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vol,.
84, NO.
Ag
l.
INrnopucrroN
Long-delay
echoes
(LDE),
defined
as radio
echoes
received
seconds
after
transmission,
have
been reported
in
the
literature
almost from
the discovery
of
the ionosphere
to
the
present
time. The
first
observations
were
apparently
made
by
Hals
U9341,
who
informed
Stdrmer
ll929a).
Some of the
latest
reports
have
been by
radio
amateurs
lRasmussen,
1975,
1976;
Goodacre,
1976;'
Yurek, 1978].
The most
convincing
case for LDE has
been made
by radio
amateurs in
an
impressive
collection
of
reports
tabulated
by
Villard
et
al.
U969,,
1970,
l97ll. However,
Villard
et
al.
[1971]
point
out
that
there
is a
very
real
possibility
that LDE
are
a
result
of hoaxes
and
practical
jokes.
Also, LDE have
not
yet
been
generated
at
will.
Until
this happens
there
will
be
skep-
tics.
Sears
U974)
has
used the
amateur
reports
(l
14
in
all) col-
lected
by
Villard
et al.
U970,
l97ll
to
do statistical
studies. No
reliable
dependence
of the
occurrence
of LDE
on latitude,
operating
power
or magnetic
activity
could
be
determined.
However,
there did appear
to be a significant
difference
be-
tween the
time
delay
of the
LDE in
the
3.5 MHzband and
the
delay
for
the
other amateur
bands
(7,
14,21,
and 28 MHz).
Of
the l7 LDE
in
the 3.5 MHz
band
only two
had
delays
in
excess
of
6
s and ten
(60Vo)had
delays
of
about
I s
or
less.
In
the
other
4
bands
the
number
of
echoes
with
delays of
about
I
s or
less
varied
between
9Vo and
l4%o.
In
Villard
et al.
[1970]
there are
two
reports
at
frequencies
below 3.5
MHz
(0.85
MHz),
one
with
a delay of 0.5-2
s and
the other
with
a delay
of
0.25-0.5
s.
f his
finding
(that
there
is
a
different
occurrence
frequency with
delay
at
frequencies near
and
below
3.5 MHz)
has
physical
significance,
which
will
be discussed
below. It
may
also
in-
dicate
that not
all
of
the
LDE
are the result
of hoaxes
and
practical
jokes.
It
seems unlikelv
that hoaxers
and
practical
Copyright @ 1979
by the
American
Geophysical Unron.
Paper number 9A0567.
0148-0227
/79 /0094-0567$01
.00
SEPTEMBER
I, 1979
jokers
would
operate
in
such
a way
as to
generate
a
different
occurrence
frequency
with
delay
on the 3.5
MHzband
than on
the
other
bands. H
owever,
there is
the
possibility
that
the
delays
of
about
I
s or less
on
the 3.5
MHz
band are a
real
effect
which
does
not
occur
on the
other
bands. When
this
real
effect
is
removed,
a
similar
occurrence
frequency
with
delay occurs
on
all
bands.
Sears
U9741
points
out that round-the-world
ech
oes
flsted,
1960J
have
delays
of about
0.
14
s
and
tend
to
occur
more
frequently
at
frequencies
above
3.5
MH
z than
near 3.5
MHz.
Hence round-the-world
echoes cannot explain
the different
occurrence
frequency.
A
n
explanation
for
echoes
of delay
about
I
s or less
at frequencies
of
3.5 MH
z
or less
is
given
in
the section
on electromagnetic
ducting.
Controlled experiments
have
been
carried
out by Budden
and Yotes
119521,
Crowford
et
al.
[1970]
and by
Duffett-Smith
il975].
Budden
and Yates,
in
about 27,a00
transmissions,
did
not
detect
a single
LDE nor
did
Duffett-Smith
in
about
one-
half million
transmissions.
Crawford
et
al.
believe
they re-
ceived several
good
examples
of LDE
which
were
Doppler
shifted
and
distorted.
Explanations
of LDE
have
been many
and
varied.
Perhaps
the
most
far-fetched idea
is
by
the
science-fiction
writer
Lunan
U9731.
He
suggested
that
a number
of
transmissions
by
Stor-
mer
and
van
der Pol
luan
der Pol,
1929)
were
received
by an
extraterrestrial
vehicle
in the
vicinity
of
the
earth
and
retrans-
mitted with
varying
delays
to
signal its
presence.
The
retrans-
missions
were
received
by
Stormer and van
der
Pol
as LDE.
The varying
delays
were
a
code
indicating
that the
craft
was
from
near
the star Epsilon
Bobtis.
Reflections
of the
signals from
ionization
clouds
fstdrmer,
1930b;
Rasmussen,
19751,
particles
fClark,
l97l;
Cohen
et
al.,
1978J
and natural
or artificial
satellites in
the
interplanetary
medium
have
also
been
proposed.
Doppler
shifts
would be too
great
and received
signals
too
weak
for
these
explanations
to
JOURNAL OF
GEOPHYSICAL RESEARCH
Generation
of Long-Delay
Echoes
D.
B. Mulnnrw
Communications Research
Centre, Department
of Communications,
Ottawa,
Canada K2H
852
Long-delay
echoes
(LDE),
defined as echoes received
from a fraction
of a second
to several seconds
after a radio
signal
is
transmitted, have
been observed
off and
on for about
50
years.
A variety
of
explanations has
been
proposed
in the
past
but none is
completely
satisfactory. The
following models are
presently proposed
for LDE:
(
l) Radio waves
of frequency
less
than about 4 MHz
can become trapped in
magnetic
field-aligned ionization
ducts with
l,
values less
than
about 4. These waves
after being
trapped
can
propagate
to the opposite hemisphere
of the earth where
they
become reflected in the topside
ionosphere.
They
can then
return
along the duct, leave it
and
propagate
to the receiver.
Delays
of
up
to 0.4
s
result
and they
probably
account for most of the LDE at frequencies
below 4
MHz
with
estimated delays
of l-2
s.
(2)
The
signals from two separated
transmitters T,
and Tr,7,
transmitting
a CW or
quasi-CW
signal, interact nonlinBarly
in the ionosphere
or magnetosphere.
Ifthe
wave
vector
and frequency ofthe
forced oscillation
at
the
difference frequency
of the two
signals satisfies
the dispersion relation for
electrostatic
waves,
such a wave
would
exist and begin to
propagate.
This wave
eould
grow
in amplitude
due to wave-particle
interaction. At
a
later
time it
could interact
with
the
CW
signal
from 7, and if the
wave vector
and
frequency
of the forced oscillation
at the
difference frequency
(frequency
of
I,)
satisfy
the dispersion relationship
for electromagnetic
waves,
such
a wave would
exist and
could
propagate
to fl,
or some other receiving
station tuned to
the frequency of 7r. Reasonable
ionospheric
and magnetospheric
plasma parameters
lead
to delays of up to
about 6 s
with
this model.
(3)
A large
percentage
of LDE
have
been reported
with
delays
of tens
of seconds. These
delays could be explained
if the model in
(2)
is applied
to
a magnetospheric
ionization duct.
Electrostatic
waves
could
propagate
for
about 1000 km
or more over
the magnetic
equator
in
such a duct and delays
of about 40 s
are
possible.
Dispersion for
a
finite
frequency
bandwidth would
probably
not be so large in
cases
(l)
and
(2)
as to make voice
unrecognizable.
Dispersion
in model
(3)
for
delays
greater
than
about l0 s
would
normally
be too severe
for
voice
modulation,
but occasionally compensating
effects
might
occur
for
which
voice would
be recognizable.
5199
s200
be
plausible.
Electromagnetic
wave
propagation
around
the
earth
via
multiple
reflections
from
the
ionosphere
fAppleton,
19291,
or
slow
group
velocity
luan
der
Pol,
1929), has also
been
proposed.
