290 maximum, 27, 39, 41, 138, 140, 147, 261, 266, 274 minimum, 27, 38, 41, 140, 147, 261, 266, 274 number, 130, 143, 147, 253, 274, 279, 290, 291, 297, 298, 322 Sweep frequency, 103, 170 System loss, 217, 218, 289, 294, 300, 337, 338, 347

T Take-off angle, 167, 186, 189, 194 Temperature, 1, 3, 5 distribution, 1, 13

variation, 4 Theorems:

absorption, 163

Breit and Tuve's, 161, 165

equivalent height, 162

Green's, 53 Martyn's, 162, 163, 165, 232

Stokes', 53

Theoretical MUF, 180 Thermal equilibrium, 385, 386 Thermosphere, 1, 2, 4, 366, 368, 369

Threshold, 366

Tilt, 114, 182, 186

angle, 78

ionospheric, 284, 330 Time, equation of, 19 Time of flight, 98 Time, recorder, 109 Time of travel of wave crest or wave front, 90 Time, transmission, 192 Topside:

profiles, 129, 390

soundings, 204, 205, 206, 207

Total bending of ray, 208

Total electron content, 209, 212, 213, 214
462 INDEX

Total internal reflection, 160

Transequatorial propagation, 131, 178, 181, 184, 187, 229, 245

Transfer, equation, 87

Transmission:

curve, 166, 170, 171, 181

distance, 174, 178, 188, 201, 439

line, 217, 218

path, 165, 166, 173

Transit time, 96

Transmitter, 162, 173, 345, 384

Transponder, 174 Transverse component of magnetic field, 70

propagation, 73, 74, 78, 87, 181, 239

wave, 55, 58, 61, 70 Tropospheric scatter, 285 True height, 124, 160, 161 Turbulence, 1, 5, 344 Turbopause, turbosphere, 2 Two-hop path, 325 U

Ultra-violet, 4, 8, 37, 38, 43, 258, 259

Unreliability of HF propagation, 393 URSI (International Scientific Radio Union), 101 V

Valley, 125

Variations of the ionosphere diurnal, 4, 18, 19, 125, 128, 138, 140, 147, 148, 153, 173, 253, 279, 291, 301, 340, 347, 364, 370, 371, 372, 377

geographic, 130, 140, 229, 271, 349, 374, 377

seasonal, 130, 138, 140, 149, 173, 253, 267, 291, 347, 364, 377

solar cycle, 4, 131, 303, 323, 347

sun-spot, 138, 140, 149, 173

Velocity: average, 84

electron, 84

phase, 90, 91 wave, 96

Velocity distribution, 87 Maxwellian, 87

Vertical dipole source, 396

Vertical polarization, 240, 395, 405 VHF forward scatter, 265, 277, 343, 345, 346, 351, 437 VLF (very low frequency): antennas, 393

emissions, 413

noise, 393

spectrum, XIII, 393, 413

uses of, 409, 440, 441 W

Warning service, 285 Water vapor, 5 Wave, composite harmonic, 91, 217 Wave, guide theory, 394, 402, 417, 420, 440 Wave:

backward, 411

crest, 90
INDEX 463 Wave—Continued

extraordinary, 45, 73, 75, 76, 77, 78, 79, 83, 84, 85, 110, 117, 118, 121, 125, 145, 176,

180, 185, 197, 198, 199, 200, 201, 202, 203, 204, 205, 209, 210, 219, 236, 237, 238, 239, 243, 245, 261, 263

forward, 4, 11

free space, 90, 91, 211

front, 94, 95, 249

height of reflection, 418

length, 90

normal, 70, 95, 96, 197, 198, 202, 203, 220

ordinary, 73, 76, 77, 78, 79, 82, 83, 84, 85, 87, 93, 110, 116, 117, 118, 121, 125, 145,

176, 180, 181, 197, 198, 199, 200, 201, 202, 203, 204, 205, 209, 210, 219, 236, 237,

