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Volume^ 3

CONFERENCE ON NON-LINEAR

PROCESSES IN THE IONOSPHERE

DECEMBER 16-17, 1963

fsi

EDITORS

DONALD H. MENZEL AND ERNEST K. SMITH, IR.

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technical *92ote 2ff, Volume 3

Issued April 19, 1964

CONFERENCE ON NON-LINEAR PROCESSES

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DECEMBER 16-17, 1963

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PREFACE TO THE PAPER BY V. A. BAILEY

At the Xth General Assembly of URSI in Sydney, in 1952, on the

motion of the President, Sir Edward Appleton, a Sub -Commission was set

up to prepare for publication a Special Report on the subject of

"ionospheric Wave Interaction. " The membership of the Sub-Commission

was as follows:

Professor V. A. Bailey, Chairman (Australia);

Mr. J. A. Ratcliffe (Great Britain);

Professor L. G. H. Huxley (Australia);

Dr. M. Cutolo (Italy).

Owing to a serious illness, the Chairman was unable for some time

to commence his duties. Then at two informal meetings in 1953 and 1955

it was agreed by the Chairman and Mr. Ratcliffe that the time was not

ripe to prepare the Report. However, at a formal meeting of the SubCommittee in Boulder during the Xllth General Assembly (l957), Mr.

Ratcliffe and Professor Huxley indicated that they were unable to

continue as members on account of the demands on their time made by

other work. The remaining members of the Sub- Committee then agreed to

recommend to the Executive that three nominated members be added.

The General Secretary subsequently informed the Chairman that the

Sub- Committee was free to co-opt those or any other members of the Union

that it desired.

The Chairman then began a first draft of the Special Report for

submission to other members of the Sub- Committee, but was unable to

complete it in time for the next meeting of URSI. As a resiilt the

whole matter was allowed to lapse.

The present communication may perhaps also be regarded as a brief

substitute for that Report, prepared by the author alone and brought

up to date. It is not intended to be completely exhaustive. He wishes

to acknowledge his indebtedness to Dr. R. A. Smith for val-uable criticism,

of the matter that is here presented in the sections 1 to 5*

IX
Volime III

Table of Contents

Session 1. Colllsional Eadio-Wave Interactions^ I^rt I

1.4 Some non-linear phenomena in the ionosphere.

V. A. Bailey, University of Sydney iv

Remarks hy Donald H. Menzel with reference to Bailey's

comments on solar electric fields 6l

1.5 Ionospheric cross -modulation at the geomagnetic

equator, W. K. KLemperer, Central Radio Propagation

Laboratory, National Bureau of Standards, Jicamarca

Radar Obse2Pvatory, Lima, Fern 63

Editors' Note 83

Session 2. Collisionless Radio-Wave Interactions.

Chairman: Jules A. Jtejer

2.3 VLF noise bands observed by the Alouette I satellite,

J. S. Belrose and R. E. Barrington, Radio Physics

Laboratory, Ottawa, Ontario, Canada 85

2.5 The interaction of an antenna with a hot plasma and the

theory of resonance probes, J. A. Fejer, Southwest Center

for Advanced Studies, Dallas, Texas 101

Session 1 papers continued from Volume I, Technical Note

No. 211.

Ill
SCME NON-LIKEAR PHENOMENA IN THE IONOSPHERE

V. A. Bailey,

Emeritus Professor, University of Sydney

A paper presented to the Conference on Non-Linear Processes in the Ionosphere

at Boulder, Colorado, on December l6-17^ 19^3

ABSTRACT

The historical development is described of the idea that sufficiently

strong radio waves can modify the properties of the ionospheric regions

which they traverse.

The modified primary properties are the electron temperature and

collision- frequency, the rates of electron attachment and recombination

and excitation and ionization of molecules.

The resulting changes in the collision frequency and electron

density modify the region's absorption coefficient and refractive index

for any wave, including the modifying wave itself. These lead to the

phenomena of wave- interaction and self-distortion, respectively.

The associated mathematical theory includes the important effects

of gyro-waves due to the presence of the Earth's magnetic field. The

principal predictions of this theory and their subsequent experimental

verification are discussed.

Applications of this theory to the study of the ionosphere and

laboratory plasmas are indicated. These include control of the ionosphere and the generation of artificial air-glows (or aurorae) by means

of powerfiil gyro-waves.

The possible modification of the ionosphere by low- frequency extraterrestrial radio waves is also considered; such waves include geomagnetic disturbances. They may arise from hydromagnetic disturbances

in the solar wind and from fluctuating screening by plasma clouds of

post\alated electric charges on the Sun.

IV
SECTION 1

imRODUCTION

In a letter to "Nature" B-D.H. Tellegen (1933) reported that the

transmissions of the Swiss radio station at Beromunster (65O kc/s)

received in Holland appeared to be modulated in the ionosphere by the

radiation from the nevly erected powerful station at Luxembourg

(200 kW, 252.1 kc/s).

This and an earlier report by Butt (1933) are examples of the

phenomenon of ionospheric wave interaction-?^ "which was subsequently

a soTirce of annoyance to European broadcast listeners. The observations reported by B. van der Pol (1935) and others all indicated that

a powerful station of sufficiently low frequency can impress its

modulation on the wave received from another station (the wanted wave)

when the latter traverses ionospheric regions whose projections on the

ground lie within about 100-200 kms of the disturbing station. The

two waves are now commonly called the disturbing wave and the wanted

wave . The observed depth of impressed modulation could amount to about

ten percent.

It is worthy of note by applied physicists that the accepted

theory of this phenomenon arose exclusively from a "thoi:ight escperiment"

which occurred to the present author while officially examining a

doctoral candidate's exposition of the magneto-ionic theory of ionospheric waves. This theory was first mentioned in a letter to Nature

(Bailey & Martyn, 193^) and more precisely developed in subsequent

^Also known as the "Luxembourg Effect" & the "Tellegen Effect".
publications (Bailey, 19JJ^y t), c, d; 1938a, b). A brief account of

this development is given in a Supplement to "Nuovo Cimento" (Bailey,

19513.

Since most of the experimental work on wave- interaction has been

guided by these mathematical developments it is here desirable to

present the theory first.

The two fundamental concepts on which the theory is based are

as follows

I. Any electric field of intensity E (volts/cm) applied to free

electrons in thermal equilibrium with a gas at pressure p (m.m. Hg) and

temperature T ( K ) will impart energy to the electrons and so raise

their temperature to a higher value T. This results in an increase of

the rms value u of the random velocities of the electrons and so to a

change in v the mean frequency of collision of an electrom with molecules

of the gas; in general this change is an increase of the collision

frequency.

II. The absorption coefficient fj of a radio wave which traverses

a particular region of the ionosphere varies with the value of the

local collision frequency v . Except for an extra- ordinary wave

of frequency near the local gyro frequency, ft increases with v ^.

It follows from I that a powerful radio wave will in general

increase the collision frequency in some region of the ionosphere

For the exceptional extraordinary gyro wave ft decreases as v

increases.
and then from II that as a result another wave (not an extraordinary

gyro-wave; traversing this region becomes more absorbed by the region.

This increased absorption of the wanted wave will reveal itself (in

general) as a decrease in the amplitude of the wave at reception.

Thus any modiolation of the amplitude of the disturbing wave at a

frequency n and to a depth M will impress a modulation of the

same fiuidamental frequency on the wanted wave.

The sam.e concepts I and II lead to the conclusion that a

sufficiently powerful wave will modify the absorption of the regions

which it traverses and so be received in a distorted form. This

phenomenon has been termed "self-distortion".

Besides explaining the observations of Tellegen^ Butt^and others^

the theory has predicted the following phenomena:

(1) The amplitude of the wanted wave is modulated by a fraction f

.

which is given by formula (hk) and (^5) and consists of a

fundamental part of frequency n , phase lag cp ^ and modulation

depth yL proportional to M and a harmonic part of frequency 2n , phase lag cp , and depth Mp proportional to M .

(2) The depths M, and Mp of the two impressed modulations decrease

in specified manners as the modulation frequency n of the disturbing

wave increases.

(3) The depths M-, and Mp increase nearly proportionally to the

mean power P of the disturbing station.

(k) The phase lags cfu and cp are eqiial to the inverse tangents _

An extraordinary gyro wave will become less absorbed 'by the region.
of the ratios n/Gvo ^^'^ Sn/Gv^ ^ respectively;, where v^ is the

value of the electron collision frequency in the unperturbed local

ionospheric region and G is a particular constant derived from

laboratory data for air; G ~ 2 x 10 .

(5) The depths M-, and IVL decrease as the angular radio frequency

m of the disturbing wave increases within certain limits.

(6) ES-ch of the depths VL and IVL passes through one or two maximum values as the angular radio frequency UJ of the disturbing wave

is varied about the local angular gyro- frequency ^ ^ i.e., resonance

occurs. Also a radiated power of 1 or 2 kw would then suffice to

produce observable interaction with an appropriate wanted wave.

(7) The depths M, and IVL increase as the region of ionospheric

reflection of the wanted wave approaches to about 100 kmy^ from the

ionospheric region vertically above the disturbing station.

(8) A pulsed disturbing wave causes the amplitude of the wanted wave

to rise and decay approximately according to a particular law which

involves the time-constant t^ = 1/gv .

(9) The observed modulation of a wave becomes increasingly distorted,

at the expense of the lower modulation frequencies, as its power

increases, i.e.^ self-distortion increases with the power.

(10

)

"Interaction atmospherics" can be impressed on a wanted wave by

the low frequency radiation from suitably located electric storms.

(11) Combination tones can be impressed on a wanted wave by two

disturbing waves with radio frequencies which differ by an audiofrequency.
The predictions (l) to (9) have been confirmed by subsequent

experimental observations. Also (k) has been used by Ratcliffe and

Shaw [ 19^8 ] to determine the height at which a particular wave interaction occurs and (8) has been used to determine the quantity Gv

which relates in part to the mean energy lost by an electron at a

collision with an ionospheric molecule. The prediction (U) appears

to accoiint for certain observations of Gill ^1935 ]•

Also it may be mentioned that the formula for IVL yielded by the

theory (and given below under (^5)) correctly accounts for the order

of magnitude of the depth of the modulation impressed on Beromunster 's

wave by the Luxembourg station as observed by van der Pol and van der

mrk [1935].

The fundamental concepts I and II have also led to the

following predictions

(12) A specified vertical beam of extraordinary gyro waves with

radiated power of 5OO kiw can generate a visible glow discharge or

artificial "aurora" in the E- region at night [iBailey, 1938a, b; 196il .

(13) A vertical beam of extraordinary gyro waves radiated with a

power of 500 kvwfrom an array of ko horizontal dipoles can penetrate

into the nocturnal E-region much more easily than a weak beam. Also,

this beam siiffices to increase the electron density near the 92 knj /s

level of the nocturnal E-region by an observable amount and thus to

determine the frequency of attachment of electrons to molecules near

this level [Bailey, 1959].
These results and the corresponding experimental studies byGoldstein et alia (1953a, b; 1955) of the effects of strong microwaves on gaseous plasma_, have led to a proposal for control of the

ionosphere by means of radio waves (Bailey and Goldstein, 1958)'

We shall now consider in detail according to the following plan

the principal theoretical and experimental results of investigations

on ionospheric wave-interaction published up to P'ebruary, 1963*

Section 2 summarises the relevant concepts, methods and experimental observations of the Townsend School which relate to the

collisions of electrons with gas molecules or atoms, under the

influence of electric fields of effective intensity E volts/cm

at gas pressures p m.m.Hg and gas temperatures T (usually about

15'' c).

Section 3 summarises the relevant concepts and experimental

observations, of the Appleton School and other ionospheric physicists,

which relate to the propagation of radio waves in the ionosphere

regarded as a magneto- ionic gaseous medium.

Section h briefly sets out the mathematical theory of waveinteraction as a logical consequence of the work described in

Sections 1 to 3«

Section 5 considers in detail the principal predictions to which

this theory leads.

Section 6 describes the experimental tests and verifications of

these predictions.
Sections 7 and 8 discuss the use of the theory as an instrument

for the study of the ionosphere and electrical gas-discharges, some

of its practical applications and some recent developments of the

subject.
SECTION 2

COLLISIONS OF ELECTRONS WITH GA.S MOLECULES UNDER

THE INFLUENCE OF AN ELECTRIC FIELD.

In the absence of an electric field, the mean energy U of an

electron in a gas at uniform temperature T^ is equal to the mean

energy U of a molecule of the gas.

Townsend and his collaborators [Townsend 19^7; Healey & Reed>

19^0], discovered that in the presence of. an electric field E, whether

constant or alternating [Tovnsend 193^ ]^ the mean energy of random

motion U of an electron is greater than U and that for a given

gas, the ratio

k = U/U^

is a function of the ratio E/p alone, "where p is the gas pressure.

By measuring, in a constant field E, the divergence in the gas

of a stream of electrons which passes through a slit, they were able

to determine the values of the Townsend factor k corresponding to

different values of E/p . Then by deflecting the same stream through

a known angle by means of a transverse magnetic field they were able

to measure the corresponding values of the drift velocity W of the

electrons in the direction of the electric field.

From these known values of k and ¥ and by means of simple

In this paper the term "molecule" is intended to include "atom"

The more complicated formulae proposed later by various workers have

not been found necessary in the present state of experimental

knowledge of wave interaction.

8
approximate theoretical formulae they then calculated the mean free

path L of an electron of energy U in the gas at the standard

pressure of 1 m.m.Hg and the mean proportion X of its own energy

which such an electron loses at a collision with a moleciole.

From the value of L corresponding to a given value of U, the mass m of an electron and the relation U = -^m u we can then

calculate in succession the corresponding mean random velocity u

and collision frequency V at a pressure p by means of the formulae

u = (2U/m)2 = (2kUo/m)2 (l)

V = u/l = up/L , (2)

since the mean free path 1 at the pressure p is given by

1 = L/p .

Also, from the corresponding value of \ we can calculate x] the mean energy lost by an electron at a collision by means of the

formula

ri = X U. (3)

The values of k, W, L and X corresponding to different values

of e/p for well dried air were first determined by Townsend & Tizard

[1913^* These are also set out in the books by Townsend [19^7] and

Healey & Reed [ L9^0] . More recent determinations of some of these

quantities have been made by Bailey [ 1925 i Neilsen & Bradbury^ 1937>

and Crompton, Huxley & Sutton, 1953] • On account of the limitations

set by the experimental methods used the lowest value of the

Townsend factor measured in air was k = k; this corresponds to a mean electron energy of ^/27 electron volts. Since the variations

of L and n with U for k < 4 are not known, the application

of the known experimental data to the lower ionosphere makes it

T] can also be obtained directly from the drift velocity W by

means of the formula t] = 1.23 mw .

•X-
necessary to extrapolate these data in some simple way to the range in

which 1 ^ k < ^. For this purpose the simplest two hypotheses

to adopt are; (l) L is independent of U and

(2) n

= G (u - uj, (k)

where G is a constant determined by the data obtained with the

lowest values of the field E. For Air the value G ~ 2 x 10

has proved the most successful.

From the first hypothesis and equations (l) and (2) it follows

that the collision frequency v in air always increases with the

intensity of the field E in the range of energies considered.

Following Townsend's work on the uniform column in high frequency

electrical discharges through gases ("Electrical Discharges",

Llewellyn Jones [l953J)"the formulae (l) to (k) may be applied to the

effects caused by a strong radio wave in the Ionosphere. But the

dependence of these effects on the field intensity E the radiofrequency oj / 2n and the terrestrial magnetic field H needs

further consideration, such as that given below in Section h and

the Appendix. This involves the determination of w , the mean work

done on an electron over a free path or, alternatively, the mean

power S = 'N \j v expended on the N electrons in unit volume.

SECTION 3

WAA/E PROPAGATION IN A GASEOUS MAGNETO- IONIC MEDIUM.