In these modes the
electromagnetic
waves would
spend a
good
fraction
of their time
in
the
dense
F
region
of the
ionosphere
where
electron-ion damping
would
be
prohibitive
lThomas,
1929;
Crawford
et
al.,
1970).
Since
the
phase
velocity
of
these
modes is
greater
than the
free-space velocity
of
light,
growth
by
wave-particle
interactions
is not
possible.
Crawford
et
al.
U
9701
and Sears
U974)
have
proposed
that a
transmitted
electromagnetic
wave
of
frequency
/
couples
into
an
electrostatic
wave
of the same
frequency near
the
height
at
which
the
plasma frequency
/n
-
f
.
This electrostatic
wave
can
then
grow
by
wave-particle interaction sufficiently
to
offset
damping.
Crawford
et
al.
estimate
the
electrostatic
wave prop-
agation
time could be of the
order of l0 s.
The
electrostatic
wave
then couples
back to an electromagnetic
wave
which
can
be
detected
as an
LDE,.
In this
paper
a
mechanism
which
is in
some
ways
related to this
is
proposed.
The mechanism involves
wave-wave
interactions in addition
to
wave-particle
inter-
actions.
It
has
the advantage
over
the
proposal
by
Crawford
et
al. that
is
can
be
applied
up
to
frequencies of
about 2000 MHz.
For higher
frequencies, ionospheric
plasma
frequencies
greater
than
about
l0 MHz are
required
to
limit
Landau
damping
of
the
electrostatic
waves.
The highest
frequency
for
a reported
LDE is
1296
MH
z
fRasmussen,
1975,
19761.
There
are two
known
echo-delay
mechanisms
which
can
occur
in
the
ionosphere and
which
have not
yet
been
presented
in the
literature
as
possible
explanations
of
LDE.
'Remote
resonance'
ech oes
lHagg,
1966;
Muldrew,
1967b)
occur at fre-
quencies
near
the
second harmonic
of the
gyrofrequency.
'Ion-
ospheric
resonance' echoes
lMuldrew
and
Hagg, 1970] occur at
frequencies
near the
plasma
frequency
resonance. LDE
have
been
observed
at
frequencies much
above
these
frequencies
and hence
these
resonance
effects are
not responsible
for
LDE.
Several
limited
reviews
of
LDE are
available
lBudden
and
Yates,
1952;
Crawford et
al.,
1970;
Villord
et al.,
1969, 1970,
197 l; Duffett-Smith, 1975;
SeArs,
19741.
The
history
of LDE
is
fascinating and
reading
the
old
papers
on the
subject
can
be
amusing
as
well as
educational.
A fairly complete history
of
LDE is
included
in this
paper.
2.
Hrsrony
In the spring
and summer of
1927,
J,
Hals received
some
long-delay
echoes
(about
3-s delays)
of transmissions from
the
Dutch
station PCJJ, Eindhoven at his
home
near
Oslo.
During
conversation
with
C. Stormer
in
December 1927 he mentioned
these and
suggested that
they
were
reflected from
the moon.
Stdrmer
ll929a)
thought
they must
be reflections from
the
toroidal surfaces
bounding
the
region
near the
earth free of
charged
particles
(see
below).
Stbrmer
asked Hals
for
a
written
report
which
he received
on
February
29,
1928
fStdrmer,
1929a).
I
n December 1927
,
Stormer
arranged
an experiment
in-
volving
the
transmitter
at
Eindhoven,
a
receiver
at Fornebo,
near
Oslo,
and H als'
private
receiver.
Oscillograms
received
January
31,
February
2, and March 29 showed
nothing re-
markable.
On
April 3,,
Hals heard
excellent
echoes.
The film
from
the oscillograph at Fornebo
'gave
very
distinct signals
from
Eindhoven,
and
also
showed
some similar
signals
which
were
either to
be attributed to atmospheric disturbances or to
echoes.' No certain conclusions
could be drawn
from
the
film
and
Stbrmer
rejected
it
as a
proof
of
LDE
lStdrmer,
1930b).
Mulpnsw: GENERATToN
oF LoNc-DELAy
EcHoss
Hals
[1934]
listed
27
of
his
observations
of
LDE made
between
April 1927
and
November
1929.
Stbrmer
and
B. van
der Pol
carried
out experiments in
July
1928
with
negative results.
After this,
they arranged
an experi-
ment
between Eindhoven and
Oslo.
A
9.55
MHz signal con-
sisting
of
3 dashes
was
to
be
transmitted
every
20
s.
Hals was
to
listen
for
echoes and if he heard
them
he
was
to telephone
Stbrmer
who
could
walk
to
Hals'
house
in l0
minutes.
Trans-
missions
began September
25.
On
October
I
I
they
heard
the
first
'undoubted
echoes.' The
following
quote
is from
Stiirmer
[
1e300]:
I observed the
phenomenon
with
Mr. Hals
the
last
quarter
of
an
hour, and
noted the approximate
interval between signal and
echo. As a rule each
signal
gave
one echo,
now
and then
several.
The
echo usually
consisted
of
3
dashes like
the
signal, but
some-
times the 3 dashes
were
joined
together,
and
it also happened
that
the echo
was
drawn out
into
a
longer note than
the
signal.
The
pitch was
the
same
as that
of
the signal. I
noted in
seconds
the
following
intervals
of
time
between
signal and echo:
15,9,4,8, 13,
8,, 12,
10,
9, 5, 8,
7,6
and 12,
14, 14,,
12,8 and
12,5,8 and
12,8,14,
14, 15, 12,,7,5, 5,
13,8,
8,
8, 13,9,
10,7,6,9,5 and
9.
With
regard
to strength,
the
signals
were
so
powerful
that
they
hurt
our ears,
and
the
echoes
were
also
very
strong even
though
they
were
far from being as
powerful
as the signals. The
atmo-
spheric disturbances
were
at
a
minimum,
so
that the
loudspeaker
could be
amplified to a considerable
extent.
Stbrmer
informed
van der
Pol
of
the echoes by telegraph;
van
der
Pol arranged a
special
experiment
in
the evening
and
received echoes
of between
3
and
15
s
delay.
There
was
no
D
oppler
sh
ift. Three dots
were
transmitted;
the
received
echoes
were
blurred
together
except
for one case
with
a
delay
of only 3
s
when the three dots
were
plainly
audible
in the
echo
luan
der
Pol,
1928, 19291.
Simultaneous
listening
periods
at Oslo
and the
two
Eindho-
ven
stations
were
agreed upon.
No LDE
were heard until
October
24,
when
a series
of
LDE
were
heard between
l6 and
l7
GMT
at
Oslo
and the
two
Eindhoven stations.
Several of
the echoes
were
heard simultaneously
at the
three
stations.
The
results
of this
experiment have
been
published
by uan der
Pol
U9291,
Stdrmer
U
955J,
and
Villard
et al.
[969].
On
November 3,
1928,
Stormer
wrote
a
letter to
Nature
lstdrmer,
1929a) and his
ideas
were presented
to
L'Academie
des
Sciences
by M.
H. Deslandres
lStdrmer,
1928a,
bl
on
November
5. Stbrmer
suggested
that
radio waves of
long delay
are
reflected from
the streams
of electrons outside
the
wall
of
the toroidal surface bounding
the
region,
free of charged
parti-
cles,
near
the
earth. According to Stbrmer,
this
region
is
formed
when
charged
particles
streaming
from
the
sun
interact
with
the earth's
magnetic field. Echoes
of
about
4-s
delay
were
from the surfaces formed by
electrons
and echoes of about
15-s
delay
were
from
the surfaces
formed
by
ions. These
were
the
regions
studied
by Birkeland
with
his terrella
lStdrmer,
19551.
At L'Acad6mie
des Sciences
meeting,
Deslandres
[928]
em-
phasized
the
importance of Stormer's
ideas. He had done
some
studies of the
sun near October
11,
1928,
and found
that
the
state
of the sun
was
favourable
to
the
emission
of electrical
particles
which
could
pass
close
to the
earth.
