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The role of the magnetosphere in satellite and radio-star scintillation
Journal of Atmmpheric and Tem&ial Phusim, Vol. 37, PP. 1089
to 1098.
Pergamon Prem,1975.Printedin NorthernIreland
The role of the magnetosphere in satellite and radiostar scixltillation HENRY G. BOOKER Department of Applied Physics end Information Science,University of California, San Diego*, La Jolla, California 92037,U.S.A. (Received
17 October 1974; in rem&dform 9 December1974)
Abstract-A theory is developed to accountfor the scintillationphenomenonobserved in equatorial regions when using communicationssatellites in the SHF band. The same theory is also used qualitatively to explain strong scintillationsin the VHF band. Instead of comiuing irregularities to a narrow interval of height in the P-region and 8aSUmiUg that they are strong, the alternative hypothesisis used that the irregularitiesare weak but extend from the P-region upwards into the magnetosphere. It is suggestedthat the irregularitiesare field-alignedand extend at least up to an L-shell of 1.3 and possibly up to 2 or more.1. INTRODUCTION It has long been established that weak scintillation of radio stars occurs in the F-region of the ionosphere (HEWISH, 1952). It has also been generally assumed that the same is true for strong scintillation in which the r.m.s. amplitude fluctuation is equal to the mean amplitude. In fact, however, the methods for assessing the height of occurrence of the irregularities are quite unsatisfactory for conditions of strong scintillation. In consequence, it is not established at this time that the imposition of strong scintillations in the VHF band is confined to a hundred or so kilometers in the vicinity of the level of maximum ionization density in the F-region. In transferring one’s attention from weak to strong scintillations in the VHF band, there are two main alternatives: Either (1) One can can confine attention to the same hundred or so kilometers of height near the level of maximum ionization density in the Pregion and increase the magnitude of the mean square fluctuation of ionization density by a power of ten or so, so (2) One can continue to use roughly the same magnitude for the mean square fluctuation of ionization density and increase the interval of height occupied by the irregularities by a power of ten or so. Although the Srst of these alternatives is the one customarily chosen, there is no present * Much of this work was performed by the author as a consultant to the RAND Corporation, Santa Monica, Californie. The remainder was supported by National Aeronautics and Space Administration Grant NGR05-009-076and National Science Foundation Grants GA-20691 and 30628.
observational reason for rejecting the second alternative. We therefore pursue the second alternstive in this paper. In recent years satellite scintillation phenomena have been observed in the SHF band (CRAFT and WESTERLUND, 1972; TAUR, 1973a; CRANE, 1974), and this phenomenon has also been interpreted on the basis of alternative 1 (CRAFT and WESTERLUN~, 1972; TAUR, 1973a, 1973b; CRANE, 1974; WERNIK and LIU, 1974; RIJFENACH, 1974). However, the Fresnel distance for irregularities that have a size of a few hundred meters is of the order of an Earth’s radius in the SHF band. Consequently, Fresnel fltering favors irregularities in the magnetosphere in comparison with irregularities in the ionosphere at SHF. It is alterntive 2 therefore, rather than alternative 1, that provides irregularities at the heights that are most effective in causing amplitude scintillation et ground level in the SHF band. Arbitrary concentration on alternative 1 therefore seems no longer to be justified. In consequence, we examine alternative 2 in this paper. 2. EXPEFtJMENTALFACTS Radio star scintillation was identiSed as a phenomenon associated with the Earth’s plasma envelope by SMITE (1950) and by LITTLE and LOVELL (1950), who found that, while the scintillations were uncorrelated for a ground separation of 100 km, a significant degree of correlation existed at 1 km. This work w&8 done before the discovery of the magnetosphere (STOREY, 1963), so that only the ionosphere was then available for explaining the scintillations.
1089
1090
H. CT.Booxxa
Using phase rather than amplitude observations, RYLE and HEWISE (1950) showed that the correlation distance, or diversity separation, for the relatively weak scintillation phenomenon commonly encountered in middle latitudes corresponds to a scale L of about 5/(2a) km, or about 800 m. Similar results have been obtained recently by BRAMLEY (1974). Somewhat greater values for the diversity separation are obtained in the northsouth direction, indicating the presence of some elongation of the irregularities, presumably along the direction of the Earth’s magnetic field (SPENCER, 1955). For the relatively weak scintillation phenomenon in middle latitudes, however, drastic elongation of irregularities along the Earth’s magnetic field was not found, and this has recently been confirmed by SINQLETON (1974). The work of Singleton and that of RUFENACH (1971, 1972) shows in addition that there is a turbulence-like spectrum of irregularities extending down to scales of less than 100 m, and that this spectrum has an inverse power-law decrease, with an index of the order of 4. An estimate of the height of the irregularities in the ionosphere was first obtained by HEWISH ( 1952) by exploiting the fact that, at wavelength II, irregularities of size L closer to the observer than the Fresnel distance vL2/1 produce phase fluctuations rather than amplitude fluctuations. By measuring both, he was able to recognize that the fluctuations associated with the weak midlatitude scintillation phenomenon occurred at an P-region level. He quoted a value of 400 km which haa since been repeatedly used as the height of the irregularities. In reality, however this height has not been determined with precision. The statement of kbRONS et al. (1971) that the irregularities “lie, for the most part, in the F-layer of the ionosphere at heights predominantly ranging from 225 400 km” is more satisfactory. The intensity of weak scintallations varies wth the wavelength of observation. At small zenith angles in the VHF band the ratio of the r.m.s. amplitude fluctuation {(AA)s}l/s to the mean amplitude A varies as i2. At large zenith angles however, the variation is believed to be aa A, although the experimental evidence is not clearly delineated in the literature. The latter behavior corresponds to a situation in which 800 m irregularities in the F-region are at a distance from the observer greater than the Fresnel distance rL2/1. From time to time in middle latitudes, and quite frequently in polar and equatorial regions, a more inmnse scintillation phenomenon is observed having
