^Kal Bureau of Standards

Library, H.W. Bldg

81962 .

^ecltnlcal ^2©te 145

EQUATORIAL SPREAD F

WYNNE CALVERT

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

cecAftical ^V^ote

145

AUGUST 1, 1962

EQUATORIAL SPREAD F

Wynne Calvert

Boulder Laboratories

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. Price
ABSTRACT

Most equatorial spread. F may be attributed to coherent scattering

by thin, magnetic -field. -aligned irregularities in the ionization of

the F layer. These irregularities occur in patches which move horizontally. The velocity of the motion may be measured by (l) the simulation of spread F observed, with a single ionosonde, (2) the timing of

the occurrence of spread F at spaced ionosondes, or (3) the measurement

of the doppler-shift imposed on scattered radio waves. The velocities

are west -to-east throughout the night, with magnitudes of 100-200 m/s

at sunspot maximum and 50-130 m/s at sunspot minimum. The instability

of the F layer giving rise to the formation of spread-F irregularities

could result from (l) upward electromagnetic drift of the ionosphere as

a whole, (2) thermal contraction of the neutral atmosphere after sunset,

(3) atmospheric gravity waves, or (h) geomagnetic support of the F

layer against gravity.

11
This technical note is based upon a thesis submitted by the

author to the faculty of the Graduate School of the University of

Colorado as a requirement for the degree of Doctor of Philosophy.

The work described here grew from that of research groups

afiliated with NBS who are currently studying equatorial phenomena.

The observations involved were performed by them; the interpretations were largely the contribution of this author. Some embryos of

the ideas developed here were conceived during numerous discussions

with Dr. R. Cohen, Dr. T. E. VanZandt, Dr. K. Davies, Dr. M. L. V.

Pitteway, Mr. R. B. Norton, Mr. S. Radicella, Mr. J. T. Brown, and

Mr. E. Stiltner. Mr. J„ T. Brown collected the velocities of

figures 26 and 27.

The author wishes to acknowledge the generous guidance of

Dr. R. Cohen and Dr„ T. E. VanZandt during this work.

111
CONTENTS

ABSTRACT

Part I

OBSERVATIONS OF SPREAD F 1

Introduction 1

Occurrence of spread F 3

The relation of spread F to other phenomena 11

Equatorial spread-F irregularities 12

Part II

THE INTERPRETATION OF SPREAD F 19

Previous interpretations of spread F 21

A scattering model for equatorial spread F 22

The simulation of equatorial 'scatter' spread F 31

Equatorial 'waveguide' spread F 37

Appendix A. Transformation relationships for backscatter

traces ^-0

Appendix B. Equatorial sporadic E simulation h-h

Part III

SPREAD-F MOTIONS 51

Methods of observation 51

Spread-F simulation 52

Spaced ionosondes I 5^

Spaced ionosondes II 58

Doppler-shifted oblique scatter 62

Appendix C. Conditions for phase coherence along thin

irregularities near the equator 72

iv
Part IV

THEORIES OF SPREAD -F IRREGULARITIES 77

Current theories 77

Electrostatic coupling to the E region 78

Amplification of drifting irregularities 8l

Electrostatic drift 83

Thermal contraction of the neutral atmosphere 85

Gravity waves 87

Gravitational instability 88

Conclusions 89

Appendix D. The motion of a cylindrical irregularity in

ionization 91

Appendix E. Geographic locations mentioned in the text 101

REFERENCES 102
ILLUSTRATIONS

1. An idealized ionogram 2

2. Equatorial spread -F configurations k-"J

3- Spread-P configurations at high latitudes 8

h. Spread -F occurrence versus magnetic latitude 9

5. Height of the equatorial F layer 13

6. South American map ik7. Transequatorial scatter signals 16

8. Direction-of-arrival of spread-F echoes 18

9. Ground scatter configuration 20

10. Equatorial scattering model: below the "base 26

11. Equatorial scattering model: between the base and the peak 27

12. Equatorial scattering model: above the peak 28

13. Projection of oblique scatter echoes 30

lk. Predicted equatorial 'scatter' spread-F ionograms 32

15. Simulation of Huancayo spread F 3^

16. Simulation of Huancayo spread F 35

17. Simulation of Huancayo spread F 36

18. Equatorial 'waveguide' s pread-F model 38

19. Scattering ray geometry ^3

20. Equatorial sporadic E at Huancayo k$

21. Simulation of equatorial sporadic -E traces ^7

22. Envelopes of equatorial slant sporadic E ^8

23. Simulation of equatorial sporadic-E intensity 50

2k

.

Simulation of spread-F sequence 53

25. Ground distance of spread-F sequence 5^

vi
26. Spread-F velocities at sunspot maximum 55

27* Spread-F velocities at sunspot minimum 57

28. Spread-F velocities deduced by Knecht 59

29* The correlation of spread F "between Huancayo and Natal 6l

30. Spread-F doppler shifts 6^-65

31. Loci of phase coherence: single-hop path 67

32. Loci of phase coherence: double -hop path 69

33. Spread-F velocities derived from doppler shifts 71

3^-. Doppler-shift geometry: vertical view 73

35» Doppler-shift geometry: plan view 7^-

36. Electrostatic coupling scale sizes 80

37- Amplification of drifting irregularity 82

38. Motion of a charged particle in a magnetic field 92

39- Ionization irregularity in cross section 95

Vll

Part I

OBSERVATIONS OF SPREAD F

Introduction . Spread F refers to a condition of the upper atmosphere

as it appears to an ionosonde . An ionosonde is simply a sweep-frequency

radar which responds to radio waves reflected by the ionosphere. It

commonly covers the range 1-25 Mc/s and records delays to about 10 c

~ sec.

The instrument produces ionograms -plots of frequency versus delay. The

delay of the radio-wave pulses is usually presented in terms of virtual

height --the delay multiplied by half the free -space velocity of radio

waves.

The free electrons of the ionosphere strongly disperse radio waves

.

The dispersion, neglecting the effects of particle collisions and the

geomagnetic field, may be represented by the refractive index u:

\? = 1 - (fN

/f f, (1)

where f is the frequency of the radio wave and f is the plasma frequency

(proportional to the square-root of the electron density). Since the

wave is reflected where f = f (where u = 0), the frequency reflected is

a measure of the electron density at the height of reflection. The group

velocity, (which determines the delay of the ionosonde pulses) derived

from equation (l), decreases with increasing electron density. Thus the

pulses are retarded by the ionosphere, and the virtual height will exceed

the true height of the point of reflection. Figure 1 illustrates how

this retardation affects the ionogram. The frequencies marked foE, foF.. ,

foF are the penetration frequencies of the various ionospheric layers

.
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from small electron -density gradients at the height of reflection. Additional traces resembling the main trace often appear on ionograms at

greater virtual heights as a result of multiple reflections between the

ionosphere and the earth. They are called first-, second-, etc. "multiples"

Spread F is said to occur when the F-layer trace on the ionogram

becomes diffuse, in contrast with the sharp trace illustrated in figure 1.

The appearance of the diffuse echoes --the configuration of spread F- -varies

with geographic location and time. Figures 2 and 3 show examples of

spread F observed at low and high geomagnetic latitudes, respectively.

The former are the topic of this work.

Equatorial spread F appears as variations of the four configurations

of figure 2. Based on their interpretation in part II, figures 2a, 2b,

2c show the three basic types of equatorial 'scatter' spread F, and

figure 2d shows equatorial 'waveguide ' spread F. The significant feature

of the configuration which distinguishes between the two is the presence

or absence of steep striations like those of figure 2d.

Occurrence of spread F. Spread F occurs in two separate geographic

regions in which its characteristics differ considerably. This leads to

the division of spread F into equatorial and high-latitude varieties, and

to the isolation of the former as the topic of this study.

Figure k shows the two regions where spread F is common. This

figure is sketched from similar figures by Singleton (i960) to show the

essential features of spread -F occurrence as a function of geomagnetic

latitude and local time. The equatorial region is bounded by + 20

geomagnetic latitude; the high-latitude region(s) by + 60 geomagnetic
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Figure k. Idealized spread-F occurrence frequency (#) for equinox,

sunspot -maximum conditions near the 75th meridian. Adapted

from Singleton ( i960 )

.
10

latitude. In the high -latitude region spread F shows a preference for

the nighttime, while in the equatorial region it is exclusively a nighttime phenomenon.

The two spread F regions have different seasonal variations. Near

the magnetic equator spread F occurs most often during the equinoxes (or

during local summer where the magnetic equator departs considerably from

the geographic equator). For example, at Huancayo, Peru extensive displays

of spread F are observed nightly from November through January, but only

on a small handful of nights during June ( Cohen and Bowles , 1961). In

the high-latitude region the occurrence frequency peaks during local

winter although it remains high year-round. This is, of course, confused

with the trend toward nighttime occurrence

.

The sunspot-cycle dependence of spread F also varies with latitude.

Spread -F statistics have been accumulated by Reber (195^-a, 195^b, 195&)

for stations within the spread -F regions and between the two:

Washington, D.C., USA; dip: 71 Nj high-latitude

Maui, Hawaii, USA; dip: 39 N; intermediate

Rarotonga Island; dip: 39 S; intermediate

Dakar, Fr. W. Africa: dip: IT N; equatorial

These data indicate that spread-F occurrence in the equatorial region

goes with the sunspot cycle; in the high-latitude region, with the reverse

of the sunspot cycle. The effect is much less marked for the former

than for the latter. At the intermediate stations the sunspot cycle

appears to alter the seasonal dependence. During sunspot minimum the

peak occurrence is in local winter; during sunspot maximum, in local

summer or equinoxes . These stations seem to exchange their role as

equatorial or high-latitude stations with the phase of the sunspot cycle.
11

The relation of spread F to other phenomena . The occurrence of

spread F has been compared with that of a number of other phenomena,

including geomagnetic activity, ionospheric scintillation, and F-layer

height changes

.

The correlation between spread F and magnetic activity is strongly

negative near the magnetic equator, positive between 20 and 60 geomagnetic latitude, and again negative near the poles. The negative

correlation at very high latitudes is probably a result of observational

selection ( Shimazaki , 1959b, 1960b), since the polar blackout or auroral

absorption occurring with high magnetic indices interferes with F-layer

observations . The strong negative correlation for equatorial spread F is

in the sense that high magnetic activity by day rarely precedes spread F

on the following night ( Wright and Skinner , 1959.5 Rao and Rao , 1961).