On
November
21, 1928,
uan
der
Pol
U929)
wrote a
letter
to
Nature and
suggested
that
Stormer's
idea couldn't
be correct
since
a
9.55
MHz
wave
would
be
reflected from
the
iono-
sphere.
He
proposed
that
the
waves
are'bottled'
in regions
of
the
ionosphere
where
the
group
velocity
is
near
zero.
On
November
27,
1928,
Appleton
U9291
wrote
a
letter
to
Nature
and
pointed
out
that
low-group-velocity
waves would
be too
severely
damped
by
electron-molecule collisions
to
remain
in the
ionosphere for
about
l0
s
unless the
waves
existed
above about
600
km
height.
He suggested
that
the
ionosphere
is a
reflecting
shell and
that
the
waves
focus
at a
point
near
the
antipode
and
near
the
transmitter.
These
points
vary
with
each
circuit of
the
earth and an echo is
heard
perhaps
several
seconds
later
when
the
focus
happens to coin-
cide
with
the
transmitter site.
Appleton
11929)
reported that
R. L.
A. Borrow
in
England
obtained
photographic
registration of
echoes
from
Eindhoven
with
delays of about
I
s.
In a letter
from Borrow to A.
T.
Lawton
lStoneley
and
Lawton,
19741,
Borrow stated that in
over
150
hours
of
listening
to
the
Morse
letter
'X'
transmitted
from
PCJJ, he heard no
more than
10
echoes.
He never
ob-
served
more
than
one echo
from any
emission
and he never
received
echoes
from
stations other
than PCJJ. Stoneley
and
Lawton
U9741
and Lawton
and
Newton
U9741
published
two
echo
sequences
they
claim
were recorded
by
Borrow near
1320
and 1330
GMT on
November 22,
1928.
In contradiction to
the
information
given
by Borrow in his
letter, a
total of 2l
LDE
are shown
in
their
diagram, including
multiple
echoes
from
a
single
transmission
in six
cases.
No
LDE
were observed
at Oslo and Eindhoven
for some
time after
October
24,
1928.
On
December 12,
1928,
Stiirmer
U929b)
suggested that
conditions
for
his
model for LDE
(see
above) are most favorable
in
the equinoxes.
Hence he
pre-
dicted
that
LDE would not
be heard until
near
the
spring
equinox
when
the angle
{
between
the earth-sun direction
and
the magnetic
equatorial
plane would
be
small.
Jelstrup
[928]
proposed
that LDE
result from multiple
hops
between
the
Heaviside layer
and/or
other
higher layers
and
the earth.
In January 1929, Thomas
U929)
pointed
out
that
it
is not
electron-molecule collisions but
electron-ion collisions
which
are important in the ionosphere and
that
the
low-group-veloc-
ity theories
of uan der
Pol
U9291,
and of Appleton
U9291above
600
km
height,
are
untenable.
In
February
1929,
Hals reported
echoes
of
4 min
20
s
and
3
min l5
s delay
fPedersen,
1929a,
b).
In March
1929, Breit
U929)
proposed
that
the
absorption
calculations of
Appleton
U9291
and of Thomar
I
19291may
be
incorrect
and
that
if
the
electron
distribution
with
height were
just
right, delays of 10 s
or
more
could
occur due
to
low
group
velocity.
Pedersen
|929a,
b)
showed
that, because
of absorption,
LDE
cannot be due to
waves
which
spend a
long
time
in
the
ionosphere.
Also, waves
guided
at
a conductive-non-
conductive ionospheric
shell boundary,
or
waves
undergoing
multiple reflections
inside
a shell
ionosphere
as
proposed
by
Appleton
U929),
would
also
suffer
prohibitive
absorption at
the
shell
and
the earth's surface. He supported
Stbrmer's
model
as
essentially
correct.
He
pointed
out
that
guiding
of
waves
around
the
'boundaries
of the tracks
of corpuscular
rays'would require
a much
smaller density
for
the solar elec-
tron streams
than
that
required by
Stbrmer's theory.
He
pre-
dicted
echoes
with
delays
of
minutes due to
reflection
from
'bands
of
ions
. . . outside the space
in
which
the magnetic field
of
the
earth
exerts any appreciable direct influence.'
He later
discovered
that Hals
did
observe
minute LDE
in
February
t929.
During
a
solar-eclipse
expedition in lndo China in May
1929,
an
incredible number
of
LDE
were
recorded in
a few-day
period
including
the eclipse date
lGalle,
1930a,
b;
Galle and
Mulonsw: GENERATToN
oF LoNc-DELAy
Ecsors
520 I
Talon,
1930].
A
sample
of data from
about an
hour
before
the
eclipse
to
about two hours
after the eclipse
is reproduced
by
Sti)rmer
[930b).
About
750 echoes were received,
fairly evenly
distributed
between the
transmitted
pulses
which
were
30 s
apart.
The
data
seem
unbelievable.
Galle and
Talon
[l930]
.
claimed
a
complete
disappearance
of
echoes
for 4.5 min
ap-
proximately
centered
on the
start
of eclipse totality which
lasted
about
5
min.
(Perhaps
no
echoes were
recorded
because
the
radio
operators
were
more
interested
in
observing
the
eclipse than
in recording
echoes.) Ferri|
[930]
stated
that
the
decrease
in
occurrence
during
totality casts
doubt
on
Stbr-
mer's
ideas
since
an eclipse
should have
no
effect on
the
path
of the
waves
to
the toroidal
surfaces
in
space and
a decrease in
electron
density due
to
the
eclipse
should not effect the
pene-
tration of the
waves
through
the
ionosphere.
He
stated that the
absence
of echoes
during
the eclipse
is
due to a
change
in
the
ionosphere
and hence
the delayed echoes must have
originated
in
the ionosphere.
He
then made the
suggestion
that
the elec-
troacoustic
oscillations reported
by Tonks and Langmuir
might
in some way
be responsible for
the
long delays of
the
echoes.
(This
idea
is related
to some
of those
presented
in
this
paper.)
He suggested
electron
oscillations
could excite similar
positive
ion
oscillations
which would propagate
with
a
velocity
of about I k*/t.
He
then asked if these ion
oscillations
could
play
a role in
the formation
of
delayed echoes due to their low
propagation
speed.
As
predicted
by
Stdrmer
ll929bl,
LDE
again appeared
near
the
spring equinox.
Hals
observed
echoes
on February 14,
15,
19,28 and
April 4,9, I
l, and
23,
1929.
Kleve
observed echoes
near
the
Arctic
circle
on
February l8
and
Appleton and
Bor-
row
atLondon
on
February
2A
$firmer,
1929c).
For all
these
cases
except
April
23,
the angle
t!
between
the sun-earth line
and the magnetic
equatorial
plane,
was
small;
r/
was
also
small
for
the
eclipse
data of
Galle. Stiirmer explained
the
absence
of
echoes
in
the
four minute
period
near
the
eclipse
as
simply
due
to the
effect
of the ionosphere
on the
waves propagating
to
the
toroidal
surfaces
lS
tdrmer,
1930a).
H
e suggested that
the
echoes
with
delays
from
15
to 30 s are reflected
from
the
annulus
outside the moon's
orbit
which
he
had
predicted
to
explain
the auroral
zone.
In
an
address
lsti)rmer,
1930b)
he
stated
that'from
the
observations
of
echoes
it seems as
if the
space
outside
the
moon's is
traversed
disruptedly
by
very
unstable
streams
of
electrons
each one
of
which
only lasts
a
short
time
only
to be replaced
by
another with
a
different
speed
and
distance
from
the
earth.'He
did
not
reconcile this
with
the
lack
of
a Doppler
frequency
shift
in
Hals' data.
Joos
[93
1]
pointed
out
that
group-velocity
dispersion
of an
ionospherically
reflected,
modulated (electromagnetic)
wave
of I
s delay
would
be so
great
that
a slow-group-velocity
type
of LDE would
not be
perceptible.