significantly different characteristics. For the intense scintillation phenomenon, amplitude fluctuations in the VHF band frequently reach 100 per cent and the statistical distribution of amplitude acquires the Rayleigh type, suggesting that all the radiation that is being received has been scattered. For intense scintillations, the methods for determining the height at which they are imposed become unsatisfactory. The diversity separation in the east-west direction is less for the strong phenomenon than for the weak. Values as low as 50-60 meters have been observed (KOSTER, 1966). Mean values near the Equator are quoted as about 400m for radio stars observed in the VHF band at substantial northerly zenith angles (KOSTER, 1963), and about 200 m for a 136 MHz satellite observed at smaller zenith angles (KOSTER, 1966). Observed values of the diversity separation near the Equator for strong scintillations are much greater in the north-south direction than in the east--west direction. The ratio is not less than 30 and could well be virtually infinite (Koster, 1966). For strong scintillations the phenomenon is not confined to the VHF band. In equatorial regions not only is scintillation observed for satellites operating in the UHF band (SESSIONS,1972), but they are sometimes observed even in the SHF band (CRAFT and WESTERLJJNIJ,1972; TAUR, 1973a; CRANE, 1974), especially in the evening hours. Scintillations have been observed at a frequency as high as 8 GHz (STEVENS, 1973). Moreover, it should be noted that these observations are not restricted to large zenith angles. The observations in the SHF band have been made with a stationary satellite, and there is no present information about what would happen in this band with an orbiting satellite. For strong scintillations near the Equator the r.m.s. amplitude fluctuation ((u)2}1’s is frequently equal to the mean amplitude A of the signal in the VHF band. In the SHF band
(( AA/A)2}1’2 is always less than unity and is proportional to 1s (CRAFT and WESTERLUND, 1972). The frequency dependence in the intervening UHF band is not precisely described in the literature. However, the fact that the occurrence of scintillations in the SHF band came
as
a surprise
is an indication that the variation of { ( AA/A)a}l12 in the UHF band is less rapid than A2. Proportionality to 1 in the UHF band is a reasonable presumption (see POPE and FRITZ, 1971). No corresponding measurements of phase-fluctuation are available. The equatorial scintillation
The role of the magnetospherein satellite and radio-star scintillation phenomenon weakens beyond 25’N geomagnetic latitude (&AFT and WESTEFCLUND, 1972); it is observed as far as 20% geomagnetic latitude, but no observations have been made further south. 3. THE SPECTRUIUOF IltItEtXlLARIl’IES
1091
r.m.s. phase fluctuation {m}u2 in the SHF band in equatorial regions,.it turns out to be large compared with one radian. We assume, however, that this is an unlikely eventuality, and that (A+)2, like (AA/A)2, is less than unity in the SHF band. On this basis the SHF scintillation phenomenon should be explicable to the first order in terms of the Born approximation. Scintillation is a forward scattering phenomenon for which there exists an angular spectrum of scattered waves that is principally concentrated within a certain beam-angle. We shall assume that waves scattered well outside this beam-angle are unlikely to be important for the communications aspects of scintillations in much the same way that the sidelobes of an antenna are usually unimportant. Just as an antenna is then characterized largely by its overall aperture-width, so the forward scattering properties of the irregularities are largely characterized by their outer scale. For the effects of a particular scintillation phenomenon, we assume that it is the value of the outer scale, and the associated scattering angle, that is likely to be of greatest importance for communications purposes. This does not rule out the possibility that two causes of irregularities can exist in the same part of space. For example, the following two causes can be considered:
Ionospheric scintillation phenomena are usually explained in terms of the concept of a phasechanging screen introduced by BOOKER et al, (1960), and further described by RATCLIFFE (1956). These authors illustrated their work with a Gaussian autocorrelation function for the irregularities, partly for mathematical simplicity but also because a correlation function of this type was thought to be reasonable at that time. This pattern was followed by many subsequent investigators. The theory of Booker et al. was originally devised to relate the field pattern observed at the ground to that existing in the ionosphere. However, for studying how the field fluctuations are created in the ionosphere, there is much to be said for the volume scattering concept adopted by BOOKER (1958). This was based on the theory of tropospheric scatter communication devised by BOOKER and GORDON (1950). These authors did not use a Gaussian autocorrelation function because such a function is inappropriate for turbulence and would have completely failed to explain the wavelength dependence of the scattering phe(1) Suppose that noise in the atmosphere nomenon then under discussion. Instead, they generates ion acoustic waves in the ionosphere used an exponential autocorrelation function, leadthat lead to roughly isotropic irregularities of size ing to a turbulence-like spectrum of irregularities L (-800 m), and that these waves are absorbed by decaying below the outer scale proportional to a turbulence-like process in which energy is passed the inverse fourth power of the spatial frequency. to progressively smaller scales, until the scale is The same theory was subsequently used by BAILEY small enough for the energy to be converted into et al. (1952) to predict the phenomenon of ionothermic motion of the ions and electrons. Such spheric scatter communication. If they had not a phenomenon is more likely to occur in the used an inverse power-law spectrum, the prediction ionosphere than in the magnetosphere. would not have been made. In explaining this (2) Suppose that plasma instability leads to phenomenon in detail, various autocorrelation functions were considered by BOOKER (1959), generation of ion acoustic waves that travel roughly leading to inverse 4, 5 and 6th power-law spectra. perpendicular to the direction of the Earth’s All such radio scattering phenomena have required magnetic field and that create field-aligned iran inverse power-law, and not a Gaussian, spectrum regularities with a transverse scale T (-300 m). to explain them, and the recent work of RUFENACH Suppose that these waves are absorbed by a (1972) and SINGLETON (1974) shows that scattering turbulence-like process in which energy is passed in the F-region associated with the weak mid- to progressively narrower field-aligned irregularities until the scale is small enough for the energy to be latitude scintillation phenomenon is no exception. It is possible to assume that the way in which the converted into thermic motion of the ions and electrons. Such a phenomenon is more likely to spectrum decays below the outer scale is important for the SHF scintillation phenomenon (RUFENACH, occur in the magnetosphere than in the ionosphere. 1974; WERNIK and LIU, 1974). However, we Indeed, it was consideration of such a phenomenon shall take a different point of view. It could be that led to invention of the term magnetosphere that, when observations have been made of the by GOLD (1959).