The effect is strong enough to suggest the prediction of spread F from the

state of magnetic activity ( Wright , 1959)

•

Spread F and radio-star scintillation have been correlated in terms

of monthly and annual means ( Dagg , 195Tb), their diurnal variation

(Ryle and Hewish, 1950; Koster and Wright , i960), and individual events

(Briggs, 1958j Brenan , i960; Wild and Roberts, 1956; Wright , Koster, and

Skinner , 1956). The correlation is clearly positive for both equatorial

and high-latitude stations. Kent (1961) has analyzed the scintillation

of radio signals from an artificial satellite. The diurnal occurrence

and the relation to magnetic activity agree with those of spread F. The

scintillation patterns at the equator correspond to magnetic -field-aligned

irregularities O.k km by 2 km in size.
12

Equatorial spread F has been related to height changes of the F

layer since the early reports ( Booker and Wells , I938). A theory by

Martyn (l959) - -<3-i scusse<3- in part IV --has recently inspired further study

( Wright , 1959 J Rao , Rao , and Pant , i960; Lyon , Skinner, and Wright , 1960b,

I96I j Rao and Rao , I96I; Rao and Mitra , 1962). The equatorial F layer

appears to rise 50-150 km just after sunset, reaching its greatest height

at a time when spread F usually starts (See figure k.). Figure 5 shows

examples of this rise for Huancayo, Peru. The curves are monthly averages

of the height of the base of the F layer with and without spread F. From

these diagrams it appears that the F layer rises farther and remains high

longer with the presence of spread F. The effect is strongest at the

equinoxes and weakest during local winter (May-July).

Equatorial spread -F irregularities . Beginning with the IGY,

Dr. K. L. Bowles and Dr. R. Cohen of the National Bureau of Standards

have conducted a series of observations of magnetic -field-aligned

irregularities in the ionosphere above Peru. This section was adapted

from their work ( Bowles and Cohen , 1957> 19^0; Cohen and Bowles , 1961).

As a part of the IGY effort, the following transequatorial scatter

experiment was conducted in South America. To study radio-wave scattering

in the F layer, a 50 Mc/s transmitter was installed at Antofagasta, Chile

to beam a steady "continuous -wave" signal north to Guayaquil, Ecuador.

The transmitting and receiving antenna beams intersected at F-region

heights above the magnetic equator, as shown in figure 6. In a late

phase of the experiment, pulse transmissions over the transequatorial

path were employed to determine the height of the scattering irregularities.

Finally, a number of additional experiments were conducted at Huancayo, Peru
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14

.GUAYAQUIL

TALARA

CHICLAYO

CHIMBOTE

HUANCAYO

-MAGNETIC

EQUATOR ~-

LAPAZ

km

ZOO 300 400 500

ANTOFAGASTA

Figure 6. A map of the west coastal area of South America with the

approximate loci of antenna beam intersections computed for

the heights indicated (130 and 170 km). La Paz, Bolivia;

Huancayo, Peru; Talara, Peru; Chiclayo, Peru; and Chimb ote,

Peru are the locations of ionosondes.
15

to supplement the data from the forward-scatter experiment.

Figure 7 illustrates the close connection between signal enhancements on the scatter path and the occurrence of equatorial 'scatter'

spread F near its midpoint. (Enhancements did not appear to accompany

equatorial 'waveguide' spread F. ) In these diagrams, time increases

from right to left. Figure 7& shows a strong E-layer signal (associated

with daytime sporadic E) decaying between 1800 and 1912 and then abruptly

giving way to a scatter signal from the F layer. Huancayo ionograms

recorded shortly thereafter show the onset of spread F. Concurrent pulse

measurements indicated that the scattering took place at the height of

the arrows --coincident with the lowest features of the configurations.

Much later, the spread-F configuration became more complicated and the

signal strength became more variable . Figure 7b shows an early morning

enhancement associated with the second type of equatorial 'scatter'

spread F (i.e. figure 2b). Both the signal enhancement and the display

of spread F at Huancayo develop between 0300 and 0400 and decay between

C4(X) and 0500. The two peaks in signal strength indicate that two

patches of irregularities came into view. In this case the pulse measurements indicated that the scattering took place well within the F layer.

The enhancement to the far left is attributed to the onset of sporadic E

in the morning. In both of the examples above, the pulse measurements

indicated that the patches of spread-F irregularities were the order of

only 50 km thick.

The observation of relatively thin patches of spread-F irregularities led to the interpretation that the spread echoes on the ionogram

at large delays do not return from overhead, but from some oblique direction.
16

(a) 16 NOVEMBER 1958

2400 2200

—2400

2000

=8 -20 —j/-*^v

(b) 25 NOVEMBER 1958

0600 0400

1

1900-

0200

"0500" "0430 0400" 0300'

Figure T« Signal strength for the Antofagasta-Guayaquil scatter path

during equatorial 'scatter' spread F at Huancayo. The height

of irregularities derived from'pulse measurements is indicated

by the arrows . Adapted from Cohen and Bowles ( I96I )

.
17

The direction of this oblique scattering was subsequently determined with

directional antennas installed at Huancayo, Peru. Figure 8 shows

"A-scan" diagrams - -plots of echo strength versus pulse delay- -corresponding

to 8.3 Mc/s beam antennas inclined 30 to the vertical and directed south,

east, west, and north ( Pitteway and Cohen , I961). The transmitted pulse

appears at the left edge of each display and time increases toward the

right. When the striations of the spread F configuration are largely

horizontal (figure 8a) the oblique echoes return from the east and from

the west. However, when steep striations like those of figure 2d are

also present (figure 8b; above the arrow on the ionogram marking the

8.3 Mc/s operating frequency) oblique echoes also return from the south.

This, and the fact that forward scatter at 50 Mc/s is not enhanced with

spread F consisting solely of steep striations, is observational evidence

for the division of equatorial spread F into the two varieties here termed

'scatter' and 'waveguide'.

The east-west oblique echoes of equatorial 'scatter' spread F are

consistent with the picture of coherent scattering by thin, north-south

irregularities (the scattering then being strongest in the plane normal

to their long dimension). Since 50 Mc/s radio waves are scattered,

irregularities the order of 6 m in cross -section (the wavelength at

50 Mc/s) must be present. Further experiments on the north-south

coherence of the scattered echoes lead to the conclusions that the

irregularities are at least 1 km in length and that they are aligned

along the earth's magnetic field.
18

15 MAR I960 2144 16 MAR I960

h'(km)

Figure 8. Spread F echoes received from various directions during the

occurrence of (a) horizontal structure and ("b) both

horizontal and vertical structure in the spread-F configuration at Huancayo. The 8.3 Mc/s operating frequency is

indicated by the small arrow on the ionogram.
19

Part II

THE INTERPRETATION OF SPREAD F

The first phase of a theoretical study of spread F should "be

the interpretation of the ionogram configuration in terms of a geometrical model. In other words, we wish to know what distribution

of electron density, scattering irregularities, etc. will give the

observed appearance to the ionogram.

As an example of such a model, Dieminger '

s

(1951) interpretation

of ground scatter will he outlined. In figure 9a > "the ground scatter

echoes are those spread echoes extending upward from the first multiple

of the F-layer trace. They seem to he always present when the ionosonde

is sufficiently sensitive. Dieminger' s interpretation involves radiowave scattering at the ground: Radio waves are reflected in the F

layer; scattered by irregularities on the ground; reflected again in

the F layer; and then returned to the ionosonde. Since this propagation circuit becomes the second-hop circuit at vertical incidence,

the ground-scatter configuration should naturally extend from the

first multiple on the ionogram. Further details of the configuration

are revealed by simple ray-path calculations. Neglecting the effects

of the earth's magnetic field and assuming horizontal stratification

of the ionosphere lead to Martyn '

s

(1935) and Breit and Tuve's (1929)

theorems. These compare vertical and oblique ray paths reflected at

the same height in the ionosphere. They state that the frequency and

delay for such rays are each proportional to the secant of the angle

of incidence (i):
20

1000

E

tt 500 — "M" ECHOES

J. "N" ECHOES

>3M

(a)

! L*-U- - -- GROUND SCATTER

SPORADIC E

10 20

1000

500 -

(b)

<jr N—CAUSTIC FOCUS

I I I 10 20

f (Mc/s)

Figure 9* ( a ) Huancayo, Peru ionogram recorded shortly before

dawn, April, i960, and

("b) The interpretation of ground scatter proposed by

Dieminger (1951): scattering by irregularities

on the ground.
21

f . := f sec 1, (Martyn) (2)

h! = h sec i, (Breit and Tuve) (3)

where the subscripts v and i refer to vertical and oblique incidence,

respectively, f is the frequency, and h* is the delay. Hence the

ratio of frequency to delay for oblique rays at a given angle of

incidence is a constant times that for vertical incidence. Thus the

contribution to ground scatter of a given angle of radiation from the

ionosonde antenna is a trace similar to the first multiple with both

its delay and frequency increased proportionately, as depicted in

figure 9b* The lower edge of the configuration should be linear

(i.e. its virtual height proportional to frequency) and is called a

caustic focus - -the tangential envelope of a set of traces.

Previous interpretat i ons of spread F. Eckersley (1937> ' 19^9)

proposed a model for spread F which is essentially that for ground

scatter, but with the scattering irregularities in the ionospheric

E layer rather than on the ground. The scattering irregularities

were considered to be local concentrations of ionization of the proper

size and of sufficient contrast with their surroundings to scatter

radio-wave energy. Echoes consistent with this model are found to

occur (e.g. on the ionogram of figure 9a )> and are called "M" and

"N" echoes. However, these configurations should not be considered

as spread F, but as part of the sporadic E configuration with which
22

they always occur. This model fails to account for the equatorial

spread F configurations of figure 2.

Renau ( 1959a, 1959b, i960) has considered a number of spread

models. Among these are sharp ledges of ionization similar to those

proposed by Whale (1951) to explain sporadic E, a scattering screen

below the F layer, and aspect -sensitive backscatter by magnetic -fieldaligned irregularities in ionization. The models, however, do not

appear to provide an adequate explanation of the equatorial spread-F

configurations of figure 2.

A scattering model for equatorial spread F. * The equatorial

spread-F configurations of figures 2a, 2b, 2c are here considered

to arise from coherent scattering by thin, magnetic -field-aligned

irregularities. The model is developed in detail for the special case

of scattering at the magnetic equator. It attributes most of the

features of the spread-F configuration to refraction and retardation

imposed on the radio waves by the ionosphere as they travel to and

from the position of scattering, and scarcely involves the scattering

process itself.

This model is based on the tracing of radio-wave ray paths

between the ionosonde and the position of scattering and the computation of the corresponding delays to form theoretical ionograms . It

utilizes the simplifying conditions that:

*The content of this and the next section was presented to URSI at

the May 1961 meeting by the author and was subsequently published

(Calvert and Cohen, I961).
23

(a) the ray-tracing approach is assumed valid

(i.e. The electron density is assumed constant

over at least a few wavelengths of the radio

wave . )

;

(b) propagation is confined to the vertical eastwest plane through the equatorial ionosonde;

(c) only the ordinary ray of magnetoionic propagation theory is considered;

(d) the ionosphere is considered horizontally

stratified;

(e) the scattering irregularities are assumed to

scatter somewhat isotropically in the vertical

east-west plane; and

(f

)

a single -scattering approximation is assumed

adequate

.