Janco
[934]
suggested
that
waves
responsible
for
LDE
be-
come
trapped
between
the
E and F layers,
become repeatedly
reflected
between
the two
layers,
propagate
around
the earth,
and
finally
return
to the
earth's surface.
I n
a series
of four
articles
in
World-Radio,
Appleton
U934a,
b,
c,
d]
discussed
the
observations
and
theories on
LDE
and
described
a
proposed
experiment
by the
World Radio
Re-
search League
(WRRL).
Transmissions
from
the
Empire
transmitter
GSB
and
League of
Nations
station
HBL
were
to
be
monitored
by radio
enthusiasts for
LDE.
Several
LDE were
reported
IWRRL,
1934-1935]
but at the
end
doubt
still re-
mained
as
to
the authenticity
of
LDE.
Dellinger
[934]
in-
formed
Americans
of
these experiments
in
QST
and
requested
5202
LDE reports
be
sent to
him for
forwarding
to the
WRRL.
There
was
apparently
no response
to
this
request.
In an odd
paper,
Ionesco and
Mihul
[1934]
stated that
there
are
many
ionospheric
layers, the
number being somehow
de-
termined by
the
electron collisional
period.
In each
layer
wherb
dN
/
dh
:
0,
where
N is the electron
density and ft
is the
height,
the
layer
acts
like
a channel and the
waves
can
go
around the
earth
several
times
in
these channels
at
low
group
velocity
and
slowly
send
their energy
back to
earth
in
the
form of
LDE.
Fuchs
U934,
19351
suggested
that
the
normal short-delay
echoes are reflected
low
in the
ionosphere
(presumably
the
so-
called
direct or low-angle
ray)
whereas
the
long-delay echoes
travel
closer to
the
peak
of
the
layer
where
the
group
velocity is
small
(presumably
the
Pedersen
or
high-angle
ray).
Collisions
are
electron-neutral
and
hence
not a
problem.
Fuchs
[935]
also tabulated and
analyzed
the
results
of
the
WRRL.
Interest
in LDE
seemed
to disappear in
1935 and did
not
reappear until
1947
when
Budden
and Yates
[1952]
again took
up the search. I n
27
,000
transmissions
from 1947 to
1949 no
LDE
were
identified.
They suggested
their choice of
frequen-
cies
(about
13.5 and 20.7
MHz)
was
too
high and
their
direc-
tion
of
transmission
too close
to
the
vertical
since initially they
thought the
echoes
were
reflected or
scattered off
large clouds
from
the sun.
They suggested
that in
further searches,
frequen-
cies
less than
l0 MHz
be
used and
that the direction of
radiation not
be
radially outward.
They tentatively suggested
that
LDE
'are
due
to the
propagation
of
guided waves
of
the
type
described
by
Pedersen . . .
over
long
curved
paths
formed
by
belts of
ions
outside
the earth
but
fixed relative
to it. .
. .'
(lt
will
be seen
below that
guided
electromagnetic
waves
can
probably
only
account
for
LDE
of
delays less
than
about 0.4
s
and
of frequencies less
than about
4 MHz.)
In his book, The
Polar Aurora, Str'ormer
11955]
again restated
his theories on
LDE,
hardly mentioning
other
theories.
How-
ever,
he
did note
the
negative results
of
Budden
and
Yates.
The
interest in LDE
again
dropped,
perhaps
due to the
negative results of Budden
and Yates,
even
though
radio
ama-
teurs were receiving
LD
E in
the
1940's,
I
950's and 1
960's
fYillard
et
al.,
1970, 19711.
Bracewell
U
960]
suggested that
extraterrestrial
probes
could
exist in
our
solar
system. To
communicate
with
us,
these
probes
might listen
to our
radio signals and
retransmit
them.
Such
replies
could
resemble
LDE.
fuI
anczarski
U9641,
in
addition
to round-the-world echoes,
received echoes on about
6-14
MHz
with
delays of about
0.5
s
or
more.
He
explained
these as
due
to
waves guided
or
ducted
along
the
magnetic
field in
the
magnetosphere,
perhaps
in the
Van-Allen
belts or
other
belts. He suggested
the
LDE
observa-
tions
of
van
der
Pol
are
of
a
similar
nature.
Experimental
programs were begun
at Stanford
University
by
Villard and students
about
1959
and
later
by Crawford
and others.
Also
Villard
et al.
[1969]
appealed
to radio
amateurs
to
send
them
documentation
of their
observations
of
LDE.
Their campaign
was very successful
and they
received
more than
I I I
reports
fVillard
et al.,
1970,
197 l;
Sears,
1974).
Villard
et
al.
[969]
listed characteristics
of
LDE as deter-
mined from
a
group
of
amateur
reports.
V
illard
and
students
at Stanford
U
niversity
monitored
WWV
when
the
carrier
left the
air
once
an
hour.
They
discov-
ered how
easy
it is
to
be
misled,
e.g.a
sticking
chart
recorder
pen
and
harmonic
radiation
from a
crystal-oscillator
produc-
tion
line
nearby.
They
found
several cases
of
what
appeared
to
be
LDE
but
because
of
other
time-standard
stations
using
the
same
frequency,
they
could
never
be sure
of
their
nesults.
For
Mulonsw: GENERATToN
oF LoNc-DELAY
EcHors
example,
extra
noise
was
sometimes observed
for
tens of sec-
onds after
WWV
turn-off.
Spectrograms
sometimes showed
signals
or echoes similar
to the
WWV
carrier
after
turn-off.
Villard
et
al.
t1969]
suggested
that
parametric
or
maser
ampli-
fication
could
overcome
ionospheric
loss
and
in
some
way
be
responsible
for
LDE.
They
also suggested that
some
effect
similar
to
plasma
resonance
echoes
lHill
and
Kaplan, 1965;
C
rawford
and H arp,
19661
or
stimulated
natural
emission
lHelliwell,
1965] might
be
involved
in
the
generation
of LDE.
The reports solicited by
Villard
et
al.
[969]
are tabulated
in
Villard
et al.
[970,
l97l]. The list
is
impressive
and
is
prob-
ably
the
best
evidence
that LDE
really
exist.
From the
reports,
they
suggested that
LDE
tend
to
occur
when magnetic activity
is
low but this
was
later shown
lsears,
19741
probably
not
to
be
the
case.
After
discussions
with
psychologists they
con-
cluded that
I
-
or
2-s echoes
could
be
psychological but
longer
echoes
would
likely
not be.
They noticed two
types
of
LDE,
one at 3.5
MHz of
l-
or
2-s
delay and one
of
longer delay
observed
in the 3.5 MHz and
higher
frequency
bands
espe-
cially
at
times of band
opening
and closing
when long-distance
propagation
conditions are
good.
Two reports
in the 0.85
MHz
band
were
of
the
former type.They
noted that, of
the
reports
in
Villard
et
al.
[1970],
only
two
mentioned
Doppler
shifts even though
a change of
20
Hz ought to
have been
recognizable. One
amateur
report
by
A. A. Simpson
is
of
particular
interest and
will
be
considered
in
detail below.
I
n
Villard
et al.
[
197 1], hoaxes
and
practical
jokes
were
outlined as the
principal
source
of
uncertainty
in LDE.
In fact,
one of
the
reports in
Villard et
al,
[970]
was found to be
a
hoax.
Crawford
et
al.
[970]
searched
for
LDE
at frequencies
near
f
oFr.
They
proposed
that
wave
energy
could, at an
electron-
density
inhomogeneity,
couple into
longitudinal
plasma
waves
which
would
propagate
along
the
magnetic
field
at
low
group
velocity.
Nonthermal electrons
traveling
along
these field
lines
could amplify
the
plasma
waves
by
beam-plasma
interaction.