238, 239, 243, 245, 261, 263, 291, 299

packet, 96, 98, 194, 197

plane polarized, 63, 210

polarization, 67, 76, 79, 217, 220, 237, 346, 399, 405, 411

properties, 63, 78

progressive, 63, 219, 411, 412

velocity, 96 Wedge refraction, 209 West-east propagation, 407

Whistler mode, 76, 411

Whistlers, 413 Wind shear, 344, 353, 364

Wolf, sun spot number, (see Ziirich), 40, 41 World data centers, 124 WWV, 115, 173, 244, 245, 246, 263, 282, 284 WWVL, 414, 415 X

X-rays, 8, 37, 38, 43, 258, 384 Z

Zenith angle of sun (x), 12, 13, 18, 262, 281, 291, 297, 317, 320, 427, 432 Zero-muf (see MUF, M(ZERO) F2). Zero-order mode, 397, 398 Zero of refractive index, 427

Z-trace, 118, 121

Ziirich relative sunspot number, 138, 143, 144

Author Index

A

Agy, v., XIV, 214, 271, 272, 273, 275, 277, 280, 283, 287, 288

Allen, A. H., 443 Anderson, L. J., 215 Aono, Y., 214

Appleton, E. V., 63, 99, 145, 146, 157,

172, 196, 214 Athay, R. G., 44 Auterman, J., 244

B Baghdady, E., 256

Bailey, D. K., 215, 287, 288, 390

Bain, W. C, 442

Baker, D. M., 287

Balser, M., 256

Barber, N. F., 442

Barron, D. W., 442

Bartels, J., 30, 33, 44 Bateman, R., 287, 379, 390, 391

Bazzard, G. H., 341

Berry, W. M., 342

Belrose, J. S., XIII, XIV, 411, 412, 422,

427, 428, 429, 430, 431, 432, 434, 435,

436, 439, 443

Bennett, W. R., 342

Berg, M. R., 391

Berkner, L. V., 287

Best, J. E., 147, 158, 442 Beynon, W. J. G., 108, 156, 172, 196, 214, 276

Bibl, K., 158

Bickle, J. E., 426, 443

Blair, J. C, 350

Booker, H. G., 44, 202, 215, 256, 287,

380, 391

Bowhill, S. A., 256

Bowles, K. L., XIV, 382, 383, 384, 385,

387, 388, 389, 390, 391, 392 Bowman, C. G., 158

Bracewell, R. N., 287, 438, 442, 443

Breit, G., 214

Brenimer, H., 197, 215, 227, 255

Briscoe, H. W., 392 Brown, G. M., 108, 156 Brown, J. N., 157 Brown, J. T., 215, 391 Budden, K. G., 73, 75, 93, 99, 124, 157,

196, 203, 215, 255, 256, 395, 438, 441,

442, 443 Burke, M. J., 88, 99

C

Cain, J. C, 24, 25

Calvert, W., 215, 391

Carpenter, R. J., 391 Chamberlain, J. R., 391 Champion, K. S. W., 44 Chapman, S., XIII, 19, 22, 44