The elongated irregularities are, at the equator, horizontal

and oriented north-south. Thus, as indicated above in (b), the

plane in which coherent scattering can occur is a vertical eastwest plane through the ionosonde. Propagation is thus transverse

to the magnetic field and the dispersion relation for the ordinary

wave is just that for the field-free case, equation (l). Furthermore, this is also approximately true for the extraordinary wave when,

as is often the case with spread F, the propagation is sufficiently

oblique to the ionosphere. (For this reason, ordinary and extraordinary features can seldom be distinguished in spread-F
24

configurations.) Thus the simplification introduced by condition (c)

is justified.

Conditions (a) and (d) allow the use of Snell's law in calculating

propagation paths.

Condition (e) implies that an echo may be obtained over any

ray path, or combination of ray paths, connecting the ionosonde

and the assumed scattering center.

Condition (f) states that the individual irregularities scatter

independently, so that the ionogram corresponding to a set of

irregularities is simply the superposition of those corresponding to

each of the irregularities alone.

The equivalent range corresponding to a pair of ray paths to and

from the irregularity is arrived at by integrating the delay along

the route. This equivalent range, as a function of frequency,

defines a 'scatter trace' on the ionogram. First the scatter traces

corresponding to a scattering irregularity overhead are discussed.

The results will then be transformed to give the scatter traces

corresponding to an irregularity east or west of the ionosonde.

For the overhead case, the (vertical) equivalent range h' is

first computed from equation (13 ) with f = f (See appendix A).

XT. This simple integration yields resulting ionograms like those of

figures 10a, 11a, and 12a for irregularities situated at or below

the base (h ) of the F layer, between the base and the peak (h )

of the F layer, and at or above the peak of the F layer, respectively.

For the first two, there are three possible 'round-trip' ray paths:
25

(i) the direct path to the irregularity and return, (ii) the path

reflected to the irregularity by the overlying ionosphere and return,

and (iii) the combination of these two—arriving by one path and

returning by the other. The 'backscatter ' modes (i) and (ii),

contribute the two added traces on the ionograms of figures 10a and

11a, above and below the regular F-layer trace. The 'combination'

mode, (iii), produces a scatter trace with equivalent ranges which

are the averages (at each frequency) between those of the backscatter

modes. Thus, in this case, the combination trace coincides with the

regular F-layer trace. With the irregularity above the peak of the

layer, no reflected ray path is possible, and only one scatter trace,

that of mode (i), is produced on the ionogram (figure 12a).

There is a point-to-point correspondence between the backscatter traces for an irregularity overhead and those for an

irregularity at the same height, but located east or west of the

ionosonde. It is represented by the transformation:

f = f (1 + R

2

/h'

2

)^, (k)

R v v

h^ = V (1 + R

2

/h'

2

)2, (5)

where h' = h' (f ) represents a backscatter trace produced by an

irregularity overhead and h' (f^) represents the corresponding backR R

scatter trace produced by an irregularity at the same height, but

at a ground distance R from the ionosonde. This transformation,

a generalization of that expressed by equations (2) and (3), is

derived in appendix A.
26

fel

cc

a

ce

v

m

in\\\

<\ cc \\ 2 O

ii ii

J I I l_ 8 £ o

<d

d . rd • G to p 0) CD ^^ d o

<H c » S o o OJ

to

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O

(D o • CO c •. to3 o H

rQ •H

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CD 0) to ,3 rci >5

-p -P

U CJ B si > s hC CD 9 o •H 3 H u <H &

CD <+H CD P HH Jh

!h

n o <+H

O ra s o a O

•P o o •H

08 OJ •H -P

-P a3 >>*-> CD Ph -P o H -P

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co- cj

H CD rn ti CO Ph

pi CD CJ M-P 03

<L) to CD

?h •H

A

d

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a •H •>

ec5 3 Fj o d Cj

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CD CD on

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u ra rM M rQ •H 03 o £ (D a -P Ph O

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CD •H bO CD d d ,3 CD »s •H Ph to rf -P CD 2 Cj H t> 3 O Ph O

CO (U o

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fHH 03 +3 H -p

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to » aj •p ^1 rH •H -P CO CD •• Ph ra ft Ph a? 1 0J CD &

CD CD EH J- K H ^—' H dH

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27

<+H

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A

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tD 5 ^ cm

CD

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rd a3

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CQ CQ ?H £ P fH -P •H 1 CD 1

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29

As illustrated in figure 13, the transformation has the effect

of projecting the backscatter traces toward greater frequencies and

toward greater equivalent ranges. On an ionogram with linear axes,

the projection is along straight lines which pass through the origin.

Finally, the combination traces for the oblique case are again

calculated by averaging the equivalent ranges of the two backscatter

traces. The middle scatter traces in figures 10b and lib were

calculated in this manner. On actual ionograms, such combination

traces might be expected to dominate over their related backscatter

traces, since (l) there are two 'round -trip' ray paths of equal

retardation combining to produce them and (2) the scattering is

through a smaller--and hence more favorable --scattering angle.

Near the penetration frequency of the layer (foF) the mode (ii)

backscatter trace for an overhead irregularity is greatly retarded

(h 1 approaches infinity as f approaches foF). It is apparent from

the transformation that the corresponding oblique scatter trace must

double back to approach an asymptote at this penetration frequency (as

h' approaches infinity, f approaches f and thus foF). The upper V K V

branch of such traces (e.g. figures 10b, lib, and 13) is a

manifestation of the "Pederson" or "high-angle" mode of propagation

engineering, the 'nose' frequency playing the role of a 'maximum

usable frequency' (MOT1 ) between the ionosonde and the irregularity.

For an irregularity embedded between the base and the peak of

the layer, scatter traces begin abruptly at a 'vertex' or 'triplepoint' where three scatter traces emerge (e.g. figure lib). When
30

a)%p

<u

-d

0) d

(U i

(U

!>» -p

•H

•Ho

Ch

to

<uo

cd?H -P

*H

CD -po

CQ

03

(1) oo

•H

ij

HB

•H«H

CHO

CU

CQo

<D p

•H ^ Pcd d

cu

CJ CD

COH

CD

•H
31

the irregularity is overhead, this occurs at the local plasma frequency

around the irregularity; when oblique, at a higher frequency. The

triple -point may even occur "beyond the penetration frequency of the

F layer (e.g. figure Ik; h = 220 km, R = 400 km).

Figure lk is a collection of predicted ionograms for individual

scattering irregularities at various heights and various ground

distances from the ionosonde. Among these the basic features of

the three configurations of equatorial 'scatter' spread F may be

found. The distinction among the three is thus interpreted in terms

of the height of the irregularities with respect to the F layer:

below the base, figure 2a; between the base and the peak, figure 2b;

and above the peak, figure 2c.

In addition, the propagation model described in this section

also applies to interpretation equatorial sporadic E (See appendix B.).

The simulation of equatorial 'scatter' spread F. Certain

observed configurations of equatorial spread F will now be interpreted on the basis of the above model. The technique employed is

that of synthesis, wherein an electron -density profile and the

positions of assumed scattering irregularities are determined so as

to obtain agreement with the observed ionogram.

The electron -density profile is derived from the regular F trace

on the ionogram. For the nighttime, Huancayo ionograms involved,

a simple parabolic distribution was usually an adequate approximation.

The synthesis enables the measurement of various parameters

of the patches of spread-F irregularities, such as their dimensions,

their positions, and the velocities of their motions.
32

hs

= 180 KM

1 ^j

2.0 3.0 50 70 10.0 10

f (Mc/s) 20 3.0 5.0 7.0 10.0 10

f (Mc/s)

2.0 3.0 5.0 7.0 10.0 f(Mc/s)

1000

800

J 600

"^400

200

°l

1000

800

-600

s

"^400

200

°l

1000

800 — 600 2^400

200

h 5

= 2IOKM

R =0 KM

_i i_

f>s = 210 KM

R 200 KM J -

n s = 2I0KM 1 R = 400 KM 1 \

i i i i i i i i i i 20 3.0 50 70 10.0 1.0 f (Mc/s)

2.0 3.0 50 70 10.0 1.0 f (Mc/s)

2.0 3.0 5.0 70 10.0 f(Mc/s)

hs

= 220 KM

R =0KM

hs

= 220KM

R = 200 KM

2.0 3.0 5.0 7.0 10.0 1.0 f (Mc/s)

2.0 3.0 50 7.0 10.0 1.0 f(Mc/s)

2.0 3.0 50 70 10.0

f (Mc/s)

hs

= 3IOKM

R =0KM

h s

= 3IOKM

R = 200 KM

2.0 3.0 50 70 10.0 10

f (Mc/s) 20 3.0 50 70 10.0 1.0 f (Mc/s)

2.0 3.0 5.0 70 10.0

f (Mc/s)

Figure 1^. Predicted 'ionograms' for irregularities at various

heights, h , and ground distances, R, east or west

of an equatorial ionosonde.
33

Occasionally, more than one spread-F configuration may appear

concurrently, as in figure 15a. Here the rectangular spread-F

configuration (attributed to low-lying irregularities) occurs at

low frequencies, while the triangular spread F configuration

(attributed to embedded irregularities) occurs at higher frequencies

The synthesis of this pair of configurations is presented in figure

l^b. The rectangular portion is calculated for a patch of irregularities located just at the base of the layer (at 328 km height),

extending from overhead out to a ground distance of 300 km. The

triangular portion was obtained with a single irregularity embedded

in the F layer at a height of 33^- kTM and at a ground distance of

500 km. (The high-frequency cutoff of each scatter trace has been

introduced arbitrarily.) The fact that no echoes are observed

corresponding to irregularities between the two patches leads to

the interpretation that they are separate

.

The ionogram in figure l6a is an example of the third configuration of equatorial 'scatter' spread F. (The descriptive term

"feathers" characterizes its form.) The synthesis (figure l6b) of

this configuration is based upon a patch of irregularities within a

ground distance of 100 km from the ionosonde, and extending in

height between 3 10 km and 350 km- -5 km to k-5 km above the peak of

the F layer. The thickness of this patch of irregularities

(around k-0 km) appears to be representative of spread-F patches.

Figure 17a is another example of equatorial 'scatter' spread F

interpreted in terms of embedded irregularities . Its partial

synthesis (figure 1Tb) is based on four irregularities at a height
34

1000

800

^600

^400

200

0,

.V

. v

J I I L_L

2.0 3.0 5.0

f(Mc/s)

(a)

70 10.0

1000

800-

^600-

400-

200

1.0 2.0 3.0 5.0

f(Mc/s)

(b)

70 10.0

Figure 15

•

(a)

00

Huancayo ionogram, recorded at 2031 EST, 21 April

i960, in which two spread-F configurations appear, and

The simulation of this- ionogram. (The parabolic F

layer used for this calculation has h = 328 km,

h = ^50 km, and f F = 8.4 Mc/s .