T
he
largest
delays
could occur
where
conditions
change
slowly,
i.e., near the
Fz
layer
peak.
A further inhomogeneity
would
allow
the
plasma
waves
to couple
back to an
O
wave.
They started transmissions in October
1967 but
it was
not until
January
and
February
1970
that
they
received
what
they con-
sidered
to be
three
good
LDE.
Two
100-ms
pulses
were
trans-
mitted 1.5
s
apart. In
one case
the
delay
was 15
s,
the
frequency
shift
was
about
-
60
Hz and the time
interval
between the
pulses was
compressed by
about
25Vo.
In the other
two
cases
the delays
were
about 20 s, the
frequency
shift
was
about
100
Hz and
the
time
spacing
between the
pulses
decreased
by
35
and
50Vo. In all
cases
the
wave frequency
was
about
equal to or
slightly below
frFr.
They
found
that
the
human
ear is
the best
instrument to identify the
echoes.
They
observed
6
more LDE
in
a
noisy background. They calculated
that
two spurious
signals
occurring close enough
together to be
mistaken
for an
LDE
would not occur sufficiently often
to
explain
their
results.
In some
of
their
initial transmissions,
Crawford
et al.
[1970]
had
problems
with
false
transmitter
keying.
As
mentioned
above,
Villard
also
had
problems
which
gave
false
results.
Hence,
it seems
quite
possible
that the
echoes
of the
late
1920's
were misinterpreted.
However, the
many
LDE reports
of
radio
amateurs and of Crawford
et al.
should
be
taken
seriously.
Clark
ll97ll
suggested that
there
are two
peaks
in the
occur-
rence of
LDE
with
delay,
one
at
about
2
to
3 s
and one at
about 8 s.
The
first
he
attributed
to
moon
reflection
and
the
second to
reflection from a
cloud
of
ionized
gas
at
one of the
earth-moon
Lagrangian
points.
Lunan
U97
3, 197 4) followed
up
B racewell' s
I
I
960]
idea
that
extraterrestrial
probes
might retransmit
terrestrial
signals
and
these
signals
received
on earth
would
appear to
be
similar
to
LDE.
He
concluded,
apparently in
all
seriousness,
that
the
series
of
echoes received
by Hals
and van
der Pol
on October
24,
1928,
were
codpd to
indicate that
the probe
was
from
a
planet
of the star
Epsilon
Bobtis.
The
probe
arrived in our
solar system
about 13,000
years
ago.
Lawton
[1973]
suggested
that a
Skylab
Apollo,command
module
be
sent to
inspect
assigned
areas of space,
such as
the Lagrangian points,
to hnd
and
identify probes.
However,
Lawton
does not believe
that
the
LDE
studied by
t
unan
were
'due
to an
alien
artifact'
fLawton,
1973;
Stoneley and Lawton, 1974).
Also,
Bracewell
[
1973J
doesn't
consider L unan's
interpretation
of
H
als'
and
van
der Pol's
echoes
to
be
a
convincing
case
that this
series of
LDE was
a message
from
an
extraterrestrial
probe.
Sassoon
U9741
analyzed
statistically
all
the
LDE
obseryed
by
Hals
[934]
and all the
radio
amateur observations
tabu-
lated
by
Villard
et
al.[1970,
l97l]
for
which
definite
observa-
tion
times
were
available.
He
concluded that
there
was
a
'statistically-significant
tendency for
echoes
to be heard when
the
trailing Moon-equilateral
[Lagrangian]
position
is
above
the observer's
horizon' and he
suggested
'that
the
echoes are
caused
by
some
phonomenon
associated
with
this
position.'
In
an addendum
to
Sassoon's
paper,
Lawton
carried
out a
chi-
squared
test
on the
data and
varified
Sassoon's result
(P
=
0.015).
However,
Hals
believed
that his
LDE
were
due
to
moon
reflection
lstdrmer,
1930b]
and hence
the moon's
posi-
tion
probably
biased his
observation
times. This
could explain
Sassoon's
conclusion.
The
data of
Villard
et
al. alone
show
that
more
LDE
were
observed
by radio
amateurs
when
the
trailing
Lagrangian
position
was
above
the
observer's
horizon.
However,
a chi-squared
test indicates
that this is
not
statisti-
cally
significant
(P
-
0.3.5).
Lawton
and
Newton
|974;
Ridpoth, 1976)
set
up
a trans-
mitter
and receiver
separated
by l0
km
to
look
for
LDE
from
a
transmitted
Morse
signal. They were
unable to
duplicate
the
reception
of
LDE
pulse
sequences
which
were
reported
in
the
late 1920's.
However,
they
received a
possible
LDE
on
137
MHz.
Possibly
because
gf
a
lack
of success
in finding
LDE
from
extraterrestrial
probes,
Lawton
and
Newton
U9741
and
Mulonsw:
GENERATToN
oF LoNc-DELAy
EcHoes
5203
Lawton
fWireless-World,
197
51
suggested
another
possibility
for
LDE
based
on the ideas
of
Crawford et
al.U970).
Ionized
matter
might
get
swept
into
the
trailing
earth-moon
Lagrange
area
and
radio waves
arriving
there
generate
a
plasma
shock
wave
which
travels
slowly
through
the region.
These waves
are
amplified
as
they
propagate
and
are
then
converted
into
radio
waves
before returning
to the earth.
Sears
U9741
reviewed
LDE,
analyzed
the data
obtained
by
Villard
et
al.
U970,
l97ll
(see
the introduction),
and
outlined
the
theory
of
Crawford
et
al.
[1970]
in
more
detail.
For
plau-
sible ionospheric
parameters
he calculated
delays
of
the
order
of
I
s
for the
model
of
Crawford
et al. He
discussed
the
observation
of
31
possible
LDE
in 3700
hours of
operation.
LDE
occurred
on
consecutive
transmissions
twice and in
four
other
cases
more
than
one LDE
occurred within
a
l5-min
period.
He concluded
that the new
experimental
evidence
com-
bined with previous
observations
'strengthens
the
belief that
LDE
are
a
genuine
ionospheric phenomenon.'
Crawford
and
Seors
U975;
wireless-world,
l976al
repeated
their
ideas
and
stated
that
calculations
indicate very
weak
fluxes
of
kilovolt
energy
electrons
could readily
cause delays
of
several
seconds.
Duffett-Smith
[975]
used a
correlation technique
to search
for
LDE
in
a
noisy
background.
In half
a million
transmis-
sions
of
a seiies
of dots and
dashes
not
a
single
LDE was
positively
identified.
He
concluded
that
'the
phenomenon
of
long-delayed
echoes should
be
treated
with
reserve.'
In 1974,
Rasmussen
U975,
1976; wireless-world,
1976b;
Lorenzen,
1976)
observed
LDE
on
1296
MHz
while
using
a
moon-bounce
technique.
He was
using
a 26-foot
parabolic
ahtenna
directed toward
the moon
in
the
south-west
at
about
30"
elevation.
The
transmitted
power
was
500 W.
His received
pulses
were
easy
to
identify
because
of a
spurious
frequency
near
the fundamental.
The LDE
had
a
delay of
about 4.6
s
and
had the
same
characteristics
as
the moon-bounce
signal
except
that
they
were
weaker.
He received
the echoes
for
a 20-min
period.
He
suggested
that his
signals
were
reflected
from
an
ionized
cloud
from
the
sun.
Calculations
based
on Rasmus-
sen's
observations
are
carried
out below.
Upon
hearing
of
Rasmussen's
observations,
Goodacre
U9761
reported
that
in
the
late 1960's
he
had heard possible
Fig. l. Plane-earth,
plane'ionosphere
geometry
for
the
nonducted
LDE
model.
s204
Mulnnrw:
GENERATToN
oF
LoNc-DELAy
Ecnors
weak
and transistory LDE
on
144
MHz
during
moon-bounce
transmissions.
The
LDE
were not noticed
at
that time
but only
later
on a
replay
of the
tape
recording.