H. G. BOOKER
1092
In both cases irregularities an
outer
inverse
scale,
would
power-law
spectrum
and would be converted inner
scale.
exist
to extend
diffusion
across
the
Earth’s
that
could
communications
but would
satellites 1974). of what
be explained
irregularities
is an important
in SHF
satellite
Substituting equation
of
for
(I),
fluctuation
(An/n)2
we
a theory in
= ~T,~~~(AN)~L~ (A(P),,~ We
now
acteristics
have
to calculate
its effect
downwards
from the screen, the phase-fluctuations
amplitude
fluctuations
may
that
somewhat,
develop
of
phenomena
7 at a height mean
h above
square
was
given
by
noted
that
his
( AN)s.
where,
for
relevant
isotropic
distance
in the
index
layer
direction
where
re is the
(2.82
x 10-15 m).
phaso introduced irregularity
classical The
of propagation
and
of h set
The
a = T.
to the ground
is
is h set
x.
x to 2, BOWHILL
shown that the mean square phase
(Aq)z
and the mean
fluctuation
(AA/A)2
square
fractional
at ground
level are
given in terms of the mean square phase-fluctuation at the screen by
These
(b)02
(6)
(ANo2
(7)
(1961).
of
outer
of thickness
electron-density
radius
/AAl
of
square
into a passing wave
Yi-= J
+’(h set x\”
1
deviation the two being such that
(1) the
\
be
jl is
r,214(AN)2
mean
the layer
of the ratio
amplitude
surface. Let the
n at wavelength
= 22
irregularities,
from
can now be made,
Then the mean square fractional
of refractive
distance
Moreover,
irregularities
in
the
errors and
of BOWHILL
the Earth’s
fluctuation
fluctuations
2 = aL2/t
fluctuation
coefficients.
scale L exist in an ionospheric
amplitude
is given by the Fresnel
In terms
by isotropic
minor, need correction.
isotropic
and
also be
is of major
a number of printer’s
that
As we move
the
involve
work
at ground level.
which
equations
in the theory
char-
over
it
some improvements
whose
(4)) and we have
distance
The fact
(1958),
based on the subsequent
screen
(1952),
systems.
also some errors in numerical
phase
HEWISII
BOOKER
errors, although
a
(4)
by
scintillation
be
from square
shown
case, the character
ionosphere
mean
set x.
are specified by equation
But we assume that
should
of (AN)2
the
As
of scintillation
the
for
decrease
in the two cases,
communications
in terms
obtain
develop.
4. SCINTfLLAl’IONS DUE TO ROUGHLY ISOTROPIC IRREQULARPHRS
Suppose
of
of phase at the under side of the layer
(1961,~.281)has
irregularities
x, a
isotropic
of the irregularities
in explaining
Although
angle
a total mean square phase fluctuation
the
phenomena
height-ranges
that, in either
the decay spectrum importance
at zenith
(TsecX)/L such irregularities,
of field-aligned
one.
must be recognized.
it is unlikely
producing
could
and LIU,
of roughly
in terms
the outer scales may be different
is
scintillation
scintillation
and
different
In
(cf. WERNIK
irregularities
the relevant
field
field.
the
in terms what
the
not
where
both phenomena
influence
question
and that
the layer
exist in
magnetic
along
BRAMLEY,
should
through
at an
into the lower ionosphere
with
and
The
might
going
The second phenomenon
of the ionosphere
coexist
frequencies, motion
In
radio wave encounters
but would not be likely to extend far
be likely
1974;
of spatial
in the magnetosphere
comparable
at
a presumably
into thermic
into the magnetosphere.
F-region
be created
via
The first phenomenon
the ionosphere might
would
decay
electron
deviation
of
by a typical
(W2 Equations focussing been
averaged
value greater unity.
is
(6) and
+ (AA/A)2 and out.
If
from
(6) and (7) gives,
the
which
(AA/A)2
than unity,
If (Av,)~ calculates
Substitution
include
defocussing,
unity, an extrapolation
(2)
(7)
= (Av)a2. have
effects
of
however
calculates
to
it should be replaced to a value greater
of the theory equation
a by
than
is involved.
(4) into
equations
for the mean square phase and
The role of the mtlgnetosphere in satallite and radio-star scintill&ion
we would then need to have
amplitude fluctuations at ground level,
+-
(Ad2
2(
-
2
L = 100m.
2
1 h see x )
h.BBCx s 2 ( )
1+
1 h BBCx 2 _2( 2 )
set x
1+
(
2
((Afff~Q~j~‘~
)
(10)
\ When set x > Z/h we have
( 11) but when set x < Z/h the formulae become, using equation (5), (Ap)’
+
4r,212(AN)2Lr set x ha 2le(AN)2 - 7 sees x.
(12) (13)
L2
The weak mid-latitude scintillation phenomenon can be explained in terms of these equations by using parameters of the order L =800m,r
=200km,h
-3OOkm
(14)
and using a value of {m}us small oompared with the average ionization density in the F-region. By using & larger value of ((ANa))1/2, let us now attempt to use the same formulae to explain the strong scintillations observed with satellites in equatorial regions (alternative 1 in Section I). In equation (10) the change from the ,X2law in equation (II) to the Eplaw in equation (13) occurs when
that is, when (equ&tion 5) I = (?7L2 COBx)/h.