In Appleton's well-known magneto- ionic theory of wave propagation^

the mediumi is a gas which contains N electrons/cc and is pervaded

by a uniform, constant magnetic field H ; also the mean collision

10
frequency v of an electron in the gas is taken as independent of the

amplitude of the wave.

The complex refractive index M = q - iX and the polarisation

number R which define a mode of propagation of a wave of angular

frequency qj in this medium are determined by means of Maxwell's

field equations combined with the equation of transport of mean

momentum, which governs the momentum Nmv of the electrons in unit

volume. When N is uniform and constant^ the latter reduces to the

eqixation

d V e m +vmv = eE + — vxH^ (5)

d t ~ ~ ^ ~ ~

where e is the charge on an electron in e.s. units and the magnetic

vector of the wave field is neglected by comparison with H .

From the dispersion equation yielded by (5) and the field

eq-uations^^lt follows that there are two wave-modes and that for each

the corresponding ray becomes attenuated as it progresses, through a

factor a defined by

s

''

ag = exp ( -f ^ ds) (6)

where s is the length of the ray path measured from its beginning

and %. is related to X as follows

= OJ x/c. (7)

11
The value of the coefficient of absorption % depends on V ,

N y and the angular gyro- frequency Q .

The theory shows that when

uj^ > > v^ (8)

^ is in general approximately proportional to the product v N. For

the exceptional case, in which the angular wave frequency uu is

nearly equal to Q and the mode is extraordinary, -ft is given by

Equation (64) and so is nearly proportional to

Nv / f V + (o) - q) } • It follows that with increasing v the

attenuation in general increases, Ijut decreases for an extraordinary

wave mode with a frequency near the gyro-frequency. The latter may

be conveniently termed an extraordinary gyro-wave.

In a slowly varying non-uniform medium a ray theory of propagation

may be used. Then along a ray path of length s j the field amplitude

is given by

E = E^exp( -

cc) where

ft ds.

'0

Since the mean power flux density is P where

= c U E^ / 4 n ,

12
where E is the rms value of the component of E transverse to

T ~

the direction of propagation^ it follows that

P / U = ( P^ / uj exp r- 2a ) (9)

and so

3(P/w)/3s = -2k(p/u). (10)

13
SECTION k

THE MTHEmTICAL THEORY OF IONOSPHERIC WAVE INTEE^CTION.

From consideration of the results mentioned In Section 2jVe see

that In the equation (5) the quantity V Is not really a constant

but must now be regarded as a function of the wave field Intensity.

It follows that the classical magneto- Ionic formulae for M and

R must now be regarded as first approximations which are accurate

only when the waves concerned are weak enough to make v closely

equal to the normal collision frequency v^ which exists in the

unperturbed medium.

The fact that at least -ft is a function of the field intensity

E Is sometimes referred to as the "non-linearity" of the medium.

In order to obtain higher approximations to M and R it is

in general necessary to apply lengthy perturbation procedures. So

in order to keep the present mathematical theory sufficiently simple

for practical purposes we shall relax its rigour to the limits allowed

by the uncertainties in the physical data Involved.

X- The experiments of King, described in section 6, show that

notable ionospheric self-distortion can occur when the radiated

power of the transmitter is at least 200 kw

.

Ik
^.1 The w'ork w done on an electron by a plane-polarised wave over

a mean free path .

It has been shown (Bailey 1937^) that

2m e A + A cos 2 m t - B sin 2 UU t (11)

where E is the effective value e/ /2 of the local electric field

e ' A' intensity E j

A = 2c

V^ + ( 0) - )^ V

+

+ ( uu + Q )^ v^ + ^

r (12)

B = -f W N

- Q

tu + Q (A) (m-Of / + (m + of V ,2V

+' ..2

UJ V

UL) is the angular frequency of the wave,

Q = H e /m c (angular gyro freq.uency),

s = sin f , c = cos ^

and iff is the angle between E and H .

The mean work w done during a complete cycle 2TT / ixi and

over a free path is therefore given by

2 _ e 2

(13)

In the following sections we shall assume that E varies

e appreciably only during a period of time which is large compared

with the period 2tt/^ of the wave.

15
k.2 The differential equation for the mean kinetic energy U of an

electron .

The equation of transport of energy in the electron gas is

^ ^^ ^^ + Nv n

= Nvv,

d t

so when the wave is not strong enough to change N appreciably

we have ^^ + V n

= V w . (Ih)

d t

When the energy U does not exceed ku we have 1 < k ^ ^

and so we may adopt the formula (k) as a working hypothesis. Then

(ih) leads to the equation

"^ ^ + ( v/ vj ( U- Uj = t^vw (15)

d T where

^0 = Vgv^

! (16) = t/t^

t^ is a time- constant and t is the time measured in units

equal to this time- constant.

Also, by (2) and (l)

v/ V, = (U/ U^)2 (L, / L) . (17)

l6

1
Kie dependence of L on U for U < 4 U^ is not yet known with

certainty. But the experiments on air of Townsend and Tizard and of

Crompton;, Huxley and Sutton indicate that no great error is likely to

result from our adopting here the original hypothesis that L is

Independent of U , i.e.

V / V^ = ( U/ Uj2 . (17.1)

By substitution for v from (17) or (17.I) in (12) and from (11

)

ve can express v -w as a known function of U and ET . Then (I5)

becomes a differential equation in the unknown fiinction U with E

e as a given slowly varying function of t _, of the form

E^ = E^^M (t) = E^^M (t^T ) (18)

where E ^ is a constant field. M (t) may be termed the modulation

function or modulation envelope.

The resultant differential equation requires some method of

approximation for its solution. From such a solution U and (17)

or (17.1) we can then obtain an approximate expression for v as

a function of "t^E,;,(ju,n,'|',G and U or V •

These expressions for U and v contain terms which vary

slowly with t and terms which are periodic in t with 2a)

as their fundamental frequency. Retention of the latter terms in the

discussion of wave- interact ion and self-distortion would lead to

similar periodic terms in these phenomena. But at radio

frequencies ^j such terms are usually negligible by comparison

17
"With the slowly varying terms, so henceforth they will be neglected.

Accordingly we will now consider only the variations of U and

V which take place in a time dt large compared with the wave period

2 TT / m • This requires the symbol w in (1^) and (15) to be

replaced always by its mean value w which is given by (I3) or by

(48) below.

4.3 The differential equation for the mean collision frequency v .

It is now convenient to base the discussion on the equation for

V . Thus, on eliminating U from (15) by means of (17.I), replacing

w by w and using (13) and (I8) we obtain — + - (o2_i)=v/2GU^=RM2(t^T) (19)

dT 2

where

a = V / v^ , (20)

R = ^1_ E^ A . (21)

4g m Uq

"^ is the collision frequency expressed in imits equal to V^ .

On account of its factor A the quantity R in (19) is a

fimction of cr such that this equation has no obvious solution

in finite terms.

However, in order to apply the theory to most of the observations

of wave interaction which have been made hitherto it is siofficient

to consider only those approximate solutions which correspond to

18
values of w/2GU or RM(tT) such that CJ varies about some

constant value O" by a small fraction of a , i.e.

CT = ^1 + 6 .

where

Thus

(22.1)

= \/ ^0 ' I 6 I < < a

1

V = v^ + v^5 , v,5I<< v-L (22.2)

These approximate solutions are then found from solutions of the

equation

d 5 d T + CJ^ 6 = R^M^ (t^ t) + i(l - o^

) (23)

where

and

(21.1)

A, +

2c

'^^ + ( i^- ^f Vi + ( cu + Q)^ v^ + ^^

(2k)

^.^ The collision frequency v in the steady state under

the influence of a continuous wave .

Here we have M (t t) = l . Then the steady value cr = v / v

19
is obtained by setting dcr/dt =0 in (I9) and solving the resultant

q-uartic in cr or setting 6 = in (23) and solving the same

quartic m cr

When E ^ is not too large we then deduce the following

approximate expression for the steady collision frequency:

^s = ^0 -^ ^0 ^0 > (25)

where

2

^0 = -r— \i ^0 (26)

kG m Up

and A- is the same as A^ in (2^) with v-, replaced by V^ .

From (25), (26) and (2k-) it follows that, except when the wave's

field vector E is only slightly inclined to the constant magnetic

field vector H , v passes through a maximum value as the wave

frequency uu is varied around the gyro frequency ^ . The

corresponding mean electron energy U behaves similarly.

These resonance effects and their consequences are of great

importance, as will be shown below.

4.5 Rise and decay of v caused by a square pulse of radio waves.

When V = v„ at t = and W (t t) = 1 for ^ t ^ T

then Equation (23) has a = 1 and its right-hand side constant.

The corresponding solution of (23) which describes the rise

of V , is

More definitely when R « •§ .

20
V = V -

( V - v^) e"^/^o . (27) S ^ S ' \ ' /

Similarly ve obtain the following solution which describes the

decay of v from ^ the steady value v

^ = ^0 + ( \ - ^0 ) e'^^^s (28)

where

For the E-region t is of the order of 1 millisecond or less.

Hence the rise and decay req[uire about 1 millisecond to be practically

completed.

Accurate expressions for the rise and decay can also be obtained,

since the Equation (19) is now exactly integrable (Bailey, 1937b,

Equation (3^)).

h.6 Modulation of v caused by a wave which is sinoidally

modulated in amplitude .

For such a wave we have

M (t) = 1 + M sin n t

where

0<M<1, n«ei)

(29)

Then

M^ (t^ t) = 1 + ^ + 2M sin (nt^T) _ ^ cos (2nt^ t). (29. l)

21
If we take

V = V

1 s

for the steady state corresponding to the mean effective force

then the constant part of the R.H.S. of (23) vanishes, i.e.

R^ (1 + i M^) + i (1 - 0^ ) = 0, (29.2)

and so the equation (23) reduces to

d6

dT

+ a^6 = 2 R^M sin (nt^T) - ^R^ cos (2n t^T), (30)

vhere

^1 =

^s / ^0 ^

and, by (25),

2

e

The general solution of (30) combined vith (22.2) leads to the

following formula for v :

^ =-^^+ BM Bin (nt - cp_^

) _ ^bM^ cos (2nt - cp^) ^ ^^-t/t^

^^2)

(1 + n^ t^)* (1 + 4 n^ t^ )i

where

22
el s s B = 2 2

t^ = 1 / GV^ >

tan cp^ = n t^ , tan cp^ = 2 n t^ _,

(33)

A is the same as A., in (2^) vith v-, replaced by v and C is

s 1^' 1 s a constant determined by the condition v = v. at t = 0.

^•7 Modulation of a wanted "wave thrbijgh the variation of the local

collision frequency.

In passing through the ionosphere the field amplitude F of the

wanted wave mode is attenuated according to the formula

F = Fo exp ( - a)

where

(3M

a = J

^ ( V ) ds.

s is the length of the wanted wave's path measured form its entry

into the ionosphere, Fq is the field amplitude at entry and •ft (v)

is the absorption coefficient corresponding to the value v of the

collision frequency at the point s in the path.

Under those conditions in which the collision frequency varies

about some constant value v^ , i.e.

23
V = V. + A V (35)

we have

a = CL + A a (36)

vhere

o, = J^ M vi ) ds

and

a = j' { M V ) - M v^ ) } ds (37)

where

Hence, by (3^) and (35)

F = F' exp ( - A a )

^^ = Fq exp ( - a)

So at the point s the amplitude of the wanted wave is

modulated according to the modulation function M. (t) where

M. (t) = exp ( - A a )

If we set

M. (t) = 1 + f . (t) (38)

2k
the impressed modiilation fraction f . (t) is given by

1

f . (t) = exp ( - A a ) - 1

When observation shows that | f . (t)

| < < 1 we will necessarily

have the approximation

f . (t) = - A a = _ J

|- ^ ( V ) - fi ( v-L ) } d s (39)

On substituting for v from (35) and expanding ^ ( v + A v )

we obtain

f. (t) = -

f ft' ( V. ) A V ds (ifO)

1 jg J.

provided that

U V f/ ( v^ )/ It' ( V3_ ) I « 2 .

When R ]yr (t) is sufficiently small for (22.2) to hold true

we have, by (35),

A V = Vq 6

where 5 satisfies the equation (23). So, on multiplying (23)

throughout by - -ft ( ^^ ) v ds, integrating with respecting to s

and using (4o) we obtain the following eq-uation for f = f . (t),

for a situation in which CJ is nearly constant throughout the region

concerned.

25
— + a f = s. M^ ( t^T ) + dT -^ -^ (kl)

vhere

Vq ds

^2 = 2 J

(0^ - 1) ft' ( v^ ) vo ds (42)

We now apply (hi) to determine the modulation fractions f and

fp of the wanted wave respectively during and after the disturbing

square pulse considered in sub- section 4.5 .

Since v = V^ at t = and M^ (t^ t) = 1 for ^ t ^ T

we then have Q = 1 and so (4l) yields the formula

^ ' -1 = ^1 ^1 )

. (^3.1)

Similarly, if v == v at t = and M (t t) = for

t > T we have a == v / v^ and so (4l) yields

f2= S^e-Vt, (43.2)

Next we apply the Equation (4l) to determine the modulation

fraction f . impressed on the wanted wave by the sinoidally

modulated disturbing wave considered in sub-section 4.6 .

As in 4.6, we now have: M (t^r) given by (29.1), v., = v i.e.

o = o = V / V , 1 S S' '

and the equation (29.2) which is satisfied by the root a = o

26
From (i|-2), (29-2) and (29. l) we obtain

S^M^Ct^T) + Sg = S^ f 2M sin (nt^r) - h^ cos (2nt^T)}

and so (kl) now becomes

+ a-j_ f = 2 S-^M sin (nt^T) - | S^M^ cos (2nt^T) . (Ifl.l)

dT

The impressed modulation fraction is given by the general

solution of this equation, namely

f . = lyL sin (nt - cpL ) - m cos (2nt - cp ) - Ce~ ' s (kk)

where cp, j, cp , t are defined under (33 )j

M^ = B^ m/(1 + n^ t^ )2 ,

M2 = i b//(1 + k r?tl )* , I

(1^5)

B3 = - 2 o-^ S^ {kG)

and C is a constant such that f . = when t =

1

Since v = v we find from (21.1) and (^(-6) that in a region

J_ s in which v and EL are constant

B3 = - ^^

I- *' (v^ )as^ (46.1)

Gm IVs

where A is the same as A^ in (24) with v replacing v and

s is the length of the path of the wanted wave, w

^ i.

It will be noted that all the quantities in {kk) which relate

27
to the wanted wave are contained in the factor B which occurs in

the quantities M, and IVL

A simple calculation shows that when, for the wanted wave, -ft (v)

is approximately proportional to v the formula (hh) confirms a

previously given formula for M^ (Bailey, 1937^ Part 1,

Equation (k2) ).

^.8 Modulation impressed by a Wave Mode .

When it is necessary to take into account the attenuation of

each of the wave modes into which a plane wave divides, the theory

given above must be modified by using in the place of the formula

(13) for w a formula for either mode which is obtained as follows

(V.A. Bailey, 1937a, Part l):

The mean power ? supplied by the wave to the N electrons in

unit volume is given by

9P

Bs

d

where P is the mean power flux density and s is the length of

the path of the disturbing wave from its place of entry.

Since this must be equal to N times the mean power V w

supplied to one electron it follows that

N V V = w (k8)

28 1
Also, when |j varies slovly with s we have from (10 ) and (9)

S = 2 ft^ P = 2 ft^ P^ exp ( - 2a^ ) (^9)

where the subscript d to a symbol relates it to the disturbing wave.

Since the amplitude of the wave mode is modulated by the factor

M(t) as in (18) therefore

Po = Pol

^

(t)

where P^^ is the mean flux density of this mode, over one period,

at entry into the ionosphere.

Hence, by (^^9)

S = S^ M^ (t) (50).

where

sd

and ft = -ft (v) when expressed as a function of v .