Chilton, C. J., XIV, 415, 417, 419, 420,

422, 443

Chivers, H. J. A., XIV, 215, 248, 252, 261 Chvojkova (Woyk), E., 196, 215

Cilhars, W. A., 443 Cohen, R. S., XIV, 379, 390, 391

Collins, C, 278, 279, 287, 288, 380, 391

Corke, R. L., 443

CorHss, W. R., 342 Cox, J. W., 214, 287

Crary, J. H., XIV

Crichlow, W. Q., XIV, 342 Crombie, D. D., XIV, 415, 420, 422, 424, 442, 443 D

Davies, K., 44, 74, 99, 103, 113, 121, 156,

157, 158, 214, 215, 287, 288, 391

Davis, R. N., 350

Bellinger, J. H., 260, 287

Dennison, J. S., 5, 7, 10, 44 De Voogt, A. H., 215

Dieminger, W., 158

Dinsey, R. T., 342

Dolphin, L., 391 Dougherty, J. P., 392, 443 Dyce, R., 381, 391

E EUyett, C, 390 Eshleman, V. R., 357, 360, 362, 390, 391 Evans, J. v., 215

F Faraday, M., 99

Farley, D. T., 392

Fejer, J. A., 392

Feidstein, Y. I., 34 Fenwick, R. C, 113, 157

Findlay, J. W., 157 Finney, J. W., 379, 391

Forsyth, P. A., 380, 391

Fowle, D., 158 Friedman, H., 44

465
466 AUTHOR INDEX

G

Gallet, R. M., 301, 341, 342, 442

Gautier, T. N., XIII, XIV, 215, 233, 234

Glover, F. N., 158

Gonzales, V. H., 215 Gordon, W. E., 384, 392

Green, J. L., 385 Greenhow, J. S., 390 Goubau, G., 63, 99

Gregory, J. B., 288 H Hagg, E. L., 157, 158, 215, 287 Hakura, Y., 287

Hall, J. E., 390 Hansen, D. R., 391 Hanson, G. H., 158, 341 Hanson, R. A., XIV

Hara, E., 87, 99

Harper, J. D., 442

Hartree, D. R., 63, 99

Haselgrove, J., 202, 215

Hatton, W. L., 214, 439, 443 Hawkins, G. S., 354, 373, 374, 390 Haydon, G. W., XIV, 290, 293, 341

Hefly, G., 443

Helliwell, R. A., 442

Heritage, J. L., 425, 426, 443

Hertz, H., 56, 99 Hewish, A., 256

Hill, G. E., 287

Hines, C. O., 367, 369, 370, 371, 372, 391 Hojo, H., 287

J Jean, A. G., XIV, 415, 420, 422, 424, 426, 442

Jelly, D. H., 278, 279, 287, 288

Jespersen, J. L., 215

Johler, J. R., 442

Jones, R. M., 287

Jones, W. B., 301, 341, 342

Josik, H., 342

Jull, G. W., 254, 256K

Kaiser, T. R., 390 Kasuya, I., 287 Keary, T. J., 371, 391

Kelso, J. M., 73, 99

Kiepenheuer, K. O., 44

Kift, F., 173, 214

King, G. A. M., 75, 99, 124, 157 King, J. W., XIV

Kirby, R. C, XIV, 287, 344, 350, 390 Knecht, R. W., XIII, XIV, 16, 44, 103,

121, 126, 138, 139, 140, 141, 144, 156,

157, 259

KomesarofF, M. M., 215

Kraft, L. G., 392 Kuper, G. P., 44

L Laby, T. H., 442 Landsberg, H. E., 44

Lauter, E. A., 437, 443 Lawrence, R. S., XIII, 209, 213, 215, 261 Leadabrand, R. L., 381, 391

Leftin, M., XIV

Leighton, H., 370

Leinbach, H., 288

Linfield, R. F., 443

Little, C. G., XIV, 108, 111, 156, 213,

215, 256, 261, 281, 288, 391

Lovell, A. C. B., 256

Lowenthal, M., 363

Lucas, D. L., XIV, 341 M

Manning, L. A., XIV, 390, 391 Margenau, H., 87, 99 Martyn, D. F., 214

Matsushita, S., 270, 287 Matthews, A. G., 278, 279, 287, 288

Maxwell, J. C, 99 Maynard, L. A., 391 McKerrow, C. A., 439, 443 McKinley, D. W. R., 391 McNamara, A. G., 391

McNeill, J. J., 442 McNicol, R. W. E., 158 Meadows, R. W., 256 Meek, J. H., 124

Minnis, C. M., 341 Minzner, R. A., 44

Moller, H. G., 214 Montgomery, C. F., 287, 373, 391 Morgan, M. G., 442 Morton, R. N., 342 Muldrew, D. R., 215, 287 N

Nawrocki, P. J., 44

Neilson, J. R., 24, 25 Newman, N., 443

Nickson, A. F. B., 442

Nicolls, F. G., 442

Norton, R. B., 5, 7, 10, 44, 255, 419 O

Ochs, G. R., 385, 391 Ogawa, T., 113, 157 Ostrow, S. M., XIV,^42

P Pack, J. L., 87, 99 Papa, R., 44

Parkinson, R. W., 442

Paul, A., 158
AUTHOR INDEX 467 Pawsey, J. L., 44

Pekeris, C. L., 442

Penton, W. A., 443

Peterson, A. M., 391

Petterson, G. W. E., 254

Phelps, A. v., 63, 87, 99

Pierce, J. A., 443

Piggott, W. R., 108, 145, 146, 156, 157,

236, 240, 255, 287

Pineo, V. C, 392

Plush, R. W., 443

Poverlein, H., 202, 215 Pond, H. L., 44 Posakony, D. J., 209, 215

Presnell, R. I., 381, 391 Pugh, R. E., 370, 291

Purcell, E. M., 287

R

RatcHffe, J. A., 44, 73, 84, 99, 147, 158, 256, 287, 438, 442, 443 Rawer, K., 156, 158, 235, 255 Rayton, W. M., 391

