U Bureau of Standards

ibrary, H.W. Bldg

JAN l 0l961

jBoulder laboratories

PB161583

^o. 82 I

A SURVEY OF SPREAD -

BY

F.N. GLOVER

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

HHBBI
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ERRATA SHEET

for

A Survey of Spread-F

by

F.N. Glover

Page No. 56 should be Page No. 53*

Page No. 53 should he Page No. 5^

Page No. 5^ should be Page No. 55

Page No. 55 should be Page No. 56

Technical Note No. 82, PBI61583

National Bureau of Standards

Boulder Laboratories

NATIONAL BUREAU OF STANDARDS

technical ^/\ote

82

November, i960

A SURVEY OF SFREAD-F

by

F.N. Glover

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A SURVEY OF SPREAD-F

by

F. N. Glover

ABSTRACT

Examples of spread-F forms occurring at different

latitudes are presented, illustrating the classification

of spread into range type and frequency type. The oc- currence patterns of spread-F at different latitudes are correlated with other geophysical phenomena. Magnetic

latitude and time within the sunspot cycle appreciably

affect the pattern of spread occurrence. Instrumental

techniques and their advantages for spread studies are outlined. The principal theoretical explanations of

spread-F are summarized. A single mechanism need not be

postulated as responsible for all types of spread occur- rence or at all latitudes.

TABLE OF CONTENTS

1

Introduc t i on

2. The Morphology of Spread-F

3. The Occurrence of Spread-F

k-. Instrumentation

5. Possible Mechanisms Responsible for Spread-F

6. Factors Responsible for Irregularities of Ionization

7. Concluding Remarks

8. Appendix A, Ionospheric Conductivity

9. Appendix B, Martyn's Theory of Vertical Drift Motions

10. References

A STUDY OF SPREAD-F

*y

F. N. Glover

1. INTRODUCTION

Spread-F, like sporadic E, is a familiar and sometimes frequent

"abnormality" encountered in radio soundings of the ionosphere. It occurs at some time or other at every station although its form and

frequency of occurrence differ widely. The existence of the phenomenon which is now commonly termed "spread-F" has been known for

more than twenty years. Booker and Wells (1938) were the first to

give a detailed account of the diffuse or spread appearance of the

F-layer echo on many Huancayo ionograms.

2. THE MORPHOLOGY OF SPREAD-F

2.1 Definition of Spread-F

Spread-F, also known as "spread echo", "scattering in the F region", "diffuse echo", etc., is usually described in terms of the

appearance of the conventional virtual height versus frequency ionogram. The annals of the IGY (Wright, Knecht and Davies, 1957) define

spread-F as follows:

"The term * spread echo* is applied to the condition

observed at middle and low latitudes, and quite often in polar regions, when the ionospheric echo

becomes quite diffuse, loses its sharply defined

structure, and extends to frequencies sometimes far

above those indicative of the actual ion density of

the layer. When it occurs in F region echoes, this

condition is called spread-F. Although spread-F is

the most frequent and most troublesome case, spread

echo is occasionally observed from all layers."

It is to be noted that spread-F is here defined in terms of the

appearance of an h* -f (virtual height versus probing frequency) ionogram, rather than in terms of some physical mechanism operative in
-2-

MEGACYCLES

SPREAD-F AT HIGH LATITUDE. ( THULE, GREENLAND, GEOMAGNETIC LATITUDE

88.1° N, DECEMBER 5, 1957, 5-01 AM) FREQUENCY TYPE SPREAD.

FIGURE I
200 ~^* -HK-4r *-— - •'J. M»><

!

MEGACYCLES

SPREAD- F AT MEDIUM LATITUDE. (FT, MONMOUTH, N.J., GEOMAGNETIC

LATITUDE 5I.7°N, DECEMBER 4, 1954, 2=54 AM) FREQUENCY TYPE SPREAD.

FIGURE 2
4-

800 v

1*

V) 600

cr

LlJ h-UJ^

o

400

200

MEGACYCLES

SPREAD-F AT LOW LATITUDE. ( HUANCAYO, PERU, GEOMAGNETIC LATITUDE 0.6°S,

SEPTEMBER 3, 1957, I MOO PM ) RANGE TYPE SPREAD.

FIGURE 3
1000 4-4-r

800

in

ji) 600

UJo

_J

400

200

1

« «

5 .

.

. Eft*

v r*

.*»_.-« — i .—-t'.y. m „*u uC !

•

MEGACYCLES

10

A LOW LATITUDE SPREAD-F IONOGRAM THE UPWARD SWEEPING TRACES

SUGGEST HIGH LATITUDE SPREAD-F, (HUANCAYO, SEPTEMBER 27, 1957, 12:59AM)

FIGURE 4
-6-

MEGACYCLES

A HIGH LATITUDE SPREAD-F IONOGRAM. THE FREQUENCY INDEPENDENCE OF THE

SPREAD OFER A WIDE RANGE OF FREQUENCIES SUGGESTS LOW LATITUDE SPREAD-F.

(THULE, DECEMBER 3, 1957, 9:30AM)

FIGURE 5
-7-

CO

o

-J

800

600

400

200

MEGACYCLES

I0N06RAM DISPLAYING RANGE TYPE SPREAD- F (SPREAD OF VALUES FOR

VIRTUAL HEIGHT, OR SLANT RANGE, OF THE F LAYER), AND FREQUENCY

TYPE SPREAD- F (SPREAD OF VALUES FOR THE PENETRATION FREQUENCY

OF THE F LAYER). (THULE, DECEMBER 14, 1957, 2^45 AM)

FIGURE 6
-8-

the upper atmosphere. The possibility is at once apparent that two or more distinct and different mechanisms in the ionosphere might each he

separately responsible for the same sort of diffuse trace on an ionogram. This possibility appears to be less remote if one recalls that

almost any kind of diffuseness appearing on the F layer trace is termed

spread-F.

2.2 High, Medium and Low (Geomagnetic) Latitude Spread-F

The common division of ionograms showing diffuse F region echoes

is that of high , medium, and low latitude spread-F (Wright and Knecht,

1957) according to the geomagnetic latitude of the station at which

certain characteristic patterns usually occur. Figures 1, 2, and 3

present examples of spread conditions found at high, medium and low

(geomagnetic) latitude stations. The traces of the high- and middlelatitude spread-F ionograms appear to sweep upward, presenting apparently a wide range of critical frequencies. In the low latitude

spread-F ionogram, the spread condition appears to be independent of

frequency over a wide range of frequencies.

Figure k, however, presents a Huancayo ionogram with upward sweeping traces, resembling the ionogram of a high latitude station whereas

Figure 5 presents a spread condition at Thule, Greenland, suggestive

of a low latitude station. These examples indicate that the division

into high, medium, and low latitude spread-F is not altogether satisfactory.

2.3 Range Type and Frequency Type Spread-F

McNicol, Webster and Bowman (1956) suggest an alternative division,

that of "range type" and "frequency type" spread-F. If the diffuseness

is pronounced along the section of the trace that sweeps upward, such

that there is some ambiguity r3garding the value of the penetration or critical frequency, the spread is to be termed "frequency type". The

ionograms in Figures 1 and 2 are examples of frequency type spread-F.

If, however, the spread is more or less independent of frequency over

a wide range of frequencies, and the diffuseness is principally along

the horizontal part of the trace, giving rise to ambiguity in virtual

height, or more generally in virtual slant range, the spread effect is

classed as "range type". Figures 3 and 5 are examples of range type

spread-F. Some ionograms appear to exhibit both range type and frequency type spread-F, as is shown in Figure 6. Although not widely

used in the past, this classification of range type and frequency type

spread-F is to be preferred to that of low, medium and high latitude

spread, since it is based on the appearance of the ionogram trace rather

than on the geographic location of the ionosonde.
-9-

1000

(SI ccUJ

ILLl O

600

..s .' A.l'-Vr',':

'V . •>

»-w•v

• •

'!•' '

400

200

MEGACYCLES

RANGE TYPE SPREAD- F SHOWING SATELITE TRACES. ( HUANCAYO, SEPTEMBER 23,1957,

4:43 AM)

FIGURE 7
-10-

to

<rUJH

LUO

800

600

400

200

MEGACYCLES

FREQUENCY TYPE SPREAD- F SHOWING SATELLITE TRACES. (WHITE

SANDS, NEW MEXICO, DECEMBER 20, 1954, 2'30 AM)

FIGURE 8
•11-

1000

j ''.. -. .,.^,«^ )«-( ^^opvr1

800

600

X

^dS*****

''»•**:

: I

r~^t^'^S«#}:.

CD

or

Lu 400 so

200

>"•«•

•• .,. -^

«. 1 ;•"*'

III llll I I >«»«»

!

io MEGACYCLES

A DOUBLE TRACE FROM THE F REGION. WITHIN 45 MINUTES THIS CONDITION DEVELOPED INTO A FULL RANGE TYPE SPREAD-F CONDITION. (HUANCAYO, SEPTEMBER 25, I957, 6:59 PM)

FIGURE 9
12-

wp

1000*'

800

600

to

<r

Ll)

UJSo

- 400

200

"in

.>

'

t~-.'

- "

;

. • *'•

« • >;

i. •• ft •"• r. .

! ••/.>

\

'

» .wh^^km****^-

sapEPraps piii >! Ki;

10 MEGACYCLES

A DOUBLE RANGE TYPE SPREAD-F CONDITION. (HUANCAYO, SEPTEMBER 24, 1957,

9:58 PMJ

FIGURE 10
-13-

800

600

<rUJH

UJso

400

200

A DOUBLE FREQUENCY TYPE SPREAD-F CONDITION. (THULE, DECEMBER 10, 1957, 12:45 PM)
-IkUJ2

o

1000

800

600

400

200

> 'f '. .- . tjr-S »

iSip

MEGACYCLES

GROUND SCATTER, THOUGHT TO BE DUE TO BACK SCATTER FROM GROUND

IRREGULARITIES VIA TWO OR MORE REFLECTIONS FROM A SMOOTH F LAYER.