On using the value of w given by (^8) and also (50) the

equation (19) assumes the form

^ + i ( O^ - 1 ) = R M^ (t^T) (52)

dT

where

^ = V / Vq, t = t / t^ = Gv^t, (53)

R = S ^

/ 2G UoNv^a (5^)

As in sub-section ^.3 "we shall be content here to consider only

those situations in which R M (tpT) is small enoijgh for the condition

29
(22.1) to hold true. Then (52) may he replaced (approximately) by

the eqioation

d6

dT

+ a^6 = R-LM^(toT) + i(l - 0^ ) (55)

where

and

^1 = ^1 K^ / 2^ ^0 ^^1 ^56)

S" (v ) is the value of S in (51) when -ft = -ft (v^ ) and

^1 ^ ^0 •

Since (55) has the same form as (23) we can now proceed, as was

done with the latter, to derive from it the equation for the

modulation fraction f = f . (t) impressed by the wave mode under

consideration when the ionospheric region concerned is nearly

\iniform in temperature and pressure and CJ is nearly constant

throughout this region.

This procedure yields the eqixation (kl) for f and the formulae

(42) but with R now given by (^6)^ I.e., S is now given by the

formiila

^0

Si = - 2G U^

fJ e-l^A ^

q/ds (57)

where

q = ft'(Vi) / NV;l (3Q)

and H is given approximately by (51) with v = v .

We thus see that the formulae (^3.1), (^3.2) and (kk) for the

impressed modulations f , f^ , f . respectively are also valid

here when S-^ is given by (57).

30
The only factor in S-, which relates to the disturbing wave is

w . For this reason it has been termed the Index of Interaction ,

w ^ also represents the mean input of power per unit volume of the

ionosphere per period of the disturbing wave.

The combined effects of the two modes which constitute a plane

wave can be similarly calculated if the distribution of the energy

flux between the modes is known.

We now consider the common case (a) in which the wanted wave

is an ordinary mode with

fe ( V ) = pWV (A)

where P is nearly constant throughout the region concerned. In

this case we generally have

2 2 2 p

OJ » V and ^ » ij- n Ne / m .

Therefore, by (58)^ <l = P / "^-i ^-^d so q is now nearly

constant throughout the region. Hence, by (57) 'we now have

; . ._^(V Js^a. (57.1)

Since, by (50) and (^7),

M^ (t) r^S ds = - fd 3ec 3^ ds (59)

'0 -^ •'0 5^ d

^d

where 3 is the angle between the elements of path ds and ds

X- contained between adjacent wave fronts of the disturbing wave , I

3f for which ds-, = ds cos p . d

31
ve cannot evaluate the integral in (57-1) in finite terms except vhen

3 is constant (or nearly so) throughout the region of interaction;

this "Will occur in the following sub-cases Al and A2 .

Al. Both waves are propagated vertically and then | sec 3 | = 1

throiJghout

.

A2. The disturbing wave is propagated vertically and the region of

interaction occurs mainly where the wanted wave is undeviated.

In these cases (59) yields

vF (t) f :^, ds = sec 3 (P- P ) Jo 1 ° s

where P^ and P are the values of the disturbing wave's flux

s^

density at the beginning and end of a length s, of its path.

Since

Pq = Pqi M^ (t) and P = P , M^ (t)

^d ^d-^

where P^_^ and P^ ^ are the mean flux densities over one period

d

at respecoively entry into and exit from the ionosphere, it follows

that

C

^ 1 ds = sec 3 (P,^ - P^^^ ) ,

and so from (57'l) that, in the sub- cases Al and A2,

* (V^) sec 3 _

Si = (Poi ^s,i ) , (6o:

2 GU^ Nv-L ^

2

,Under A we have sec 3 = sec iWWwhere i is the angle

of incidence of the wanted wave. We then obtain from (^4) and (60)

a fonnula for the depth M, , of the impressed fundamental

32
modulation, vhich is equivalent to the equation (28) given in Huxley's

"Synopsis" (1952) and is originally due to Ratcliffe & Shaw (19^8).

4.9 Gyro Interaction: Interaction caused by an approximate gyro-wave .

When the disturbing wave is plane-polarised and has a frequency

within 20 percent of the local gj^nro- frequency, i.e.

0) = Q (1 + e )

where > (61)

I e I ^ 0.2 ,

the formula (2^) with v-, = V„ shows that in a region where

1 s

v2 « q2 (62)

the q-uantity A passes through a sharp maximum as the wave's

frequency ^ is varied about the gyro-frequency ^ .

If follows from (kS.l) that B behaves similarly and that in

consequence each of the modulation depths M, and VL passed

through a sharp maximum. By (21.1), (^2) and (^3-1) "the modulation

f impressed by a pulsed gyro-wave will behave similarly.

Since the two component modes of the plane gyro-wave are

absorbed at very different rates as they propagate through the ionosphere, a more precise discussion requires the effects caused by each

of these modes to be considered separately. We may then use the

results obtained in the sub- section 4.8.

For our present purpose it is sufficient to consider only the

33
5f effects caused by the much more absorbable extraordinary component

in the lover E region of the nocturnal ionosphere, at moderate

latitudes, for which "we have

N < 800 , n = lo'^ , V ^ 10 . (63)

It has been shown (Bailey 19383-) that the refractive index

1^ of the extraordinary mode defined by (61) is closely equal to

unity and that its coefficient of absorption ^ , is given approximately by

^ K (1 + cos^ 9 ) NV ,g^x

where

K = 0.0266,

and 6 is the angle between the directions of propagation and of the

earth's magnetic field.

More recently R.A.Smith (1957) has obtained the following

closer approximation:

When

N < 500, n = 10''', 3 X 10^ < V < 1.2 X 10 , I 9

I < 65^,

then

, K (1 . cos^ 9 ) KV

^^5) d V + e^ q2 _ ^2 ^^ ^ _ ^ g2,

Po (Ai^ - A2e )

X- When required the weaker effects due to the ordinary component can

be calculated in a similar way.

3h

r

I
where

p^ = 3.19 X 10^ N

A^ = i (2 + 3 sin^ e )

Ag = 4 (1 + 3 sin 9 )

(66)

From (6k) or (65) it is clear that mider the specified

conditions ft passes through a notable maximum value as m varies

about the value ^ . On the other hand (51) shows that 3 may

then pass through either one or two maxima according as the path

length s, is shorter or longer than some particular value. As

sho^wn by (57) this behaviour will be reflected in S-, through the

integral

f - 1 q <is

and therefore^ by (^3'l) ^-nd (kk), the modiilations f impressed

by a pulsed or sinoidally modulated gyro-wave will pass through one

or two maxima as the disturbing wave's frequency varies about the

gyro- frequency. The curves representing S-, ^ IVL or IVL in terms

of e , ^ , or Uo/2n , may therefore be called resonance curves.

Whether the extraordinary gyro-wave is transmitted from the

ground or from a rocket or a satellite in (or above) the ionosphere,

calculation shows that in general the wave is almost completely

absorbed within a region of the ionosphere about 6 kms long.

Consequently we may expect the interaction to be greatest

35
when the ionospheric path of the wanted wave lies within this region.

With the gyro-wave transmitted from the ground this region at

night lies in a horizontal slab with its lower face at about 90 kms

and_, for e = 0, its upper face at about ^^ kms above the ground.

As I e I increases from to 0.2 the upper face rises from about

95 kms to about 97 kms.

Consequently, when the top of the wanted wave ' s path lies below

95 kms the resonance curve for the impressed modulation in terms of

e possesses only one maximum (dromedarian resonance). But when

this top lies above 95 kms the resonance curve possesses two maxima

nearly symmetrically situated about the minimum which occurs near

e = (bactrian resonance); for increase of | e | from initially

causes the slab to embrace an increasing portion of the wanted wave's

path and so increases the interaction.

This deduction is supported by the published curves for the

Index of Interaction " at different levels in a specified model

of the lower ionosphere (Bailey, 1938a). For these have one maximum

at the lower levels and two maxima at the higher levels.

For a particular model of the nocturnal ionosphere and the

conditions relating to experiments on gyro- interaction at Armidale,

New South Wales, during the period 1950-195^1, R.A. Smith (195?) has

carried out the computations which are needed to evaluate q. ds

and the integral in (57).

These computations led to a theoretical resonance curve for

the impressed modulation which was in agreement with the observed

36
resonance curves (Bailey, Smith et al, 1952) vithin the limits of

experimental error. Some of these curves are shown in Figure 3 helow.

When the disturbing and wanted waves are both propagated

vertically the computation of the integral in (57) is notably

simplified. The experimental work is also much simplified provided

that the power is increased sufficiently to compensate for the

reduction in interaction which would otherwise occur.

If also the wanted wave is an ordinary mode under the conditions

discussed above, the, equation (57) inay be replaced by (57-1) and so

the theoretical computations then become simpler still.

The impressed modulations pre-determined by means of this

theory of gyro- interaction have been fully confirmed within the

limits of experimental error by subsequent experiments.

37
SECTION '5

PREDICTIONS FROM THE MTHEmTICAL THEORY.

The formulae {hh), (^5) a-nd (^6.1) lead to the predictions

labelled (l) in the Section 1.

The formulae (^5) specify the manners in which M_ and IVL

decrease vith increasing n as stated in the prediction labelled (2).

These variations with the modulation frequency are similar to the

variation of the current in a choke coil as the frequency of the

applied p.d. is varied.

The formula (46.1) shows that when E is not too large

^ ' ei

B is nearly proportional to E and therefore also to the mean

power P of the disturbing station. It then follows from (^5) that

M-, and Mp are nearly proportional to P and so we obtain the

prediction (3),

The form-ulae {hk) and (33) show that

cp^ = tan"-^ (n/GVg ) , cpg = tan"^ (2n/GVg )

•

Hence, when the mean power of the disturbing wave is such that v

the steady value of the perturbed collision frequency differs only

slightly from v^ the unperturbed value, we obtain the prediction {k)

.

The formulae (45) and (46.1) show that IVL and ]yL are

proportional to A , where A is given by (24) with v replaced

s s 1

by v^ . Hence, when V differs only slightly from V^ we

obtain the predicted behaviour (5) and also the single maxima

predicted xmder the label (6). But the more precise discussion of

38
the sub- section ^.9 shows that when s, the path of the disturbing

wave exceeds a certain value each of the modulations depths passes

through two maxima. Also^ computations by means of the formulae

given in the sub-section ^.9 show that when e = a mean power

of 1 or 2 kW. radiated from a vertical aerial s-uffices to produce

observable interaction. All this is summed up in the prediction (6).

The rays from an average radio station which produce the largest

values of ET in the E-region are inclined at ^5 "to the vertical.

ei

Consequently the ionospheric regions where a wanted wave is most

modulated by the disturbing station wi3J. be about 100 kms from the

ionospheric region vertically above this station. This is the

prediction (7)-

The formulae (^3-1)^ (^3-2), (I6) and (33) show that, when the

disturbing wave is such that v does not differ much from v ,

the modulation impressed by a pulsed disturbing wave rises and falls

approximately according to the same exponential law with the time

constant t = 1/GVq • This yields the prediction (8).

As the mean power P of a wave increases the modulations of

its amplitude with the same depth M but different frequencies n

will, by (32)^ cause modulations of v of depths which are greatest

for the lowest frequencies. Consequently the modulations of the

lowest frequencies will be received with the smallest amplitudes.

This self-distortion must Increase with P and so we obtain the prediction (9). Quantitative discussions of self-distortion have been

given by Hibberd (1955, 1957 )•

39
The prediction (10 ) follows immediately from the fact that the

low-frequency radiation from an electric storm reaches the nocturnal

E-region with great intensity and so considerably increases the

local electron collision frequency for periods of the order of one

millisecond.

The same general mathematical theory (Bailey, 1937^) which

yielded the equation (11 ), for a single disturbing wave, also yielded

a formijla (there labelled (35) ) for the variation of the collision

frequency caused by two or more disturbing waves. The latter formula

contained terms representing combination tones and so the prediction

(11 ) immediately follows.

The predicted phenomena (12) and (13 ) are of great interest

and possible future importance for the study of the ionosphere and

ionospheric radio propagation. Since no experimental tests of the

prediction (12) have as yet been carried out, it is sufficient here

to refer to the original publications in which it is discussed in

detail (Bailey, I938, 1959)- The predictions (13) are under

experimental test by Professor- R. A. Smith at the University of

New England in N. S. Wales, as indicated ttn.section-S.

Il-O i
SECTION 6

EXPERIMEM!AL TESTS OF THE THEORY AW VERCTICATION

OF THE PREDICTIONS .

The principal experiments which served to test one or more

of these predictions will now be mentioned in their historical order.

Van der Pol and van der ]yfe,rk (1935) measured the depth of

modulation M impressed on Radio Beromunster by Radio iuxembourg

at four different frequencies of modulation n . Their observations

are represented by the four dots shown in the Figure 1. The

theoretical curve representing IVL as a function of n ^ with

appropriately selected values of the two constants (B M) and t

s s in (^5); is also shown there. The resulting value of

Q^ = l/t then yielded a value of Vq which was consistent with

the values of v^ previously estimated by E. V. Appleton (1932) and

S. Chapman (1932) from other experiments. This constituted the

earliest verification of the prediction (2) with regard to M-|^ • Also

the measured depths of modulation were later found to agree in order

of magnitude with the theoretical value M, given in (^5)^ ^hus

verifying a part of the prediction (l).

Under the guidance of E. V. Appleton (193^) and Ralph

Stranger (193^) the members of the World Radio Research League in

Europe made observations which roughly verified the prediction (7).

In 1935 Baumler and Pfitzer qualitatively verified

predictions (2), (5) and (7).

kl
Extensive experiments 'wnich were carried out in 1937 vith the

help of the British Broadcasting Corporation and other European authorities verified at least the last part of the prediction (6) (Bailey,

1937"i)* During these experiments E. ¥• B. Gill of Merton College,

Oxford, reported observations which appeared to verify prediction (ll).

From 19^6 onwards M. Cutolo of Naples and his colleagues

successfully made extensive observations of gyro- interaction using

disturbing waves with powers less than 1 kW. They also succeeded in

demonstrating the existence of both double- humped (bactrian) and

single-humped (dromedarian) resonance. Tnus they verified the whole

of the prediction (6).

Commencing in 19^6 L. G. H. Huxley and J. A. Rat cliffe and

their respective colleagues carried out extensive experiments, both

separately and jointly, which verified the predictions (l), (2), (3)

and (k) (excepting the proportionality of Mp to m) . Moreover,

Huxley, Foster 8c Newton (19^7) observed the gyro-interaction caused

by the 10 kW station at Stagshaw; this is consistent with the last

part of prediction (6). In addition, Ratcliffe 8c Shaw (19^8)

directly verified the fundamental concept of the theory that the

amplitude of the wanted wave is decreased when the disturbing wave

is operating. Also Ratcliffe & Shaw successfully applied the

theoretical formula for the phase lag cp

^ given under (33), to

determine experimentally the height of the ionospheric region at

which the wave- interaction took place. Since the heights so

determined were of the same order as the heights postulated in the

42
original theory^ ve inay regard this "work as an experimental verification of the prediction (k)

.

In 19^9 experiments on gyro-interaction were commenced in

Eastern Australia by V. A. Bailey and colleagues at the University

of Sydney in collaboration with R. A. Smith and his colleagues at

the University of lew England at Armidale, (N. S.W. )• These were

planned to conform as closely as possible to the published requirements of the theory (Bailey, 1937c and 19383'). Accordingly the

arrangement of stations shown in the Figure 2 was adopted. In this

the disturbing gyro-wave A was radiated vertically from a horizontal aerial at Armidale, which lies at the mid-point of the 7^0 km.

line that joins Brisbane and Katoomba. The wanted wave B was

radiated from Brisbane on 590 kc/s and received at Katoomba. The

local gyro-frequency at Armidale was estimated to be 1530 kc/s.