(18)
1
h set x a *
-
(16)
In order to explain the wavelength dependence for roughly vertical propagation at the Equator, let us assume on the basis of the observations described in Section 2 that the transition-wavelength in equation (16) has the value 10 cm for a value of cos x of the order of unity. Taking h to be 300 km,
(17)
If we now substitute this value into equations (9) and (lo), and use h = 300 km, 7 = 200 km, x = 0, we obtain, for a frequency of 8 GHz,
(9)
4r,“;l”(AN)‘Lr
1093
= I.6 x 10-‘a((AN)“)*~2-
(19)
It follows that, if { ( AN)2)1/2 can be of the order of 1011 mw3, there then would be, at 8 GHz, e phasefluctuation of 0.1 radian and an amplitude fluctuation of 1.6 per cent. It is therefore possible to explain, in accordance with alternative 1 in Section 1, the magnitude of SHF satellite scintillations in terms of irregularities in a 200 km slab in the F-region by using an outer scale of the order of 100 m and an r.m.8. fluctuation of ionization density of the order of 1Oii rne3. Plasma physists would, however, have some difficulty in explaining such behavior in the ionosphere. The needed s&e is comparable with the mean free path of ions in collision with themselves, and the needed fluctuations of ionization density are comparable with the mean ionization density in the F-region, especially at night when scintillations are more common. In addition, roughly isotropic irregularities do not explain the extreme elongation of the field irregularities observed at ground level in equatorial regions in the VHF band. It is appropriate, therefore, to turn attention to alternative 2 in Section 1 and to pay more attention to m~etosphe~~ phenomena. 6. SCDTTILLATIOIiSDUD TO FYELD-ALIWED AGUE
Consider a magnetosphere with field-aligned irregul&rities stretching from the ionosphere in one hemisphere to that in the other. Let T be the outer scale of the irregularities, measured transverse to the Earth’s magnetic field. Allowance should be made for the geometrical variation of T along a particular tube of flux. Allowance also needs to be made for the fact that a, radio wave passing through the magnetosphere is in general propag&ing in a direction making an angle p with the local line of flux of the Earth’s magnetic field. In consequence, the value of L to be used in equations (2), (3) and (4) when handling fieldaligned irregularities is T cosec qa. Furthermore, BOWHILX,(1961, p. 282) has shown that the development of amplitude fluctustions as
H. Q. Booxxn
1094
one moves away from a phase-screen that involves aligned irregularities is appreciably slower than for one that involves isotropic irregularities. As a result, the numerical coefficient a in equation (6) is not rr but lr(8/3)l12. It should also be noted that L in equation (6) is to be replaoed by T, not by T cosec rp. Bowhill also gives a more complicated function to describe the growth of amplitude scintillations in moving away from a phase-screen of aligned irregularities than that applicable for isotropict irregularities. However, to simplify the evaluation of integrals we will preserve the simpler function. We shall now be involved with phase screens stacked over an extended range of height, so that it is necessary to replace the thickness 7 in equations (9) and (10) by an element of height dh and to integrate over all relevant heights. By making all the replacements described, equations (9) and (10) become 1 h set x
l+i-
s Co
4r6212
0
1+
x (AN)2T
2
( 1 ( > h se0 x
2
z
cosec ye set x dh
magnetosphere, ( AN)2 almost oertainly increases with decrease of height. At some height in the magnetosphere, however, (AN)2 must cease to increase as rapidly as N2 because diffusion transverse to the Earth’s magnetic field becomes more important at lower levels. On the other hand, starting from below the magnetosphere, iarv)z for field-aligned irregularities must increase from zero in the lower ionosphere. It follows that, at some level in the plasmasphere, (AN)2 must have a maximum, but there is no present information as to the height at which this maximum occurs. In particular, there is no reason to believe that the maximum of (AN)2 occurs at the height of maximum ionization density in the F-region, or indeed in the ionosphere at all. In the present state of ignorance, let us assume that {(AN)2}r/2 is small compared with the maximumionization density in the F-region, and that it has a constant value between an ionospheric height h, and a magnetospheric height hM. At the height h,, N2 may be assumed to have decreased
z
-
plasmapause in the equatorial plane, (AN)2 may be assumed to be proportional to Nz and even more-or-less equal to N2. Hence, far out in the
(201
to the postulated value of (AN)2. Above the height hM it would be reasonable to assume that (AN)2 decreases with Ns. However, for simplicity of calculation, we will assume that irregularities above the height hM make no important contribution to scintillations and may be neglected.
\
x (AN)2T
cosec ly set x dh.
(21)
We have shown the integral as running from zero
We then have a model in which (AN)2 for fieldaligned irregularities is constant from an ionospheric height h, up to a magnetospheric height hM, and vanishes elsewhere. With the assumptions described, equations (20) and (21) reduce to
to infinity in height, but (AN)2 can be set equal to zero for heights that are not relevant. To simplify evaluation of the integrals in equations (20) and (21) let us confine our attention hdl1 -t 4(h/z)2dh to communication between a stationary satellite (AP)~ = ~v,~A~(A.N)~T hI 1 + (h/-V2 at the Equator and an Earth terminal vertically below it. We may then put x = 0 and y = ?r/2. hdi (h/g)2 dh (23) Furthermore, over the interval of height with = ~T,~A~(AN)~T hl 1 -t (h/Q2 ' which we are likely to be concerned, no pronounced s variation of T is to be expected at the Equator. Evaluating the integrals, we obtain Let us therefore assume that T is independent of height. A more difficult decision has to be made con(h&g) - tan-’ V+)}l (24) cerning the variation of (AN)2 with height, Well out in the magnetosphere, where diffusion transverse to the Earth’s magnetic field is small, there is no objection to assuming that field-aligned z{tan-’ (hN/Z) - tan-‘(hi/Z))]. irregularities are strong. As we come in from the (25)
-s
(22)
The role of the magnetospherein satellite and radio-star scintillation The precise numerical value of h, in equations (24) and (25) is in fact unimportant. If one has integrated through a considerable part of the plasmasphere, it makes little numerical difference whether one stops the integration at a height of 500 km, 150 km or 0 km. We may therefore simplify equations (24) and (25) by putting h, = 0. If at the same time we substitute for the Fresnel distance 2 from equation (5), we obtain 1 + $ tan-’ t
(26) 0
1 - $ tan-‘:
(27) 0
where 1, = ~(8/3)l’~ T2/hM. Since, in equation (27),
l-
!!? tan-l1
I
1 N
10
1 1 2 0 ( 33,
if
1 > 1,
(29)
if
1 Q 1,
(30)
we see that (AA/A)2 is proportional to A2 at long wavelengths and to ;(a at short wavelengths, the break between the two behaviors coming where
where 1, = 5.77 X 10e2 m.
(36)
At a frequency of 8 GHz this gives = 1.0 x 10-11((AN)2)“2 {(AA/A)2}1’2
(37)
x 10-12{(AN)a)1’2.
= 2.5
(38)
We therefore see that the scintillation phenomenon at 8 GHz can be explained in terms of fieldaligned irregularities having an r.m.s. fluctuation of ionization density small compared with the maximum ionization density in the P-region. However, these irregularities need to exist over a few thousand kilometers of height rather than a few hundred kilometers. Using the value 300 m for the transverse scale T of the field-aligned irregularities and the value 8000km for the magnetospheric height hB, to which the irregularities extend, and taking the lower bound of the irregularities to be at a negligibly small height (say, a height in the P-region), the r.m.s. phase fluctuation at ground level in radians calculates, in accordance with equation (34), to the values shown in Fig. 1; the part of the Wavelength, i-2
rz=
1095
rn
I
IO-’
1/3A,
or (equation 28) L = 2d27rT=/hM.