SPREAD ECHOES WERE ALSO PRESENT ON THE I F TRACE A FEW HOURS

PREVIOUS. (HUANCAYO, SEPTEMBER 16, 1957, 3:45 AM)

FIGURE 12
15-

1000

iji " i 4nn'i r t : »«ifl»:jdllt^auisa^i*at

MEGACYCLES

SUNRISE EFFECT, FOLLOWING SEVERAL HOURS OF NIGHT TIME SPREAD-F.

THE CONDITION ONE HOUR EARLIER IS SHOWN IN FIGURE 7. (HUANCAYO,

SEPTEMBER 23, 1957, 5:49 AM)

FIGURE 13
-16-

2.4 Multiplets or Satellites

Many ionograms exhibiting spread conditions actually present a number of multiplet or satellite traces lying close to the main F re- gion trace, and only imperfectly resolved from it. Figures 7 and- 8 are examples of this multiplet structure in range type and frequency

type spread-F. Webster (1958) has considered in some detail this

multiplet structure of the F trace. Frequently a well developed spread

condition is preceded by a number of weaker satellite traces adjacent

to the main trace.

2.5 Double Traces

At times a spread condition is preceded by, or associated with,

double traces from the F region. Figure 9 shows such a double trace,

at a greater virtual height than the main F trace. The additional

trace is too low to be two hop F, and since no E region trace is

visible, a combination of E and F layer reflection is excluded. The

condition in Figure 9 later developed into full range spread in less

than forty-five minutes. It should be recalled that the "vertical

incidence" ionosondes look not only toward the zenith, but also "see"

somewhat obliquely. This oblique seeing, along with ionosphere variations in the horizontal plane, may, in part, be the explanation of the

double traces in Figure 9* Figures 10 and 11 exhibit double traces

for range type and frequency type spread-F conditions.

2.6 Special Spread-F Effects

The Huancayo ionogram in Figure 12 shows no spread on the 1 F

trace but pronounced spreading on higher order traces. Such a condition is termed ground scatter, and is thought to result from back

scatter from ground irregularities via two or more reflections from

the F layer. Dieminger (1951) reports that this ground scatter can always be observed at Lindau, provided sufficiently high transmitter

power and receiver sensitivity are employed.

The ionogram in Figure 13 shows diffuseness on frequencies above

the F layer critical and at virtual heights greater than those asso- ciated with the normal F layer. Such ionograms are not uncommon at ' Huancayo just at dawn following several hours of spread conditions.

Booker and Wells (1938) suggest that this is due to a gradient in ionosphere conditions in the east-west direction just at sunrise. Looking

west the ionosonde views the nighttime spread conditions, and looking

east it views the fresh ionization formed by the rising sun. Figure 7

shows the condition of the ionosphere one hour prior to Figure 13.
-17-

800

600

or

LxJ t ^OO so

200

• ftrf

* . • ^ • *

.• jj . : u : -v

%•*-. V

t

...

\.

'.

I I > -~m 10 MEGACYCLES

RANGE TYPE SPREAD-F SUPERIMPOSED ON A WELL DEFINED

(HUANCAYO, SEPTEMBER 22, 1957, 8:59 PM)

TRACE.

FIGURE 14
-18-

o

-J

800

600

400

200

MEGACYCLES

A MILD FREQUENCY TYPE SPREAD-F CONDITION AT A HIGH LATITUDE STATION, (THULE, DECEMBER 5, 1957, 12:55 PM)

FIGURE 15
-19-

A range type spread-F condition with the ordinary and extraordinary trace showing through the spread is shown in Figure 1^. It

is possible that the ionosonde is looking in two different directions

and sees two different sets of ionosphere conditions. At 1800 local

time, some three hours prior to the ionogram shown in Figure lk, a ground scatter condition prevailed, similar to that in Figure 12. At

2000, some 200 km above the main trace there appeared a double trace

(as in Figure 9) which rapidly descended and became diffuse. Subsequent to the ionogram in Figure lb the range type spread condition

continued to descend to about 325 km. By 23OO this spread developed

into a clearly defined F trace, while the former F trace, at about

550 km dissolved into range type spread at this same virtual height.

2.7 Use of Hourly Tabulated Data

The presence of spread-F is Immediately apparent on viewing the

ionogram. However, most statistical studies of spread-F are based on

the tabulated ionospheric hourly values rather than directly from the

ionograms. The presence of spread-F can be known by the symbol F

attached to, or in place of, the values for foF2, F2 M3000 or h'F.

Spread-F on the ionogram is a necessary, but not sufficient, condition

for the symbol F to appear in the tabulated hourly values. Singleton

(1957) made a detailed comparison of ionograms with tabulated foF2

values over a nine month period. He found that over fifty percent of

the occurrences of range type spread-F over Brisbane were not indicated

by any qualifying symbol associated with the tabulated foF2 values.

The mild spread conditions shown in Figure 15, as well as the

ground scatter shown in Figure 12 do not have any F qualifications in

their tabulated values. The spread condition of Figure 13 is recorded

only by UF (value uncertain due to spread condition) associated with

the F2 M3000 value, and the spread condition of Figure k is recorded

by the symbol F in place of the h*F value. In no one of these four

cases is the occurrence of spread conditions indicated by the tabulated

foF2 critical frequency values.

The f-plot is usually a more reliable indication of the presence

of spread conditions than is the tabulated data. However, for the four

ionograms in Figures 12 - 15, only the f-plot corresponding to the ionogram of Figure 13 gives an indication of the presence of spread-F.

2.8 Degree of Spread Condition

The degree of the spread condition may vary from a slight spread

not obscuring the critical frequencies, as in Figure 15, to a heavy

blanket of spread, as in Figures 3 an<i 1, which completely obliterates
-20-

o

O

40

30

UJ

1 < 20

o ?

o

o

V)

18 20 22 2 LOCAL TIME

(b)

1953-55- _ W\

1956- 58

JAN MAR MAY JUL SEP NOV

MONTHS

PROBABILITY OF OCCURENCE OF SPREAD- F AT BAGUI0

(a) DIURNAL VARIATION

(b) ANNUAL VARIATION

FIGURE 16
-21-

TABLE 1

Various Methods Employed to Classify the

Degree of Spread-F Appearing on an Ionogram

Scale of Spread-F Reference

to 3 Wright, Koster, and Skinner

(1956)

Briggs (1958)

to k Singleton (1957)

1 to 8 Meek and McKerrow (1951

)

"faint", "moderate" and

"strong"

Reber (1954 a)
-22-

TABLE 2

List of Studies Treating of Spread-F

at Particular Locations

Mag.

Lat. Location Authors

7U°N Baker Lake Meek, (1952)

7^°N Spitzbergen Whatman, (19^9)

57°N Ottawa Hartz, (1955)

54 °N Slough Briggs, (1958 a, b);

Dagg, (1957 c)

50°N Washington Reber, (195^ b

)

25 °N Japan Kasuya, Katano and Taguchi, (1955

)

21 °N Hawaii Reber, (195^ a)

lU°N Ahmedabad Kotadia, (1959)

11°N Ibadan Lyon, Skinner and Wright, (195$)

1°S Huancayo Wells, (195^)

Booker and Wells, (1938)

10°S Singapore Osborne, (1951

)

36°S Brisbane McNicol, Webster and Bowman, (195&

)

McNicol and Webster, (195^)

Singleton, (1957

)

Bowman, (i960)
-23-

the F region critical frequencies. A number of different systems have

been employed to record the amount of spread appearing on the ionograms

(see Table l). Such methods are desirable for detailed studies of

spread-F, particularly for those of a comparative nature. However,

variations in equipment, antenna design, transmitter output and receiver

gain, as well as the human factor in scaling records must all be given

due consideration.

3. THE OCCURRENCE OF SPREAD-F

The diurnal and seasonal pattern of spread-F occurrence changes

markedly with magnetic latitude and sunspot cycle. Shimazaki (1959)

has made a comprehensive world-wide survey of the probability of

spread-F occurrence for 195^- (year of sunspot minimum) and for the IGY

(sunspot maximum). Reber (195^) made a briefer study on a world-wide

basis. Table 2 lists a number of studies of spread-F at particular

stations.

3.1 Diurnal Variations

Spread-F is generally a nighttime occurrence except at polar or near polar stations, where it occurs also during the day. Figure l6

(a), representing the diurnal variation of spread-F occurrence probability at Baguio- (5°N geomagnetic) at times of sunspot minimum and

sunspot maximum, illustrates the relation of the sunspot cycle to the

diurnal pattern of spread-F occurrence. The Baguio data are roughly

typical of other equatorial stations (see Shimazaki, 1959)* In. middle

latitudes, there appears to be a consistent tendency for spread-F oc- currence to peak somewhat in the post midnight hours.

3.2 Seasonal Variations

For stations near the geomagnetic equator the occurrence of

spread-F is significantly greater during local summer than during

local winter. Although the seasonal pattern may vary with the sunspot

cycle, as indicated in Figure l6 (b) (see also Kotadia, 1959) generally

the occurrence of spread-F in this equatorial region is greater in summer than in winter. For higher (north and south) magnetic latitudes

just the opposite is usually observed, with spread-F more frequent in

the winter than in summer. However, it has been observed (Reber, 195^;

Shimazaki, 1959) that the region where spread-F occurs more frequently

in summer than in winter also includes, besides the equatorial stations,

a number of high northern latitude stations in the Pacific area, and a corresponding number of high southern latitude stations in South

America. The dividing lines separating those high latitude stations

where spread-F predominates in summer from those where it predominates

in winter lie roughly along a great circle, defined as the "spread-F

equator". The position of this spread-F equator varies with sunspot
-21*-

activity. The nearest approach of the spread-F equator to the magnetic equator occurs at sunspot minimum.