The g3nro-wave was radiated ^0 times per second as a square

pulse of length 1 millisecond and power 36 kW. Its frequency f

was kept constant for 2 minutes at each of 8 values lying within

± 23fo of the gyro- frequency 1530 kc/s. I&,ch of the cycles 1, 2 and

3 ran throiJigh the middle 6 frequencies and lasted 17 minutes. Cycle k

ran throi:igh all the 8 frequencies and lasted 23 minutes.

In order to provide a standard of comparison for the depth

of the modulation Impressed on the wanted wave B the latter was

modulated at its source for 30 seconds in each 2-minute period with

a standard tone of 80 c/s to a depth of 5?^« This depth was chosen

because computations based on our mathematical theory of gyro-

^3
interaction had indicated in advance that the experimental arrangement

shown in Figure 2 "would impress on B modulation depths of the order

of 5^. This prediction was nicely verified by the experimental

obseiTvations.

A detailed account of these Australian experiments on gyrointeraction was published in 1952 by Bailey, Smith, Landecker, Siggs

and Hibberd. A briefer account was published by Bailey in 1956.

Examples of the experimental resonance curves are shown in the

Figure 3* It will thus be seen that these experiments not only

verified the predictions (6) and (8) but also confirmed the theory

quantitatively in every particular.

The theory of interaction, including gyro- interact ion, was

also thoroijghly verified by the experiments on micro-wave interaction

in gas-discharge tubes of Gfoldstein, Anderson and Clarke (1953) and

of Anderson & Goldstein (1955^ 1956). In some of these .experiments

Goldstein was able to demonstrate also the self-distortion of a

powerful wave (Private communication, 1955) thus verifying the

prediction (9) for a plasma.

The prediction (9), that self-distortion in the Ionosphere

increases with the power and does so at the expense of the lower

modulation frequencies, was verified by J. W. King (1957) .

In this publication King inadvertently contradicts the statement

on "Ionospheric self- interaction" previously made by Hibberd (1955)

namely: "its existence was first predicted by V.A.Bailey in 1935,..."

kk
In carrying out his experiments he vas guided by the quantitative

theory of self-distortion developed by F. H. Hibberd (1955; 1956).

Other tests of the theory arose from the experimental study

of wave-interaction by J. A. Fejer (1955) in which both the wanted

and disturbing waves were pulse-modulated. This study demonstrated

the existence of interaction during the day at heights between 70

and 90 km and also that a modification of the theory suggested by

Huxley was not valid.

The prediction (5) is now verified by the fact that during

the last 30 years the greatest disturbance by interaction backgrounds

has been produced by the radio stations with the lowest wavefrequencies.

From the whole discussion given above we see that

experimental observations have verified the ten predictions (l) to

(9) and (11). The predictions (10 ), (12) and (I3) remain to be

tested. We may therefore conclude that in the form presented here

the theory of wave-interaction is experimentally established.

45
SECTIOK 7

SOME APPLICATIONS TO RESEAECH ON THE IONOSPHERE

AND GAS DISCHARGES AND TO RADIO COMMUNICATION.

The experiments mentioned above "by van der Pol and van der

lyferk, Cutolo, Huxley, Ratcliffe & Shaw, Bailey Ss Smith, Fejer,

combined with the theory, have between them served to measure the

following important quantities relating to the Ionosphere

The electron collision frequencies v , the electron densities

N , the local magnetic fields H , the constant G (relating to the

mean loss of energy by an electron at a collision with a gas molecule)

and the heights at which the wave-interact ion occurs.

Similar applications, to the D-region, have been made more

recently by Fejer & Vice (1959), Bjelland et al. (1959) and by

Barrington & Thrane (1962).

The experiments by Goldstein and his associates mentioned

above also demonstrate the value of the phenomenon of wave- interaction

and its theory for investigating several fundamental processes in a

gas - di s charge

.

As an illustration of its practical value for radio- comm.'unication it may be mentioned that the author has been consiilted about

it more than once by the leading broadcasting organisations in

Europe and the U.S.A. Also, in the U.R.S.I. Information Bulletin

No. 73, on p. 59, it was reported that the CCI.R. stressed the

practical importance of information on non-linear effects in the

Ionosphere.
The present trend towards the use of increasingly powerful

beams in connexion with the reception of irregularly scattered

waves has also compelled attention to the possible occurrence of

observable wave- interaction and other non- linear phenomena at very

high frequencies.

Lastly^ the possibility mentioned by Bailey & Goldstein (I958)

of controlling the Ionosphere in various ways by means of powerful

radio waves has attracted some attention.

^7
SECTION 8

SOME RECEm' DEVELOPMEIWS

Filling in the gap between the two situations corresponding

to wave-interaction caused by moderate powers and ionospheric airglows

caused by extremely high powers and large aerial arrays, an investigation was made (Bailey, 1959) of "the possible increases of both the

collision frequencies v and the electron densities ~N caused by

a powerful extraordinary circular gyro-wave in the nocturnal lower

E-region and in the daytime D-region. The theory was based on the

most reliable available experimental data on the behaviour of free

electrons in air with energies up to 1.22 ev . The principal process

then freshly Introduced was the attachment of electrons to molecules

in some collisions.

It was found that some of the resultant effects, of such

increases in v and N , on this wave or on other waves are remarkable

in magnitude or in kind. Thus, when the gyro-wave produces near the

92 km. level at night a reduced equivalent electric force (z/p) equal

to 2.5 v/cm per mm Hg (measured at 288 K) it causes notable selfdistortion and extremely large wave- interaction; also within 3 milliseconds its penetration into the E-region increases considerably.

Other possible observable effects which may be caused at

night when z/p has a value between 2.5 and 8 are changes

in the visible e,nd infra-red airglow, in parts of some trails of

meteors and fast particles of solar or cosmic origin, in the radar

echoes from such trails and in the local magnetic elements.

I1-8 1
The theory also sho'wed. that a pulse of gyro-waves such as

that specified above could be used to determine by experiments on

the ground the rates of attachment of electrons and other electroncollision data pertaining to the regions near the 92 and 75 km levels.

For these and other reasons it was therefore suggested that

experiments be carried out with gyro-wave pulses beamed from an array

of at least 80 horizontal dipoles connected to a generator of at

least 500 kW power.

As a result of this work and of my recommendation to the

Air Force Cambridge Research Center at Bedford (yhss.)^ the University

of Few England is under contract with this Research Center to carry

out a project to "Modify the Ionosphere by means of Gyro-waves" using

an array of ^0 dipoles connected to a generator of 5OO kW power. The

results of this project are being reported by Professor R. A. Smith.

The power density req,uirements for the excitation of an

artificial airglow by means of gyro-waves (Bailey, 1938h) have been

reconsidered (Bailey, I961) in the light of later information. One

important conclusion was that- an array of 80 dipoles radiating

vertically a beam of gyro-waves with a mean power of 5OO k¥ would

produce an easily observable enhancement of the nocturnal airglow

overhead within a solid angle of 32 sqixare degrees. Another conclusion is that from the same array pulses of power 3500 kW and length

about 0.2 ms would each produce a flash of airglow that is ^0 times

as bright as the night sky.

h9
An extensive report on non-linear phenomena in a plasma was

published by Ginzburg & Gurevich in I96O and is available in an English

translation (1961). The theory is based on the Boltzmann equation for

the energy distribution function of the electrons, thus folloving the

classical examples of H. A. Lorentz and F. B. Pidduck. The authors

point out that "to disclose the physical picture" the simpler

"elementary theory" is "convenient and useful". Our present account

of the "elementary theory" confirms this opinion.

Similar discussions based on Boltzmann equations for the

electronic distribution functions are contained in reports by Megill

(1961), Carleton & Megill (I96I) and Moljnud et al (I962). These are

directed towards special problems of considerable interest such as,

respectively, the generation of artificial airglows and a method to

reduce the electron density in the D-region, by means of powerful

radio transmitters on the ground. In all these discussions the use

of simplifying approximations was found necessary.

An interesting new way of using wave-interaction for studying

the Ionosphere has been proposed independently by Vilenski (1962) and

Perraro, Lee & Weisbrod (1963). This depends on measurement of the

phase changes in the wanted wave that are caused by the disturbing

wave.

Ferraro and his co-authors mistakenly attribute the origin of the

theory of v/ave- interaction to its discussion in 19^8 instead of to

the correct date 193^.

50
A remarkable new example of the Interaction of combination

tones of two high-frequency waves with a third (wanted) wave, similar

to that mentioned under prediction (ll) in Sections 1 and 5^ has

been reported by Cutolo (I962).

The waves concerned and our theoretical processes were

as follows

(1) Disturbing wave; A carrier wave of frequency (Ju/2Tr

between 50 and 75 Mc/s was modulated at a frequency of ^/2'n' between

1000 and I3OO Kc/s which lies near the local gyro- frequency of

1200 Kc/s; the peak power was 80 kW and the modiilation depth m about

h2fo. Thus the (Yagi) aerial used simultaneously radiated three waves

of the angular frequencies 0) + ^ , uj and OJ - Q . Two pairs of

these produced in the Ionosphere electric currents which contained

components with frequencies equal to the combination tones

(ou + n) _ (JU and UO - (uu - Q) i.e., equal to the gyrofrequency ^ . These ionospheric current components generated

secondary waves of the frequency ^ which in turn caused gyroresonance variations of the local collision frequency v .

(2) The wanted waves were selected so as to be reflected at

or above the 90 km level in the Ionosphere in accordance with the

requirements for gyro- interaction given in our Section 4.9*

Cutolo 's experiments demonstrated that in this way modulations

of depths from 'pfo to 20^^ could be impressed on the wanted waves near

the 90 km level of the Ionosphere when the modulation frequency

approximated to the gyro-frequency.

51
Lastly we may consider the waves that could be generated in

the interplanetary plasma by the large negative charge on the Sua

which has been postulated in recent years to account simultaneously

for a number of important phenomena (Bailey, I960). The evidence in

support of this hypothesis has recently been strengthened by the fact

that three predictions (based on this hypothesis) that were published

in i960 have now been verified by the data on the interplanetary

magnetic field obtained by means of the space probes Pioneer 5^

Explorer 10, Mariner 2 and Explorer 12 (Bailey, 1963)'

The electrostatic field E due to the Charge -Q on the ^ s ^ ^s

Sun is radial to the Sun and has the magnitude

o E = fQ. /r e.s.u.

s s'

at the radial distance r , where f is a niimber between and 1

which represents the partial screening of the solar charge by the

interplanetary plasma clouds.

Any fluctuations in the emission by the Sun of these plasma

clouds will cause corresponding fluctuations E in the field Eg .

In certain frequency bands the radial components of E are particularly

liable to amplification by the mean static field E since they

may be regarded as forming longitudinal wave-modes.

These longitudinal waves may be sufficiently strong to produce,

or help produce, certain notable non-linear effects in the E&,rth's

Ionosphere which are at present attributed to other causes. For

52
•5f example, some geomagnetic disturbances may be caused by such longitudinal waves (Heirtzler, I962).

This possibility deserves further study, both by means of

instrumented satellites and theoretically (Bailey, 19^8, 1951)-

For example the micropulsations of shorter Type A waves (period ^

1 sec) modulated by Type C waves of periods about 20 sees. (Sci. Am.,

206, 128 (March I962) ).

53
SECTION 9

CONCLUSION

The foregoing account of the theory of wave- interaction and

other non-linear processes in the Ionosphere in the form developed at

the University of Sydney shows how the ideas and methods of the

Townsend School on the motions of electrons in gases and of the

Appleton School on magneto- ionic wave propagation have led to a

relatively simple mathematical theory which has proved fertile in

predictions of new phenomena that have subsequently been verified

by experiment.

It may therefore be used, and has been used, with confidence

as the basis of new experimental methods for investigating processes

in the Ionosphere and in electrical gas-discharges. It has also

suggested methods of controlling parts of the Ionosphere for particular

purposes by means of beams of radio waves.

The present trend towards increasingly large power-densities

in radio beams has made this theory, and its mathematical elaborations,

of increasing practical importance.

These elaborations, which are based in part on Boltzmann's

equation for the distribution of electron energies, are distinctly

onerous, but they serve both to check the simple mathematical theory

of the Townsend School and to study ab initio those phenomena which,

like the artificial airglow, depend strongly on the actual distribution

of the electron energies. On account of continual and non-uniform

fluctuations of the Ionosphere and the lack of precision in the

5^
necessary auxiliary laboratory data, it is probable that for some time

to come the simple theory will serve for most purposes quite as veil

as the elaborations.

The present account also si;iggests that certain types of lowfrequency longitudinal waves of extra-terrestrial origin may produce

some modifications of the Ionosphere that are at present attributed

to other causes.

Also called, by Ginsburg, the "elementary theory".

55
REFERENCES

Anderson, J. M. & Goldstein, L., Phys. Rev., 100, 103? (1955);

102, 388 (1956).

Appleton, E. V., World Radio, November 30 & December 7, 193^4-.

Appleton, E. V., J.I.E.E., l^cxl , 642 (1932).

Bailey, V. A., Phil. Ifeg., 50, 825 (1925)-

Bailey, V. A., Nature, I39, 68 (1937a).

Bailey, V. A., Phil. Lfeg., 23, 77^ (l937h).

Bailey, V. A., Phil. Mag., 23, 929 (1937c).

Bailey, V. A., Nature, 139, 838 (l937(i).

Bailey, V. A., Phil. Mag., 26, 425 (l938a).

Bailey, V. A., Nature, 1^2, 613 (l938t))

Bailey, V. A., Aust. J. Sci. Res., 1, 35I, (19^8).

Bailey, V. A., Phys. Rev., 83, ^39 (1951)-

Bailey, V. A., Nuovo Cimento, k (Suppl. 4), 1^30 (1957).

Bailey, V. A., J. Atmos. Terr. Phys., l4, 299 (1959)-

Bailey, V. A., Proc. Roy. Soc. N.S. Wales, 9^, 77 (I960).

Bailey, V. A., J. Research N.B.S., 65D, 321 (1961).

Bailey, V. A., Nature, 199, 1029 (I963).

Bailey, V. A. & Martyn, D. F., Nature, 133, 2l8 (193^).

Bailey, V. A. & Martyn, D. F., Nature, 135, 585 (1935).

Bailey, V. A., Smith, R. A., Landecker, K., Higgs, A. J.

and Hibberd, F. H., Nature, 169, 9II (1952).

Bailey, V. A. & Goldstein, L., J. Atmos. Terr. Phys., 12, 2l6 (I958).

Barrington, R. E. & Thrane, E., J. Atmos. Terr. Phys., 24, 3I (I962).

Baumler, M. & Pfitzer, W., Hochfreq.. Elektroak., 46, 8I (1935).

56
I

Bjelland, B.^ Holt_, 0.^ Landjmrk, B. and Lied^ F., Nature^ iQh, 973

(1959).

Butt, A. G., World Radio,. April 28, 1933-

Carleton, N. P. & Megill, L. R., "Electron Energy Distributions in

Slightly, Ionised Gases under the Influence of Electric and

Magnetic Fields", N.B-S. Boulder Laboratories, (I961).

Chapman, S., Proc. Roy. Soc, 137, I69 (1932).

Crompton, R. ¥. , Huxley, L.G.H. & Sutton, D. J., Proc. Roy. Soc,

A 218, 507 (1953).

Cutolo, M., Nature, 160, 83^+ (19^7).

Cutolo, M., Nature, I66, 98 (1950).

Cutolo, M., Nuovo Cimento, 9, 39I (1952).

Cutolo, M., Istituto di Fisica Tecnica, University of Naples,

(June 1962).

Cutolo, M., Carlevaro, M. & Gherghi, M., Alta Freq.., I5, 2,

p. 111(19^6).

Fejer, J. A., J. Atmos. Terr. Phys., 7, 322 (1955).

Fejer, J. A. & Vice, R. W., J. Atmos. Terr. Phys., 16, 29I (1959).

Ferraro, A. J., Lee, H. S. & Weisbrod, S., J. Geophys. Res., 68,

1169 (19^).

Gill, E.W.B., Private Communication, March I7, 1937.