(31)
If, on the basis of the observations described in Section 2, we take this transition wavelength to be 10 cm, and put T = 300m,
(32)
hM = 8000 km.
(33)
we deduce that We are therefore dealing with the part of the plasmasphere extending out more than an Earth’s radius. If we now substitute these values for T and hM into equations (26), (27) and (28), we obtain for the mean square phase and amplitude fluctuations at ground level (A#)2
= 3.82 x 10-20i12(AN)2
I
I
Frequency.
I20 Pan-
12 n0
I
I
I
100
1000
10000
MHz
Fig. 1. The frequency variation of r.m.8. phase fluotuations at ground level for field-aligned irregularities of outer scale 300 m existing in the plasmasphere to a height
of
8000 km.
Vertical
propagation
et
the
Equator is assumed. The portion (A+)2 > 1 is an extrapoletion.
H. G,
1096
BOOKRR
diagram for which (A$)2 > 1 should be viewed with caution. Likewise, on the basis of equation (35), the r.m.s. fluctuation in the fractional amplitude at ground level calculates to the values shown in Fig. 2. These values are in general aocord with the observational facts for scintillation phenomena observednear theEquator using stationarysatellites more-or-less overhead. 0. TEE REWETS AT WHICH SCINTILLATIONS m =OSED To examine the heights in the plasmasphere that are responsible for causing scintillations when the phenomenon is strong we need to plot the integrands in equations (22) and (23) as functions of height. This is done in Fig. 3 for phase scintillations and in Fig. 4 for amplitude scintillations. The ordinates in Fig. 3 and 4 are the coefficients of the expression 29
ile (AN)2 T
I
(39)
in the integramls appearing in equations (22) and (23) respectively. The same parameters have been used as for Figs. 1 and 2. The nerves have not been plotted for heights greater than 8000 km because our crude model of the plasmasphere assnmes that there are no irregularities above this height. Likewise the curves have not been plotted below a ~v~~~gth, -2 K)
10-l
m I
to
I 0
I
I
t
4000
6000
6000
I
2000
Height,
I 10000
km
Fig. 3. The height-weighting in the plasmaspherefor phase tluctuationsat ground level due to field-aligned irregularitiesof outer scale 300 m. Vertical propagation at the Equator is ~~~WTXKL height of 400 km because the field-aligned irregularities presumably do not extend below the a-region. It is olear from Fig. 3 that the whole range of heights up to the assumed cut-off at 8000 km is ~otenti~ly important in causing phase scintillations. On the other hand, Fig, 4 shows that, for amplitude scintillations, irregularities at clistanoes closer to the ground than the Fresnel distanoe 2 tend to be suppressed. The assumption of a uniform value of (alv)z extending from a height of 400 km up to a height of 8000 km is, of course, unlikely to be correct. But the notion that one is concerned at the Equator with the first few thousand kilometers of the plasmasphere, rather than the first few hundred kilometers, should be taken seriously. A more
1000
IO0
MHZ Fig. 2, The frequency variation of T.M.B. fracrtioti amplitude flu&u&one at ground level for &&Migned irregularities of outer so& 300 m existing in the Freawncy ,
plasmasphere to a height of 8000 km. Vertioal propagation at the Equator is assumed.
plausible distribution of (AJJ)2 in the plasmasphere would involve rough uniformity between a height of 400 km and the L shell of 1.3, with smaller values for higher I;-shells, The &-shell of 1.3 intersects the 400 km level at the latitudes f26’, which are the approximate locations where the
The role of the magnetosphere in satellite and radio-star scintillation
1097
Thus, when (A#)2 is large compared with unity, there are about ( A#)2 scatterings in passing through the plasmasphere. On a random walk basis the total mean square scattering angle is then {A/(2nT)}2 (A+)2, leading to an outer scale in the field pattern at the ground of the order of T/(( A+)2}1/2. We may conveniently allow for both the single and mulitple scattering situations by defining the diversity separation transverse to the magnetic meridian as
1
;-~
0
D=
T -. (1 + (A$)2}1’2
If we use the estimates
(40)
of (A#)2 in Fig.
1, we
derive for the diversity separation in equation (40) 2000
4oco
Height,
6000
8000~
10000
km
the estimates shown in Fig. 5. the
Fig. 4. The height-weighting in the plasmasphere for amplitude fluctuations at ground level due to fieldaligned irregularities of outer scale 300 m. Vertical propagation at the Equator is assumed.
diversity
separation
In the SHF
is simply
outer scale of the field-aligned
equal
band to the
irregularities,
this we have assumed to be 300 m.
and
In the VHF
band, however, multiple scattering can reduce the diversity separation substantially.
equatorial
scintillation
phenomenon
is observed
to decrease (CRAPYCand WESTERLUND, 1972). In accordance with equations (20) and (21), useful information about the dependence of ( AN)2 T upon height should be obtainable by measuring the ratio of (AA/A)2 to (A$)2 as a function of frequency at frequencies such that both quantities are less than unity.
It should be noted estimate
of
the
that expression
diversity
separation
(40) is an for
phase
and that, for amplitude fluctuations,
fluctuations,
Wavelength, I
IO-' I
m I I
I
1
7. THE DIVERSITY SEPARATION A point of interest for communications purposes is the minimum distance by which antennas must be separated in order to receive more-or-less uncorrelated fading. For the field-aligned irregularities that we have postulated in the plaamasphere, it is only separation perpendicular to the magnetic meridian that is involved. So long as m < 1, only single scattering is involved and it may be assumed that the diversity sepsxation is given by the outer scale T of the field-aligned irregularities. The scattered waves constitute a fanbeam of half-angle il/(%T) and, as shown by BOOKER et al. (1950), these waves synthesize at ground level to a field pattern having an outer scale T. If, however, s
is appreciably greater then unity, multiple scattering is involved. As a rough guide for experimental purposes, the path may then be divided into sections for each of which (A+)3 is equal to unity. The number of sections is then roughly the number of scatterings involved. 3
RMS. fluctuation in ionization density
I 10000
I
I
I 1000
Frequency,
! loo
MHz
Fig. 6. The frequency variation of an estimated east-west diversity separation for field-aligned irregularities of outer soale 300 m existing in the plasmasphere to a height of 8000 km. Vertical propagation at the Equator is assumed.