Eickerman
U976I
suggested
that Goodacre's
LDE
might
be due to magnetic tape
print-through;
the
magnetic
alignment
in
one
layer
of tape
can
be induced
into the
adjacent layers.
Garibaldi
U97
61
discounted Rasmussen's
explanation
of
LDE
because
of
the Doppler effect
.
Fletcher
U9771
suggests
that Rasmussen's
explanation
could
still be
right
provided
the
ionized
cloud
at the time of observation
had no velocity
com-
ponent
toward
the earth.
Simpson
ll978l
indicated
the unlike-
lihood
of Rasmussen's explanation
because a varying
echo
delay
(in
the
20-min
observation
period)
and
a large Doppler
shift
would
occur and an
unreasonably
large
electron
density
would
be
necessary.
Incoherent
scatter
signals
would
also
be
too
weak
to
be
detected. He
concluded
that the
echo
mecha-
nism
must
be
fixed
relative
to the
earth.
Cohen
et
al.
[1978]
stated
that the
reflector
for Rasmussen's
signals
must have
been extraterrestrial
because the
ionosphere
is
not
sufficiently
dense to reflect
1296
MHz. They suggested
that the solar
wind
ionized
dust
clouds
near
the
Lagrange
points
sufficiently
to
reflect
R
asmussen's signals.
Wolking
[978]
suggested
that
ions
of the
solar
wind
follow
various
paths
around the magnetosphere
and meet
down-
stream
to
form
a turbulent area at some distance
from
the
earth.
Rasmussen's
signals could
have
been
reflected from
such a
region.
On April
l,
1977, Yurek
[1978]
recorded
LDE
of about
6-s
delay on both
paper
chart and
magnetic
tape.
During
moon-
bounce
communications
on
432 MHz he
observed LDE
both
on his
signal
and
on
those
of
an amateur in Rhodesia with
whom
he was
communicating.
He had
also
observed
LDE
on
and
off
throughout
March and April
1977.
Frank
et
al.
[1978]
calculated, using
Y
urek's chart
recording,
that the echoes
could
not
be two-hop
moon echoes.
J.
P.
Bagby
(personal
communication to H. L. Rasmussen,
1978)
suggested
that the
results
of Rasmussen
in
particular,
and
LDE in
general,
might
be
explained
by
a
reflecting
cloud
of
particles
surrounding
ephemeral,
natural-earth
satellites
in
translunar
orbits.
He
claimed to have
proved
the existence
of
one such
natural-ephemeral
satellite
lBagby,
19661
although
not
in
a translunar
orbit and has correlated
received
enhance-
ments in the
Ottawa time
signal
CHU
at7.33
MHz with
this
satellite
fBagby,
1967).
On the basis
of observations
over the
last
200
years,
of
transits
of
the
Sun
by small dark
bodies,
Bagby
U972,
19731 suggested
that
there
is
also a
family
of
retrograde
earth satellites in
translunar orbits.
C.
Anderson
lRidpath,
19761
suggested
that
visitors
from
outer space might leave a reflecting
device
in
orbit
about
a
planet
or moon
of the
Solar
System.
A much stronger
echo
could
then be
returned than from a
small
natural satellite.
J.
P.
Bagby
(personal
communication
to H. L.
Rasmussen,
1978)
also
pointed
out
that the date
of July
7, 1974,
given
by
Rasmussen
[975]
for his
observations is incorrect
since
the
moon
was
not in the location
indicated
by Rasmussen at that
time. H. L. Rasmussen
(private
communications, 1978)
stated
that the
correct
date
was
May 28,
1974.
In
1959
and 1960, A.
Goodacre
(private
communications,
1978) believed he
observed about
68 LDE
on
paper
chart
recordings
of
signals transmitted at 50
MHz
during six
moon-
bounce trials.
Statistical analysis indicated
that the
echoes
were
harmonically
related; in
one
case,
he found the
delay
times
to
be multiples
of
138
ms and
postulated
that the
waves
were
launched into
interlayer
ionospheric
ducts
and
circled the
earth
several
times.
I n I
977
,
he
also
recorded
several
possible
LDE
on 14
MHz
which
also
appeared
to
be harmonically
related
with
delay
times
which
were
multiples
of 133
or 144
ms.
He
has
recently
recorded
(A.
Goodacre,
private
communica-
tions,
1979)
several LDE
on
28 MHz,
these
were
identified
by
transmitting
a
train
of about
five
short
pulses.
3.
Ducrnp
ElrcrRoMAGNETrc
PnopncATroN
Radio
waves
of frequency
less
than
about
4 MH
z
can
be
ducted
from
one
hemisphere
of the
earth
to the other in
ionization
ducts
aligned
with
the earth's magnetic
field lines
fMuldrew,
1963, 1967a).
Such ducting
above
4
MHz is very
rare
although
on
one
topside ionogram
conjugate ducting was
observed
up to about
7
MHz.
Medium
frequency
ducting is
common
at L < 2.5
and occasionally
can
occur
for
L
values
up
to 4.
A
radio wave
can enter
a
duct in
one
hemisphere
of the
earth,
be
reflected
in
the topside ionosphere
at the
other end,
return
along
the
duct, leave it,
and
then
propagate
to the
transmitter.
The
distance along
the
field line
from one
hemi-
sphere
of
the earth to
the other
and
back
is
about
62,000
km
at
L
_
2.5
and
I 15,000
km
at L
-
4. The average velocity
of
the
waves
in
the
duct
would
be
very
close to the speed
of
light
so
that
the
propagation
times
would
be
0.20
s
for L
_
2.5
and
0.38
s for L
-
4.0.
Hence
this could explain delays
of about
0.4
s
or
less, but
apparently
can
not
explain
delays of about I s.
The
delay times
submitted to
Villard
et al.
by
radio
amateurs
were
subjective
estimations made
after
the
fact.
It
is
quite
possible
th
at
a
delay of,
say,
0.3 s
would
be
so
astonishing
to
the
radio
operator
that
he would
estimate
the
delay to be
about
l-2
s.
A test
carried
out
by
O. C.
Villard
(private
communications, 1979)
with
radio
amateurs
indicated
that
a
person's
ability
to estimate
time
delay,
when
unprepared,
is
surprisingly poor.
It is
thus
proposed
that the majority
of
delayed echoes
on
0.85
MHz
and on
3.5 MHz
with
an
esti-
mated
delay
of
about l-2
s
or
less
are ducted
echoes. This
would
explain the different
occurrence distribution of LDE
for
the
3.5 MHz
band.
An
echo
in
the
3.5
MHz
band
with
a delay
of 0.25
s
was
recorded
by Ricks
on magnetic
tape
[see
Sears,
1974,
p.
2l).
This was
likely
a
ducted
echo.
Also,
Villard
reportedlBlakes-
lee,,
1978]
that
a
whole
network
of
stations
at
about
4
MHz
on
the
U nited
States
west
coast heard
an
echo effect
lasting
sev-
eral minutes.
A remarkable
sonogram
recording
Isee
Blakes-
lee, 19781
shows
the delay to
be
0.21 s. Villard
indicated
that
the
echoes might
be
caused by electromagnetic
ducting in
a
way
similar
to that
described
above.
Sears
U974)
found
that about
all
of
the LDE
in
the
3.5 MHz
band
occurred
during
the nighttime.
LDE
resulting from
duc-
ted
propagation
would
not normally
be detected during
the
day
because
of high
D region
absorption.
waves
transmitted
from
topside
sounders
can
become
trapped in
ducts
and
bounce
back and
forth
between
hemi-
spheres
several times.
This is not
as
likely
to
happen for ducted
MF
or [{F
waves
transmitted from
the
ground
since, if
they
enter
a duct
at
one
end, and are reflected
at the
other
end,
they
will probably
leave
the duct
upon
returning
to
the
end at
which
they
entered.
4.