Ginzburg, V. L. & Gurevich, A. V., Soviet Physics, Uspekhi, 3,

115 and 175 (19^1).

Goldstein, L., Anderson, J. M. & Clarke, G. L., Phys. Rev., 90^

151, (1953).

Healey, R. H. & Reed, J. W., "The Behaviour of Slow Electrons in

Gases", A. W. A. Ltd., (Sydney, 19^0).

Heirtzler, J. R., Scient. American, 206, 128 (March I962).

Hibberd, F. H., J. Atmos. Terr. Phys., 6, 268 (1955).

Hibberd, F. H., J. Atmos. Terr. Phys., 8, 121 (I956).

57
Hibberd, F- H., J. Atmos. Terr. Phys.^, 11, 102, (1957)-

Huxley, L.G.H., Proc Roy. Soc, A200, 486 (1950).

Huxley, L.G.H., Nuovo Cimento, 9 (Suppl. Series 9), 59 (1952).

Huxley, L.G.H., Foster, H. G. & New-ton, C C, Nature, 159

300 (19^7).

Huxley, L.G-H., Foster, H. G. & Ne^^ton, C C, Proc. Phys. Soc,

61, 13^ (19^8).

Huxley, L.G.H. & Ratcliffe, J. A., Proc. I. E. E., 97, I65 (1950).

King, J. W., J. Atmos. Terr. Phys., 10, I66 (1957)-

Llewellyn Jones, F., "Electrical Discharges", Reports on Progress in Physics, 16, 2l6 (1953)-

Megill, L. R., "Expected Upper Atmospheric Effects in the Presence

of High Frequency Fields with High Power Density",

C.R.P.L., N.B.S., Boulder Laboratories (I96I).

Molmud, P., Altshuler, S. & Gardner, J. H., "The Study of a Method

to Reduce Electron Density in the Ionospheric D-region by

means of High-powered Ground-based Transmitters". Space

Technology Labs., Inc., Final Report, September I962.

Neilsen, R. A. & Bradbury, N., Phys. Rev., 5I, 69 (1937).

Ratcliffe, J. A., J. I. E. E., 95, 325 (19^8).

Ratcliffe, J. A. & Shaw, I. J., Proc. Roy. Soc, A, 193, 311 (19^8).

Smith, R. A., Doctoral Thesis, University of Sydney, (1957).

Stranger, Ralph, World Radio, December ik, 193^.

Tellegen, B.D.H., Nature, I3I, QkO (1933).

Townsend, J. S., Phil, mg., 13, 7^5 (1932).

Townsend, J. S., "Electrons in Gases", (Hutchinson's Publications, 19^7).

Townsend, J. S. & Tizard, H. T., Proc. Roy. Soc, A, 88, 336 (1913)-

Van der Pol, B., Tijdschrift Nederland Radiogenootschap, 7, 93 (1935 )•

Y=in der Pol, B. , and van der Mark, J. , Tijdschrift Nederland, Radiogenootschap, 7, 12 (1935).

Vilenski, I. M. , Radiofizika, 5, 468, (1962).

58
200 400 600 800 MODULATION FREQUENCY, c/s

000

Figure I

Bailey, V. A. , and D. F. Martyn, Nature 135 , 585, 1935

530 kc/s

KATOOMBA BRISBANE

59
o

tr

Qin

UJ

2000

Figure 3

Bailey, V.A. , R.A. Smith, K. Landecker, A.J. Higgs, and F. H.

Hibberd, Nature 169, 911, 1952.

60
Remarks by Donald H. Menzel

with Reference to Bailey's Comments on Solar Electric Fields

Professor V. Bailey has postulated the existence of a large

negative electric charge on the sun and refers to apparent experimental

verification of his hypothesis.

I regret to say that I completely disagree with Professor

Bailey. Since electrons have velocities higher than those of the ions

they wo\ild tend to escape more readily and leave the sun with a positive

rather than a negative residual charge. But my objection to Bailey's

hypothesis rests on the magnitude rather than the sign of the charge.

For when the positive (or negative) charge attains a value such that the

electrostatic repulsion on the proton (or electron) equals the gravitational

attraction, the two oppositely charged particles will thereafter escape

in pairs.

This condition requires that

Qe _ GMm

wherein Q and M are the respective electric charge and mass of the

sun, r the solar radius (which cancels out), and G the constant of

gravitation. The quantities e and m refer respectively to the

charge and mass of proton (or electron).

61
Thus the voltage at the surface of the sun is

Q G M m G M m V = — esu = =:— esu = 300 =;;— volts

r e R e R

This equation leads to potentials of

V = 6.64 esu = 2000 volts, if positive

or

-3 V= 3.6x10 esu = 1.08 volts, if negative.

These potentials are naany orders of magnitude smaller than

1 7

those postulated by Bailey, 10 volts or higher. No process of

producing an electric field could possibly reconcile this disagreement.

Bailey has based his conclusion on the postulate that cosmic

1 7

ray energies occasionally attain the figure of 10 electron volts. But

if cosmic rays actually derived these energies by falling through a

solar electric field, they would be highly directional. One concludes

that the most energetic cosmic rays do not derive from solar phenomena.

I do not preclude the possibility that cosmic rays of low energy may be

produced by an electromotive force resxilting from changing solar

magnetic fields.

The space probes that Bailey refers to have measured only

magnetic, not electric fields. No one denies that the sun possesses

high electric currents. But these currents must be galvanic in

character and not the result of a rotating charged sun. A sun carrying

so high a charge would be violently unstable.

62
IONOSPHERIC CROSS -MODULATION

AT THE GEOMAGNETIC EQUATOR

W. K. Klemperer

Jicamarca Radar Observatory, Apartado 37^7^ Lima, Peru

Various experiments to detect radio wave interactions in the lower

ionosphere have been carried out using the 22 acre antenna and k megawatt transmitter of the Jicamarca Radar Observatory. Although equatorial

sporadic -E severely limits observation time, reduction in the amplitude

of 3 Mc/s F layer echoes by as much aS 25^ is readily obtained from the

classical Luxembourg effect. Cross -modulation of 50 Mc/s cosmic noise has

also been obtained. In this experiment the lower ionosphere is first

heated with a 3 millisecond, k megawatt rf pulse. A decrease in sky

brightness temperature (about 6,000° K, well away from the galactic

center) of 30° ± 10° K is occasionally observed with a recovery time on the order of 2 milliseconds. Both the Luxembourg and cosmic noise

observations indicate that the interaction height is above 75 km, and

essentially no cross -modulation was observed below 65 km. The lower

boundary of the D region thus appears to be substantially higher over

the geomagnetic equator than in other parts of the world. This is in

agreement with theories of D region formation attributing most of the

lower level ionization to cosmic ray and solar particle influx, which is

significantly less at the geomagnetic equator.

Three other experiments of an exploratory nature for the detection

of "sidebands" or combination frequencies near the electron gyrofrequency

were carried out. No such effects were obsearved.

X-A cooperative project of the Central Radio Propagation Laboratory,

National Bureau of Standards,' Boulder, Colorado, and the Instituto

Geofisico del Pfemi, Lima, Peru.

63
1. Introduction

The lower ionosphere remains a challenging frontier. Because of

atmospheric drag, it is a region inaccessible to satellites, so that

one must rely on rocket probes or traditional radio-wave methods to

obtain information about the environment at altitudes in the ij-0-90 km

range. In a masterful review of all ionospheric knowledge, Ratcliffe

and Weekes [1960] published suggested electron density distributions for

the D region based on various sources. In their words, the results were

somewhat disappointing. The power of radio and rocket techniq[ues has

measurably increased over the past years, yet it is still very difficult

to obtain D region electron density profiles.

The purpose of this note is to describe some of the radiowave interaction experiments carried out at the Jicamarca Radar Obseirvatory in

Peru. This station is the location of an antenna of 8^,000 m aperture

fed by a 50 Mc/s, k megawatt pulse transmitter. Although the frequency

is somewhat higher than one would normally employ for cross -modulation

work, the field strength attainable at E region heights is sufficiently

intense to produce an order-of-magnitude increase in the electron temperature. "With this "disturbing transmitter", the detection of cross

modulation using a 3 Mc/s "wanted transmitter" (to use the terminology

of the Luxembourg effect) is not at all difficult, and some fairly

spectacular effects have been observed. Cross -modulation of 50 Mc/s

cosmic noise, on the other hand, is extremely difficult to detect, but

some results have been obtained. No effects due to gyrofrequency

"sidebands" at 50 Mc/s as reported by Cutolo [1963] have been observed

at Jicamarca. The experiments will be described, as well as a few

preliminary results which have been obtained. The cosmic noise modulation experiment will form the subject of a later paper.

6k
2. "Luxembourg" Experiments

Fejer [1955] demonstrated that the extremely weak radiowave interactions occurring in the lower ionosphere between pulsed transmissions

on about 2 Mc/s could be detected, using a disturbing transmitter of only

5 kw peak power. This techniq.ue has been followed by Barrington and

Thrane [1962], Bjelland, et al. [1959]^ Landmark and Lied [I961], Rumi

[1962a and 1962b], and Smith [196k].

Cross -modulation effects were obtained using the Jicamarca radar

as early as I96I, with only a portion of the antenna completed [Bowles,

private communication]. Because of the radar's narrow beam (l between

half-power points when operated on axis and using the full k8X x kQ\

aperture), ra.y paths for the wanted wave occasionally fall outside of

the heated region due to normal ionospheric layer tilts and irregular

reflection effects. To ensure that data would be taken at the proper

times, two interferometer systems of 6\ spacing operating at 3 Mc/s were installed on N-S and E-W baselines and operated continuously as direction

finders . The wanted wave was generated by a 20 kw pulse transmitter

(also at about 3 Mc/s) and beamed vertically using an array of four

folded ^ dipoles. This short 50 M-sec probing signal was sent out twice

as often as the 50 Mc/s disturbing pulse, and F layer reflections were examined on alternate sweeps for evidence of the heating produced. When

using short disturbing pulses, a phase sensitive detector was used to

search for the weak cross -modulation produced. The sensitivity and

stability of the equipment in this mode of operation -were sufficiently

good to detect as little as 0.3^ cross-modulation, using a long integration time of 50 seconds. Usually an integration time of 1 second was

used, for which 2^ of cross -modulation gave a deflection which was

in excess of 10 times the noise level. One of the advantages of working

so near the geomagnetic equator is that a single magneto-ionic

component can be selected, using simple linear polarization. All the

wanted wave antennas were aligned N-S. A serious disadvantage is

the presence of equatorial sporadic E (E ) in the daytime. These

65
E region irregularities caused by the equatorial electrojet [Bowles et_

al., 1963; Farley, I963] forward scatter the wanted wave to such an

extent that measurement of cross -modulation becomes difficult or even

impossible. This has severely limited observation time. Nevertheless,

enough data has been obtained using F layer reflection of the wanted

wave to show that usually as much as 12^ cross -modulation is obtained

using 3 millisecond pulses of 2 megawatt peaj£ power and half of the

available antenna aperture for the disturbing transmitter. Spectacular

(25^) cross -modulation is observed occasionally. By varying the disturbing pulse length, one can estimate the time constant for heating.

It is on the order of 1-2 milliseconds. Two examples of cross -modulation

using F layer reflections are shown in figure 1. No effects have been

observed at heights of less than 70 km using shorter disturbing pulses,

in spite of greatly increased sensitivity (phase -sensitive detection)

and diligent searching.

A sizeable increase in sensitivity can be attained by using E

layer rather than F layer reflections. Although smooth E layer reflections at our latitude occur but rareHy, the wanted wave can then be made

to transit the disturbed region twice before much cooling takes place

and thus double the amount of cross -modulation produced. Examples of

cross -modulation of E layer echoes are shown in figure 2. As with the

F layer reflections, the time constants were found to be long; and

practically no cross -modulation was detected below 65 km, although the

eq.uipment was certainly capable of detecting it. By working close to

the E layer critical frecLuency, cross -modulation in excess of 50^

(6 db) could be obtained. Examples of this are shown in figure 3- This

indicates that most of the cross -modulation is taking place at the level

of reflection, in agreement with the interaction height estimates from

the short pulse experiments . When interaction takes place near the

level of reflection, the retardation in the medium (difference in group

and phase path) enhances cross -modulation according to the relation

[Ratcliffe, I959, p. II6]

eo
- log p = ^

(Pg - Pp), (1)

where: p = reflection coefficient,

V = collision freq.uency for electrons,

P = group path,

O

P = phase path,

o c = 3 X 10 m/sec.

Under these conditions (copious amounts of cross -modulation and

long time constants) near the E layer critical frequency, the experiment can be set up to measure time constants directly by passing three

probing pulses through the disturbed region in rapid succession. This

is illustrated in figure k. Note that the echo from the lower height

shows a shorter recovery time.

3. Cross -modulation of Cosmic Noise

It occurred to Rumi [Benson, I963] while working at the Geophysical

Institute of the University of Alaska that a simplification of the usual

pulse interaction experiment of the type just described should be possible by using cosmic noise as the wanted wave. In addition to removing

the requirement for the wanted transmitter, this permits operation during

ionospherically disturbed periods (such as strong absorption at high

latitudes or E at the geomagnetic equator). Observations of the cross

modulation of cosmic noise have been reported by Benson [1962 and I963]

.

An experiment to observe this effect at 50 Mc/s was set up in the

fall of 1963. The k Mw transmitter of the Jicamarca Radar was connected

to one linear polarization (NE-SW) of the 8^,000 m antenna, and a wide

bandwidth receiver was connected to the orthogonal polarization (NW-SE).

In this way the entire 2 Mc/s bandwidth capability of the large antenna

could be exploited without TR problems, since the attenuation between

polarizations is greater than 60 db and the receiver is blanked during

67
the transmitter pulse. Normal incoherent scatter echoes from the F

region (Faraday rotated) as well as cross -polarized components of the

E reflections were removed by a 10 kc/s wide notch filter tuned to the

sq.

' operating freq.uency.

The sensitivity req.uired to detect modulation of cosmic noise at

50 Mc/s even with such a powerful system approaches the statistical

limit of detectability given "by

T

AT=yJ=, (2)

VBr

where T = sky brightness temperatuxe at 50 Mc/s

(minimum ~ 5^000 IC, maximum ~ ^5^000 °K),

B = system bandwidth (imited to 2 Mc/s by the antenna),

T = integration time,

At = ims fluctuations in temperature.

We can neglect receiver noise contributions in comparison with the

5^000 K minimum sky brightness temperature, 'f is limited by the range

resolution required and the ninnber of range sweeps which can be con- veniently integrated. For example: with a detector time constant of

150 p.sec, a sampling interval of 133 l-isec, and integration of 10,000

sweeps, T is about I.5 seconds. The flucutations in temperature

according to (2) would then be at least 3.5 °K for a T of 6,000 K and

a two megacycle bandwidth. Under the conditions of the experiment, the

fluctuations were about 10 K, the additional "noise" being due to

receiver and integrator gain fluctuations and digitizing errors. Figure

5 shows the change in the cosmic noise level caused by heating with a

3 millisecond pulse. The decrease in sky brightness amounts to only

30 °K in 6,100°.

68
h. strong, Non-linear Effects (gyro sidebands)

Three experiments of an exploratory nature for the detection of

"sidebands" or combination freq.uencies of the electron gyrofreq.uency

with the carrier -or carriers were carried out and will be briefly described. The first of these was motivated by a report that Cutolo

[private communication] in 19^3 had succeeded in detecting the effect

on the lower ionosphere of a small 50 Mc/s radar modulated at the gyrofreq.uency. After the 50 Mc/s and 3 Mc/s pulsed interaction experiments

at Jicamarca showed easily detectable results, it was decided to try to

duplicate the experiment of Cutolo using higher power. Accordingly, two

of the four one -megawatt transmitters were detuned slightly, one to

50.^ Mc/s and the other to k^.6 Mc/s, so that the frequency separation

was near the predicted gyrofrequency . The Luxembourg effect experiments

were repeated with this arrangement to see if there was any enhancement

of the modulation transferred to the 3 Mc/s signal. The frequency of

separation was varied from 750 to 9OO kc/s in small increments. The

pair of one -megawatt transmitters remaining on 50 Mc/s was frequently

substituted for the pair separated at the gyrofreq.uency to show that

the normal cross -modulation was produced. No detectable difference (to

within 10-20^^) could be observed between the two methods of heating the

lower ionosphere.