H. G. BOOKER
1098
the diversity separation can be greater. Figures 3 and 4 show that, in general, a smaller thickness of the plasmasphere is important for amplitude fluctuations than for phase fluctuations, and in the VHF band this reduces the number of successive scat&rings that are important for amplitude fluotuations. However, the resultingnumerical changes in Fig. 5 are not major. ’ It should also be noted that the value of 300 m that we have used for the transverse outer scale of field-aligned irregularities is in fact bssed on observations that show a spread in the values of the east--west diversity separation extending from 430m down to 50m (KOSTE~, 1966), measured with a stationary satellite at a frequency of 136 MHz. It would not be unreasonableto assume that the transverse scale of the irregularitiesin the plasmasphereis around 430 m and that the smaller
values of diversity separation observed at ground level are associated with various degrees of multiple scattering. This interpretation would increase still further the value of hM derived in equation (33), and make it even more important to considera substantial depth of the plasmaspherein seeking an explanation of equatorial scintillation phenomena. 8. COECLlJsIOEs While weak mid-latitude scintillation is undoubtedly due to roughly isotropic irregularities in the F-region of the ionosphere, the most reasonable explanation for strong scintillations in equatorial regions is in terms of field-aligned irregularitiesin the plasmasphere. Such irregularities appear to be potentially important for scintillation purposesat least up to the magnetospherio L-shell of 1.3, and possibly up to 2 or more.
REFERRECES AARONS J., WHITNEY H. E. and ALLEN R. S. BAILEY D. K., BATEMAN R., BERKNER L. V., BOOKER H. G., MONTGOMERYG. F., PURCELL E. M., SALISB~Y W. W. end WEISWER J. B. BOOKER H. G., RATCLIFFE J. A. and SHINN D. H. BOOKER H. G. and GORDON W. E. BOOKER H. G. BOOKER H. G. BOWHILL S. A. BRAMLEY E. N. BRIQ~S B. H. and PARKIN I. A. GOLD T. HEWISE A. KOSTER J. R. KOSTER J. R. LITTLE C. G. and LOVELL A. C. B. POPE J. H. and FRITZ R. B. RATCLIFFE J. A. RUPENAOH C. L. RUFENAOE C. L. RUFENACH C. L. RYLE M. and HEWISH A. SINGLETON D. G. SmTH F. G. SPENOER M. STOF#ZYL. R. 0. TAUIZ R. R. WERNIK A. W. and LIO C. H.
Referen
1971 1962
Proc. IEEE 59, 169. The PhyaiGd Review 88, 141.
1960 1960 1968 1969 1961 1974 1963 1969 1962 1963 1966 1960 1971 1966 1971 1972 1974 1960 1974 1960 1966 1963 1973a 1974
Tram. Sot. AM!?, 579. Proc. IEEE 58,401.
PTOC.IEEE 46, 293. J. geophys. Res. 64, 2164. J. Res. natA. BUT. Stand. 66D. 276. J. atmoa. terr. Phya. 36, 1603: J. atmoa. terr. Phys. 25, 339. J. geophya. Rea. 64, 1219. Proc. R. SOG.214, 494. J. geophy8. Rea. 68,2679. An& &?ophye. 22. 436. NatUT6, Lo&. 165, 423. Ind. J. Pure Appl. Phye. 9,693. Rep. Progreaa Whys. 19, 183. J. atmoa. tew. Phy8. 85, 1941. J. geophys. Rea. 72, 4761. J. geophye. Reu. 79, 1602. R. Astron. SGG.110,384. J. atmoa. terr. Phys. 36, 113. Nature, Land. 166, 422. PTOG.Phya. SOG.6SB, 493. Phil. Trans. R. SOG. A&6, 113. Cornsat. Tsohn. Rev. 8,146. J. atmos. and terr. Phye. 86,871.
ie a&o made to the following unpublished matwial:
&AFT H. D. and WESTERLUND L. H. CIUluE R. K. SESSIONSW. B.
1972 1974 1972
STEVENS R.
1973
TAG
1973b
R. R.
AIAA 10th AerospaceSciencesMeeting,Paper179. AIAA 12th Aerospace Sciences Meeting, Paper 62. Goddard Spaoe Flight Center, Tech&al Rept. X-810-72-282. Electromagnetic Systems Laboratory, Memorandum 6319. Comsat Leboratories Technical Memorandum CL29-73.
to 1098.
Pergamon Prem,1975.Printedin NorthernIreland
The role of the magnetosphere in satellite and radiostar scixltillation HENRY G. BOOKER Department of Applied Physics end Information Science,University of California, San Diego*, La Jolla, California 92037,U.S.A. (Received
17 October 1974; in rem&dform 9 December1974)
Abstract-A theory is developed to accountfor the scintillationphenomenonobserved in equatorial regions when using communicationssatellites in the SHF band. The same theory is also used qualitatively to explain strong scintillationsin the VHF band. Instead of comiuing irregularities to a narrow interval of height in the P-region and 8aSUmiUg that they are strong, the alternative hypothesisis used that the irregularitiesare weak but extend from the P-region upwards into the magnetosphere. It is suggestedthat the irregularitiesare field-alignedand extend at least up to an L-shell of 1.3 and possibly up to 2 or more.1. INTRODUCTION It has long been established that weak scintillation of radio stars occurs in the F-region of the ionosphere (HEWISH, 1952). It has also been generally assumed that the same is true for strong scintillation in which the r.m.s. amplitude fluctuation is equal to the mean amplitude. In fact, however, the methods for assessing the height of occurrence of the irregularities are quite unsatisfactory for conditions of strong scintillation. In consequence, it is not established at this time that the imposition of strong scintillations in the VHF band is confined to a hundred or so kilometers in the vicinity of the level of maximum ionization density in the F-region. In transferring one’s attention from weak to strong scintillations in the VHF band, there are two main alternatives: Either (1) One can can confine attention to the same hundred or so kilometers of height near the level of maximum ionization density in the Pregion and increase the magnitude of the mean square fluctuation of ionization density by a power of ten or so, so (2) One can continue to use roughly the same magnitude for the mean square fluctuation of ionization density and increase the interval of height occupied by the irregularities by a power of ten or so. Although the Srst of these alternatives is the one customarily chosen, there is no present * Much of this work was performed by the author as a consultant to the RAND Corporation, Santa Monica, Californie. The remainder was supported by National Aeronautics and Space Administration Grant NGR05-009-076and National Science Foundation Grants GA-20691 and 30628.