MoDELS
FoR LDE
WrrH
Drleys
oF Asour
I
s
on Monr
Model
for
nonducted
propogation.
Two
types of
LDE have
been
reported.
The first is where
transmission and reception
of
an LDE
or signal are
at
the same
station 7r.
The
second
type
is
where
the
signal
is
transmitted
at one
station 7, and
a
different
station 7, receives
an
LDE
in
addition to
the
normal signal.
NORTH
Fig. 2. Geometry
The basic
assumption
in this
paper
is
that
in
addition
to Tt
and
Tr,
there is
another station T2
transmitting a
CW
(or
approximately
CW)
signal at a frequency which
is
close to
but
different than
the
operating
frequency
of fr. The
waves
at
frequencies
/,
(frequency
of
7n,
)
and
/,
(frequency
of Tr) inter-
act
nonlinearly
(wave-wave
interaction)
in the ionosphere
or
magnetosphere
to
generate
an electrostatic
wave
at frequency
fr,
_
f,
f
,.
An
electrostatic
wave generated
in
the
topside
ionosphere
can
propagate
for many kilometers
and
behave in
a
predictable
manner
lM
cAfee,
1968]. This wave whose
fre-
quency
f
,,
A/
f
*,
where
/ru
is
the
plasma
frequency,
grows
through
wave-particle interaction.
When
the
conditions are
right,
this
wave
can
interact
nonlinearly with
the
CW
electro-
magnetic
wave
of frequency
f
,
to
generate
an electromagnetic
wave
of
frequency
f
,
:
f
,
-
/r,
whose
wave
normal
is
such
that
it can
propagate
to T, or
G
where
it is
detected as
an
LDE.
In
the
amateur
bands it is not unlikely
that CW
signals
can
exist for
a few minutes
(A.
A.
Simpson,
private
communica-
tions,
1978);
amateurs often
transmit
a
CW signal
while
tuning
their
antennas to the appropriate
frequency
or
while
adjusting
their
transmitters. The more
common
situation, of
course,
would
be
a
keyed
signal
(O.
C.
Villard,
private
communica-
tions, 1979).
If it is assumed
that
actual transmission
occurs
50Vo of the
time during
which
a Morse message is
sent,
then
for
the
above model,
the electrostatic
waves
carrying
voice
modu-
lation
would
also be keyed
50Vo
of
the
time
and resulting
LDE
would
contain about
25Vo
of the original
voice
transmission.
A
'chopped
up' LDE
of
this
type
might not
be
recognizable
to
the radio
operator.
The
above
model
is illustrated
in Figure
1.
The
three sta-
tions
Tr,
Tr,
and
7s,
the
ray
path,
and all the
wave
normals
are
assumed
to
be
in a magnetic
meridian
plane.
For
simplicity
plane-earth, plane-ionosphere
geometry
is used here. This
il-
lustrates
the
second
type of LDE.
The flrst
type
of
LDE
is a
special case
where
Ds
_
0.
At
the
origin of the
(x, y)
coordinate
system,
the
electromag-
netic
waves
from
T,
and
T2 having
angular
frequencies
c.r1 and
c.r2 and
wave
vectors
k,
and
k,
can
interact
nonlinearly
lDysthe
et al.,
1978]
to
produce
a
forced
oscillation
with
angular
fre-
QUeflc!
{rr12
and
wave vector
k*
given
by
0)n:
0)2
-
0)1
krr:kr-k,
520s
I
f
(r,r,
kr,
)
satisfy the dispersion relation for
electrostatic
waves,
such
a
wave
will
exist
and
begin to
propagate
away
from
the
interaction region.
Other
restrictions to
wave-wave
interactions
do
not apply
lrHarker,
19771.
The approximate
dispersion
relation
given
by
(
l5)
of
Fejer
and Caluert
Ug64)
which
is valid
for
&R
(l
I whereR
-
(KT,/
m)trz
/ar,
K is Boltzmann's
constant, 7", ffi,
and cor are the
electron
temperature,
mass and
angular
gyrofrequency,
is
sometimes
used in
this
paper.
The more
commonly
used
ap-
proximation
given
by
(l)
of
FejerU972)
is
valid
for kR
((
l,
frequency,
and is
ko/an)':
(,rs*/r*)'+
sinzp+
3k2R2
(2)
where
0
is
the angle
between
the
wave
vector
k
and
magnetic
field
B.
This
equation is not
always
used
because
in
some
of
the
calculations
presented
below the
second
condition
is not
satis-
fied. Ray
tracing of
the
electrostatic
wave
is
carried
out using
one of
these
dispersion relations
and
Snell's law. For more
detail
on ray-tracing
see
Muldrew
ll978a,
b).
The electron
density
gradient
VN
is assumed to be
constant
along
the
path.
The variation
of
cor aloog the
path
is only
partially
taken
into
account;
Y r,
is assumed
to be
parallel
to
V,nf.
The ray is
traced and
its wave
normal
k,
position (x,
y),
and
propagation
time
t
from
the origin is determined
along the
path.
In addition
a
wave
vector
k, is
calculated
at
each
point
along
the
ray
path
(see
Appendix l)
such that
k,
_
kr'
kt
(3)
where
at
a
point
(x, y),
kz' is the
value
of the
wave
normal
for
the
CW signal
and ks
is
the
wave
normal
required
for a
hypothetical
electromagnetic wave
to
propagate
from
the
point
to Ts. By
varing
e
,
the
angle
between vertically
down-
ward
and
Vtrr, a ray
path
can
be
found
by
trial and
error,
for
which
at some
point
on
the
path
the electrostatic
wave
normal
k_
k..At
this
point
the
forced
oscillation
between the elec-
trostatic
wave
(c.r,
k) and
the electromagnetic wave
from Tr,
(rr,
kr')
satisfies
the dispersion
relation
for
the
electromagnetic
wave
(rr,
kr) which
can
propagate
to Is.
Mulnnnw:
GENERATToN
oF
Loxc-DELAy
Ecnoss
D=
254
km
SOUTH
for a
particular
solution
which
can explain the LDE
results
of
Rasmussen.
,
o,,
o
o
'or')
'r,
-t
t.d
oo
?
(4)
(s)
(l)
s206
Mulpnnw:
GENERATIoN
oF LoNc-DELAy
EcHons
-30 -20 -ro
o to
20
30 40
HORIZONTAL
DISTANCE, r
(km)
E
:
u;
()
z
F
U'
6
J
o
l-
E,
lrj
Hence such a
wave
will
exist and
propagate
to Tr.It
is
assumed
thato)1
:
ors
))
cory
and
hence that kr: o)r/c
and
lkr I
:
kr.
The electrostatic
wave
at
P
(Figure
1)
is very
weak.
In
propagating
from P
to
Q
the
wave must
grow
by
wave-particle
interaction
(see
conclusion
section below,
Crawford
et
al.
[970],
and Sears
U9741)
sufficiently to
overcome
electron-ion
damping
and
to be sufficiently
strong
so
that the
generated
electromagnetic
wave
(rr,
kg)
is
strong enough
to be
detected
at Ts. Landau damping due to a background
Maxwellian
electron
distribution along
the
path
PQ must also be negligible
or
it is
unlikely that
sufficient
growth
could occur.
This
Landau
damping
can be calculated at certain
points
along the
ray
using
an accurate form
of the dispersion
relationship
for a hot
magnetoplasma
lMuldrew
and
Estabrooks,
1972).
Unless
noted,
for
the
raypaths
used in the results
presented
below,
M axwellian
Landau damping
is
negligible.
Model
for
ducted
propagation.
An attempt
was
made
to
obtain
long
propagation
times
for
electrostatic
waves propa-
gating
in
a unif<rrmly
varying
plasma
between
the
two
points
at
which
the conditions
given
by
(l)
and by
(4)
and
(5)
are
satisfied. Reasonable
plasma
parameters
for
the
ionosphere
and magnetosphere
were
used.