A second experiment was carried out, using the same transmitters

(50.^ and k^.6 Mc/s) separated by the gyrofreq.uency, but with reception

at the sum frequency (lOO Mc/s). The receiving antenna was a ^ x ^ array

of dipoles over a reflecting screen. No effect was detected.

The most sensitive test for a strong, non-linear effect was the

search for "sidebands" on the E echoes. These echoes are often 100 db

scL above the noise when the entire radar is beamed perpendicular to the

magnetic field over Jicamarca. Under conditions of strong E , the

receiver was detuned and a search was made for echoes at 50 Mc/s

_'7 ± 150-900 kc/s. No "sidebands" were detected down to parts in lO" of

the echo power received at 50 Mc/s.

69
5« Discussion

An interesting feature of the cosmic noise cross -modulation

observations (figure 5) is the decrease in sky brightness temperature

and the long recovery time. Although the 3 millisecond disturbing pulse

increases the electron temperature in the lower ionosphere by an oirder

of magnitude (the rms E field during the pulse at 100 km height near

the center of the antenna beam is about 15 volts per meter), the

ionospheric contribution to total sky brightness temperature observed

at 50 Mc/s remains negligible. A decrease in sky brightness is observed

at 50 Mc/s. This is because the ionosphere remains essentially transparent to 50 Mc/s radiation so that any increase in temperature is not

directly apparent. An analogous situation is found in the solar corona

which, at a temperature of a million degrees Kelvin, has a brightness

only a few millionths as great as the 6,000 photosphere. The decrease

observed in the 50 Mc/s cosmic noise level is evidently due to an

increase in V, the electron collision frequency, which has the effect

of increasing the absorption slightly. The recoveiy time is related to

the time constant for ionospheric heating which in the simple theory is

t = 1/g V (3)

where G is the fractional energy loss per collision and is a small factor

-3

X 10 . Figure 5 shows two time constants, one of approximately

5 2 milliseconds, corresponding to a collision freq[uency of 5 x 10 or a height of about 8o km, and a weaker component with a longer time constant

which may be of E region origin.

The approximately 2 millisecond time constant found in the cosmic

noise data agrees with the time constant for heating found in the

Lxixembourg type experiments performed at Jicamarca. By the technique

shown in figure h, the time constant can be determined to considerable

precision for several heights. Values are all in the range 1.5 to 2

milliseconds for the echoes from 80 km and above, while an occasional

70
echo from the lo"wer 70 to 75 km height shows a time constant of less

than one millisecond. There are seme indications that G in (3) may not

be a constant but depend on energy [Phelps, private communication] and

if so this complicates the analysis considerably.

A comparison can be made between the large cross -modulation produced at 3 Mc/s and the very weak effect detected in the 50 Mc/s cosmic

noise. The 3 Mc/s effects were produced using but one -half of the

available transmitter power and one -half of the 22 acre antenna. The

cosmic noise experiment made use of the whole system. The 50 Mc/s

sky brightness changed by 0.02 db. If the 3 Mc/s experment —which

showed, on the average, a 15^ change in the F region echo amplitude

(1.5 db)--had been performed under the same conditions as the cosmic

noise experiment with four times the gain, the cross -modulation would

have been 6 db. The ratio of these two numbers is 1:300, which is

approximately equal to the reciprocal ratio of the squares of the

frequencies (9:2500). This variation as f is a characteristic of

non-deviative absolution for the case f > V.

Although only preliminary data is available at the present time,

it is of some interest to speculate on the sort of D region electron

density profile one might expect to find at the geomagnetic equator

that would agree with the observations. It is fairly clear from the

preceding experiments that what little ionization does exist below

65 km must be less than that reported at high latitudes [Rumi, 1962b

j

Benson, I963] by a large factor or it would have been detected. Figure

6 is a noon-time model, D region profile constructed by Nicolet and

Aikin [1960] for a geomagnetic latitude of 50 . Considerably higher

electron densities than shown can be produced at low heights from the

influx of energetic solar protons in addition to the cosmic ray flux.

At the geomagnetic equator we are effectively shielded by the earth's

field from all such activity of less than I5 Bev energy (for particles

arriving from the zenith). Accordingly there is apt to be less lower

71
D region ionization over the geomagnetic eq.uator than anywhere else in

the world. Whether this is also the reason for the failure to detect

gyro "sidebands" or strongly non-linear effects remains to he seen.

72
Acknowledgments

The author wishes to acknowledge the very substantial support and

encouragement given during the course of this work "by K. L. Bowles, who

showed the feasibility of cross -modulation with the Jicamarca Radar as early as I96I. The author also wishes to thank his colleagues, especially

J. L. Green and D. T. Farley, Jr., and personnel of the Instituto

Geofisico del Peru for invaluable aid and advice.

73
References

Bailey, V. A., and D. F. Martyn (193^)^ The influence of electric waves

on the ionosphere, Phil. Mag. l8, 369*

Barrington, R. E., and E. Thrane (Jan. I962), The determination of

D-region electron densities from obseivations of cross -modulation,

J. Atmos. Terrestrial Phys. 2h, 31-^2.

Benson, R. F. (June I962), Cross modulation of cosmic noise, J. Geophys.

Res. 67, 2569-2572.

Benson, R. F. (May I963), The cross modulation of cosmic noise: A

technique for investigating the disturbed D region. Scientific

Rept. No. 1, Contract AF 19(60^)-8833, University of Alaska,

UAG-RI3I.

Bjelland, B., 0. Holt, B. Landmark, and F. Lied (Sept. 26, 1959), The

D region of the ionosphere. Nature l8^, 973-97^.

Bowles, K. L., B. B. Balsley, and R. Cohen (1963), Field aligned E

region irregularities identified with acoustic plasma waves,

J. Geophys. Res. 68, 2^1-85-2501.

Cutolo, M. (1963), On seme new properties of the lower ionosphere. Report

of II Centre di Studi di Fisica dello Spazio, Univ. of Naples,

Naples, Italy.

Farley, D. T., Jr. (Nov. I5, I963), A plasma instability resulting in

field-aligned irregularities in the ionosphere, J. Geophys. Res.

68, No. 22, 6083-6097.

Fejer, J. A. (Dec. 1955)^ The interaction of pulsed radio waves in the

ionosphere, J. Atmos. Terrestrial Phys. 7, 322-332.

Fejer, J. A., and R. W. Vice (Nov. 1959), An investigation of the

ionospheric D-region, J. Atmos. Terrestrial Phys. I6, 29I-306.

I

74
Ferraro, A. J., H. S. Lee, and S. Weisbrod (1963), Phase interaction:

A new tool for D-region studies, J. Geophys. Res. 68, II69-II7I.

Landmark, B., and F. Lied (Dec. I96I), Observations of the D region

from a study of ionospheric cross modulation, J. Atmos. Terrestrial

Phys. 23, 92-100.

Nicolet, M., and A. C. Aikin (I960), The formation of the D region of

the ionosphere, J. Geophys. Res. 65, 1^69-1^83.

Rumi, G. C. (Sept. 1962a), Experiment Luxembourg: Cross modulation at

high latitude, low height. Part I: Theoretical aspects, IRE

Trans., Antennas Propagation AP-10, 60I-607.

Rumi, G. C. (Sept. 1962b), Experim.ent Liaxembourg: Cross modulation at

high latitude, low height. Part II: Experimental aspects, IRE

Trans., Antennas Propagation AP-10, 60I-6OT.

Smith, R. A. (Dec. 1963)^ Ionospheric wave interaction using gyrowaves. Part II: The D-region, Paper k.6, Conference on NonLinear Propeirties of the Ionosphere, held at Boulder, Colorado,

Dec. 17, 1963.

75
Figure Captions

Figure 1. Examples of cross modulation F layer reflection.

Figure 2. Cross modulation of E layer echoes.

Figure 3' Cross modulation of E layer echoes using two different

disturbing pulse lengths

.

Figure k. Triple pulsing (3 E layer echoes in succession).

Figuire 5* Recovery of 50 Mc/s sky brightness temperature after h megawatt, 3 millisecond disturbing pulse.

Figure 6. Theoretical curves for electron density (after Nicolet and

Aikin )

.

76
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82
Editors' Note

Dr. Cutolo remarked, in informal sessions after

the meeting, that Dr. Klemperer's experiment was not

identical with his, in that it relied on entirely different

means for detecting the effect.

83

VLF Noise Bands Observed by the Alouette I Satellite

J. S. Belrose and R. E. Harrington

Defence Research Telecommunications Establishment

Radio Physics Laboratory

Ottawa, Ontario, Canada

A surprising feature of the signals observed by the VLF receiver

aboard the Alouette I Satellite are bands of noise which show

systematic variations vdth the position of the space craft in the geomagnetic field. Sometimes this is a variation of the lowest

frequency at which noise is found, sometiiiies it is a variation of one

or more discrete bands, but in all cases it is a variation which shows

a frequency decrease with increase in the latitude of the satellite.

The most regular noise bands are found within the zone defined by the

geomagnetic L values between 2,6 and 3*6, but bands with a stronger

dependence on the geomagnetic field are sometimes found at higher

latitudes. The polar chorus zone is well defined by the observations

between L values of 4 and 9.

These observations are compared with present theories of

generation of VLF exospheric noise (hiss) (Dov^den^ 1962, 1963). The

observed spectral distribution of the noise is perhaps more consistent

with the doppler shifted cyclotron theory of generation, but the dependence on the geomagnetic field is in better agreement with the

travelling wave tube amplification theory. Although both theories can account for narrow, wide and very wide band noise, neither seems to

adequately explain all features of the observational data.

85
1. Introduction

Bursts of VLF ionospheric noise or "hiss", which occur in the

audio frequency range 0.1 - 15 kc, and last for periods ranging from

several minutes to a few hours, have been studied at DRTE and elsewhere

(Ellis J 1959.1) and Watts, et al.j 1963) for several years. Hiss occurs

in broad bands or in one or more narrow bands. The narrow bands often

have bandwidths of 1 kc or less. The most common type, "isolated

bursts", is typical of magnetically quiet conditions. These are also

sometimes associated with isolated magnetic bays, and ionospheric radio

wave absorption. A second type occurs as an extended series of hiss

bursts or noise storms. All major magnetic storms are accompanied by

noise storms. Hiss has been correlated with airglow (Duncan and ELliSj

1959) , with aurora (Martin et al,,.19pO) , and with abnormal D-region

absorption (V/atts et al,t 1%3)

.

Although the ground observations have revealed much information

on the occurrence of the hiss bursts, there are difficulties in interpreting detailed studies of their characteristics. This is partly

because ionospheric attenuation affects the noise intensities that can reach a ground based receiver, and partly because propagation under

the ionosphere allows observation of hiss generated in a wide range of

field line latitudes.

Only by means of a satellite travelling vdthin (or above) the

ionosphere, can noise generated on particular field lines be properlj''

studied. In addition there is no ionospheric loss to contend with,

and the amplitude-frequency spectra would be as generated. On

September 29, 1962, the Alouette satellite was launched into orbit,

and, although primarily designed as a top-side sounder, a broad band

(C.5 - 10 kc) VXF receiver vras included in the pay load. The satellite

moves in a nearly circular orbit at an altitude of 1025 + 20 km and

has an inclination of 80° to the equator^ This allows observation of

the VLF spectrum over a wide range of latitude, while the nearly circular orbit simplifies the interpretation of the results, e.g., over North America the height of the satellite can for most purposes be

considered constant at 1.16 + 0.02 earth radius and the position of the

spacecraft in the geomagnetic field can therefore very simply be determined. It is the purpose of this paper to discuss, in somewhat more

detail, some of the results so far obtained (Barrington, et al,,.1963) j and to compare these observations with cresent theories of the generation

of VLF noise (Do^Mien, 1962, 1963). .

86
2. The Observations

In this paper the data are sorted according to the magnetic

parameter L (Mcllwainj, 1961) , The parameter L is constant along a line of force and labels the magnetic shell on which an electron boimces

in latitude and drifts in longitude. Numerically L is such that for a perfect dipole field, it would be the equatorial radius to a magnetic

shell, expressed in units of earth radii. In coraparison of the observations with current theories of the generation of VLF noise (^ection 4),

it will be necessary to refer to geomagnetic latitude. In the case of a perfect dipole, the magnetic latitude measured to the point where the

line of force passing through the satellite cuts the earth's surface

(R = 1) is

A = cos -^^IaT

L is however calculated from the real magnetic field as approximated by

Finch and Leaton (1957) > and therefore A is calculated simply from L as indicated above. The discrepancy between A and geomagnetic latitude is

at most about 2° over North America,

Fig. 1 shows the track of a pole-to-pole pass recorded once per

week, which gives full coverage from SO^^N to 80**S latitude. Other passes,

not so complete in continuous coverage are recorded at other times (about

2| hours of recordings are made each week); e.g., a pass extending from

i\!E of Bermuda, over Newfoundland, passing midway between Narsarssuak and

Godhavn, and ending N and E of Spitsbergen, is recorded in co-operation

with ground recordings made by the Danes; and a recording beginning over

the Queen Charlotte Islands and ending at about 20°H latitude over the

Pacific is recorded at Stanford for comparison with ground recordings

made there. The purpose of this figure is to show the asymmetry of the

satellite track with respect to the geomagnetic field. The contours are constant magnetic L values at 1025 km (the satellite height). The pass

shown covers a range of L values from about 6 in the north to about 7 in

the south.

A surprising feature of the signals observed by the satellite VLF

receiver are bands of noise which show systematic variations with the

position of the space craft in the geomagnetic field. Fig, 2 shows one of the early examples of ionospheric noise which exhibited systematic

changes in the spectral distribution of noise with satellite latitude.

In this example the noise is sporadic but shows a systematic tendency

for the lowest frequency at which noise is found to decrease as the

satellite moves to high latitudes, over a range of L between about 2,5 - 3.

Above this latitude sporadic noise is found throughout the entire frequency range of the VLF receiver with no well defined lower limit. Fig, 3

is another example, but shows two bands of sporadic noise observed over

87
the same range of L values, both of which decrease as the latitude of the

satellite increases. Fig. 4 is an example recorded at higher latitudes.

Fig. 5 is an outstanding example, made on 31 January, 1963^ from

1057 to HUB UT, while the satellite passed through its full range of

latitude. A narrow noise band was observed, the low limit of v;hich changed

from about 2'| to 9 kc as the satellite moved from L values of about 3.5 to

2o5. To a very high degree the noise observed at the same L value in the

northern and southern hemisphere was the same in spite of the fact that

the observations in the two hemispheres are separated by at least 30 minutes

in time, several degrees in longitude, and the local gyro-frequencies at

the points differ by as much as 30^. These facts suggest that such noise

bands must be due to conditions in the exosphere which are relatively

stable and uniform over a large region.

f Other features worthy discussion shown in Fig. 5 are: <

(1) The relatively constant noise bands from the lower edge of the

receiver pass band (about 400 c/s) to 2,5 kc which were observed

when the vehicle was in a region where the magnetic parameter L was greater than 9.

(2) Similar noise bands were found in the region where L was less than

2o5 (even at the equator, not shovm, vriiere L . — 1.1), ' ' ' mm

(3) In the region where L lies between 9 and 4, the noise was very

erratic both in amplitude and frequency.