Reber, G., 158

Reid, G. C, 288

Rice, S. O., 243, 256

Rolf, W., 215

Roof, R. B., 391 Roubique, C. J., 342

Russell, S., 157

S Saha, A. K., 157 Salaman, R. K., XIII, 214

Salisbury, W. W., 287

Salpeter, E. E., 392

Sandoz, O. A., 214 Schlobohm, J., 391

Schneider, O., 35 Seddon, J. C, 157, 158

Sen, H. K., 63, 87, 99

Shiniazaki, T., 158

Shinn, D. H., 256

Silberstein, R., 155, 215, 281, 288

Skinner, IN. J., 158 Smerd, S. F., 44

Smith, D. F., 342

Smith, E. K., 158, 214, 379, 391

Smith, F. G., 215

Smith, IS., 166, 214

Smith, W. B., 256

Spaulding, A. D., 342

Spies, K., 403, 404, 405, 406, 407, 408,

409, 410, 442

Sprenger, K., 443

Stein, S., 215

Steele, F. K., 417. 419

Stevens, E. E., 214

Stiltner, E., 215, 391

Storey, L. R. O., 75, 99, 157

Straker, T. W., 287, 438, 442, 443

Stratton, J., 99

Sugar, G. R., XIV, 351, 354, 363, 368,

373, 390, 391

Sulzer, P. G., 214

T Tao, K., 158

Taylor, E. W., 157

Taylor, W. L., XIV, 442

Thain, R. S., 439, 443 Thomas, J. O., 125, 157, 158, 214 Thomas, L., 255, 276, 287

Titheridge, J. E., 157, 202, 215 Tuve, M. A., 214

Tveten, L. H., 379, 391 V

Van Mieghem, J., 44 Van Zandt, T. E., XIII, 2, 5, 7, 10, 12,

16, 18, 44, 157

Villard, O. G., 113, 157, 215, 288

Vogen, E. L., 391 W

Wait, J. R., XIV, 395, 403, 404, 405,

406, 407, 408, 420, 441, 442, 443 Waldmeier, M., 42, 44

Walters, L. C, 410 Warren, E. S., 157, 214, 256, 287 Warwick, C. S., 44 Watson-Watt, R., 1 Watt, A. D., 443 Watts, J. M., XIII, 113, 120, 157, 379,

390, 391 Webster, H. C, 158 Weekes, K., 44, 438, 443 Weisbrod, S., 215, 426, 443

Wescott, C. H., 442 Wheelon, A. D., 390

Wieder, B., 170

Wilkes, M. v., 44, 442

Wilkins, A. F., 214

Winkler, G. M. R., 443

Wirth, J. H., 371, 391 Wright, J. W., XIII, 44, 103, 121, 127,

128, 129, 131, 132, 156, 157, 215

Wright, R. W., 158

Wyller, A. A., 63, 87, 99 Y

Yeh, K. C, 215, 288Z

Zacharisen, D. H., 142, 143, 157, 342
I

II I ii . I i I
Place Index

A

Accra 177, 247 Adak (lonad) 122, 123

Africa 182, 185 Ahmedabad 148 Alaska 122, 123, 261, 272, 278, 282, 286,

383, 419, 420

Alert 278 America 148, 149, 185 Amsterdam 31 Anchorage 282, 283, 284, 285, 286 Arabian Sea 426

Arctic 282, 349

Ascension Island 178, 179, 189, 192

B Baker Lake 119, 148, 278, 282 Barrow 281, 381, 421, 422 Belgrano 35

Berlin 430 Bismarck 283, 284 Boston 285, 441 Boulder XIII, 115, 175, 176, 177, 178,