3.3 Solar Cycle Variation

The yearly average spread-F occurrence probability is dependent

on geomagnetic latitude and on sunspot activity. At geomagnetic latitudes above 60° the occurrence probability of spread-F increases with

sunspot number. At lower magnetic latitudes, the correlation between

yearly average spread-F occurrence probability and sunspot activity is

inverse (Shimazaki, 1959 )•

3.4 Correlation with Magnetic Activity

The correlation of spread-F with magnetic activity is dependent

on latitude as well as sunspot cycle. Shimazaki (1959) found that the

correlation between the occurrence probability of spread-F and magnetic activity is strongly negative for magnetic latitudes lower than 20°,

shifting to strongly positive for latitudes between 20° and 60°, while

at latitudes higher than 60° it again becomes negative.

In the equatorial regions (Wright, Koster and Skinner, 195&; Lyon,

Skinner and Wright; 1958, 1959; Wright, 1959) spread-F during IGY was regularly present on magnetically quiet days, but markedly inhibited on magnetically disturbed days. For several African stations in the vicinity of or north of the magnetic equator during 195 2 ~53> Wright and

Skinner (1959) find an enhancement of spread-F on magnetically quiet

days to be pronounced only during the summer solstice. From an analysis of spread-F data at Baguio from 1953 to 1958 Marasigan (i960) notes

that magnetically disturbed days generally inhibit spread only during

the years of high sunspot number.

For magnetic latitudes between k0° and 60° North a direct cor- relation of magnetic activity with the probability of spread-F occur- rence increases with increase of latitude (Dagg, 1957 c; Hartz, 1955

i

Appleton, Naismith and Ingram, 1937)* F°r magnetic latitudes over 60°

the correlation again becomes negative. However, as Shimazaki (1959)

points out, at such high latitudes, magnetic disturbances are usually

associated with polar blackouts, which preclude the possibility of

spread-F observations.

Additional studies over complete sunspot cycles and at various

locations would be desirable. Cohen (1959) has suggested investigating some possible connection of spread-F at a given height above the

magnetic equator with the magnetic activity at the base of the field

line passing through this region.
-25-

3. 5 Correlation with the Virtual Height of the F2 Region

There is a marked correlation "between the virtual height of the

F2 layer and spread-F occurrence (see, for example, Bowman, i960).

Spread usually occurs only when the virtual heights are relatively

high for the station in question. Kasuya, Katano and Taguchi (1955)

observed that in Japan the diurnal peaks of spread-F occurrence coincide with the times of virtual height maxima for the F2 layer. At

Baguio the evening onset of spread-F is preceded by virtual heights

of kOO km, higher on the average than at any other time. The disappearance of spread is frequently correlated with the decrease of

virtual heights (Booker and Wells, 1938). Osborne (1952 ) a"t Singapore

found a striking positive correlation between the mean monthly rate of

increase of the virtual height of the F2 layer between 1800 and 1900,

local time, and the occurrence of spread-F at 2000. He also found that

the virtual height of the F2 layer attained its peak height at the

moment of sunset at the 400 km level, and that the time of greatest

rate of increase of virtual height is the period from terrestrial sun- set till sunset at the 400 km level, some hour-and-a-half later.

3.6 Inverse Correlation with the Maximum

Critical Frequency, foF2

There is a rather marked inverse correlation between the probability of occurrence of spread-F and the maximum critical frequency

foF2. Kasuya, Katano and Taguchi (1955) correlated spread-F occur- rence at four Japanese stations over a six- year period with the reciprocal of the monthly mean noon values of foF2. The correlation coefficient was + 0.82.

The evening onset of range type spread-F, characteristic of many

equatorial stations, is normally preceded by a significant drop in the

value of foF2 (Wells and Stanton, 1938, 1939). However, it is to be

noted that there is a much sharper decrease in foF2 during the predawn period at equatorial stations, and yet the probability of spreadF decreases toward sunrise. Brisbane (38°S geomagnetic) lies in a re- gion where spread-F has a pre-dawn peak, but the diurnal variation of

foF2 is not as great there as at equatorial stations. Singleton (1957)

reports that significant pre-dawn frequency spread occurs at Brisbane

only when the value of foF2 falls below k Mc.

3.7 Correlation with Radio Star Scintillations

Although the existence of spread-F has been known for over twenty

years (Booker and Wells, 1938), it is only since its connection with

the scintillation of radio stars was pointed out (Ryle and Hewish; 1950;

Little and Maxwell, 1951) that significant attention has been given to

spread-F.
-26-

Galactic radio noise was first identified by K.G. Jansky in 1932

(Haddock, 1958)* Later work showed that this radiation comes from discrete sources (Bolton and Stanley, 19^) and that it exhibits irregular

short period fluctuations. (Hey, Parsons and Phillips, 19^6). Such fluctuations of "radio stars" can "be shown to "be either fluctuations in the

apparent position of the discrete source, "phase scintillations"; or fluctuations in the intensity of the received radiation, "amplitude

scintillations" (Lawrence, 1958)* Under highly disturbed conditions,

the shift in apparent position of a radio star can be as great as one- half a degree (Hewish, 1952). The question arose early as to whether

the fluctuations were due to actual intensity variations in the source

itself, or were imposed on the signal by some property of the medium

traversed by the signal. Little and Lovell (1950) showed that if the

scintillations are observed by two receivers 100 meters apart, there is

complete correlation of the scintillation patterns. Increasing the

separation of the receivers decreases the correlation, which indicates

that the cause of the fluctuations is not located in the source. In

seeking a cause for these fluctuations in the ionosphere, it was found

that a definite correlation can exist between the occurrence of spreadF and that of radio star scintillation (Ryle and Hewish, 1950; Little

and Maxwell, 1951 ).

Whatever the mechanism responsible for the scintillation phenomena,

it must be operative essentially along the line of sight from the ob- server to the source. When the radio star is near the horizon, the line

of sight passes through the F region at a point many hundreds of kilometers away from the observer. Also, the spread echoes returning to a vertical incidence ionosonde need not always return from directly over- head (McNicol, Webster and Bowman, 1956). The difficulty in correlating accurately the occurrence of spread-F and scintillation is therefore

apparent.

Little and Maxwell (1951) found that, for high angles of elevation,

the occurrence of scintillations coincided with the observation of

spread-F 75 percent of the time, even though the scintillation measurements were made at Jodrell Bank while the ionosonde was located at

Slough, some 230 km to the south. For radio sources located close to

the horizon, continual scintillations are observed. Similar results

have been reported (Mills and Thomas, 1951). For low angles of arrival,

however, of the order of 10° or less, Dueno (1955) at Ithaca, and Bolton,

Slee, and Stanley (1953) i*1 Australia found only a small correlation of

scintillation with spread F, but a rather good correlation with sporadic

E (see also Wild and Roberts, 1956).

The difference in results is probably closely connected with the

angle of observation, which modifies the effective thickness of the

disturbing region, and with the increased separation of the disturbing
-27-

TABLE 3

Experimental Procedures for

Obtaining Data on Spread-F

Method Reference

h' -f ionogram Conventional

A -scan Conventional

h'-t Conventional

h

1 -t, swept gain McNicol, Webster and Bowman, (1956)

h

, -t, swept frequency Nakata, Kan and Uyeda, (1953 a)

f -t

c Nakata, Kan and Uyeda, (1953 b)

Direction of Arrival Thomas and McNicol, (1955 ) Miya, et al, (1957)

Bibl, Harnishmacher and Rawer, (1955

)

Phase Path Findlay, (1951

)

Jones, (1953)

Yuhara, Koseki and Aono, (195^)

McNicol, Webster and Bowman, (195^

)
-28-

region from the location of the observer (Little, Raytort and Roof, 1956).

The correlation of the occurrence of spread-F with the scintillation of radio stars has been useful, since a fair amount is known about

the conditions of the ionosphere at the time of scintillations. The

dimensions of the irregularities in ion-density in the F region thought

to be responsible for scintillation are of the order of five km in

width (Bolton, Slee, and Stanley, 1953)* often quite elongated, with a tendency to lie in bands parallel to the magnetic field (Spencer, 1955)*

The irregularities have a horizontal drift motion in an approximately

east-west direction, with a drift velocity reaching at times several

hundred meters per second (Salzberg and Greenstone, 1951; Skinner, Hope

and Wright, 1958).

3.8 Correlation with Scintillations

of Radio Signals from Satellites

The character of radio signals received from artificial satellites

provides information on the state of the ionosphere along the path of

propagation. Parthasarathy, Balser and DeWitt (1959) detected irregularities in ionization in the auroral zone up to heights of 800-1000 km,

by employing two spaced receivers. Yeh and Swenson (1959) suggest that

the region producing scintillations on the satellite signals is between

200 and 300 km, and find a strong positive correlation between such

scintillation and the occurrence of spread-F, see Table 3«

4. INSTRUMENTATION

Spread-F is usually defined with respect to the appearance of the

trace on the conventional virtual height versus frequency ionogram

(h'-f). In making detailed studies of the occurrence and nature of

spread-F a number of other experimental techniques have been employed.

Table 3 presents some of these.

Ij-.l A-scan

At times it is helpful to present an A-scan pattern of the returned

echo at a fixed frequency, by displaying the intensity of the returned

echo versus the delay time on the face of an oscilloscope tube. This

procedure yields information on the relative intensity of the different

portions of the spread echo, which may exhibit a multiplet structure.

A-scan, used in conjunction with the conventional sweep-frequency ionosonde, can serve as a useful indicator for adjusting the receiver gain

setting to minimize the effect of background noise.
-29-

k.Z Virtual Height Versus Time (h'-t) Records

The conventional h

8 -f ionograms are usually taken at fifteenminute intervals. It is sometimes desirable to have a continuous rec- ord of the conditions of the ionosphere. However, successive h'-f

sweeps can produce possible local interference, and also necessitate

additional scaling time to obtain the data from the successive ionograms. For the purpose of spread-F studies it is frequently satisfactory to employ a single pulsed frequency rather than the swept frequency

method. In this method of fixed frequency probing, the recording film

is continually moved to produce a time base, while the returning echo

intensity modulates the electron beam, which is deflected at right

angles to the direction of film travel to indicate virtual height.

The result is an h'-t plot. Such a procedure is useful in studying

range type spread-F, since, over a wide range of frequencies, the degree

of range- spread is independent of frequency.