)

m o—
35

3.0 5.0

f(Mc/s)

(a)

IWU

_ 800 -

_600

^400

-

i i i 1 1 1 I 1 1

200

-

1 .0 2.0 3.0 5.0 7.0 10.0

f(Mc/s)

(b)

Figure 16. (a) Huancayo ionogram, recorded at 0100 EST, 15 October

i960, in which a configuration called 'feathers'

occurs, and

(b) The simulation of this ionogram. (The parabolic F

layer used in this case has h

Q

= 215 km, h^ = 305 km,

and f F = 7-3 Mc/s.)

m

c—
36

1000

800

_600

^400

200

1 L 3.0 5.0

f(Mc/s)

(a)

1000

800

.600-

400-

200-

1.0 2.0 3.0 5.0

f(Mc/s)

(b)

70 10.0

Figure IT- (a)

(*)

Huancayo ionogram, recorded at 0015 EST, IT June i960,

which exhibits a configuration similar to that of

figure 2"b, and

The simulation of this ionogram. (The parabolic F

layer used in this case has h

Q

- 220 km, h

m

= 320 km,

and f F = 6.8 Mc/s.)

o—
37

of 227 km and at ground distances of 250, 300, 350, and ^-00 km from

the ionosonde. (The base of the F layer in this case was at a height

of 220 km. ) Thus this patch of irregularities had an east-west

extent of 150 km.

The above interpretation of equatorial 'scatter' spread-F is

made more convincing in part III where a sequence of ionograms is

synthesized. For Ig" hours a patch of spread-F irregularities,

remaining at a constant height, moved first toward, then away from,

the ionosonde. During the period of observation it covered a

ground distance of 600 km with a constant velocity of 113 m/s.

Equatorial f waveguide ' spread F. An interpretation of the fourth

equatorial spread-F configuration (figure 2d) has been proposed by

Pitteway and Cohen (1961). The model, sketched in figure 18, invokes

north-south ducts adequate to contain radio energy in a waveguide

mode: The waveguide mode is excited by incident radio waves where

they are propagating parallel to the duct (at the ray reflection

level in the equatorial case). Radio energy in this waveguide mode

then travels to the 'end' of the duct and is reflected. The

reflected energy which leaks out of the duct near the original

position of entry is then able to return to the ionosonde to form

a spread echo. The delay for such echoes is thus the sum of the

delay to the duct entry and the delay accumulated 'rattling around'

within the duct. Each striation of the configuration is attributed

to a separate duct; the portion with the greater delay attributed to

more oblique propagation.
38

•cZmtW&ZZZ

(a)

SSSSSSSSS SS S S S SS S SSS s s ss ss

Figure 18. The equatorial 'waveguide' spread -F model proposed by

Pitteway and Cohen (1961): (a) Duct entry, and (b)

Schematic ray paths for f > f >" f .
39

In contrast with that of equatorial 'scatter' spread F, the

oblique propagation of equatorial 'waveguide' spread F is north-south

rather than east-west. The slight dip (2 ) of the magnetic field at

Huancayo, Peru appears to allow an easier entry into the ducts toward

the south (figure 8).

The 'waveguide' irregularities are similar to the 'scatter'

irregularities except that (l) they must have larger transverse

dimensions and (2) they must have electron densities less than that

of the ambient medium (to act as waveguides ) and thus can only occur

embedded in the layer.
40

Appendix A

TRANSOFRMATION RELATIONSHIPS FOR BACKSCATTER TRACES

The equivalent range from an ionosonde to a. scattering irregularityis

h' = f

u' ds (6)

ray

where u' is the group refractive index and ds is the element of pathlength .

If the magnetic field is neglected, the dispersion relation has

the form

^ (f ) = l - 4/?

2

, (T)

where \i is the phase refractive index, f is the local plasma

frequency, and f is the exploring frequency. It can be shown using

(7) that p. \i' = 1. (8)

From figure 19, it can he seen that

ds = dz/cos <J>. (9)

Substitution of (8) and (9) into (6) gives

h

! = / |dz|/u cos <t> = / |dz| (\i

2

- n2sin2

4>)" 2

. (10)

ray ray

By Snell' s law,

\i sin $ = constant = u , (ll)

where |~i is the index of refraction at the apex of the ray-path; i.e.,

from (7),

^ = 1 - ^/f2

. (12)
41

Substitution of (7) and (12) into (10) yields

h' = tj |dz| (f

2

- f2)"2 (13)

ray

The integral of (13) is constant for rays that traverse the same heightinterval as long as these rays have reflection-points at the same

height (the height characterized by the plasma frequency f

fl ). Thus,

for such a family of corresponding ray-paths, there is the relationship

h'/f = constant. (ik)

Let the subscript V refer to a ray at vertical incidence, and the

subscript R refer to a corresponding ray at oblique incidence. Then

from (1*0,

K

/f

V

m Vf

E- < 15 >

Another useful relation may be derived by integration in terms of

the horizontal coordinate. From figure 19,

ds = dx/sin <t>, (l6)

so that (6) may be written, in view of equations (8) and (ll),

h' = f dx/u sin 0> = f <WnA

= R/nA

, (IT)

ray ray

where R is the ground distance of the irregularity. Substitution of

u = R/h' from (17) into (12) yields

h'

2

= (f./ff h'

2 + R

2

. (18)

At oblique incidence, h' becomes h', and f becomes f . Also, from (12),

2

since normal-incidence reflection occurs where u =0,
so that (l8) "becomes

42

f

A

= V (19)

h

R

2

= W" ^ + r2 « ( 2°)

Using (15)^ this equation can be written

h

R

2= H

2

+ r2 = H

2

(1 + r2/^

2 ^

or

h^ = h^ (1 + E

2/hff (21)

Alternatively, (15) may be expressed, following (21) as

f

R

= f

v

(1 + R

2/h^

2

)2. (22)

Equations (21) and (22) are recognized as the transformation used in the

text, equations (k) and (5)«
43

CD P UH

Ph

-P

CO¥

p>W

cd<D H

ctf oH

-P

5h

CD

t>

-Pqm

-p

•HO

Ph

-P

ctf

-P

•HU

-P

03

CO •H

CD H

hi

d)

cd -P

-P

•H

O

Ij CD P W 3 cd

UD

(U ££•H

tQO

P> cd •H Sh

cd 0) H ,PP> a0)

5h HP ^s

cd

O Cho

-p I A CD M^J

•H cd 0) -P

0)

CD rP

t»0 W) P -H

PI

cd

a

0)Ph

p> pq >d P

•H

S3

cdo

p>&O 'H tl) jj P> O -H O ft

0) 0) "-0-P TJ ,3

cd cd P

5h

O -p

-P 0) CQ ,P I r& O M

t>s P 51 -H

cd

O

O CD pq CQ -H ,p

CA o

CDu

•HPR
44

Appendix B

THE SIMULATION OF EQUATORIAL SPORADIC E *

The above model for the interpretation of equatorial 'scatter'

spread F applies as well to the interpretation of equatorial sporadic E.

Figure 20 shows the typical equatorial sporadic E configuration

observed at Huancayo, Peru. Two parts of this configuration have been

classified: 'equatorial sporadic E' (q-type) and 'equatorial slant

sporadic E' (s-type). The former is the diffuse trace at a constant

equivalent range of about 100 km. The latter is the diffuse trace

emerging from the former at a low frequency and rising in equivalent

range proportional to frequency. No term has been adopted for the

spread echoes bounded by these two traces.

It was shown by Cohen , Bowles , and Calvert (1962) that the echoes

comprising the q-type trace arrive from overhead, while those

comprising the s-type trace arrive from a considerable angle to the

vertical.

There is strong evidence for thin, magnetic -field-aligned

irregularities in the ionization of the E layer ( Bowles and Cohen ,

1962a, 1962b; Cohen , Bowles , and Calvert , 1962; Egan, i960; Bowles ,

Cohen , Ochs , and Balsley , i960; etc.). They are the order of 6m by

200m in size and lie in the region between 95 and 110 km height.

* The content of this appendix was presented to URSI at the May 1961

meeting by Dr. Cohen and subsequently published ( Cohen , Bowles , and

Calvert, 1962).
45

k! I I i I 1 I m

H

a5 •H

*HO

Id

g>

0) H

COo

•H

ft

!>» +3

-P

•HX

CD -PHO

voON

•H

<!ONH

EHCQH

ON

CMCJH8d

CDO o

•H

O -p

CD cd

g>

CVJ

CD *H M Si O O

sd o o

•H pq| O o

CO

d CJ CD 3 o £W ftco

IT3

(UJM) ,M o

CJ

CD
46

Equatorial sporadic E is interpreted as scattering by a thin

stratum of irregularities at E-region heights. In order to produce

the observed (s-type) slant trace, this stratum must be embedded in the

equatorial E layer below its peak ionization density. This situation

is simulated in figure 21 for several irregularities located slightly

above the base of the E layer and at various ground distances from

the ionosonde.

Figure 21 faithfully reproduces the width of the slant trace of

figure 20. The upper envelope of the trace is generated by the

'triple -points ' of the individual configurations as the ground distance

of the irregularities is increased. The edge is expected to be enhanced on the ionogram, since it corresponds to scattering at the ray

reflection level, where the ray paths converge. The lower envelope

of the trace is formed as the caustic focus (like the ground-scatter

caustic focus) of the center traces of the 'triplets'.

This interpretation of equatorial sporadic E predicts that the

upper envelope of its slant trace should be linear (i.e. its equivalent range should be proportional to its frequency). This is

a direct result of the projection involved in transforming, after

equations (k) and (5), echo delays from the overhead case to the

oblique case. Figure 22 shows this feature for the observed slant

trace in figure 20. The linearity of slant -sporadic -E traces has

been noticed previously by Agy (private communication to Smith and

Knecht, 1957) and by Whale (1951).
47

if) O

OJ

<z> <=> c=>

O o o <=> o

10 ^*- ro CSJ

("M) ,M

a!

d -p -P ctf Pi

a

Si! ^

•H ,Q

H

ft

d o d

(U -PH

d

d

Pi szj i-9 a a

0) -P rM

CQ 0)

g o

Pi Pi r3 o

ctf

H

Pi o

a) cq o P1 -p u OJ d

P> 0) d U

d

O CD PI CO

CD P d

d

p P O cti »s P> o o co

co LT\ p>

bD

H •H

fl cu d Ieh

O P>

<H •H O H >

ft • CQ >J •N

O

CD P>

O •H

Pi -H U"\ p-l Pi cq O O £ •s r^ O (D o 03 d Pi

<+H n3

w

a o ft

a o

cd 5m CQ CO

Pi

p •H • M O O jEj O CD a OO C-j a h cfl CM O CD p -d" •H CO H — ri •H Pi H 3 d 3 -P d -H d •H d

pi

X s <H

d eg 3 CO •H S o d"

!>u Pi o

•H Ch

w

d S d o

PI -p

O

•H P>

d Pi • ,3

CD bD

d §>

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49

The simulation of the equatorial sporadic-E configuration may

he carried a step further by accounting for the relative strength of

the echoes. Figure 23 was produced by adjusting the density of

points (each produced by an electronic computer and plotted

automatically) proportional to an estimate of the expected echo

intensity. This estimate considered attenuation with distance,

ionospheric defocusing of rays, and the efficiency of scattering

( Cohen , Bowles , and Calvert , 1962). There is striking agreement

between this synthesized configuration and that of the observed

equatorial sporadic E.
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Part III

SPREAD-F MOTIONS *

Methods of observation . The motions of F-layer irregularities

are often detected through the observation of radio diffraction

patterns moving along the ground. Radio stars and local radio transmitters are commonly -used sources of radio waves. With this

technique, fluctuations in the signals received with spaced antennas

are displaced in time and compared for similarity. The time displacement giving the greatest correlation, combined with the known separation

of the antennas, thus determines the velocity of the moving irregularities .