198, 199, 200, 209, 244, 245, 246, 315,

414, 417, 418, 419, 421, 422, 424, 429, 441 Bueno Aires 35 C

Cambridge 422, 430, 436 Canada 119, 148, 174, 178, 274, 282 Canary Islands 340, 341 Cedar Rapids 373 Cheltenham 260

Churchill 148, 278, 279, 282, 433, 435 Clyde River 278

College 261, 282, 283, 284, 383, 381 Comfort Cove 433, 435 CRPL (Central Radio Propagation

Laboratory) XIII, XIV, 31, 39, 120,

124, 130, 145, 148, 149, 258, 282, 285,

287, 289, 301, 302, 303, 304, 305, 310, 331 D

DeBilt 30, 31 Decca 441

Delhi 148, 178, 179 Droitwich 441 DRTE (Defence Research Telecommunications Establishment) 119, 179, 282, 303

England 108, 418, 423 Europe 149, 185, 281, 349

F Fairbanks 285 Far East 377, 378

Fort Belvoir 118, 138, 140, 143, 144, 286

Fort Monmouth 268, 269

Frankfurt 424

Freiburg 148 G

GBR 416, 418, 419, 420, 421, 422, 423,

424, 441 Genoa 148 Germany 174 Goose Bay 374, 433, 434

Gottingen 30, 31, 33 Grand Bahama 128 Great Britain 174 Greenland 152, 285

Greenville 185 Greenwich 30 H

Halifax 254, 255

Halley Bay 35 Hawaii 282, 426 Huancayo 101, 127, 128, 151, 152, 154

Ibadan 148

India 148 Indian Ocean 426

Ithaca 385

J Japan 174 Jicamarca 386, 387 K Kalundborg 428, 430 Kenai 278

L Lima 386, 388, 389 Lindau 188 London 240, 285, 330, 341 Long Branch 384 Loran C 441 469
470 PLACE INDEX

M

Maine 285 Maui 282, 283, 284 Meanook 278

Millis (WIXK) 260 MIT (Massachusetts Institute of Technology) 384 Moscow 34 Motala 430 Munich 185 N

National Bureau of Standards XIII,

258, 286, 303 NBA 418, 419 Newfoundland 128, 433 New York 285 New Zealand 418

Nigeria 148 North Africa 185, 285 North America 281, 435 North Atlantic 286, 426, 441 North Pacific 286 NPM 424 O

Onna (Okinawa) 379 Ottawa 119, 179, 254, 255, 278, 282, 374,

429, 433, 434, 435

P

Pacific 286, 426 Panama 418, 419

Paris 285

Pennsylvania State University 412, 413

Point Barrow 281, 381, 419, 420

Polo Geomagnetic 35 Poro 379

Prince Rupert 148 R Radio Research Laboratories (Japan) 303 Radio Research Station (England) XIV,

137, 145, 179, 240, 303

Resolute Bay 148, 271, 278, 282 Rugby 416, 417, 424

S

St. Louis 180 San Francisco 285 Scandanavia 272

Seattle 285

75° geographic meridian 132, 133 Shackleton 35

Siberia 36

Singapore 36, 206

Skelton 228

Slough XIV, 101, 137, 145, 146, 147, 148,

178, 179, 189, 192

Slutsk 101 South America 377 South Ice 35 South Pole 151, 154

Sterling 175, 176, 177, 178, 180 Swansea 228 Sydney 148 Syowa 35

T Tokyo 148, 285

Tripoli 177, 247 U United States 148, 149, 174, 181, 182, 202, 349, 350 W

Washington, D. C. 101, 148, 152, 260,

261, 285, 314, 315, 330 Watheroo 101 Western Russia 149 White Sands 126, 151 Wingst 33 Winnipeg 271, 278 World Data Centers 124 WWV 115, 173, 224, 245, 246, 263, 282 WWVL 414, 415 Z