U.3 Swept Gain h'-t Records

Since the extent of spread-F appearing on an ionogram is somewhat

gain- sensitive, McNicol, Webster and Bowman (1956) included a swept

gain technique in their h'-t records. They permitted the gain of the

receiver to fall in steps of 2 db through a total of 80 db over a period of two minutes, after which the receiver is returned to maximum

gain and the cycle repeated. They find that as the gain decreases,

what at first appeared to be a diffuse spread resolved itself into a set of multiplets.

k-.k Swept Frequency h'-t Records

Depending on the fixed frequency selected, either the E, F, or F

? regions may be studied. Usually blanketing by the lower layers prevents

the viewing of several layers at the same time. Nakata, Kan and Uyeda

(1953 a ) combined a limited but rapid variation in the probing frequency

together with the h'-t procedure. In one experiment the frequency was varied from 1.8 Mc to 3-5 Mc in ten seconds, while the film speed was only about 3*5 centimeters per hour. This rapid variation of frequency

over a limited range, superimposed on the h'-t records, does not cause any appreciable blurring of the record. Good resolution is thus obtained, and the film shows layer thickness, spread echoes absorption,

and the minimum height. of each layer.

^•5 Critical Frequency versus Time (f -t) Records

c Another variation by this group (Nakata, Kan and Uyeda, 1953 "b

)

yields a continuous record of the maximum critical frequency. The

method may be visualized by considering first the standard h*-f
-30-

ionogram. Let the h

1 axis "be collapsed. The film is then continuously

moved at right angles to the horizontal or frequency axis, while the

oscilloscope is z-modulated by the returning echo. The resulting pattern on the film is a plot versus time of the maximum frequency re- turned from the ionosphere. Frequency type spread-F will readily show

up on such records.

k.6 Direction of Arrival

In any detailed study of spread echoes it is important to know the

direction of arrival of the returning echo. The normal delta antenna

system used on vertical incidence equipment has its maximum sensitivity

in the direction of the zenith, but it still has appreciable gain in

directions other than the vertical.

Thomas and McNicol (1955) employed two sets of parallel loop an- tennas separated by one -half wave length. Each of the two sets is

mounted at right angles to the other set, one north- south, and the

other east-west. An echo returning from directly overhead will arrive

at all four loop antennas in phase. However, there will be a relative

phase difference at the different loop antennas if the wave returns

from any direction other than the zenith.

For the north- south pair of antennas, the phase difference * of

the echo pulses in the two antennas will be proportional to the angle

the returning wave makes with the north. Thomas and McNicol show that

the ratio of the absolute value of the difference of the signals in

the two antennas to the absolute value of the sum of the two signals

is proportional to <S> and therefore proportional to the angle of arrival.

In practice the sum and difference voltages are applied to the Y and X

plates of an oscilloscope, and the slant of the resulting trace indicates the angle of arrival the returning echo makes with the north.

A similar arrangement is also used for the east-west pair of antennas.

A more sophisticated version of the above has "been developed by

Miya, Sasaki, Ishikawa and Matsushita (1957) • They use four vertical

antennas instead of the loops, and insert a fifth vertical antenna in

the center of the array to remove a 180° ambiguity in the direction of

arrival of the returning echo.

A rather simple arrangement that can be used with the already es- tablished vertical incidence sounding equipment is described by BIbl,

Harnischmacher, and Rawer (1955 )• This procedure consists in interchanging the antenna feeding arrangement for the rhombic antennas, so that the antenna will alternately have a null and a maximum In the

zenith direction. With such an arrangement traces on the h'-f ionogram

produced "by echoes returning from directly overhead will have an
-31-

interrupted appearance, -while oblique echoes are more continuous.

There is, however, no indication of azimuth on the ionogram.

4.7 Phase Path Measurements

The conventional vertical incidence pulse technique measures the

time taken for the transmitted pulse to return to the receiver via a particular path from the reflecting region. The accuracy of this

measurement -will depend on the pulse width, receiver characteristics,

focus of the oscilloscope, film grain-size, etc. Small height variations, of a kilometer or two, can he detected only with difficulty

from successive h* -f ionograms. The "phase path" measurement, however,

indicates any small variation in phase path in the medium through which

the signal is passing.

Let the probing frequency of a fixed frequency h*-t vertical incidence sounder be f. A signal of frequency (f - e ) from a stable

local oscillator is fed into the detector stage of the receiver along

with the returning echo from the ionosphere. The injected signal has

an angular dependence given by

cos (ft - et) ,

while the angular • dependence of the returned echo signal is

cos (ft - P/\) ,

where P is the total phase path of the signal and \ is the wave length.

Due to the non-linearity of the detection process in the receiver a difference frequency is generated, with an angular dependence given by

cos (et - P/\) .

With suitable low pass filters, if there is no returned echo signal

there will be no output signal from the receiver. When there is a returned signal, the receiver output can be approximated by a wave

packet, where the number of cycles in the packet will depend on the

value selected for e, the original duration of the transmitted pulse,

and the pulse deformation during the time of travel in the ionosphere.

This means that the usual h'-t echo traces will then appear to be

striated, and any change in the phase path length will cause the striations to be inclined with respect to the horizontal or time axis. The

whole process is much like the counting of interference fringes in an interferometer, and each striation corresponds to a phase path difference of \. However, it is to be recalled that \ is itself a function of the index of refraction and therefore will differ with changes

of the ion density along the path of propagation. With this type of
-32-

equipment small changes of phase path are readily detected.

k.Q Indirect Methods

Other observational methods have been employed in conjunction

with studies of spread-F. These methods, while they do not measure

spread-F directly, do study phenomena that appear to have an intimate

connection with spread-F occurrence. Some of these are listed in

Table k.

5. POSSIBLE MECHANISMS RESPONSIBLE FOR SPREAD-F

It is generally felt that spread-F owes its origin to irregularities in the electron density of the ionosphere. In this connection

two questions arise:

(1) What is the configuration of electron density which

produces the observed spread-F patterns?

(2) How does such a configuration arise?

The patterns of spread-F occurrence suggest the possibility that

the responsible mechanism may differ with season, location and spreadF type. The first question will be discussed in the present section,

while the second question will be treated in the section following.

Table 5 lists several proposed mechanisms thought to be responsible

for the appearance of spread-F on certain ionograms.

5.1 Reflections from Horizontally Moving Fronts

A detailed study of range type spread-F has been carried on by a Brisbane group (McNicol and Webster, 19^>6; McNicol, Webster and Bowman,

1956). Evidence is presented to indicate that range multiplets have

their origin In reflections from horizontally moving fronts in the F

region, with dimensions of up to several hundred kilometers, and that

range type spread-F is generally a series of closely spaced multiplets

in the vicinity of the main F trace. Frequency type spread-F is not

considered, as it is thought to have its origin in another mechanism.

McNicol and Webster (1956) fit their theory of range type spreading into the pattern of large scale ionospheric movements. They con- sider in some detail three types of irregularities, an inverted trough

(Munro, 1953 )> a SaP> an<i a step, and suggest that each satellite trace

is a reflection of the incident pulse from such irregularities.

By the use of three pulse transmitters located at the corners of

a right triangle of 95 km base and altitude, simultaneous measurements

were made of slant virtual range, R

1 , of the satellites of the main F
-33-

TABLE h

Indirect Methods for Obtaining Data

Relative to Spread-F Occurrence

Method Reference

Radar echoes

Oblique incidence

pulses

Radio Star

scintillations

Horizontal drift

motions

Peterson, Villard, Leadabrand

and Gallagher, (1955

)

Bateman, Finney, Smith, Tveten

and Watts, (1959)

Booker, (1958)

Briggs and Spencer, (195^)
_ 3lH

TABLE 5

Some Proposed Mechanisms

Responsible for Spread-F

Mechanism References

Reflection from horizontallymoving ionospheric fronts

Reflections from large irregularities in ionization

Reflection from horizontal

stratification

Forward scatter plus re- flection

Backscatter

Aspect sensitive backscatter

McNicol and Webster, (1956)

Uyeda and Ogata, (195U

)

Singleton, (1957)

Eckersley, (1953

)

Sung and Kwei, (1938)

Eckersley, (1937)

Renau, (1959)

Booker and Wells, (1938)

Renau, (1958)

Bowles and Cohen, (1959)
-35-

trace. Taking the virtual height of the main F trace as h

1 , the horizontal displacement, x, was deduced from the relation

1 x = (R'

2

- h'

2

) 2

(1)

for each of the three transmitters.

It was found that if three points, T , T

? and T are plotted to

represent the geographical location of the transmitters, one can draw

about these points circles of radius x, , x~ and x_ respectively, cor- responding to the echo measurements at a given time. There is rarely,

if ever, a common intersection of these three circles, but it is usual

for the three circles to have a common tangent. Continued observation

showed the common tangent to move roughly parallel to itself, although

at times this direction was somewhat changed. The azimuth of the re- turned echo corresponded roughly to a normal to this common tangent.

Variations in the zenith angle, Q, of the returned echo conformed quite

closely to the relation

R' = h' sec B . (2)

The h'-f ionograms indicate that for range type spread-F the

separation of the satellite traces from the main trace is independent

of frequency over a wide range of frequencies. McNicol and Webster

were able to obtain a good deal of data from h'-t measurements at a fixed frequency, sufficiently low to eliminate any effect of ordinary

and extraordinary trace separation. Detailed studies of the results

show the motions of these irregularities, indicating the time and distance of closest approach. The intensity of the satellite trace decreases with increasing slant range, obeying approximately a linear

relationship of -O.k db/km. The average length of these moving fronts

in the F region was found to be of the order of 300 km, with a mean

duration of from one to two hours. The speed generally varied from

150 to 350 km/hr, with the mean direction toward a little north of

west.