Another technique revealing F-layer motions is that of following

large-scale ionospheric distortions as they occur at spaced ionosondes.

These "traveling disturbances", observed extensively at temperate

latitudes, appear to possess many features of wave motion.

The two techniques above are discussed more fully by Ratcliffe

and Weekes (i960.)

In this part, three techniques are discussed which reveal the

motions of spread -F irregularities. They involve (l) the analysis of

ionograms recorded at a single station, (2) the timing of the

occurrence of spread F at spaced ionosondes, and (3) the measurement

* Here the term "motion" implies the horizontal movement of ionospheric

structure (ripples, distortions, irregularities, patches of

irregularities , etc . )

.
52

of the doppler shift of radio waves scattered by spread F irregularities.

Spread-F simulation . In part II the position of spread-F

irregularities in the east-west plane was determined from the

configuration of spread F at a single ionosonde. From a sequence of

ionograms it is thus possible to study the east-west motion of

patches of equatorial 'scatter 1 spread-F irregularities.

As an example of this technique, figure 2k shows two ionograms

recorded IT minutes apart, together with their partial syntheses

(i.e. those computed as if the patch were a single irregularity). A

height of 26l km and ground distances of k6o and 3^-0 km give good

agreement. The additional traces in these diagrams above the second

and third multiples of the F-layer trace are attributed to propagation

paths involving additional F-layer and ground reflections en route

to the scattering region. They are indicated by dashed curves in the

simulations and were calculated for one (the lower) and two (the upper)

additional ground reflections. Five more ionograms of this l^-hour

sequence were analyzed. The height of the patch of irregularities

remained constant, and its ground distance varied as shown in figure 25

<

The linearity of this plot indicates that the velocity was constant,

and the slope indicates that its east-west component was 113 m/s

.

Figure 26 presents spread-F velocity measurements obtained by

this technique for sunspot maximum (1958-1960) data from Huancayo, Peru

and Natal, Brazil. A nocturnal trend is apparent in these results.

The velocities decrease with time of night from about 200 m/s at

2100 LT to about 80 m/s at 0600 LT. A few velocities of 100 m/s
53 o o o o o o o o o o o co ID <fr CJ (W>D,M oo 8 8 oo

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23 JUNE I960

300 -

Co

200 -

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100 - \

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i 0300

1 \ ' 0400 0500

\ TIME

100 - \

200 - \

Figure 25. The ground distance of a patch of irregularities plotted

against the local time of the Huancayo ionogram simulated.

(The first and third points result from figure 2^.)
55

(s/uj) A±I00T3A J-QV3ddS

s (1) H

-p o o !h ft •H

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56

occurred prior to 2100 LT. The trend agrees remarkably well with the

spaced-receiver observations of Skinner , Hope , and Wright (1958).

Figure 27 presents similar measurements for sunspot minimum

(1955-1956) data from Huancayo, Peru. In this case the nocturnal trend

is considerably moderated, with the velocities varying through the

night from 130 m/s to 60 m/s

.

Further data are required to establish whether these spread-F

motions are east-to-west or west-to-east. The transequatorial scatter

experiment of Cohen and Bowles (1961) provided such data for motions

at Huancayo between December, 1957 and November, 1958- This

experiment (described in part i) employed beam antennas which limited

the scatter volume to that shown southwest of Huancayo in figure 6.

The sense of the motions are thus indicated by which occurs first,

the enhancement of transequatorial scatter signals or the overhead

passage of irregularities at Huancayo. Of the spread-F motions which

could clearly be sensed in this manner (eight cases occurring between

2130 LT and 0600 LT) all were directed toward the east .

Spaced ionosondes I. From the routine scalings of IGY ionograms,

Knecht (i960, 1962) has found that the onset of spread F often occurs

in sequence along the chain of ionosondes in Peru (See figure 6.).

With the assumption that this is a manifestation of spread-F motions,

the delay in onset and the spacing of the ionosondes yield the northwest-southeast component of the spread-F velocity. With the further

assumption that the motion is along the magnetic equator (inclined

some 37 to the chain of ionosondes), the observed delays are

consistent with the spaced-receiver measurements of Skinner, Hope, and
57

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O

<0O

u

O

flO

•HO

3

o

o

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CD

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58

Wright (1958) and with the velocities determined above by the simulation

of spread F. The results of Knecht's analysis for September 1958 are

reproduced in figure 28. The 15-minute interval between observations

introduces the large scatter in the measurements and causes the

tendency to group about certain velocities. Nonetheless, the trend

toward lower velocities later in the night is apparent.

Spaced ionosondes II . Provided the patches of spread-F

irregularities last long enough, the above technique may be applied to

stations more widely spaced along the magnetic equator. Such an

analysis is presented in this section for two stations --at Huancayo,

Peru and Natal, Brazil.

Huancayo and Natal are separated by the whole width of South

America, roughly Mj-00 km. With the spread F velocities thus far

determined, it should take roughly eight hours for spread-F

irregularities to travel this distance . Thus evening spread F at

Huancayo was compared with morning spread F at Natal. This pair of

stations was chosen because they use similar ionosondes and similar

scaling techniques. The latter is important, since the occurrence of

spread F was taken to be that indicated in the tabulations of ionospheric

data produced as a routine of the station.

The occurrence of spread F at the two stations was compared by

counting the coincidences and contradictions corresponding to a

given delay between their observation. Monthly totals were then

recorded as contingency tables of the form below.
59

300

s

E

o

o

-1

LJ

>

<

€0

<

UJ

-

-300

-i 1—t

1 . r-

• • •

• • • • ••

• /

A • •• •\r -«-

:

•

•

•

11 •

1

1

1

V•

\

\

1 \-

1 \

1 \

1 •

•

••

•

' t

• • •

_.—,—1—.—, ._ 1800 2400

LOCAL TIME

0600

Figure 28. The spread -F velocities determined by Knecht (unpublished

material) compared with the spaced-receiver measurements

obtained at Ibadan, Nigeria (dashed) by Skinner , Hope , and

Wright (1958).
60

Huancayo, Peru

Spread F No spread F

Spread Fa b

Natal,

Brazil

No spread F c d

The correlation indicated "by this scheme is positive when a and d

greatly exceed h and c, negative when "b and c greatly exceed a and d.

The degree of correlation implied by a given contingency table may be

measured by the probability that the distribution within the table

occurred purely be chance. When this is large the correlation is

weak; when it is small the correlation is strong.

Figure 29 shows the contingency -table probability associated

with various delays between spread-F observations. October, 1958 data

recorded for the hours 2000-2300 LT (evening set) and 0200-0600 LT

(morning set) were used. The solid line indicates the correlation

between spread F in the evening at Huancayo and spread F in the

following morning at Natal. For comparison, the dashed line indicates

the corresponding correlation between evening and morning spread F

at the same station (Huancayo). The Huancayo -Natal correlation

becomes very strong with a three-hour delay and reaches a maximum

with a five -hour delay. The sharp drop in correlation beyond the

five -hour delay results from the sun's rising at Natal and attenuating

spread F. For this reason, the delay corresponding to the peak

correlation does not represent an average transit time for the spread -F

irregularities . The excellent correlation at the peak of the graph
61

*C I h *

N0I1V13UU00 30NVH3 JO AlHIGVaOdd

oO

H

£hH

13

u

PhM

a

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Spread F 19

Natal,

Brazil

Wo spread F Ik

62

(10 probability) was obtained from the contingency table below.

Huancayo, Peru

Spread F No spread F

30

The zero in this table seems to indicate that evening spread F at

Huancayo is a prerequisite of morning spread F at Natal. The

mechanism ultimately responsible for spread F thus operates only

near sunset, since the spread F observed later in the night appears to

occur only by virtue of its eastward motion.

Doppler- shifted oblique scatter . This section is a preliminary

analysis of data from an experiment performed under the auspices of

the Voice of America and the National Bureau of Standards . This

experiment was conducted by Dr. K. Davies and Father J. R. Koster

during September and October, I96I. It involved an oblique propagation

path between Tripoli, Libya (transmitter) and Accra, Ghana (receiver).

The 20 Mc/s transmitted frequency was controlled by a highly stable

oscillator at Tripoli, and the received frequency was compared with

that of a similar oscillator at Accra. In this manner, it was possible

to detect the relatively small doppler shift imposed by the ionosphere

and record it on slow-moving magnetic tape. Upon playing the tape at

full speed (1500 times the recording speed) doppler shifts of a few

cycles per second are transformed into audio frequencies acceptable

to standard audio-frequency spectrum analyzers . Davies , Watts , and

Zacharisen (1962) have discussed this technique in greater detail.
63

Figure 30 presents some examples of nighttime doppler shifts

as they appear in the result of the spectrum analysis. The dopplershift frequency increases upward, and time increases to the right.

In these figures, the daytime signal, visible at the far left, is

narrow; having a width the order of 0.2 c/s . Just after sunset this

often gives way to very broad signals which may cover as much as 18 c/s,

The broad signals occurring before midnight usually consist of

striations sloping downward to the right.

The large nighttime doppler shifts are attributed to spread-F

motions occurring near the southern terminal of the path where it

crosses the magnetic equator. The largest doppler shifts arise by

scattering from spread-F irregularities when they are first observed

west of the path. As the eastward velocity of a given spread-F

patch carries it closer to the path, the component of the motion

producing doppler shifts decreases, and hence the patch appears as a

sloping band on the records. This interpretation is further

strengthened by the fact that broad signals fail to develop on

evenings following strong magnetic disturbances --a well-known feature

of spread-F occurrence.

Since no absolute frequency calibration was attempted, a

reference frequency for the doppler shifts is lacking. However, its

position on the records may be estimated where the narrow signal

corresponding to normal propagation is superimposed (e.g. 27-28 Sept.,

29-30 Sept., 6-7 Oct.; figure 30). Assuming that such narrow signals

are not appreciably doppler shifted leads to the feature that spread-F

irregularities appear to approach the path but not leave it. This will
64 t : 1 i) i

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65

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66

be attributed to the aspect-sensitivity of the spread-F scattering.

Since spread-F irregularities are thin and long, radio waves will

be scattered strongest when they add in phase from the whole length

of the irregularity. In other words, the irregularity must be

oriented so that there is phase coherence along its length. For the

simple case where ionospheric refraction is neglected, phase coherence

occurs when the irregularity is tangent to an ellipsoid of revolution

having the path terminals as foci (since this is the figure on which

the path length has a stationary value ) . Since spread-F irregularities are magnetic -field aligned, and their orientation is thus

fixed, they produce phase coherence only when they are in the proper

places. In the case of the Tripoli-Accra path, which crosses the

magnetic equator, phase coherence is possible for spread-F

irregularities above the ground only in two sectors --those roughly

northwest and southeast of the point where the path crosses the

magnetic equator. Furthermore, the latter sector is also excluded

because F-layer heights there are below the horizon from Tripoli.