We have not recorded enough examples of noise bands and noise storms

to come to any firm conclusions about the morphology of such distiirbances,

but a few comments, particularly in regards to the disturbance pattern of

hiss bands shown in Fig. 5 can be made. Ground station recordings of VLF

noise made at Ottawa (L - 3*6) on a slowly moving paper chart record,

employing narrow band receivers- centred on ?> 4j and 1^ kc, and an asymmetrical detector circuit to minimize effects on the recordings due to

atmospherics are shown in Fig. 6. It is clear that the satellite recording, made at the time shown by the cross-hatched rectangle, was made

during a series of noise bursts (in fact noise bursts of much greater

amplitude were recorded before and after the making of the satellite

record) . This series of noise bursts began, after a period of magnetic

and VLF noise calm, at about 09 UT on 30 January, and continued in varying

degrees of intensity until about 04 UT on 2 February. The noise storm was correlated in time with a geomagnetic disturbance observed in local and

planetary k-indices. It seems likely that the electron streams causing the

geomagnetic disturbance also produce the hiss, although an experiment to

test any possible detailed correlation has not yet been done. A satellite

VLF recording made at 0044 - 0049 on 1 February, 1963, while Alouette

passed through a range of L values from about 2o5 - 6, is also pertinent

88
to our discussion of the 30 January, 1963? noise storm. Although

magnetic activity was less at this time, ground recordings of VLF hiss

at Ottawa (L '^ 3.6) showed greater activity (see Fig. 6 which shows

records up to just before the making of the satellite recording). The

satellite observations did not show on this occasion the two zones clearly evident in the previous recording (Fig. 5)j viz. the noise band

whose frequency changes with latitude in the range where L is between

2,5 - 3»5, and the auroral disturbance zone where L is between 4-9.

The satellite observations showed two quasi constant noise bands for L

between 3-6. The upper one (2,5 - 4 kc) became somewhat erratic above

L '^ 5. The lower one (below 1.5 kc) was less regular and weaker.

These results, as well as more detailed comparisons between ground

station observations and satellite data reveal that there is no close

correlation. This may be due to absorption or total internal reflection

of these noisy signals in the ionosphere, the noise arising only in the

immediate vicinity of the satellite, or due to the fact that the ground

stations can observe VLF signals which have emerged from the ionosphere

over a large area.

As mentioned above detailed correlations between particle streams

(of the appropriate energy range) and VLF hiss have not yet been made.

It is unfortunate that with the Alouette I satellite the VLF receiver and

the particle detector recorders are not operated simultaneously. Nevertheless comparisons can be made between the VLF data and average properties

of the intensity distributions for particles. The two places where interesting features are sometimes found in VLF data, viz, L between 2.5 - 3.5

and L between 4 - 9, are also places where features are found in the intensity distribution of trapped (and dumped) electrons. HcDiarmid et al (1963)

have shown that the intensity distribution of trapped electrons (in the

lowest energy range observed, viz. E 1^ 40 kev) observed by Alouette

exhibits two maxima separated by a minimum atL = 3.2(A ~ 56°). The

minimum is not always present. Large fluctuations occur around L = 2,2

( A = 48°) J the approximate position of the lower latitude peak: (in the

so-called slot between the inner and outer radiation belts). The second

peak at L = 5.6 (A = 65°) corresponds approximately with a peak found

in the average intensity of precipitated electrons having similar energies

(which occurs atL = 6,5 (y\ = 6?°)). Thus the VLF noise bands which exhibit

a systematic change with the earth* s field are observed at a latitude near

the slot between the inner and outer radiation belts, while the higher

latitude disturbance zone corresponds approximately with L values at the

edge of the magneto-sphere, and the horn of the outer Van Allen belt.

3. Analysis of the Data

In an effort to obtain more quantitative information on these

noise bands, several of their features were scaled and plotted as functions

of different parameters of the geomagnetic field. It was found that to a

89
good approximation the frequency of the lower edge of the noise band was inversely proportional to the cube of the L parameter at which the noise

band was observed for L values between 2,5 and 5. Since the cube of L is

inversely proportional to the magnetic field where the L shell crosses

the magnetic equator, the frequency of the lower edge of the noise band

f, is proportional to the magnetic field B or the gyro-frequency f„

at the peak of the line of force on which the noise is observed. This

fact is illustrated in Fig. 7 in which results from noise bands observed

on several different occasions are combined. At high latitudes, or B

between 0.003 and 0.01 (L values of 3 to 5)> f-, varies approximately

linearly with B but shows no consistent trend from day to day. At lower

latitudes B between 0.01 and 0,02 (L values between 3.5 to 2o5) fn

is not only proportional to F but the slope of the points on the

(f^ , B ) plots is about the same for all events. Moreover, in this

latitude range the points appear to cluster about two frequencies separated

by about 3o5 kc.

At very high latitudes, or B less than 0.002 (L values between

5o5 to 7), a noise band is sometimes found which shows a systematic increase in frequency with decrease in latitude, but the slope of the points

on the (f^ > B ) plot is very much steeper than at lower latitudes.

The times of occurrence of all events so far recorded, although

not sufficient in nurriber to be statistically significant, cluster near 10 UT, or 05 LST, which is the time for the maximum of occurrence of the

4 kc noise bursts observed in our longer statistical study,

4, Discussion

It is not possible, at present, to give any final explanation of

these noise observations but certain features are suggestive. Recently

two theories have been advanced in explanation of the generation of VLF

noise or hiss

.

The first (Dovjden^ 1962) explains hiss as amplified Cerenkov

emission from electron streams by analogy with the travelling wave tube

(Tl'JT process). It was shown that an electron stream in the exosphere

acts as a narrov/ band amplifier if the stream is "weak" but as an over loaded amplifier for "stronger" streams. Fig. 8 shows calculated results

based on this theory, in which the interaction parameter s/^v, (which is

proportional to the amplification of the TaT in nepers) is plotted for

stream particles of small pitch guided along the field line terminating

at a geomagnetic latitude of oO". At other latitudes frequencies will

scale so the maximum s/>. occurs at the frequency shown by the dotted

line. In these respects the theory seems to explain the observational

results, i.e.: for geomagnetic latitudes between about 65° and 50°, the

90
theory predicts centre frequencies should range from about 1 to 10 kc.

Observed hiss frequencies vary between 3 and 9 kc for L values betvreen

3^ and 2^ (A = 56 - 51°). ^^he maximum amplification which occurs at

0»15 fiT is quite closely the same as observed. This is evident in Fig. 7

where the dashed line is drawn assuming that f = 0.15 fu (or f = 4»2 x lO'^B , n O

where B is in gauss). The departure between the lower set of data points

and the dashed line for L greater than 3 •3 is at least partly because a

noise band which does not vary with the position of the satellite is

usually observed for frequencies below about 2,5 kc, and the noise band

whose frequency does vary with latitude disappears into this regular noise

band at about L = 3«>3«

It is clear, however, from Fig. 8 that frequency response is

not symmetrical, in that the amplification falls off much more slowly at

the low frequencies than at the high frequencies. Consequently "strong"

streams would produce noise having a xvider bandwidth but shifted toward

low frequencies. The fact that it is the lower edge of the noise bands,

rather than their central frequency, which for several events has a constant relation to the geomagnetic field suggests a cut-off mechanism

may be involved. Such a cut-off could be due to propagation conditions

which determine what frequencies are trapped on a given field line, or may be associated with a cut-off in the spectrum of the energetic particles which radiate in the VLF band.

Doppler shifted cyclotron radiation could produce hiss having

such a low frequency limit emission cut-off (Dowdenj ,1963) . In this

theory cyclotron radiation from a receding electron in the exosphere can

be doppler shifted to a frequency much less than the local gyro frequency,

A stream of electrons will produce band limited white noise. Computed

amplitude-frequency spectraT^iss generated on field lines of 60** and

63| geomagnetic by mono-energetic electron streams of 1 kev, 6 kev, and

30 kev are shown in Fig. 9. Thus the soft particle fluxes produce the

narrower hiss spectra, and the peak amplitude occurs at 0,55 frjo These

spectra exhibit the required feature that the low frequency cut-off does

not change much with electron energy (except for high values of electron

energy), whereas the upper frequency limit is quite variable. Unfortunately the dependence of the peak frequency on the geomagnetic field is

quite different from that found.

Thus neither theory can account for all the detailed features that

are observed. The TVJT theory is perhaps the most hopeful, and it should

receive further study.

5, Acknowledgements

We wish to thank Mr. W. E. Mather for operating the VLF ground

station recorders, and for making the spectrogrammes from the satellite

data, which are shown in this paper. We are also endebted to I^Ir. W. E.

Thompson for the recordings made with the VLF noise burst receiver.

91
References

Barririgton, R. S,, Belrose, J. 3. and Keeley, D. A,

VLf Noise Bands Observed by the Alouette I Satellite,

J.G.R., 63, 6339, December, 1963.

Dowden, R. L.

Theory of Generation of Exospheric Very-Low-Frequency Noise (Hiss),

J.G.R., 62, 2223 - 2230, June 1962.

Dowden, R. L,

Doppler Shifted Cyclotron Generation of Exospheric Very-Low-Frequency Noise

(Kiss),

Planet. Space Sci., 11, 36l - 369, April 1963.

Duncan, R. A. and Ellis, G. R.

Simultaneous Occurrence of Subvisual Aurorae and Radio Noise on 4.6 kc/s.

Nature, 18^, I6l8, 1959.

Ellis, G. R. A.

Low Frequency Electromagnetic Radiation associated with Magnetic Disturbances,

Planet. Space Sci., 1, 253 - 25S, 1959.

Finch, H. F. and Leaton, B, R.

The Earth's Main Magnetic Field-epoch 1955.

Monthly Notices Roy. Astron. Soc, Geophys. Suppl., 7 (6), 314 - 317, 1957.

Martin, L. H., Helliwell, R. A», and Marks, K. Ro

Association between Aurorae and VLF Hiss Observed at Byrd Station, Antarctica,

SEL, Tech. Rept. 1, Stanford University, April 29, I960.

McDiarmid, I. B., Burrows, J. R,, Budzinski, E. Eo, and Wilson, M. D.

Some Average Properties of the Outer Radiation Zone at 1000 km.

Can. J. Phys., L^, 2064 - 2079, December 1963.

Mcllwain, C. E.

Co-ordinates for lapping the Distribution of Magnetically Trapped Particles,

J.G.R., 66, 3681, 1961.

Watts, J. M., Koch, J. A., and Gallet, R. M.

Observations and Results from the "Hiss Recorder", an Instrument to Continuously Observe VLF Emissions,

J. Res. Nat. Bur. Standards, 67D, 569, 1963.

92
Fifflire Captions

Fig. 1 Polar map showing contours of constant L at 1025 km, and the

track of particular satellite pass which recorded VLF data

discussed in this paper.

Fig. 2 Example of ionospheric noise which exhibits systematic changes

in the spectral distribution of the noise with satellite

latitude.

Fig.. 3 (same caption as for Fig. 2).

Fig. 4 (same caption as for Fig. 2)

.

Fig. 5 Spectramme of VLF ionospheric noise observed in Alouette 1 on

31 January, 1963, 1057 - 1U8 UT. The track of the satellite

for this recording is shown in Fig. 1. The captions on the

three segments shown refer to the telemetry station where the

data were recorded (the equatorial segment is not shown).

Fig. 6 Recording of VLF hiss made on three narrow band noise burst

receivers at Ottawa (L '^ 3 •6) at the frequencies shown. Time

narks are put on the record at hourly intervals. The base line

for no (or little) noise can be seen at the beginning of the

recordings.

_Fig. 7 Plots of f, (the lower edge of the noise band that shows

systematic changes in spectral distribution with satellite

latitude) versus B (the minimum value of the strength of the

earth^s field on the field line at which the noise was observed)

for several different events- The dashed line is drawn for

f = 0.15 fu (or f = 4.2 X lO'^B ) which is discussed in the text.

n o Fig. 8 Amplitude-frequency spectra in nepers (which is proportional to

the interaction parameter s/>, for the TVJT process as shown) for

stream particles of small pitch guided along the field line

terminating at geomagnetic latitude 60**. At other latitudes

frequencies scale so that maximum amplification occurs at the

frequency given by the dashed curve.

Fig. 9 Amplitude-frequency spectra of hiss generated on field lines of

60° and 63.5° geomagnetic by the doppler shifted cyclotron processes by mono-energetic electron streams having a pitch angle

distribution produced by isotropic injection in the equatorial

plane, A finite stream width would smooth out the discontinuity

which occurs at 0.55 fir.

93
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100
The Interaction of an Antenna With a Hot Plasma and

the Theory of Resonance Probes

J. A. Fejer

Southwest Center for Advanced Studies

P. 0. Box 8478, Dallas^ Texas

The impedance and the radiation field of a short antenna, which

consists of two spherical conductors excited through very thin wires

in phase opposition, is calculated. In the calculations the pressure

tensor is replaced by a scalar pressure. A discontinuous model of the

ion sheath is used.

The losses due to the radiation of electromagnetic and electronacoustic waves are calculated and are expressed in terms of equivalent

series resistances. The operation of resonance probes is discussed.

It is shown that their resonant frequency is well below the electron

plasma frequency if the probe radius is much larger than the Debye

length. The significance of this result to both past and future

ionospheric rocket probe experiments is pointed out. The limitations

of the present treatment are discussed.

Presented at the Conference on Non-Linear Processes in the

Ionosphere, Dec. 16, 17, 19^3^ Boxilder, Colo.

101
1. Introduction

Antennas Impedance measurements in the ionosphere during rocket

flights show the presence of a much larger resistive component (Whale^

1963) than is predicted by the type of antenna theoiy, in which the

surrounding plasma is treated as cold. In principle the interaction

of an antenna with a hot and very tenuous plasma could be treated by

solving a combination of the collisionless Boltzmann equation with

Maxwell's equations. The mathematical difficulties of solving these

equations and staisfying the appropriate boundary conditions appear

to be formidable.

In this paper the problem is considerably simplified by the use of

certain approximations. The first of these is the use of a scalar

pressure (Spitzer 1962; p.. 24). The problem is further simplified by

the rather crude assumption that the plasma surrounding the antenna is

sharply bounded and that outside the boundary the plasma is uniform.

These approximations are applied here to a simple "spherical" dipole

antenna that consists of two spheres excited in phase opposition through

wires whose capacity -is neglected. For other applications of the same

type of approximations the reader is referred to papers by Gould (1959),

Fejer (1963), and Nickel, Parker, and Gould (1963). The present

analysis and its conclusions are entirely different from those of Whale

(1963) who also treated the excitation of electron-acoustic waves by

102
introducing the concept of an isotropic pressure. Whale assumed the

existence of interaction between the fluctuating quasi-electrostatic

field and the electron-acoustic waves throughout the uniform plasma.

In the present treatment the only interaction is taken to occur at

the inner boundary (in reality in the sheath). Within the uniform

plasma the electron-acoustic wave and the electromagnetic wave (or in

the present limit the quasi-electrostatic field) propagate independently

(c.f., for example Ginzburg 1961) and therefore cannot interact in terms

of the hydrodynaihic approximation.

2. The Excitation of Electron-Acoustic Waves

It is only necessary to consider one of the two spheres of the

antenna described in the introduction here. It is assumed that the

unperturbed electron concentration vanishes for r < R, and has the

constant value N for r > R, where r is the distance from the center

of the sphere. This is admittedly a rather artificial model of the

unperturbed ion sheath. It effectively assumes an abrupt potential

barrier (this could be visualized as a hypothetical double-layer

formed from infinitely heavy positive and negative ions) at r = R

which prevents the penetration of electrons inside the sphere at r = R.