The explanation of range multiplets as reflections from horizontally moving disturbances, as presented by McNicol and Webster

(1956) is inviting. The authors restrict themselves to range spread

alone. Their explanation fits most clearly the case of a single satellite trace, although the extension to a number of such satellites

all closely spaced is immediate

Using continuous observations of virtual height at a fixed frequency interval, Uyeda and Ogata (195*0 obtained evidence of apparent
-36-

ionospheric undulations moving with a horizontal speed of from 300 to

i+20 km/hr. The length of the undulations was about 300 km and the

maximum depth appeared to "be greater than 100 km. The corresponding

virtual height versus frequency ionograms indicated a range multiplicity and at times a diffuse range type spread-F. There may, therefore, be some connection between spread F and systematic ionospheric

drifts.

Horizontal drift motions of the ionosphere have been recognized

for some time. Pawsey (1935 ) separated two receivers by 170 meters

and noted that on occasion the recorded fading curves were displaced

from each other by up to one second. This he interpreted to be the

result of an ionospheric wind. Munro (l9*J-8), employing a more elabrate arrangement, utilized three transmitters placed at the corners of

a right triangle with legs of 13 and 27 miles. He estimated winds

with speeds of up to 100 m/sec. Mitra (19^9 )> with a single pulse

transmitter and three receivers spaced 100 and 200 meters apart at the

corners of a right triangle, found the most frequent velocity to be

about 5° m/sec. Much work has been done along these lines, both ex- perimental and theoretical, and excellent summaries are given by

Ratcliffe (1955) and by Briggs and Spencer (l95 1 +).

Tilts in the F layer were first noted by Ross and Bramley (19*1-9)

and subsequently Price (1953) reported large scale traveling disturbances, responsible for peaks and dips of F layer virtual height, and

splitting of ordinary and extraordinary rays. Such disturbances are reported to have an average speed of about 100 - 200 m/sec, and the

velocity of the disturbance to remain substantially constant over distances of up to several thousand kilometers.

In general these F region ripples drift in such a way that the

east-west component of their motion is eastward by day and westward by

night, with an appreciable increase of velocity in times of magnetic

disturbance. The maximum vertical displacement of the ripple is of

the order of 5 km- There are few points understood concerning these

irregularities. It is not clear if the movement involves the neutral

air as well as the ions, and electrons, and if there is any net transfer

of ionization or merely a wave motion, as the name ripple seems to

suggest. The origin of these large scale movements and their ultimate

decay process is still undetermined.

5.2 Reflection from Large Irregularities in Ionization

Singleton (1957 ) suggested that frequency type spread-F is, due to

reflections from irregularities in the F region large, compared to the wave length of the incident wave. Noting the correlation between

spread-F occurrence and the scintillation of radio stars, he assumes
-37-

that the same ionization irregularities are responsible for both effects.

A. Relative Ion Density of Irregularities Responsible

for Radio Star Scintillations

The irregularities in the F region ionization thought to be res- ponsible for the scintillations of radio stars are taken to be of the

order of 5 km in diameter (Ryle and Hewish, 1950; Little, 1951; Booker,

1958). Little (1951) has shown what must be the difference in plasma

frequency between the irregularity and the surrounding medium for

scintillations to occur. The difference in phase path for a wave

traveling through the irregularity or through the surrounding medium

must amount to one-half wave length for destructive interference to

occur. From the definition of the index of refraction, \±, the change

in wave length, A \, of a wave of length A. due to a change A \x of the

refractive index of the medium is given by

AX = ±-^. (3)

For an irregularity of diameter t the total path difference required

for scintillation is given by

(l/\) A\= (i/\) ( ^-^ ) * V2 • 00

Provided that the refractive index of an ionized medium does not depart appreciably from unity, it may be expressed as

1

n - -[1 - (f/f f } =i-| (f

p

/f ) + . . . (5)

For scintillation observations, a plasma frequency, f , of 3 Mc and

XT an observing frequency, f, of 50 Mc are not unreasonable, and justify

dropping the additional expansion terms in (5). The difference in

refractive index, A |i , between the background region and the irregularity of plasma frequency f , is

*"-l?r-<V.-V- (6)
-38-

Using this value of A p. in (h) we obtain the inequality

2 2

f5" (f

P

- f

P

> s l- (7)

For an irregularity diameter of 5 ^^ "the difference in plasma

frequency between the irregularity and the background ionization

necessary for scintillation may be as small as 0.5 Mc. This value

is comparable to the extent of frequency type spread encountered on many ionograms.

B. Reflection and Interference

On the assumption that the irregularities which produce scintillation are identical with those responsible for spread-F, (5 km in extent, differing in plasma frequency from the background by about 0.5

Mc ) wave from the ionosonde will be reflected since the dimensions are large compared to the incident wave length. However, interference will

occur between the reflections from several irregularities and the background layer. Also, a spread of critical frequencies will be obtained.

The angular power spectrum for a wave reflected from a screen of

irregularities has been given by Booker, Ratcliffe, and Shirm (1950)

and also by Briggs and Phillips (195O). The reflected power falls

off rapidly for directions at large angles to the normal to the re- flecting screen. If the F region is to be considered as such a screen

above a vertical incidence sounder, the irregularities directly over- head will reflect back maximum power (with a minimum delay time ), while those at greater lateral distances will reflect back proportionately less power (and with a greater delay time). The reflected waves

from each irregularity will interfere to produce marked fading.

Suppose an arbitrary minimum power, determined by the sensitivity

of the receiving and recording equipment, is required of the wave

returned from the individual irregularity in order that its contribution affect the ionogram. The ionosonde can then observe only those

irregularities lying within a certain cone whose semi-angle is a function of the height of the irregularities and their mean dimensions.

Singleton has shown that the number of irregularities, n, observable

in a layer at a height, h, above an ionosonde using a probing frequency,

f, is of the form

n cc h

2 /bV , (8)

where b is the average horizontal distance between the irregularity

centers. Under conditions obtaining in the ionosphere, n can be
-39-

great enough to account for the rapid fading of the returned spread

echoes.

The degree of frequency spread in the penetration frequency is,

in general, independent of any assumptions regarding the horizontal

distribution pattern of the irregularities. Rather, it is a function

of the extremes of ion density along the horizontal layer. According

to (8), a small decrease in probing frequency below the maximum penetration frequency implies that effectively the ionosonde can view more irregularities, and these at slightly greater virtual ranges. This

would result in a slight range broadening of the echo trace, and also

fading due to interference of the echoes returning from the different

irregularities. Further decrease in the probing frequency would

heighten this effect. However, since the irregularities are thought

to be embedded in the F region ionization, a decrease in the probing

frequency means that irregularities embedded more deeply in the F re- gion will not be observed. This effect will be the more pronounced

the greater is the zenith angle of the irregularity.

An increase in receiver gain has the effect of increasing the semiangle of the cone of admissible echoes. This should increase the

density of the diffuse trace, and also the virtual range. In general

this will not result in a spread of penetration frequencies, provided

the variations in peak electron density are randomly spread throughout the horizontal layer.

C. Scintillation and Spread-F

Irregularity in ionization is a necessary and sufficient condition for radio star scintillation. However, according to Singleton's

explanation it is not a sufficient condition for frequency type spreadF. If the irregularities exist above the F layer maximum ion density,

scintillations will be observed, but not spread-F. Hewish (1952) has

pointed out that fluctuations in the intensity of cosmic radio noise

start in the evening, reach a maximum shortly after midnight, and decay slowly, lasting late into the following morning. Spread-F, however, appears to be predominately a nighttime phenomenon. The sharp

cutoff of spread-F with local sunrise may be associated with the predawn drop in virtual height, so that irregularities are obscured by the

F layer maximum beneath them (Booker and Wells, 1938). The world-wide

summer increase in the virtual heights of the F region might be a factor expected to account for the seasonal variation of spread. In

latitudes less than 20°, this seems to be the case. However, for latitudes greater than 20°, spread-F is more common in the winter than in

the summer. At present insufficient knowledge is available concerning

the heights of the irregularities responsible for scintillations to

clarify these matters completely.
-40-

5.3 Reflection from Horizontal Stratifications

A. Simple Stratification

A much oversimplified explanation of range type spread-F would

suggest that the region above the F layer maximum is stratified, which

somehow accounts for satellite traces above the main trace of the

ionogram. There are, however, indications that this explanation is

not correct.

Irrespective of spread, the main trace frequently remains un- changed in appearance, suggestive of a well defined layer maximum of

uniform consistency. For range type spread there is at times a single

sharply defined critical frequency which indicates a definite uniformity in the structure of the layer. It is difficult to see how the

probing wave could actually penetrate this F layer to get to the stratification above the F region maximum. Yet considerable penetration

would at times be required to account for the observed intensity of

the spread echo.

A second factor against the simple stratification hypothesis, at

all but polar latitudes, is the angle of arrival of the returning echo.

For satellites of large range separation, McNicol, Webster and Bowman

(1956) have found that the returning signal arrives at a considerable

angle with the vertical. In many instances, the virtual height of the

main trace, h', of the satellite trace, R

1 , and the zenith angle 6, of

the returning satellite echo follow the simple relationship,

cos 9 = h'/R* , (9)

which is what would be expected if the satellite echoes are all re- flected from the same height as the main trace.

B. Stratification in the Polar Regions

Eckersley (1953) points out that spread-F in the polar regions is

frequently a daylight occurrence, and that spread echoes in these re- gions generally return from the zenith. When the effects of vertical

radiation are neglected, solar radiation, on a simple Chapman theory

(Chapman, 1931) will produce the usual well defined E and F layers.

If charged particles from the sun approach the earth, their easiest

path of approach will be in the polar regions, due to the action of

the earth's magnetic field. If the ionizing effect of these incoming

particles is to be included in a simple Chapman theory, Eckersley points

out that the vertical diffusion term can no longer be neglected.
-inEckersley believed that the vertical distribution of electron density, p (z), is governed by the equation

dz

where q accounts for the ionizing effects of solar radiation and the

incident particles, Ot is the recombination coefficient, and D is the

diffusion coefficient, including the effects of the magnetic field.