Figure 31 shows the positions where phase -coherent scattering

should be detected with this experiment and the simple model above.

The solid curves correspond to irregularities at the heights indicated,

and the dotted curve is the limit imposed by the horizons from the two

terminals . The approximations involved in this calculation are

indicated in the derivation, Appendix C.

Figure 31 does not appear to be consistent with the sloping

striations apparent in figure 30. It would predict, from the fact that

its constant -height contours are nearly parallel to the path,
67

Tripoli

Figure 31 • The height at which spread-F irregularities would produce

phase -coherent echoes on a one -hop model. This figure and

figure 32 are based on magnetic charts of the U. S.

Hydrographic Office.
68

that thin patches of spread-F irregularities should give rise to a

relatively constant doppler shift corresponding to the off-path distance

and the velocity of the irregularities. Furthermore, concurrent

results from an oblique ionosonde experiment (similar to vertical

sounding, but with the transmitter and receiver separated) between

Tripoli and Accra indicated that the doppler shifts should be

associated with two-hop transmission, rather than one-hop transmission.

It appears from this, and from vertical-incidence ionograms recorded

at Tamanrasset (See figure 32.), that the ionosphere just south of

Tripoli is dense enough during these times to reflect 20 Mc/s radio

waves back toward the ground near the midpoint of the path. For

radio waves thus reflected at the ground and subsequently scattered

by spread-F irregularities at the same height as the initial ionospheric

reflection, the positions where phase coherence may be attained become

those of figure 32. These contours, being inclined to the path, allow

the observation of a patch of irregularities as it approaches the path,

and thus are consistent with the presence of sloping striations in

the doppler-shift records

.

Since this second interpretation requires an exceptionally strong

ionosphere at 30-^-0 magnetic dip (the observed "subequatorial

anomoly"), it accounts for the disappearance of the doppler-shift

signals at 0200-0300 LT, just when the concentration of ionization

there is observed to dissipate suddenly.

The interpretation that the doppler-shift signals arrive by twohop transmission, and thus that the scattering occurs at roughly onequarter the total path length from the Accra terminal, leads to an
69

Tripoli

Figure 32. The height at which spread F irregularities would produce

phase -coherent echoes on a two-hop model. The ionospheric

reflection is assumed to occur at the same height as the

scattering.
70

estimate of the spread -F velocities from the sloping striations. The

doppler shift is

D = (f/c) dP/dt, (6)

where f is the frequency (20 Mc/s), c is the speed of radio waves

o (3 x 10 m/s), and dP/dt is the time derivative of the total path

length. If the scattering region is a distance x perpendicular to the

great -circle path from a point one -quarter of the way between the two

terminals (which are separated by the distance P ),

dP/dt = (32/3) (x/P

q

) dx/dt, (7)

where x is assumed small. Hence, approximately,

D = 2 x 10"T

(x dx/dt), (8)

in MKS units. The slope of the striations should then be

dD/dt = 2 x lO""7" (dx/dt) 2 cycles/sec2. (9)

A number of velocities determined according to equation (9) were

extracted from the month's data and plotted in figure 33* For

comparison, the results from the spread-F simulation described

above have been added to the figure as open circles (sunspot minimum)

and open triangles (sunspot maximum). Considering that the dopplershift observations were made as the sunspot cycle is approaching its

next minimum, there is reasonable agreement between the two sets of

results
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72

Appendix C

CONDITIONS FOR PHASE COHERENCE ALONG THIN, MAGNETICFIELD -ALIGNED IRREGULARITIES NEAR THE MAGNETIC EQUATOR

Figure 3^ shows the cross -section of the earth (with radius a)

and straight ray paths (of lengths r, , r ) "between the terminals

and a scattering irregularity (at height h). The great-circle arcs

indicated (of lengths s , s ) subtend the angles s_/a and s /a at the

center of the earth. From the law of cosines,

2 2 r = h + 2a(a + h)(l - cos s/a), (10)

with the subscripts 1, 2 on r and s.

Figure 35 shows both ray paths in plan view. The two great

circle arcs from the terminals make the angles p and q_ with the horizontal component of the geomagnetic field (the vector B). Considering

the variations of s^ s , and h as the position of scattering is varied

along the geomagnetic field leads to the identifications

ds /dl = cos p, (ll)

ds /dl = cos q., (12)

dh/dl = -tan I; (13)

where dl is the increment of the horizontal position of the scattering

and I is the dip angle of the geomagnetic field.

The condition for phase coherence along a magnetic -field-aligned

irregularity is that the variation of the total phase -path length is

zero for variations of the scattering position along the magnetic

field. With the assumption that the ionosphere has little effect, the

phase path is approximately the geometric path of figures 3^ and 35>

and its length is approximately (r, + r ).
73

fto

•H-P

in

l> P

•HI

fciD

ft

CD

•H
74 >

•H

!>aH

fts

•H

+31

+3ft

00

•H
75

Thus for phase coherence

:

divj/ai + dr /dl = 0. (Ik)

Differentiating equation (10) and substituting from equations

(11), (12), and (13) gives

r (dr /dl) = -tan I (h + a(l - cos s/a))

+ (a + h) sin s /a cos p, (15)

r (dr /dl) = -tan I (h + a(l - cos s/a))

+ (a + h) sin s /a cos q. (l6)

Substituting for the (l - cos s/a) factors from equation (10) and

applying the law of sines,

(a + h) sin s/a = r cos t, (17)

gives

dr /dl = -tan I (h/i^ - (h

2

- r

1

2

)/2r

1

(a + h))

+ cos t cos p, (l8)

dr

2

/dl = -tan I (h/r

2

- (h

2

- r

2

2

)/2r

2

(a + h))

+ cos t cos q; (19)

where the ray take-off angle (t) is measured to the horizon.

If the height is a small fraction of the earth's radius, h may be

neglected in comparison with a. With this approximation, the

substitution of equations (l8) and (19) into equation (l^-) gives the

condition for phase coherence:

(cos t cos p + cos t cos q) cot I

1 1 rn + rp
76

The further approximations that the take-off angles are small and

that the path lengths (r , r ) are approximately equal to their greatcircle arc lengths (s , s ) simplifies the calculation of figures 31

and 32 by providing the formula

S 1

S

2

S 1

S 2 h =

^s—+~s~")( COS P + COS ^ C0t I

2a~' ^ 21 ^

Figure 31 is obtained by using the distances to the terminals for s

and s ; figure 32 by using the distance to Accra for s and one -third

the distance to Tripoli for s .
77

Part IV

THEORIES OF SPREAD -F IRREGULARITIES

Current theories . A number of theories have "been proposed to

account for the irregularities causing equatorial spread F, although

only two have had any measure of acceptance. These two, Martyn's

(1959) electrostatic instability and Dagg '

s

(1957&) coupling to

turbulent E-region structure, will he treated later. The others will

be briefly mentioned now.

Dessler (1958) suggested that hydromagnetic waves excited by the

solar "wind" of particles would concentrate at the level where their

velocity is greatest and produce a stratum of irregularities . Later

calculations ( Francis , Green, and Dessler , 1959) indicated that this

height was 2000 to ^000 km, much too high for agreement with observed

spread F.

Dagg (1957c) and Glover (i960) have surveyed the remaining theories

Irregular accretion of interstellar matter (gyle and Hewish , 1950)

would be inconsistent with the observed sunspot-cycle effects and with

the occurrence of spread F in rather well-defined patches. An influx

of charged solar particles ( Shlmazaki , 1959a :> 19^0a) would be deflected

away from the equator to cause spread F only at high latitudes. Ryle's

suggestion of charged-particle streaming forced by solar radiation

pressure ( Ratcliffe , 195^) predicts spread F just in the sunrise and

sunset regions and contradicts the observation that the onset of

spread F is delayed an hour or so after sunset.
78

Turbulence in the F region has not "been considered among the

theories, since it is thought to be quite weak at these heights. There

is considerable evidence that the atmosphere above 120 km is not mixed

by turbulence, but rests in diffusive equilibrium with each constituent

distributed according to its own mass ( Nicolet , i960).

Electrostatic coupling to the E region . Dagg (l957d) suggested

that irregular structure would be coupled strongly along the earth's

magnetic field by the great anistropy of the conductivity in the

ionosphere. The high conductivity along the magnetic field lines

(compared to that across) tends to make them equipotential lines so

that they can transmit transverse electrostatic fields . Presumably

such electrostatic fields can control the distribution of ionization.

An estimate of the strength of the coupling to be expected

results from the following simple analogy: Two adjacent field lines

play the role of a lossy transmission line on which the attenuation

follows the law

d(ln E)/ds = (R G) 2

(22)

where E is the electric field between the lines, R and G are the line

resistance and the shunt conductance per unit length along the transmission line, and s is the distance along the lines (from transmissionline theory of electrical engineering). With the analogy, G

corresponds to the transverse conductivity a, , and R corresponds to

2 the 'wire area' L divided by the longitudinal conductivity a . Here

L represents the transverse scale size to be transmitted. The

expected attenuation is then
79

d(ln E)/ds = (a

t /a

Q

) 2 (l/L). (23)

Finally, considering the electrostatic coupling to an e-fold drop in E,

the minimum scale size which can he transmitted over the distance s is

L . = (a./o fs. (2k) mm x v o

v

'

Figure D 36 shows the height variation of L . /s for two choices mm'

of the transverse conductivity ( Chapman , 1956): Curve A for the

Pederson conductivity (Hall currents allowed) and Curve B.for the

Cowling conductivity (Hall currents prohibited). The former applies

at high latitudes and to vertical electric fields at the equator.

The latter applies to horizontal electric fields at the equator, since

the horizontal stratification of the ionosphere prohibits Hall currents

in this case. The figure indicates that the coupling from 100 km

(the height of the E region) should be some hundred-times stronger for

vertical equatorial structure than for horizontal equatorial structure.

Furthermore, since the E region is some 1000 km distant along the

earth's magnetic field, structure no smaller than 100 m in cross

section should be expected in the equatorial F layer.

The calculations of Spreiter and Briggs (1961), involving

detailed solutions for the potential distribution having Fourier

wavelength L, agree in substance with these results . Their limiting

scale size in the transverse direction is somewhat larger, the order

of 5 km.

The mechanism proposed by Dagg must be discarded as the mechanism

creating equatorial spread-F irregularities. On the basis of the

above estimates, it is inconsistent with the observation of spread-F
80

ra

UJ

w o -P a 3

cS o

P>

d CO -p

•H •H -d £ a <d

fl !> co •H

bO,c.-P

ctf •H rd

CD bO H 3

ft •H 3 H O ft o g

!>s o HH o

cti

p o

•H

d +^ £

ct5

O

-P ft

CO CO oU u

-P

U o O

CD o H

PQd

r^

fl

ctf <n o

CO rdo

•H £ 1 a

fl • •r+d -£H • h3 co V ' •H P

<+H ti

IS3O f-i •H •H ?H

CO -P

do £ H $ HH o e CtJ CO o W ^ tiD <+- H o

sd »H ^ £ £ -P o

•H

H S tifltH ao a AP

VD

OOU

S>

•Hpq
81

irregularities as thin as 6 m in cross -section ( Cohen and Bowles , 1961)

Amplification of drifting irregularities . This section provides

a basis for the discussions below which treat the instability of the

ionosphere resulting from (l) electrostatic fields, (2) thermal

contraction of the neutral atmosphere, (3) gravity waves, and (k)

geomagnetic support of the ionosphere against gravity.