observational reason for rejecting the second alternative. We therefore pursue the second alternstive in this paper. In recent years satellite scintillation phenomena have been observed in the SHF band (CRAFT and WESTERLUND, 1972; TAUR, 1973a; CRANE, 1974), and this phenomenon has also been interpreted on the basis of alternative 1 (CRAFT and WESTERLUN~, 1972; TAUR, 1973a, 1973b; CRANE, 1974; WERNIK and LIU, 1974; RIJFENACH, 1974). However, the Fresnel distance for irregularities that have a size of a few hundred meters is of the order of an Earth’s radius in the SHF band. Consequently, Fresnel fltering favors irregularities in the magnetosphere in comparison with irregularities in the ionosphere at SHF. It is alterntive 2 therefore, rather than alternative 1, that provides irregularities at the heights that are most effective in causing amplitude scintillation et ground level in the SHF band. Arbitrary concentration on alternative 1 therefore seems no longer to be justified. In consequence, we examine alternative 2 in this paper. 2. EXPEFtJMENTALFACTS Radio star scintillation was identiSed as a phenomenon associated with the Earth’s plasma envelope by SMITE (1950) and by LITTLE and LOVELL (1950), who found that, while the scintillations were uncorrelated for a ground separation of 100 km, a significant degree of correlation existed at 1 km. This work w&8 done before the discovery of the magnetosphere (STOREY, 1963), so that only the ionosphere was then available for explaining the scintillations.
1089
1090
H. CT.Booxxa
Using phase rather than amplitude observations, RYLE and HEWISE (1950) showed that the correlation distance, or diversity separation, for the relatively weak scintillation phenomenon commonly encountered in middle latitudes corresponds to a scale L of about 5/(2a) km, or about 800 m. Similar results have been obtained recently by BRAMLEY (1974). Somewhat greater values for the diversity separation are obtained in the northsouth direction, indicating the presence of some elongation of the irregularities, presumably along the direction of the Earth’s magnetic field (SPENCER, 1955). For the relatively weak scintillation phenomenon in middle latitudes, however, drastic elongation of irregularities along the Earth’s magnetic field was not found, and this has recently been confirmed by SINQLETON (1974). The work of Singleton and that of RUFENACH (1971, 1972) shows in addition that there is a turbulence-like spectrum of irregularities extending down to scales of less than 100 m, and that this spectrum has an inverse power-law decrease, with an index of the order of 4. An estimate of the height of the irregularities in the ionosphere was first obtained by HEWISH ( 1952) by exploiting the fact that, at wavelength II, irregularities of size L closer to the observer than the Fresnel distance vL2/1 produce phase fluctuations rather than amplitude fluctuations. By measuring both, he was able to recognize that the fluctuations associated with the weak midlatitude scintillation phenomenon occurred at an P-region level. He quoted a value of 400 km which haa since been repeatedly used as the height of the irregularities. In reality, however this height has not been determined with precision. The statement of kbRONS et al. (1971) that the irregularities “lie, for the most part, in the F-layer of the ionosphere at heights predominantly ranging from 225 400 km” is more satisfactory. The intensity of weak scintallations varies wth the wavelength of observation. At small zenith angles in the VHF band the ratio of the r.m.s. amplitude fluctuation {(AA)s}l/s to the mean amplitude A varies as i2. At large zenith angles however, the variation is believed to be aa A, although the experimental evidence is not clearly delineated in the literature. The latter behavior corresponds to a situation in which 800 m irregularities in the F-region are at a distance from the observer greater than the Fresnel distance rL2/1. From time to time in middle latitudes, and quite frequently in polar and equatorial regions, a more inmnse scintillation phenomenon is observed having
significantly different characteristics. For the intense scintillation phenomenon, amplitude fluctuations in the VHF band frequently reach 100 per cent and the statistical distribution of amplitude acquires the Rayleigh type, suggesting that all the radiation that is being received has been scattered. For intense scintillations, the methods for determining the height at which they are imposed become unsatisfactory. The diversity separation in the east-west direction is less for the strong phenomenon than for the weak. Values as low as 50-60 meters have been observed (KOSTER, 1966). Mean values near the Equator are quoted as about 400m for radio stars observed in the VHF band at substantial northerly zenith angles (KOSTER, 1963), and about 200 m for a 136 MHz satellite observed at smaller zenith angles (KOSTER, 1966). Observed values of the diversity separation near the Equator for strong scintillations are much greater in the north-south direction than in the east--west direction. The ratio is not less than 30 and could well be virtually infinite (Koster, 1966). For strong scintillations the phenomenon is not confined to the VHF band. In equatorial regions not only is scintillation observed for satellites operating in the UHF band (SESSIONS,1972), but they are sometimes observed even in the SHF band (CRAFT and WESTERLJJNIJ,1972; TAUR, 1973a; CRANE, 1974), especially in the evening hours. Scintillations have been observed at a frequency as high as 8 GHz (STEVENS, 1973). Moreover, it should be noted that these observations are not restricted to large zenith angles. The observations in the SHF band have been made with a stationary satellite, and there is no present information about what would happen in this band with an orbiting satellite. For strong scintillations near the Equator the r.m.s. amplitude fluctuation ((u)2}1’s is frequently equal to the mean amplitude A of the signal in the VHF band. In the SHF band
(( AA/A)2}1’2 is always less than unity and is proportional to 1s (CRAFT and WESTERLUND, 1972). The frequency dependence in the intervening UHF band is not precisely described in the literature. However, the fact that the occurrence of scintillations in the SHF band came
as
a surprise
is an indication that the variation of { ( AA/A)a}l12 in the UHF band is less rapid than A2. Proportionality to 1 in the UHF band is a reasonable presumption (see POPE and FRITZ, 1971). No corresponding measurements of phase-fluctuation are available. The equatorial scintillation
The role of the magnetospherein satellite and radio-star scintillation phenomenon weakens beyond 25’N geomagnetic latitude (&AFT and WESTEFCLUND, 1972); it is observed as far as 20% geomagnetic latitude, but no observations have been made further south. 3. THE SPECTRUIUOF IltItEtXlLARIl’IES
1091