He solved this equation for the steady state (dp/dt = 0), and found

that the admissible solutions for p (z) involved doubly periodic elliptic functions. Physically this means that while the solar radiation causes layers to be formed that are many wave lengths thick with

respect to the probing frequency of the ionosonde, the incident particles cause the formation of very thin layers, only a few wave lengths

thick, embedded in the background of the thick layers. Eckersley also

showed mathematically that this type of layer structure would cause a single incident pulse to return a series of delayed echoes, sufficient

to account for the spread effects on an ionogram. This theory applies

only to polar spread, where the geomagnetic field is predominately

vertical.

Additional angle of arrival studies and correlations with solar

flares and radio noise outbursts should prove enlightening. It would

seem that some seasonal variation of polar spread-F should be predictable on this theory due to the changing length of the polar day.

C. Multiple Reflection Between the Fl and F2 Layers

Sung and Kwei (193&) noted from a limited number of observations

that a spread condition resulted after the coming together of the Fl

and F2 layers in the evening. They suggested that the spread effect

might result from multiple reflections between closely adjacent layers.

Such an explanation, if correct, would account for only a very limited

number of occurrences of spread-F.

5.4 Forward Scatter Plus Reflection

A. E Region Scatter with F Region Reflection

An early suggestion advanced by Eckersley (1937) attributed spreadF to scatter from moving irregularities in the E region followed by a regular reflection process in the F region (or alternatively, F reflection followed by E scatter). Evidence of this mode of propagation has

been presented by Meek (1952) in observational data obtained at Baker

Lake, Canada. He even noticed a brief return directly from the E
-112-

region at the moment when the sporadic E cloud was computed to be

directly overhead. Meek (1952) observed a difference in critical frequency between the main trace and the satellite traces, which is con- sonant with the different angle of arrival of the main trace, reflected

vertically from the F layer, and the satellite, reflected obliquely via

the E scatter.

In a great number of range spread instances, McNicol and Webster

(1956) find no difference observable between the critical frequency of

the main trace and of the satellite traces. There are many occasions

when Es echoes occur with no spread-F, and vice versa. Also McNicol,

Webster and Bowman (1956) present instances where the F + Es echo is

either absent or quite weak, while the satellite traces are of high

intensity.

However, from the observational data presented by Meek (1952) it

is clear that the process suggested by Eckersley can actually be operative on certain occasions.

B. A Postulated Scattering Screen Below the F Region

A theory of spread-F involving an F layer reflection coupled with

a scattering process below the F region has been considered by Renau

(1959)* A thin scattering screen, invisible on the ionograms, is

postulated to exist above the E region. Propagation is considered to

be that of forward scatter from this screen followed by F layer reflection. A parabolic F region of arbitrary semi-thickness and height

is assumed, and a thin scattering screen is set beneath it at an arbitrary height above the flat earth. Delay time as a function of probing

frequency is calculated for various sets of parameters. Depending on

the position on the thin screen of the forward scatter, a family of

admissible delay times are obtained, bounded by a suitable envelope.

Comparison with ionograms shows that some cases of spread actually do

admit of such an analysis. However, in general, the minimum delay

times exceed those actually observed on the ionograms, even with all

possible variations of the height of the thin scattering screen below,

and even coinciding with, the F region maximum.

In a transequatorial transmission experiment Bowles and Cohen

(1959) found that propagation via F scatter occurred only about 10

percent of the time along their 258O km propagation path, and this

during evening hours, generally before midnight. A sufficient and

nearly necessary condition for the occurrence of such oblique F scatter was found to be the presence of range type spread-F on the vertical incidence Huancayo ionograms, located close to the midpoint of the transmission path. By variation of the ionosonde antenna pattern, and by

oblique incidence pulse delay measurements, the height of the propagation medium sustaining this F scatter was established, in general, as
43-

the lowest height of the associated equatorial spread-F on the Huancayo

ionograms. Such results are not compatible with the scatter plus re- flection theory of Renau (1959).

5.5 Back Scatter

An early attempt to explain the spread echoes on the Huancayo records by hack scatter is due to Booker and Wells (1938)* They point out

that, to a first approximation in Rayleigh scatter, the ratio of the intensity of the scattered radiation, i, to the incident radiation I, is

given by

2

i/1 « t

k {/ - a/) , (11)

where f is the frequency of the radiation in question, and \± and u are

the refractive indices of the scattering medium and the surrounding

medium respectively. However, for Rayleigh scatter it is necessary that

the scatterer be small with respect to the incident wave length.

Equation (ll) appears to indicate a definite frequency dependence

for the scattered radiation, but the Huancayo ionograms do not bear this

out. It should be recalled, however, that to a first approximation the

index of refraction of the ionosphere may be expressed in terms of particle charge, mass and density as

M- = 1 - 2 2~ > ( 12 ^ (jtm/e ) f

and therefore

2 2

v o

(N N) (e

2

/TM)

f

2 (13)

Substituting (13) in (ll) we find that the ratio of scattered to

incident radiation is independent of frequency but depends on the relative difference of ion density in adjacent regions of the ionosphere

i/1 « (N - N

q

) 2

(e

2

/*m)

2

. (ik)

This is valid as long as the wave length of the radiation is large

compared to the dimensions of the scattering areas. On the Huancayo

ionograms the spread becomes weaker toward the higher frequencies and

generally disappears entirely at 11 or 12 Mc, corresponding to a wave
-kklength of about 25 meters. Therefore irregularities in ion density of

some 25 meters in diameter are postulated to explain this spread phenomena .

These irregularities are thought to exist above the F layer maximum during the early evening. For probing frequencies below the

penetration frequency of the F layer maximum, these irregularities are effectively out of sight, while for higher frequencies, the irregularities are too large, in comparison with the small wave length, to

permit appreciable scattering. However, later in the evening, the F

region maximum rises above the level of these irregularities and

Rayleigh scatter can take place for frequencies below 12 Mc accounting

for the spread echo occurring on the ionograms at that time . Wells

( 195*0* however, questioned the importance of this masking effect in

accounting for the diurnal characteristics of spread-F.

This theory was advanced before radio star scintillations were

observed. Such scintillation effects seem to suggest irregularity

sizes of the order of five kilometers. Bowles and Cohen (1959) suggest the scale size of the irregularities measured normal to the magnetic field lines can be as small as 10 meters.

5.6 Aspect Sensitive Back Scatter

Renau (i960) has suggested that the observed spread-F ionograms

may be the outcome of aspect sensitive back scatter from columns of

ionization aligned along the earth's magnetic field. In accord with

the work of Chapman (1953) and- Booker (195& t> ) this back scatter is

assumed to be most intense when the incident ray is perpendicular to

the field aligned column of ionization.

For an ionosonde at the dip equator the geometry is quite simple

and echoes would be returned only in a plane in the east-west direction. The varying delay times responsible for the spread effect would

depend on the existence of such field-aligned irregularities and their

height relative to the F layer maximum. At stations away from the dip

equator a wider selection of admissible paths is possible. North of

the dip equator, a ray returned from the magnetic north should have

the minimum delay time, while one returned from the south should have

a maximum, and all intermediate delay times should be possible for

other azimuth values of the returning echo. Bowles and Cohen (1959)

report that at Huancayo, polarization measurements indicate that range

spread echoes arrive from the magnetic east-west direction.

The theory is attractive and a number of ionograms lend support

although others do not conform to this analysis. At middle latitudes

Peterson et al (1955 ) obtained aspect sensitive echoes over a frequency
-45-

TABLE 6

Factors Suggested as Being Responsible

for Irregularities in Ionization

Factor Reference

E region turbulence communicated

to the F region

Instability of drifting ionization configurations

Corpuscular matter of inter-

•stellar origin

Charged particles of solar origin

Evaporation of terrestrial atmosphere

Dagg (1957 a, b

)

Martyn (1959 a, b, c)

Clemmow, Johnson and

Weeks (1955

)

Ryle and Hewish (1950

)

Shimazaki (1959)

Ratcliffe (1956)
-k6-

range of from 6 to 30 Mc, provided the line of sight of the transmitter

intersected a magnetic field line at a height corresponding to that of

the E or F layer maximum. Attempts were made to correlate the times

of these echoes with the occurrence of spread-F, since the aspect sen- sitive echoes are essentially a nighttime phenomena. Detailed correlation, however, was lacking, due perhaps to the fact that the spread-F

observations were made in the vicinity of the transmitter, while the

slant range of the aspect sensitive echoes varied from 600 to 17OO km.

{See also Nichols (1959)}.

6. Factors Responsible for Irregularities of Ionization

All the foregoing possible mechanisms for spread-F postulate some type of irregularities of ionization. Several suggested processes for

the formation of suitable irregularities have been advanced (Dagg,

1957 a )> and are listed in Table 6.

6.1 E Region Turbulence Communicated to the F Region

A. Turbulence below 120 km

Visual observations of meteor trails and noctilucent clouds

(Millman, 1959) an(i radio echoes from meteor trails (Greenhow and

Neufeld, 1959) suggest that turbulence is a common occurrence in the

ionosphere at least up to 100 km. Golitsyn (1959) has shown that the

influence of the earth 1 s magnetic field has little influence in suppressing turbulent motions in the lower atmosphere, and Howells (1959)

has pointed out that a combination of turbulence, diffusion, and a magnetic field cannot alone be expected to produce irregularities that

are strongly elongated along the magnetic field, certainly not with

dimensions much in excess of two to one. It is to be recalled that

the ratio of neutral to charged particles is never less than 1000 to 1.