Zurich 42, 138, 143, 303

a U. S. GOVERNMENT PRINTING OFFICE : 1965 O - 737-179
I

I

IONOSPHERIC RADIO PROPAGATION

BY

KENNETH DAVIES

Page

12 Equation (l-l^) (c)

13 Equation I.I8

13 Equation I.I9

ih Equation 1.23

17 Equation 1.3^

22 Figure 1.6

25 Figure 1.8 (title)

kk

58 Equation 2.1+2

62 Line 6

70-71 Equations 2.73,

2.7^, and 2.76

7h Figure 2.9 (b)

76 Line 11

79 Figure 2.11 (a

Figure 2.11 (b

80 Equation 2.95

8k Equation 2.103

85 Figure 2.ll+ (a)

Figure 2.1^ (b)

Errata as of December 17, 1965

Correction

XA in place of XY

h

f Ncjdh

00h

;

00r N dh = = h

2

Nmax

ctNT mg

is incorrect (F isosurfaces should be

rotated through 90^

}

(1) should be (l)

Kuper should be Kuiper in 13, I5, 18. —.should be

Mo ' ^

WB/m cm ^ not Wo/

Extend root sign to include hx\

Curve through X = 1 should be d.

Curve through X = 3 should be x. (interchange o and x)

Use small "c" on Budden ref . Bracket at

end of sentence

3 should be on left.

3 should be on left

- before v W not Ny . 1; not subscript, should be as in 2.98.

3 on left

2 on top, 3 on left.

Errata as of December I75I965

86 Table 2.1 (title)

92 Figure 2.l6

126 Figure 3.I3

137 Figure 3.199

160 Figure k.l

161 Line 17

162 5th line from bottom

of page

162 Equation ^.6

163 Equation ^.7

172 Line 11

175 Figure k.l2

178

179 Figure k.lQ

Figure ^.19

182 Figure k.2Z (caption)

195 Figure ^.3^

206 Figure k ,h3

208 " Figure h,k'^

220 Equation 5.^

231 Line 7. 9

233 Figure 5-12

257 Line 8

258 Line 6

262 Line 2h

IONOSPHERIC RADIO PROPAGATION

should be same as equation (2.IO5) on page 88.

Insert "nearly" between of and equal

Defence spelled with c (Norwegian)

One "t" in Britannic

Insert letter G at midpoint of TR

Parentheses within parentheses, remove

inner set.

Expression for replace AD with AG

P'(f) = 2 h'(f^) sec 0o

Bmudge on parentheses

Insert "analytically" after determined.

Time should be 2112 not 2012

Pedersen

One "t" in Britannic

Add, [Sterling-St .Louis, II50 km, O957

(75''WMT) May 15, I962]

Replace 0 with i, as in equation ^.l8.

One "t" in Britannic

Redraw

Add a term Laa^ antenna aperture loss

Parentheses within parentheses, remove

inner set

.

hg - 80 km should read hj^ = 80 km (2 plac

Should read, (see section I.7.2)

Same as above

Section 3-2.3.2 not 2.5-3, add "and the

theory is given in section 2.5.3".

Errata as of December 1?, I965 - IONOSPHERIC RADIO PROPAGATION

285 Line 2 Parentheses within parentheses 5 remove inner set.

298 Figure 7-6 This nomogram is based on the equation

- _ 61^.^ n sec 0 [1 + .0037R][cos .881 x]"^'^

n = niimber of reflections. Note that it is

inaccurate for frequencies less than about 5 Mc/s

30^ Figure 7.9 (a) Title should read I8OO UT not O8OO

313 Figure 7. 10 (b) & (c) Abscissas shcaild be labeled Mc/s.

325 Line 10 Change Eg ^ to Eg

329 Figure 7-19 ("b) & (c) Insert figure title. Abscissas should be labeled

Mc/s. Should be consistent with figure 7* 10.

3^2 Jasik not Josik

360 Line 9 (IO.8) should read (8.8)

388 Last line (IO.I8) should read (8. I8)

kOl Line 5 V smudge

kl3 2nd line under (see sec. 7-2.2) should read (see sec. 7'5.l)

section 9 '3.1

hh'J Chapman layer, reference to page 3^ should be

page 13^ .

^+^9 E layer — note repetition

Under height — phase repeated, real or true

split.

^57 Pedersen

466 Hefley not Hefly

466 Last Line Kuiper not Kuper
, I;