The
maximum
propagation
time
that could be obtained was
about
6
s. About 40Vo
of
the
amateur
observations have
delays in
excess of this
lS
ears,
19741,
and hence
an alternate
explanation
is required
to
ex-
plain
these observations.
A study
of electrostatic
wave
propagation
in magnetic-field
aligned ducts was
carried
out.
Muldrel4,
[
19791
discusses
this
type
of
propagation.
Various
parameters
such as H
t
(scale
length
perpendicular
to the earth's
magnetic
induction
B
),
H
,,
(scale
length
parallel
to
B),
7",
f
N,
LN/N
(fractional
decrease
in
electron density from
ambient at
the centre
of
the
duct)
were
varied
over
large ranges.
Long
delay times,
of
the order
of tens
of seconds,
could not be obtained. It
turned
out
that
in
order
to
get
delays
of 30 s, say,
I/11
had
to be extremely large. At
some
point
in
a field-aligned
duct, close to
the
dip equ ator,
H
11
goes
through an
infinite value.
It
was
thus
decided
to
carry
out
ray tracing near
the dip
equator
in
a
field
aligned duct.
With
this
model
propagation
times of about
40
s and
perhaps
larger
are
possible.
Only 7Vo of the
amateur observations had delays
exceeding
35 s
[Senrs,
1974).
'
50 60
SOUTH
Near
the
dip equatot,
H
11
coooot
be assumed
constant.
The
equation
of
a magnetic
dipole
field line is
(6)
where
r
is
the
distance
;-rr';::Jrrr of the earth,
r
is
the
magnetic latitude,
and
a
-
r at
^y
:
0o.
Near
the dip
equator
r
=
a(l
:y').Assuming
a
vertical
density
gradient
H,
-
N/
QN/
0r) and
taking the
distance
along
the field
line
s
_
r^y,
near
the
dip equator
H
rt_
N/l
aN/ asl
-
Hula/2sl
tzl
The
program
used
by MuldrewU9T9l to do
ray
tracing
in
a
duct
with
constant
H
I
was
modified
so that H
11
varied
as
given
by
(7).
Field
line curvature
was
neglected.
Each time the ray
crosses
the axis of the
duct, the
resultant
density
gradient
is
calculated from
FI,
and
^F/,1
and
this
gradient
is
assumed to
remain
constant
until
the ray again
crosses the
duct
axis.
The model
is
similar
to
that
discussed above for the
non-
ducted case.
The
waves
from
7, and
Tz
interact nontinearly in
the duct
to
generate
the electrostatic
wave.
As
it
propagates
along the
duct
it
grows
in
amplitude
due to
wave-particle
interaction.
A few
tens
of
seconds later
or
less
the
wave
propa-
gates
to
where
the
conditions
(4)
and
(5)
satisfy
the dispersion
relation
for
an
electromagnetic
wave.
This
electromagnetic
wave
is
generated
and
propagates
to
T,
where
it is received
as
an LDE. It is
also
possible
that
the
wave
could
penetrate
the
upper
boundary of
the
duct and
then
propagate
to
where
these
conditions
could
be
satisfied
in
the ambient
plasma.
5.
CnlcuLATroNS
There
are
two
amateur LDE reports
(one
by
Rasmussen,
one
by
Simpson)
which
are of
particular
interest
because of the
experimental
detail
which
is available.
Also,
in the literature,
these
reports
are
treated
with
considerable confidence.
Below,
an attempt
will
be made
to
explain
these using
the model
for
nonducted propagation.
An explanation
of
the
various
ama-
teur
observations
of
LDE
with
delays of
tens of
seconds will
also
be
presented
below using the model
for
ducted elec-
trostatic
wave
propagation.
Rasmussen's
obseruations. It
was
mentioned
above that
Rasmussen
|975,
1976J,
while
receiving moon-bounce echoes,
-40
NORTH
Fig. 3.
Electrostatic ray
path
for the Rasmussen calculation.
The arrows
protruding
from the
path
are
wave vectors.
observed
an additional echo
with
a
delay
of
about 4.5 s.
The
nonducted
propagation
model
presented
here is
applied
to
Rasmussen's
observations
to see
if
reasonable
ionospheric
pa-
rameters
can be
found
which will
explain his
results. The
purpose
of the
present
calculation
is only
to show that
these
parameters
can be
found;
the actual
values
should
not
be
taken
too seriously.
There are several
parameters
or
conditions
which
are known
or must be
satisfied.
The frequency
of
the transmitter
f
,:
1296
MHz.
Tt
and Ts coincide
(Figure
l)
so
that
Ds
_
0.
The
propagation
time
is 4.5
s.
The angle of
incidence
0t:
60o.
His
dish
antenna is
26 ft in
diameter
so that
the
beam
width
is
about
2o.
The
electrostatic
wave
referred to above
must, after
propagating
for
4.5
s, return to the
region illuminated by his
beam
(and
the beam
of
the
CW
transmitter)
and
have
the
appropriate
wave vector in order to
produce
a
signal
which
can be
detected as an
LDE.
Electron-ion collision
damping
can
be
quite
severe
near the
Fz layer
peak
density; the
assump-
tion
is made that
wave
growth
by
wave-particle interaction is
more than sufficient
to overcome this
damping
lCrawford
et
al.,
19701'
Sears,
19741.
The unknown
parameters
which
can be
varied within reason
are
the
direction e and
scale length
H of the density
gradient
V/f,
the distance
D
between
Tz and Tr, the
plasma
electron
temperature T, and the
frequency
f
z
of the CW
transmitter
T,
(this
and the
geometry
determines
the
value
of the
plasma
frequency
/ro
at the origin.r
-
0,
y_
0).
The
height of
the
origin fto
is
also
variable
provided
it is
consistent
with
/r.
The
dip 1 and
gyrofrequency
are
determined by
the
location
of
f,
and
the
geometry.
It
is
assumed that
Tr, T, and all
propagation
paths
are
in
the same
magnetic
meridian
plane.
This,
of course,
is
not a
necessary
condition
and this extra degree
of
freedom
would
make
the occurrence of
LDE more likely
than
it
would
be for the
restricted
case considered
here. In fact
Rasmussen's
antenna
was
pointing
to
the
south-west,
not
magnetically
southward as
assumed
here.
Rasmussen's
signal
produced
a
'distinctive
note'
due
to a
spurious
frequency near
the
fundamental;
this
note
was
repro-
duced
in
the echoes.
Hence, since this
note
was
heard in
the
LDE,
another
condition
is that
time
dispersion of
the signal
must
be small over
the
500
Hz
bandpass of
his
receiver.
By
trial
and
error
using
the electrostatic
ray tracing
pro-
gram,
a
particular
solution
was
found
satisfying all the above
conditions.
The
parameters
for
this
solution
are:
f
,
_
1296
MHz,0t:
60o,
Ir
_
4.5
s,
xt:
54
km,
lr
:
31
km
(where
xr,
lt
and
/,
are
the coordinates
and
propagation
time
of the ray
when
(4)
and
(5)
are
satisfied),,
-
61.25", H
:
1800
km,
D
-
254
km,
T,:800 K,fr:
1303 MHz,f
ru:
6.91
MHz,ho:300
km,.f
:
66o
and
f
,
:
l.2l MHz. Figures 2
and
3 illustrate this
solution.
The
electron
density
gradient
VIf
has
a
large
scale
length
and
is
directed at
a large
angle to
the
vertical. This
should
be
possible
on occasions
near the
peak
of the
layer. The
scale
length
at
the
peak
of
the
layer is,
of
course,
infinite
but
nor-
mally for
a
vertical
gradient
it falls
to
roughly *
1000
km
at
* l0 km
in height from
the
peak.
The
calculation
was
made
assuming
a constant
scale
length
of
1800
km;
the
vertical
height range
covered
by the ray
was
about
40
km.
Hence
normally
an
'average'
scale