On the experimental side, Nichols (1959) presents evidence based on radio observations of back scatter from ionospheric irregularities

that there do exist at heights of from 80 to 300 km, small scale irregularities definitely elongated along the earth's magnetic field. There

is general feeling (Booker, 1959) that turbulence does not exist in

any marked degree above 120 km (See Maxwell, 195^ )•

B. Richardson's Criterion

In the upper regions of the earth' s atmosphere there are drift

motions (Ratcliffe, 1955; Briggs and Spencer, 195*0. Their horizontal

velocity, u, varies with height and therefore laminar flow and shear can be envisioned, and under certain conditions laminar flow may

develop into turbulence.
-klIn turbulent motion a mass of fluid may be moved upward into a region of lower density. Work is required and therefore the displaced

mass can be considered to have increased potential energy. Due to the

velocity gradient with height, the fluid mass will be swept along in

the higher region with increased velocity, and therefore its kinetic

energy will also be changed. A dimensionless quantity, Richardson's

number, R., is defined for a unit mass of displaced fluid as

Change in Potential Energy / * i

" Change in Kinetic Energy

*

\ s >

Thus for a large value of R., the potential energy change, and

hence the work required for such a vertical displacement is many times

greater than the increased kinetic energy resulting from such a displacement. This implies a high degree of stability and the suppression

of turbulence. However for R. appreciably less than unity, the kinetic

energy increment arising from a vertical displacement is greater than

the work required for the displacement and turbulence is possible and

even fostered. Thus, Richardson's number is a criterion for turbulence.

It may be expressed as

R -

< »/*>

( 1

+

2

F }

, (16)

( 51 )

where T and g are the absolute temperature and the acceleration due to

gravity; ^— is the vertical velocity gradient, and r is the adiabatic

lapse rate.

With sunset the upper atmosphere cools with a corresponding de- crease in the temperature gradient, tending to make R. smaller.

Although, as Lowan (1955) nas shown, during the first two-and-a-half

hours after sunset the drop in temperature at 360 km is of the order of

ij-00°K, yet at heights below l60 km the temperature has hardly changed

during this same period. Moreover the adiabatic lapse rate, r, is

generally several times larger than the temperature gradient term.

Since the velocity gradient appears to the second power, this term has

a greater effect on the value of R . Dagg (1957 *>) finds R. to be

700 at 90 km, and not much different at 135 knu Such a large value indicates that turbulence should be greatly inhibited at these heights,

which is apparently not the case. This points up the approximate
-48-

nature of Richardson* s criterion as applied to the upper atmosphere,

and of the present state of the question of turbulence in the ionosphere .

C. Magnetic Field Lines as Equipotentials

Dagg (195 7-b) suggests that turbulence of ionization below 120 km

sets up a varying electric field, superimposed on a mean electric

field arising from the interaction of the tidal flow of ionization

with the geomagnetic field (Baker, 1953; Baker and Martyn, 1952, 1953;

Chapman and Bartels, 19^0). Since the conductivity along the magnetic

field lines is so much greater than that transverse to them, these

magnetic field lines determine lines of equal electric potential.

Thus the variations in the electric field in the E region are transmitted up along the magnetic field lines into the F region. In this

region of enhanced ionization, irregularities in the ion and electron

density result. It is not necessary to postulate a turbulent motion

of the unionized atmosphere at F region heights, and indeed such turbulence of the neutral air is thought not to occur.

Such a propagation of the electric field from the dynamo region

up into the F region via the so-called equipotentials is thought to be

quite possible by Martyn (1959 a, b, c ). Horizontal electric fields

produced in the dynamo region, of the order of 1000 km in extent can

readily be thought to produce an effect in the higher F region via the

magnetic field lines. However, field variations a few kilometers in

extent in the dynamo region could much less readily be propagated the

requisite distance into the F region. Farley (1959) has considered

this question and finds that such a process is theoretically possible,

but it depends rather critically on limited conditions of source height, and to a lesser extent, on temperature and ionization profiles.

Such small fields propagated into the F region can be shown to vary by

one or two powers of ten for plausible diurnal variations of the ionosphere parameters. Such variations may be associated with the diurnal

behavior of spread-F.

If the above explanation offered by Dagg is substantially correct,

at least some effects of the turbulence in the dynamo region should be

observed at the time of occurrence of spread-F. . However, there is

little or no consistent correlation between the occurrence of spreadF and sporadic E (Lawrence, 1958)*

6.2 Instability of Drifting Ionization Configurations

It might be objected against Dagg that the perturbing fields com- municated to the F region from below may not be sufficient to produce

the irregularities thought to be responsible for spread-F. A theory
-49-

advanced "by Martyn (1959 a > b, c ) explains how such small perturbations in the F region may become appreciably enhanced under certain

circumstances.

Martyn considers that the F layer as a whole will drift vertically, under the action of large scale electric fields from below and

interactions with the earth's magnetic field. He shows the perturbations in ionization on the undersurface of an upward drifting layer

are inherently unstable, and will move, relative to the drifting

medium, in such a way as to enhance their difference in ionization

from the surrounding medium.

A. Development According to Martyn

Martyn considers the ionosphere as a thin ionized sheet. He notes

that while currents can flow in the plane of the sheet, a current flow

normal to the sheet will be inhibited due to the finite thickness of

the ionized region. At the dip equator the magnetic field is running

north-south in the plane of the ionized sheet. A horizontal east-west

electric field would tend to set up vertical Hall currents . However,

due to the finite thickness of the ionosphere, these vertical Hall

currents will at length be inhibited by polarization effects at the

upper and lower surfaces of the layer. At other regions away from

the dip equator the situation is more involved. Here, there will be

a magnetic component both in the layer and also normal to it. The

resultant conductivities are a function of the magnetic dip angle and

also of the heights, since the different conductivities have a different dependence on v, the collisional frequency, which is itself a function of height (see Appendix A). Due to this polarization, Baker

and Martyn (1953) show that in the F region the Hall conductivity is

much less significant than the Pedersen conductivity and therefore may

be neglected.

Let a cylinder of neutral ionization be embedded in a region of

differing ion density, and be aligned with the geomagnetic field. Let

the entire region be drifting vertically under the action of an electric field. If the surrounding medium were non-conductive, Chapman

and Ferraro (1931 ) showed that the cylinder would be free to move at

right angles to the magnetic field. Viewed from the outside the cylinder is electrically neutral. Inside, the walls of the cylinder

become polarized in such a way that the effect of the magnetic field

is neutralized within.

However when the surrounding medium has a non-zero conductivity

some of the polarization will leak away, giving rise to a leakage cur- rent in the medium and also within the cylinder. Martyn assumes that

this leakage current will be divergenceless. Physically this means

that while there may be accretions or depletions of (neutral) ionization at the boundary of the cylinder, yet there will be no build up
-50-

of un-neutralized positive or negative charge. The plausibility of

such an assumption stems from the fact that the electrostatic forces

opposing accumulations of free (un-neutralized) charge are much

greater than the diffusion forces opposing concentrations of neutral

ionization.

If the background medium of ionization density N has a vertical

drift velocity V, then Martyn states that the cylinder of ionization

density N + A N will move relative to the background medium with a velocity given by

-v(2-Hr> , (17)

where e = A N/N . (see Appendix B).

Suppose the F region as a whole to be drifting upwards , and that

somewhere on the underside of this region is a field aligned blob of

ionization of differing density. If this blob is slightly denser than

its surroundings, then V > and € > and therefore by (17) this blob

will drift downwards with respect to the medium, into regions of still

less dense ionization. Likewise an underdense blob (e < 0) would drift

into regions of greater ionization. Conversely, should the layer as a whole be drifting downwards , such an overdense blob on the under

surface would move relatively upward into regions of comparable ion

density, and become identical with its surroundings.

Martyn thus shows that spread-F should occur only if the F region

is moving upwards, and should be inhibited if the F region is moving

downwards. Also a steep ionization gradient on the underside of the

F layer should enhance spread-F occurrence. The upper surface of the

F layer is thought to have a gentle ionization gradient. For a descending F region, an overdense blob of ionization (V < 0, e > 0) above

the F layer maximum would move into regions of still less electron

density. Since this is on the upper surface, the effects should not be

manifest as spread-F but possibly as radio star scintillations. However,

this effect for a descending F region should be less pronounced since

the top- side ionization gradient is more gradual than the underside.

B. Development According to Clemmow, Johnson and Weeks

An alternate approach to this same problem of instability has

been taken by Clemmow, Johnson and Weeks (1955 ) • They make no assumptions regarding the smallness of the Hall conductivity, but do assume

that not only is the net ionization current divergenceless, but also

that the positive ion current and negative ion current are each separately divergenceless. They seek a steady state solution in which

the irregularity will retain its original shape over the given period
-51-

of interest. They find such a solution possible provided that the

cylinder has a velocity with respect to the surrounding medium. No

steady state solution appears possible for a three dimensional irregularity due to the high conductivity along the magnetic field lines

(Ratcliffe, 1959) • While their conclusions differ from Martyn' s in

detail (especially that there is no build up of neutral ionization at

the boundary of the cylinder), the general results of movement with

respect to the surrounding medium remain the same. The occurrence of

spread at times of increasing F layer virtual height appears to be in

accord with this explanation.

6.3 Corpuscular Matter of Extraterrestrial Origin

The irregular ionization of the E region has been correlated with

the incidence of meteors (Appleton and Naismith, 19^7 J Love11, 19^8).

However, there appears to be no general relation between the occurrence

of spread-F, and known meteor showers.

Interstellar corpuscular matter, other than meteors as a possible

cause of scintillations and spread-F has been proposed by Ryle and

Hewish (l950)» Such matter would be attracted by the sun's gravitational field and would tend to impinge on the dark side of the earth.

Due to the orbital velocity of the earth, this would occur from about

2000 to 0800 local time, with a maximum at 0200. The earth's magnetic

field might possibly modify this diurnal distribution, and seasonal

variations in spread-F occurrence could be accounted for by the general

motions of the solar system with respect to this interstellar matter.

The shift in seasonal characteristics of spread-F occurrence with

sunspot cycle (see Figure l6) is not accounted for by the above ex- planation. Such a process should be operative from night to night.

Also it is not clear how such a mechanism would produce patch-like

irregularities only a few kilometers or less in extent.

6.k Charged Particles of Solar Origin

Charged particles approaching the earth find their easiest path

of approach at high latitudes. Shimazaki (1959) suggests that such

charged particles are the cause of spread-F at high latitudes. He

notes for latitudes in excess of 40° the gradual increase of spread-F

occurrence probability with latitude, and also the correlation, at

higher latitudes of spread occurrence with geomagnetic disturbances,

especially striking if the masking effects of "blackouts" are considered.