It is clear that the radial component of the mean electron velocity must

vanish at r = R. Immediately inside the sheath there is assumed to be

a spherical conductor whose (quasi-electrostatic) perturbation potential

is taken to be a harmonic function of the time. (In principle the

radius of the conductor could be taken as smaller than R without essentially

modifying the analysis; this will not be done here.) Since there is

no mean radial motion of the electrons at r = R, there is no fluctuating

103
charged surface layer there and therefore both the perturbation potential V

and its normal derivative must be continuous at r = R. Inside the

plasma the equation

nc^f^'di^At- Ae 7V- YKTvn (1)

is taken to be valid where m is the mass, e the absolute value of the

charge, N the unperturbed number density and n the perturhation in

the number density of electrons (factors e are taken for granted in

n and in V) K is Boltzmann's constant, T is the temperature, and where

the ratio ^ of the specific heats is taken as 3 (Spitzer 1962). A

combination of the divergence of equation (1) with the equation of

continuity (satisfied by the velocity v, of the electron gas)

Y.(l\!v-)^-S^/B't (2)

leads to

A combination of equation (3) and Poisson's equation in spherical

coordinates and with spherical symmetry:

leads to

y^= 5^ ^r 5^=^^ (5)

where O^ ~ ^^ '^^/^J ^kl^V 'vsW ^^ ^^^ electron plasma

104
frequency and 11/ ~ \ C n i /^y is the velocity of electron-acoustic waves

in the high frequency limit (CO»CJ^).

The general solution, which vanishes at infinity, of the differential

equations (4) and (5) has the form

e

m. -t

^

(7)

where that part of the solution which is associated with the constant C^

,

describes an electron-acoustic wave, whereas the part associated with C.

describes a quasi-electrostatic field (the so-called induction field)

which is a good approximation to the electromagnetic wave field within

distances very much shorter than a wave length from the antenna.

The boundary condition v = at r = R yield with the aid of

equation (1)

Substitution of n and V from equations ^,6) and (7) into equation (8)

leads to the relation

Q-^'rr^h^>o-<^T^y'"^Q (9)

'2 ^' ^.H^/-^y N ^ a/ Substitution of C„ from equation (9) into equations (6) and (7) leads to

the following relationship between the perturbation in the number density

and the perturbation potential V at r = R:

105
Similarly, the effective, complex capacity of the conductor, defined

here as the ratio of the charge on the conductor to the potential V(R)

is given by

Wr

v^) '-''^''^T'Rj^FaJ^--'

''''

Equations (6) , (7) , (9) , (10) , and (11) represent the main results

of this paper and a discussion of their significance follows here.

Equation (11) may also be used to calculate the impedance Zl.rr~ [t^L rjj

of the antenna. The energy loss due to the radiation of electromagnetic

waves has not as yet been included in the analysis; this will be done in

a subsequent part of the present paper. The resistive part of the

impedance Z ,, represents only the energy loss due to the "radiation"

of electron-acoustic waves.

It is convenient to express the impedance Z ^.^ as a function of

the parameters / ~ \^ ICg lOj/ (the free space reactance of a sphere of

radius R), Q~ /V^^(the ratio of the radius R to ^^ times the Debye

length^, and j ~ CJ/uJ^ (the ratio of the frequency to the electron

plasma frequency). The result is y

It is clear from equation (12) that Z ^^is pure imaginary for

T'^ I ox Cj'^oJ . The absence of a loss term is explained in this case

by the absence of propagating electron-acoustic waves. It may be seen

from equation (12) that the impedance becomes infinitely high at the

plasma frequency and vanishes at the frequency where

106
I O I \l r ^ (y . More will be said about the significance

of this frequency later. At very low frequencies Z j-r: = - 1/(1 + S)~ >

and thus the impedance is smaller than the free space impedance by a

factor (1 +S) • It is understandable that the effective capacity of

the sphere is larger at low frequencies than the free space capacity

because the alternating electric field does not extend to infinity but

is confined to within the plasma sheath which in the case of large a

is much smaller than the radius. Figure 1 shows for 7 "^ / the ratio

of the imaginary part of Z ^.^ (the real part is zero for r'<- 1) to the

magnitude / of the free space reactance as a function of the ratio

/ ~ OJ/^^i^ of the frequency to the electron plasma frequency for

different values of the ratio <3 of the radius to C^ Debye lengthi The

curve for<J ~ *^^ represents the well-known approximation in which thermal

motions are neglected and the plasma is treated as a dielectric with an

effective dielectric constant ^o\\ ~~ ^hil^J'

Fory^>/ it is convenient to write equation (12) in the form

^-ff i + s'c^'-o ^7+g^r)i.^-7r

Figure 1 also shows the real and the imaginary parts of Z ^.^ for

(in units of/ ) as a function of / , for different values of ^, for ^ >1,

The case of <j='0<5 again represents the approximation in which thermal

motions are neglected and the plasma is regarded as a dielectric. The

curves of Fig. 1 show the presence of a resistive component of the

impedance for finite values of <0 . The resistive, ohmical component

represents the energy loss caused by the generation of electron-acoustic

107
waves.

3. The Radiation of Electromagnetic Waves by Two Spherical Conductors

Excited in Antiphase

The analysis of this paper can be extended to include radiation

losses due to electromagnetic waves. The analysis of electromagnetic

radiation by spheres oscillating in antiphase is of course somewhat

artificial because in practice antennas resemble cylindrical conductors,

rather than two spherical conductors excited in antiphase through thin

wires whose capacity is neglected here. It is, however, relatively

simple to extend the present analysis to cylindrical conductors, at

least in an approximate manner; this extension, whose results may be

expressed in terms of Bessel functions, is not carried out in the

present paper. The analysis of spheres oscillating in antiphase is

considerably simpler and it illustrates the nature of the problem

rather well.

If the distance D between the two spheres is much smaller than the

electromagnetic wavelength (and at the same time R <::^ D) then the

quasi-electrostatic field at a distance r >>> D on the line connecting

3 the spheres is 2C„D/r , where C„/r is that part of the potential given

by equation (7) which could be regarded as an approximation to the

radiation field of a spherical radiator at distances much smaller than

the wave length. At distances much longer than a wavelength and in

the plane that perpendicularly bisects the line connecting the two

spheres, the magnitude E of the radiation electric field of the dipole

108
(14)

antenna is then given by

The radiation magnetic field H is given by

^

(s, QDA^[((v^-^^V A^\ (15)

where k is the wave number and c is the velocity of electromagnetic

waves in vacuum. Equations (14-) ai^d (15) were derived by fitting the

quasi-electrostatic dipole field to the radiation field of a dipole

(Stratton 1941) in a medium with a dielectric constant £" { XT ^'^^u /OOJ

Equations (6) , (7) , and (9) can then be used to express C„ in terms of

V(R) , the alternating potential of one of the spheres or in terms of

the current supplied to the spherical conductors I = iCjC rfV(R) where

C j-c, is given by (11) . The Poynting vector E x H may then be expressed

in terms of I, and the total radiated power P may be found by integration

over a very large sphere. The result is

?= ^Tey'D'oo c'(o^'-^,') 'I^ (16)

and therefore the resistive component of the antenna impedance (the

radiation resistance) due to the radiation of electromagnetic waves is

f„

= (c re/Di c-'fcv'-o)/) ^

(17)

The resistive component due to electron-acoustic waves is given by

/ equation (13) as ^ ,r 2 ,^ Z

K^^ i^i'(f-i)

109
Equations (17) and (18) show that P is zero at the electron plasma

) lY) frequency and increases rapidly with frequency whereas O is infinitely

high at the plasma frequency and decreases rapidly with frequency.

It is interesting to note that the expression (17) for O is the

same as the expression for the radiation resistance of a short antenna

of length D (whose capacity is entirely at its extremities) situated in

a medium with a dielectric constant^f (/—^^^/^ y. This is a significant

result in view of the fact that in the calculation of the series reactive

part of the antenna impedance the plasma can not be replaced by a medium

with a dielectric constant ^,(\-^M

4. Application to Resonance Probes

The results of the previous section may be used to draw some

tentative but very important conclusions about the behavior of resonance

probes (Miyazaki et al, 1960). In such probes the change in the collected

direct current,, caused by the application of a radio frequency voltage

is measured as a function of the radio frequency. It has been usually

accepted (Miyazaki et al, 196Q) as an experimental fact that the change

in the collected current shows a resonant increase at the plasma frequency.

In this section the point of view is taken that the change in the

collected direct current is due to rectification cause by the non-linear

characteristic of a Langmuir probe. The amplitude of the radio frequency

variations in the collected current will be proportional to the

fluctuations n(R) in the number density (in a more accurate treatment

the fluctuation in temperature would also have to be taken into account

110
but these would in any case be proportional to the fluctuations in

number density) and therefore equation (10) should really give the

characteristics of a resonance probe. Using the parameters o and

/ equation (10) may be written in the form

01 CR) = Ycr) T^fh 777^,

J

(15) ^f I / (j- y'JEquation (19) shows that n(R) becomes infinitely large at the frequency

for which

^-{frfii-ci^^&f/f

I

(20)

This shows that resonance occurs near the electron plasma frequency

(jr^ I ) only when^*^"^^ ; for large values of <j the resonance occurs

well below the plasma frequency. Fig. 2 shows (t iV/(^u ^J I ^

fT^)/ VH^-^

as a function of f for two values of h . Fig. 2 illustrates that

resonance occurs well below the plasma frequency when the probe radius

is much larger than the Debye length. The resonant frequency given by

(20) is the same as the previously discussed frequency where the impedance

of the probe vanishes.

The present analysis clearly leads to the conclusion that the

resonant response of the probe does not occur at the plasma frequency,

as laboratory and space experiments are claimed to show, but always

below the plasma frequency. Large errors could thus occur in rocket

investigations of electron concentration in which the resonant frequency

was identified with the plasma frequency, especially if the radius of the

probe were much larger than the Debye length. Fortunately a relatively

111
I

small sphere (R = 1 cm) was used in the ionospheric experiments (Aono

et al, 1962) reported so far.

A discussion of the physical nature of this resonance sheds some

light on the reasons for the occurrence of the resonance well below the

plasma frequency. It is clear from equation (7) that the electric field

of the probe consists of two parts. One is simply a quasi-electrostatic

field, which at short distances is the approximate form of the radiation

field for frequencies above the plasma frequency whereas the other is the

field associated with an electrorwacoustic wave which is evanescent at

frequencies below the plasma frequency.

At very low frequencies the quasi-electrostatic field becomes very

small compared to the field of the evanescent electron-acoustic wave.

This means that the alternating charge on the conducting sphere is almost

perfectly shielded by a suitable (continuous) modification of the sheath.

As the frequency is increased, the shielding becomes less perfect and

a potential C„/r appears outside the sheath. The present theory shows

that the outside field opposes in phase the field within the sheath.

With increasing frequency a situation is reached eventually where the

potential drop outside the sheath just balances the potential drop

inside so that no exciting voltage is required on the conductor and

resonant oscillations occur.

This explanation of the resonance is strongly supported by the full

agreement, in one special case, of the present approximate calculation with

Landau's (1946) more accurate analysis utilizing the collisionless Boltzmann

equation. Landau considered the penetration of an alternating electric field,

that is normal to a plane boundary, from empty space on the one side of the

112
boundary into a uniform plasma on the other side. He showed that at

frequencies slightly below the plasma frequency the field asymptotically

approaches a value which is equal to (1-6A//6J) times its value at the

boundary. The field deep inside the plasma is thus out of phase with the

field at the boundary. Equations (6), (7), and (9) of the present paper

lead to the same asymptotic value if R and r-R both approach infinity and

at the same time satisfy the inequality R>^r-R. Landau also showed that

the asymptotic value is approached according to a simple exponential law

expressed by his equation (45) . Essentially the same exponential law

with the same exponent (-o(r in equation 6) results from equations (6),

(7), and (9) of this paper.

An alternative, simpler but less quantitative, explanation is that

the resonance frequency of the probe is lowered by a tight coupling to

the medium. For a very small probe which is weakly coupled to the

medium, the resonant frequency will be nearly equal to the plasma

frequency. A larger probe has a lower resonant frequency because it

is more tightly coupled to the plasma.

5. Conclusions

The simple analysis of this paper leads to certain interesting and

significant results about the behavior of antennas in plasmas and about

the interpretation of observations with the aid of resonance probes in

plasmas. It is shown that resonance does not take place at the plasma

frequency and that previous measurements made by the resonant probe

method may have to be reinterpreted. In principle both the concentration

and the electron temperature could be determined by simultaneous

measurements of the resonant frequencies of two resonant probes of

different size. The same information could be obtained from a single

probe if an additional measurement (such as the additional direct

current at very low frequencies) was made besides the determination Of

the resonant frequency. Impedance measurements (not necessarily above

the plasma frequency) could also be used to determine the electron

113
concentration and the electron temperature. It is to be remembered,

however, that the results of this paper must be regarded as merely

semi-quantitative in view of the oversimplified nature of the underlying assumptions.

The present treatment could, in principle, be further refined by

using a more sophisticated model of the sheath even if the use of a

scalar pressure term were retained. The treatment could also be applied,

in principle, to conductors which have other shapes than spherical.

The most severe shortcoming of the present approach is undoubtedly the

use of a scalar pressure term and it is to be hoped that a calculation

with the aid of the collisionless Boltzmann equation will be attempted

in the future. It is also to be hoped that the conclusions of the

present paper will be submitted soon to an experimental check.

ACKNOWLEDGMENTS - The benefit of discussions with Drs. J. E. Midgley,

H. B. Liemohn, and W. B. Hanson is acknowledged. Thanks are due to

Miss J. Ligon for assistance with the computations. This research was

supported by the National Aeronautics and Space Administration under

grant NsG-269-62.

114
REFERENCES

Aono, Y. , K. Hirao and S. Miyazaki (1962), "Profile of charged particle

density in the ionosphere observed with rockets," Space Research III ,

221 (North-Holland Publishing Co. , Amsterdam)

.

Fejer, J. A. (1963), Scattering of electromagnetic waves by a plasma

cylinder, Phys. Fluids . In the press.

Ginzburg,, V. L. (1961), Propagation of electromagnetic waves in plasma,

(Gordon and Breach, New York).

Gould, R. W. (1959), Experiments on plasma oscillations. Proceedings

of the Conference on Plasma Oscillations (Linde Company, Indianapolis,

Ind.).

Latidau, L. (1946), On the vibrations of the electronic plasma, J. Phys .

I

U.S.S.R. , 10, 25.

Miyazaki, S. , K. Hirao, Y. Aono, K. Takayama, H. Ikegami and T. Ichimiya

(1960) , Resonance probe--a new probe method for measuring electron

density and electron temperature in the ionosphere--. Rep. lonos .

Space Res. Japan, 7_, 148.

Nickel, J. C. , J. V. Parker and R. W. Gould (1963), Resonance oscillations

in a hot nonuniform plasma column, Phys. Rev. Letters , 11 , 183.

Spitzer, L. , Jr. (1962),, Physics of Fully Ionized Gases (Interscience

Publishers, New York and London).

Stratton, J. A. (1941), Electromagnetic Theory (McGraw-Hill, New York

and London)

.

Whale, H. A. (1963), The excitation of electroacoustic waves in the

ionosphere, J. Geophys. Res . , 68 , 415.

1

115
CAPTIONS

Fig. 1. The ratios of the real (interrupted line) and imaginary

(solid line) parts of the impedance to the magnitude of the free space

reactance as functions of the ratio Y °f the radio frequency to the

electron plasma frequency.

Fig. 2. The dimensionless quantity (EW/^i^^jl^Cl^)/VCjw'n.ich is

proportional to the number density fluctuations |^ (R) produced by a

given rf voltage V(R) , as a function of the ratio [ of the radio

frequency to the electron plasma frequency.

116 1
}-l

(1) rt ri ti +j , . <+-( <u o a

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r—t

•r-( o

rn

m^

>^u

l/J

a rt a (1)

9,

>>u

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u 0)

rtt

d

'd <u cr ^

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ua rH CO to T3 1> (D

(U

r-la, VH ti

>H (U

u

t->

(-> ()

•H

CD

4)

i-H0) rH T) (U lO ;i si

U)

u -M ^ 1-1d

(D 00 -«->

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>+-(

a

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)-> cr

•iH o <u

4->

u tl> C)

O

J3

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ct

H XI

(Ua (U 1—t P -£} ^ (U o

117
«

o

«

p6>

&

mu

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a

m>

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uu

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|(d)A/(d)u|(°3^/2na)

118


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