An irregularity in the ionization of the ionosphere may drift

relative to the ambient ionization as a result of the above causes.

If such a drift carries the irregularity to a region where its contrast

with the ambient density is increased, it is, in effect, amplified.

In other words, the relative strength of the irregularity

e = A n/n (25)

is increased in magnitude (N and N + Al are the ionization densities

outside and inside the irregularity.) Where irregularities are

amplified the ionosphere is unstable; where attenuated, stable.

An overdense irregularity is illustrated in figure 37 drifting

through the distance dz and, as a result, increasing its strength

from A N,/N, to A N /N . It is thus amplified by the factor

H = (AN

2/N

2

) / (AI^). (26)

With the assumption that dz is small, this may be written

u = (1 - A dz/e) / (1 + A dz), (27)

where A is the logarithmic gradient of the ionization density in the

direction of the drift:

A = (l/N) dN/dz. (28)
82

W

AMBIENT DENSITY

dz DRIFT

IONIZATION DENSITY

Figure 37. Amplification of an irregularity in ionization density as it drifts vertically.
83

Further, with (A dz) much less than unity, the amplification is

u = 1 - A dz/e. (29)

In the cases considered below, where |e| is small, the drift

velocity of the irregularity relative to the surrounding medium will be

shown to be proportional to e

.

H = -i € U, (30)

where U is a velocity related to the mechanism involved.

The irregularity covers the distance dz in the time dt = dz/u,

during which it increases its strength by de:

de = (u - l)e = -A u dt. (31)

Substituting from equation (30) and integrating yields the overall

amplification of the irregularity:

*2

6/s = exp (/ i At dt). (32)

Hence the ionization profile is stable where (A U) is negative and

unstable where it is positive. Furthermore, the time constant of the

instability growth or decay is

T = l/<i AU).

Electrostatic drift . Martyn (1959) has proposed that the source

of equatorial spread-F irregularities is an amplifying drift arising

from an east-west electrostatic field in the F layer. This electric

field causes both the ionosphere and its irregularities to drift

vertically, but with slightly different speeds . The differential

velocity between the two derived by Martyn is also derived in appendix

D (equation (85)). For weak irregularities (e < < 2) its vertical
84

component is

where U is the upward electrostatic drift velocity of the F layer

(equation (83)). From equation (32), the overall amplification of

irregularities is thus

e/e = exp (| A U

Q

t). (3*0

Under this mechanism, the F layer should be unstable below

its peak when drifting upward and above its peak when drifting downward. Furthermore, irregularities should be formed more readily near

the base of an F layer drifting upward, since the logarithmic gradient

of ionization density (a) is greatest there. These predictions agree

with the morphology of the spread F that forms just after sunset:

The onset of spread F corresponding to irregularities near the base

of the layer is immediately preceded by a rise of the F layer.

If the sudden rise in the F layer after sunset is entirely due

to an electrostatic field, (U t) may be as large as 200 km. With an

observed value of 0.1 km for the logarithmic gradient (a) near

the base of the nighttime F layer, the corresponding overall

k amplification may exceed 10 .

Unfortunately, this theory does not present an adequate source

of the electrostatic field. To produce the desired effects, a field

of 500 uV/m must exist shortly after sunset, abruptly reversing

in sense when the F layer reaches its greatest height (at 2100-2200 LT).

Martyn originally suggested that the electric field driving the

daily Sq current system of the E region might be adequate . The
85

diurnal range in the strength of this electric field (determined from

the strength of the Sq currents) is the order of 800 uv/m near the

equator. However, the electric field attains its greatest magnitude

near noon, and apparently dwindles to a weak field by sunset (Hirono

and Maeda , 1955)- In short: The diurnal variations of this Sq

electric field are of the wrong phase . Two alternate sources for

the required electrostatic field- -a charge concentration at sunset

and induction by the changing equatorial electrojet current--are of the

wrong sense and of insufficient magnitude, respectively.

Thermal contraction of the neutral atmosphere . An alternative

to Martyn's theory is proposed in this section. It is based on the

cooling of the atmosphere after sunset.

Lowan (1955) assumed that the upper atmosphere cools after

sunset principally by downward thermal conduction. His calculations

indicate that the atmosphere above 200 km should remain nearly isothermal as it cools from 1250 K to 850 K during the two hours following

sunset. Recent satellite measurements of the electron temperature

( Serbu, Bourdeau , and Donley , 1961) bear out Lowan s predictions

remarkably well. The nocturnal temperatures at F-region heights

range from 1800 K at dusk to 1000 K at dawn, with most of the decrease

occurring abruptly after sunset.

The neutral atmosphere should contract as it cools . Its downward motion gives rise to an instability in the ionosphere quite

similar to that of electrostatic fields.

The analysis of the motion of ionization irregularities in

appendix D tacitly assumes (through the simple definition of particle
86

mobilities) that the frame -of-reference is fixed to the neutral atmosphere. Hence , with this analysis, effects of the moving neutral

atmosphere enter the picture as effects caused by the use of a moving

frame -of -reference

.

The motion of the frame -of-reference across the geomagnetic field

produces, in that frame, an induced electric field given by

E = V x B, (35)

where V is the velocity of the frame -of -reference and B is the magnetic

field. Exactly as indicated in the previous section, this electric

field causes a differential drift and thus an instability in the ionization profile. In this case the proper value of U for equation (30)

is approximately V, the velocity of the frame -of -reference, and the

overall amplification of irregularities is

e/e

o

= exp (/ i A V dt). (36)

The vertical drift of the ionosphere as a whole is also approximately

V (from equation (83) and the assumption of small collision frequencies)

relative to the moving frame -of-reference. Upon transformation back

to fixed coordinates, this drift overcomes the motion of the frame

and the ionosphere is practically stationary (its motion being

-2 h, roughly (x X V"), where x and X are the order of 10 -10 ).

If the neutral atmosphere is in hydrostatic equilibrium throughout

its contraction, its vertical velocity can be shown to be

V = (H + h)(l/T)dT/dt, (37)

where H is the scale height of the neutral atmosphere (assumed constant
87

with height), h is the height above the level where the density is

not changing (near 200 km in this case), T is the temperature, and t

is the time. Its integral in time (for substitution in equation (36 ))

as the scale-height changes from H, to EL is

-/ V dt = E

1

- H

2 + h In (Ej/H ). (38)

J

l

The amplification of irregularities thus increases exponentially with

height. If H, = 50 km, A = 0.1 km (appropriate for the base of

the nighttime F layer), and the reference level for h is at 200 km,

the results obtained by Serbu, et . al. (1961) give the following overall amplifications (from equations (36) and (38)):

Height: 300 km hOO km 500 km

e /G „

: 58 103

' 2 x 10

The post -sunset rise of the F layer- -now attributed mostly to

recombination and lateral diffusion away from the equator ( Norton and

VanZandt , 1962)- -contributes to the formation of equatorial spread F

simply by bringing the F layer to greater heights where the irregularity amplification is greater.

Gravity waves . The instability mechanism described above is not

limited to thermal contraction. It would arise with any appreciable

motion of the neutral atmosphere across the contours of equal ionization density.

For instance, such an instability could arise with gravity waves

possessing vertical motions of sufficient amplitude. Such gravity

waves, excited in the F region by the relatively sudden adjustment
88

of the neutral atmosphere after sunset, might well explain the spread -F

motions described in part III. The calculations on internal gravity

waves in the ionosphere by Hines (1953; 1959* 19&0) indicate that the

observed spread-F velocities should correspond to 100 km wavelengths

in the east-west direction. It is curious that striations of nearly

this spacing often occur in configurations of equatorial 'scatter'

spread F (e.g. figures Ja, 8a, and 2^1-c).

Gravitational instability . A final source of instability arises

from geomagnetic support of the F layer. A plasma supported against

gravity by a horizontal magnetic field is analogous to a dense fluid

supported by a weightless fluid --it is unstable ( Chandrasekhar , i960).

The downward velocity of ionization irregularities under gravity

is calculated in appendix D (equation (91)), and is approximately

u = -2 e g/v

±

, (39)

where g is the acceleration of gravity and v. is the ionic collision

frequency. Thus, in equation (30),

u - g/v.

.

(ho)

With the logarithmic gradient used earlier, A = 0.1 km , the time

constant of this instability at 300 km is the order of 1/2 hour by day

and 2 minutes by night (using Chapman '

s

(1956) collision frequencies

for hot (1500 K) and cold 85O K) models of the thermosphere ) . These

time constants should decrease with height along with the density of

the neutral atmosphere --exponentially with a scale height the order

of 50 km.

This instability gives rise to the "convective diffusion"

described by Johnson and Hulburt (1950) and Dungey (1956). This
89

hypothesis allows the downward transport of ionization in the

equatorial ionosphere to be carried by these gravitational irregularities

Presumably the irregularities would coalesce at a lower height where

the time constant 'of the instability is greater. This mechanism is

consistent with the observation that the equatorial F layer often

starts to fall when spread F first forms (figure 5)- Observations

where the F layer falls without the occurrence of spread F might be

disclaimed with the apology that the observing equipment was insensitive

to either the scale size or the strength of the irregularities present,

(improved ionosondes have done much toward increasing the occurrence

of spread F.

)

Conclusions . The minimum scale size which could be electrostatically transmitted from the E region is too large to account

for observed equatorial spread-F irregularities

.

Martyn's drift theory would account for the equatorial spread F

observed shortly after sunset if the existence of the required electrostatic field could be justified.

Thermal contraction of the neutral atmosphere, based on the

observed atmospheric cooling after sunset, provides an adequate

degree of instability.

Additional sources of instability are possible, resulting from

(l) geomagnetic support of the F layer or from (2) vertical motions

of atmospheric gravity waves excited by the thermal adjustment after

sunset.

More than one type of instability may combine to provide the

nocturnal display of equatorial spread F. The sudden onset of
90

spread F might be attributed to thermal contraction; its maintenance

as the F layer falls to gravitational instability; and its occurrence

late in the night to wave motion.
91

Appendix D

THE MOTION OF A CYLINDRICAL IRREGULARITY IN IONIZATION

Introduction . The mobility of a particle is defined as the ratio

of its velocity to the force causing the motion. In the presence of

a magnetic field, the mobility of a charged particle may depend

strongly upon direction. This being the case, the mobility is

treated as a tensor with three independent components. In the

geometry of figure 2>Q, "the magnetic field is parallel to the z-axis

and the assumed force lies in the xz -plane. Then the longitudinal

mobility is

v = v

z /fz

, (in)

the transverse mobility is

and the Hall mobility is

T* = V

x

/Fx

, (k-2)

H' = V /F ; (1*3) y' x

v '

where F is the force and V is an average of the particle velocity.