The suggestion is inviting, and a fuller explanation is desired,

indicating in what way the incident particles produce the variations

in electron density apparently required for spread-F.
-52-

6.5 Evaporation of Terrestrial Atmosphere

A different approach suggested in a symposium by Ryle has been

reported by Ratcliffe (195&). Ryle discussed the work of a group in

the USSR on the counterglow or "gegenschein". The tenuous outer re- gions of the earth* s atmosphere are repelled by the radiation pressure

of the sun much like the effect on a comet* s tail. This process would

occur on the dark side of the earth and, Ryle suggests, the streaming

would tend to occur along the lines of magnetic force. Irregularities

in the ionization of the upper regions of the atmosphere could be caused

by such a streaming, or "evaporation" process.

This model does have the advantage of explaining nicely the field

aligned orientation of these irregularities. However, it would seem

also to require that spread-F and scintillation should occur every

evening rather than randomly, as is actually observed. Daytime spread, an occasional occurrence, is difficult to explain. In the equatorial

regions the magnetic field lines are almost parallel to the earth*

s

surface, making the escape of charged particles a difficult process.

Moreover the onset of spread-F and scintillations is frequently delayed

until several hours after the F region has entered the earth's umbra,

and it is hard to see how radiation pressure could have the desired

effect in the F region at this time.

7. CONCLUDING REMARKS

(1) The division of spread-F into high-, middle-, and lowlatitude type is not completely satisfactory. The designation of spread

as range type and frequency type is desirable, although even this division is not necessarily comprehensive.

(2) Statistical studies of spread-F occurrence based solely on the

qualifying symbols appearing with the tabulated data of foF2, F2 M3000

and h'F, leave something to be desired.

(3) The pattern of spread occurrence changes over the sunspot

cycle. Care must be used in generalizing from records covering only

a part of one cycle. Further studies at particular locations over a full sunspot cycle will be useful.

(k) More direction of arrival studies for spread echoes should

prove significant in determining the extent of spread areas and some- thing of the nature of the spread mechanism.

(5) A single mechanism need not be postulated to explain all

types of spread occurrences. The same phenomena may be produced by

significantly different mechanisms.
-53-

as

J = a f_. + o\.f,+ cr (H x E) H'

1

. (A3)

o 11 1 -L 2

J

The current density may also "be expressed in terms of the density of

charge carriers, N, as follows

l=Mev. (Ak)

By combining (Ak) with (A3) and using the solution of (A2 ) in

terms of v, the following values for the conductivities are obtained:

cr = , Longitudinal conductivity (A5-a)

Ne

m

1

V

}

= Ne

2 m

V

°1 2

O) +

2

V

>

=

2

Ne

m

Oi °2 2

U) +

2 V

>

Pedersen conductivity (A5-b )

Hall conductivity, (A5-c )

where a> = eH/m. If more than one type of charge carrier is significant, additional terms involving the charge, mass, number density and

collision frequency of each type are included. Note that the longitudinal conductivity is appreciably greater than the conductivity

transverse to the magnetic field. This tends to make the magnetic

field lines act as equipotentials.

9. APPENDIX B

Martyn1 s Theory of Vertical Drift Motions

The following is a simplification of the treatment presented by

Martyn (1953) since the original paper is somewhat condensed.

Consider a cylinder of ionization density N + A N of radius r , aligned with a magnetic field H directed along the negative z-axis

in a medium of ion-density N. Suppose a uniform, constant electric

field, E, is perpendicular to H (a z-component of the electric field
is of no particular interest here as the resulting motion is well

understood), and assume that in the surrounding region the Hall con- ductivity is effectively neutralized.

The external electric field may be expressed in polar coordinates

as

E = E cos <D , (Bl-a)

E = -E sin <D . (Bl-b

)

Since the medium is of non-zero conductivity a leakage current of

ionization will develop which is assumed to be divergenceless. The

ionization distribution gives rise to a polarization potential S, and

a corresponding electric field, - grad S, which is imposed on the constant field given by (Bl). The resultant current pattern, employing

the Pedersen conductivity, is given by

J = a (E cos - ||-) , (B2-a)

J = a (-E sin --±-§f ) • (B2-b)

The requirement that the ionization current be divergenceless leads to

v- ?- °--r-i? <*. y> -r -! <v • (B3)

By using the current distribution of (B2 ) in (B3) we find the restriction that must be placed on the polarization potential S:

!i|_ + _i_ _|b_

+

i afs . . (Bk) ^2 r or 2 >2

or r o<t>

To obtain the solution for (B^), assume that

S = R(r) 0(d)) , (B5)
-55-

which yields the pair of equations

" 2 $ (<D) = -\ $(<D) , (B6-a)

r

2

R (r ) + rR (r ) - \

2

R (r ) = , (B6-b

)

2 where K is the separation constant. The solution of (B6-a ) is of the

form

$ = A cos (<t> + r\ ) , (B7)

where A and r\ are constants of integration ("by symmetry considerations,

\ = l).

For the radial equation (B6-b ) we require R (o) = from symmetry,

and also Lim R (r) = 0. Since <j , the conductivity of the medium, is r -* oo a function of ion-density, it will differ within and outside the cylinder and therefore two solutions will be sought, for r < r and

r > r . Clearly we expect continuity of the two solutions for r = r . The simplest solutions that will satisfy these requirements are

it R(r) = A r for r ^ r , (B8-a

)

.t 2

R(r) = A r /r for r ^ r . (B8-b

)

x o

' o

v

The full solution of (B^) is

S = Ar cos (<i> + T]) for r ^ r , (B9-a

)

S = A (r /r) cos (* + r\) for r 1 r , (B9-b

)

where primed quantities refer to the region external to the cylinder.

Since the dimensions of S, the polarization potential, are (field

strength) x (length), A may be expressed as QE, where Q is a dimensionless constant and E is the electric field strength of the uniform
-56-

(6) The explanations of McNicol and Webster (1956) for range

type spread, and of Singleton (1957) f°r frequency type spread, seem

to be valid for the observational data presented. However, it is

quite possible that other mechanisms may be operative in other re- gions .

(7) The theoretical work of Dagg (1957) and of Martyn (1959)

need not be contradictory, as both processes may be operative at the same time. Additional investigations on the occurrence of turbulence,

and also on layer height changes with spread-F occurrences are des irable

.

8. APPENDIX A

Ionospheric Conductivity

The conductivity, cr , of a unit volume of a substance may be ex- pressed in terms of the applied electric field, E, and the resultant

current density, J, as

J = of , (Al

)

where o is in general a tensor and a function of the number of available charge carriers and their mobility. In the ionosphere, the more

free electrons and ions present, the greater the conductivity. Even

in the more highly ionized regions, however, the ratio of neutral to

charged particles is hardly ever less than 1000 to 1, and therefore

collisions of charged particles with neutral particles will significantly affect the conductivity.

Since the net force acting on a particle is equal to the rate of

change of the particle's momentum, we obtain the equation of motion

of a particle of charge e, and mass m in an electric and magnetic

-* -* field, E and H, as follows:

—> --*-> -> Ee + evxH = mv+vmv,* (A2)

-* where v is the collisional frequency with neutral particles and v is

the particle velocity.

If E is resolved into two components, E and Ej_ , parallel with

and perpendicular to the magnetic field, equation (Al ) may be expressed
-57-

external field. By using (B9) in (B2-a) we obtain J (r ) and J (r),

the radial current distribution inside and outside the cylinder.

Since it has been assumed that no net un-neutralized charge accumu- lated at the boundaries of the cylinder, we require that for all values

of <$> ,

J (r

Q

) = J (r

Q

) . (BIO)

The condition (BIO ) determines Q and q as follows

Q

= \ <X + <T /

,-! = (Bll)

The Pedersen conductivity is directly proportional to N, the ion

density. To a first approximation we have

N + A N

N

(B12)

and therefore

n _e . AN

Q = TTT , where e = — , (B13)

and the expressions for the components of the current become

J = a E ( 1 - -^— ) cos 4> , r 2 + e

' (Blij-a)

J = 'ot'e I 1

2 !- : { 2 ) j

J = - o-E (l -

v r

2 + £

2 COS <t> ,

) sin ,

(Bll+-b )

(Bl4-c )

J. = -

t <r E 1 -

2 + e

2

2 r J

sin (Bl^-d)
-58-

Note that each first term on the right side of (Bl4) represents the

current flow due to the static external electric field, while the

second term represents the "leakage" current, due to the non-zero

conductivity of the medium. Since these currents flow in a plane

perpendicular to the magnetic field, a lateral drift motion is to be

expected. Let the velocity of this lateral drift "be expressed by U

and the resultant current as NeU. Since the conductivity is cr , the

electric field must be NeU/cr, and the lateral force on a single charge

is Ne U/cr . But such a lateral force, produced by a velocity perpendicular to the magnetic field, must be equal to J x H/N and therefore

U = J x H

cr 2 2

N e (B15)

and

U =-^_

r AT2 2 N e N e

e + 2

) sin <I> , (B16)

t u = r Ha

w2 2

N e

J. =

,2

Her E

2 2 Ne

1 -

€ + 2

sin <t> (B17)

The desired result is given by (B17). This motion is in the direction

of <t> = it/2, at right angles to the external electric field. For

r » r , (BI7) represents the drift motion of the medium as a whole.

For r = r we have a picture of the absolute drift motion of the cylo inder, which is somewhat different than that of the surrounding medium.

If V is the velocity of the medium as a whole, and v the absolute

velocity of the cylinder, then

v = V - 2 + e V , (B18)

while the drift velocity of the cylinder relative to the surrounding

medium is given by

-V ( 2 + e

) • (17)
-59-

10 . ACKNOWLEDGMENT

This present work has been partially supported by the United

States Information Agency under Agreement IA-^586. The assistance

of the director and the staff of the Manila Observatory is gratefully

acknowledged. This study was undertaken at the suggestion of Dr. E.K.

Smith of the National Bureau of Standards.

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