A simple calculation of these mobilities (after Ratcliffe , 1959)

is presented below.

Between collisions with other particles, the charged particle

is assumed to follow the well-known cycloidal path (superimposed on

its random thermal motion):

V = (F /eB) sin wt, (kk)

V = -(F /eB)(l - cos wt), (k-5)

y x
92

H

0) H

cho

•H

-P

<D

of

•Ho

•H

-P

P)

<u Ao

SO

9hog

•Ho

CO

•H
93

V

z = (Fz /m) t; (k6)

where e is the charge of the particle (sign included), B is the

magnetic field strength, m is the particle mass, w is the angular

gyro-frequency (= eB/m), and t is the time. Since a collision will

randomize this orderly motion, the particle is, in effect, stopped

"by each collision; whereupon it restarts the cycloidal motion again.

The net motion of the particle due to the applied force is thus the

average of its instantaneous motion, weighted by the time between

collisions. The probability of collision is taken to be

exp (-vt),

where v is the collision frequency of the particle. With this,

equations (kh), (^-5); and (h6) yield the following average velocity:

V

x

= (v/m(v2

+ w

2

))Fx

, #75

7 = - (w/m(v2 +w2

))F , (*&)

V = (l/mv) F . (lj-9)

From this, the mobilities are

L' = l/mv, (50)

T' = v/m(v2 + w

2

), (51)

H' = -w/m(v2 + w

2

). (52)

Where the force may not lie in the xz -plane, the average particle

motion is

V = T'F - H'F , (53) x x y \

'

V = H'F + T'F , (5*0

y x y'

V

z - I/Fz

. (55)
94

In the equations which follow, it will be convenient to use the

symbols h and t for the Hall and transverse mobilities of the electrons,

and H and T for those of the ions. Further, with

x = |v1 /w [, X = V./w.', H = l/eB;

e' e" r 1/ o

'

these mobilities are

2 h = H /(l + x^), t = x H /(l + x^),

H = - H

q

/(1 + X ), T = X H /(l + X ).

(56)

Derivation . The method employed below to arrive at the drift of an

irregularity in ionization is that started by Martyn (1953) a*id

finished by Clemmow, Johnson , and Weekes (1955)* In addition to the

electrostatic drift treated by them, gravitational drift will be

considered.

The motions of ions and electrons are examined relative to an

irregularity in the form of an infinitely-long circular cylinder with

its axis parallel to the earth's magnetic field. The motions arise

from (l) an applied force field, and from (2) an electrostatic field

of induced charges residing on the surface of the cylinder. In

applying the condition that the irregularity should be stable, it is

found to drift through the surrounding medium.

The applied force, assumed to be perpendicular to the irregularity, defines a reference direction for the cylindrical coordinate

system employed, the r0-plane of which is shown in figure 39- Its

components are thus

F = F cos 9, (57)
95

-p

CO>»

to

CD p

•HoO " o

ina} HO

Ph CD

-P

•p

•HH

-POPo

t3

0) po

CD •H

?H CQ •H -H

>> *d -P H

s.

(Do

•H

-P

(ti

tsi •Hao

•H

el

"in p> O Xo

•H-POI

(D P>

CD

rC5

S3o

•H•PO -p

0)

cq

a I -H

CQ

CQ rjj OO

(1)

&H CD

CO

CDU

•H
96

F = - F sin 6. (58)

Under applied forces, the ions and electrons in the ionized

medium will tend to move differently, according to their individual

mobilities. In a non-uniform medium, this leads to charge separation,

and thus to an induced electric field. Hence particle motions are

dictated by a combination of two force fields; one applied and the

other induced.

The ionization is assumed to be uniform both inside and outside

the cylindrical irregularity. Hence induced charges should develop

only on the surface of the cylinder, as a result of the discontinuity

in the density of ionization. Elsewhere, electrical neutrality is

assumed. The electrostatic potential (P) of the induced charges

should thus satisfy Laplace's equation

V

2

P = 0. (59)

This equation is easily solved, giving

P = \ (Cn

rn

+ D

n

r"

n

) cos (n G + pj + C

q

In r + D , (60)

'n

where C^, D , and pn

are integration constants. The part of this

solution corresponding to a uniform field within the cylinder (n = l)

seems to be appropriate, and the remainder is arbitrarily discarded.

Further requiring that the potential be finite and continuous leads to

the following solutions inside (P) and outside (P f ) the cylinder:

P = Q r cos (6 + p), (61)

P

1 = Q (a

2

/r) cos (0 + p); (62)
97

where a is the radius of the cylinder and Q, p are the two remaining

integration constants. The forces on a particle with the charge e,

given by

- eVP or - e V P

1 ,

are thus

F

Sr

= - Q e cos (0 + p), (63)

F^ = Q e sin (0 + p) (6k)

inside the cylinder, and

*£' = Q e (a/r) 2 cos (0 + p), (65)

Fg' = Q e (a/r)

2 sin (0 + p) (66)

outside the cylinder.

The total force acting on a charged particle (either ion or

electron) is thus (F + F ) inside the cylinder and (F + F ) outside

the cylinder. The two unknown constants (Q and p) remaining in these

expressions are determined from the conditions that the particle

fluxes must each be continuous across the boundary of the cylinder.

In this process it is necessary to superimpose a velocity U, representing

the drift of the irregularity, upon the particle velocities. Where V

and V' are the particle velocities on the two sides of the boundary

and k is the ratio of ionization densities across the boundary, this

continuity condition is

k (Vr +UJ = (V; + U

r

). (67)

Calculating the particle velocities according to equation (53) a*id

substituting them into equation (67) gives
98

(FT' + (QeT'/<l) cos p - QeH' sin p + U ) cos Q

+ (FH* - (QeT'/cL) sin p - QeH' cos p + U ) sin = (68)

where U and U are the cartesian components of U, and

d = (1 - k)/(l + k), (69)

In order to satisfy equation (69) all around the boundary of the

cylinder, the coefficients of (cos 0) and (sin 9) must separately

vanish. Thus there are two equations for electrons and two for ions;

a total of four equations to be solved for Q, p, U , and U . Using the

abbreviations

C = Q |e| cos p, S = Q |e| sin p, (70)

and the notation that F and f are the applied forces on the ions and

electrons, respectively; these four equations are FT=-T/dC+HS-U, (71)

ft = t/d C - h S - U , (72)

.X.

FH = H C + T/d S - U , (73)

fh = - h C - t/d S - U . (7*0

The components of the drift velocity may then be found in terms

of ratios of determinants

:

U = [x]/[D], U = [y]/[D], (75)

where [D] = (T + t

)

2

+ d

2

(H + h) (76)

[x] = - T t (T + t) (F + f)

- d (Th - tH) (FH - fh)

- d

2

(H + h) (FTh + ftH) (77)
99

[y] = - (T + t) (FHt + fhT)

+ d (Th - tH) (FT - ft)

+ a

2

H h (H + h) (F + f

)

(78)

Electrostatic clrift . If the appliea forces are those of an

electrostatic fieia E,

F = |e| E, f = - |e| E. (79)

This gives the result previously arrivea at by Clemmow, Johnson , ana

Weekes (1955):

. . (d + d

g )(Th - tH)(H ±

h)

X

|e| ^

(T + t) 2

+ d

2

(H + h)2

(1 + a)(Th - tH )(T + t) |e|E- (81)

* (t + tr + a (h + \y)

When a is zero, equations (80) ana (8l) give the electrostatic

arift of the ambient meaium:

U =0, (82) ox s

U

Qy

= (Th - tH) |e| E/(T + t) = (E/B)/(l + xX). (83)

If the irregularity is relatively weak (i.e. if a is small), the

velocity of the cylinarical irregularity relative to the ambient meaium

is

u = - (a + a

2

) ^-4 u = —^—. x " x u . (84) T +t °y

(2 + ef 1+xX °y

u = a u = - ~=— u , (85)

y oy 2 + e oy' v Jl

where e is the fractional aeviation of the ionization aensity (e = k - l)
100

Gravitational drift. If the applied forces are those of a

gravitational field g:

F=Mg, f = m g, (86)

where M, m are the ionic, electronic masses, respectively.

Neglecting m compared to M gives the result:

U

- Tt(T + t) + dH(Th - tH) + d

2Th(H + h) Mg^ (8?) X

(T + t)

2 + d

2

(H + h)

2

U

- Ht(T + t) - dT(Th - tH) + d

2Hh(H + h) M g> (Q8)

y (T + t)

2 + d2

(H + h)

2

When d is zero, equations (87) and (88) give the gravitational

drift of the ambient medium:

= T t M g = xX g /qqn ox T + t 1 + xX v. + (m/M)v ^ y}

1

v

' e

U = - n - S S - AI ( Qn \ oy T + t 1 + xX v. + (m/M)v Ky J

If the irregularity is relatively weak (i.e. if d is small), the

velocity of the cylindrical irregularity relative to the ambient

medium is approximately

u = - H (Th - tH) d M g / (T + t)

2 x d (1 + x

2

N ) (U /xX) ' v ox

(e/(2 + e)) (g/v,), (91)

u = T (Th - tH) d M g / (T + t)

2

•J d (1 + x

2

) U ' oy

= - (e/(2 + e)) (g/w.), (92)

where e is the fractional deviation of the ionization density (e = k - l).
101

Appendix E.

GEOGRAPHIC LOCATIONS MENTIONED IN THE TEXT

Name geog. coord. mag . dip Remarks

Ac era , Ghana

Antofagasta, Chile

Chiclayo, Peru

Chimb ote, Peru

Dakar, Dr. W. Africa

Guayaquil, Ecuador

Huancayo, Peru

Ibadan, Nigeria

La Paz, Bolivia

Maui, Hawaii, USA

Natal, Brazil

Rarotonga Island

Talara, Peru

Tamanrasset, Algeria

Tripoli , Libya

Washington, D. C, USA

5°^5'N, 0° 8'W

23

QljVs, T0°l5'w

6

cVf , S, 79

CV'w

9° It's, T8°3^'W

l4°36'N, l7°2Vw

2°36'S, 80°2VW

12° 3'S, T5°20'W

T°26'N, 3°53'E

16°30'S, 68°10'W

20°50 , N,l56°30 , w

5°l8's, 35° 6'W

2l°l5 , s,l59°1t5 , w

^°3^'S, 8l°15'W

22°50'N, 5°31'E

32°55'N, 13°25'E

38°55'N, 77° 0'w

i3°s D

17°S T

9°N I

5°N I

17°N I

17°N T

2°N I

8°S I

5°S I

39°N I

2°N I

39°S I

13°N I

28°N I

k6% D

71°N I

Doppler Shift Station

Ionosonde

Transequatorial Scatter Station
102

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U.S. GOVERNMENT PRINTING OFFICE : 1962 —658328

U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the -following listing of the divisions and sections engaged in technical work.

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