r.m.s. phase fluctuation {m}u2 in the SHF band in equatorial regions,.it turns out to be large compared with one radian. We assume, however, that this is an unlikely eventuality, and that (A+)2, like (AA/A)2, is less than unity in the SHF band. On this basis the SHF scintillation phenomenon should be explicable to the first order in terms of the Born approximation. Scintillation is a forward scattering phenomenon for which there exists an angular spectrum of scattered waves that is principally concentrated within a certain beam-angle. We shall assume that waves scattered well outside this beam-angle are unlikely to be important for the communications aspects of scintillations in much the same way that the sidelobes of an antenna are usually unimportant. Just as an antenna is then characterized largely by its overall aperture-width, so the forward scattering properties of the irregularities are largely characterized by their outer scale. For the effects of a particular scintillation phenomenon, we assume that it is the value of the outer scale, and the associated scattering angle, that is likely to be of greatest importance for communications purposes. This does not rule out the possibility that two causes of irregularities can exist in the same part of space. For example, the following two causes can be considered:
Ionospheric scintillation phenomena are usually explained in terms of the concept of a phasechanging screen introduced by BOOKER et al, (1960), and further described by RATCLIFFE (1956). These authors illustrated their work with a Gaussian autocorrelation function for the irregularities, partly for mathematical simplicity but also because a correlation function of this type was thought to be reasonable at that time. This pattern was followed by many subsequent investigators. The theory of Booker et al. was originally devised to relate the field pattern observed at the ground to that existing in the ionosphere. However, for studying how the field fluctuations are created in the ionosphere, there is much to be said for the volume scattering concept adopted by BOOKER (1958). This was based on the theory of tropospheric scatter communication devised by BOOKER and GORDON (1950). These authors did not use a Gaussian autocorrelation function because such a function is inappropriate for turbulence and would have completely failed to explain the wavelength dependence of the scattering phe(1) Suppose that noise in the atmosphere nomenon then under discussion. Instead, they generates ion acoustic waves in the ionosphere used an exponential autocorrelation function, leadthat lead to roughly isotropic irregularities of size ing to a turbulence-like spectrum of irregularities L (-800 m), and that these waves are absorbed by decaying below the outer scale proportional to a turbulence-like process in which energy is passed the inverse fourth power of the spatial frequency. to progressively smaller scales, until the scale is The same theory was subsequently used by BAILEY small enough for the energy to be converted into et al. (1952) to predict the phenomenon of ionothermic motion of the ions and electrons. Such spheric scatter communication. If they had not a phenomenon is more likely to occur in the used an inverse power-law spectrum, the prediction ionosphere than in the magnetosphere. would not have been made. In explaining this (2) Suppose that plasma instability leads to phenomenon in detail, various autocorrelation functions were considered by BOOKER (1959), generation of ion acoustic waves that travel roughly leading to inverse 4, 5 and 6th power-law spectra. perpendicular to the direction of the Earth’s All such radio scattering phenomena have required magnetic field and that create field-aligned iran inverse power-law, and not a Gaussian, spectrum regularities with a transverse scale T (-300 m). to explain them, and the recent work of RUFENACH Suppose that these waves are absorbed by a (1972) and SINGLETON (1974) shows that scattering turbulence-like process in which energy is passed in the F-region associated with the weak mid- to progressively narrower field-aligned irregularities until the scale is small enough for the energy to be latitude scintillation phenomenon is no exception. It is possible to assume that the way in which the converted into thermic motion of the ions and electrons. Such a phenomenon is more likely to spectrum decays below the outer scale is important for the SHF scintillation phenomenon (RUFENACH, occur in the magnetosphere than in the ionosphere. 1974; WERNIK and LIU, 1974). However, we Indeed, it was consideration of such a phenomenon shall take a different point of view. It could be that led to invention of the term magnetosphere that, when observations have been made of the by GOLD (1959).
H. G. BOOKER
1092
In both cases irregularities an
outer
inverse
scale,
would
power-law
spectrum
and would be converted inner
scale.
exist
to extend
diffusion
across
the
Earth’s
that
could
communications
but would
satellites 1974). of what
be explained
irregularities
is an important
in SHF
satellite
Substituting equation
of
for
(I),
fluctuation
(An/n)2
we
a theory in
= ~T,~~~(AN)~L~ (A(P),,~ We
now
acteristics
have
to calculate
its effect
downwards
from the screen, the phase-fluctuations
amplitude
fluctuations
may
that
somewhat,
develop
of
phenomena
7 at a height mean
h above
square
was
given
by
noted
that
his
( AN)s.
where,
for
relevant
isotropic
distance
in the
index
layer
direction
where
re is the
(2.82
x 10-15 m).
phaso introduced irregularity
classical The
of propagation
and
of h set
The
a = T.
to the ground
is
is h set
x.
x to 2, BOWHILL
shown that the mean square phase
(Aq)z
and the mean
fluctuation
(AA/A)2
square
fractional
at ground
level are
given in terms of the mean square phase-fluctuation at the screen by
These
(b)02
(6)
(ANo2
(7)
(1961).
of
outer
of thickness
electron-density
radius
/AAl
of
square
into a passing wave
Yi-= J
+’(h set x\”
1
deviation the two being such that
(1) the
\
be
jl is
r,214(AN)2
mean
the layer
of the ratio
amplitude
surface. Let the
n at wavelength
= 22
irregularities,
from
can now be made,
Then the mean square fractional
of refractive
distance
Moreover,
irregularities
in
the
errors and
of BOWHILL
the Earth’s
fluctuation
fluctuations
2 = aL2/t
fluctuation
coefficients.
scale L exist in an ionospheric
amplitude
is given by the Fresnel
In terms
by isotropic
minor, need correction.
isotropic
and
also be
is of major
a number of printer’s
that
As we move
the
involve
work
at ground level.
which
equations
in the theory
char-
over
it
some improvements
whose
(4)) and we have
distance
The fact
(1958),
based on the subsequent
screen
(1952),
systems.
also some errors in numerical
phase
HEWISII
BOOKER
errors, although
a
(4)
by
scintillation
be
from square
shown
case, the character
ionosphere
mean
set x.
are specified by equation
But we assume that
should
of (AN)2
the
As
of scintillation
the
for
decrease
in the two cases,
communications
in terms
obtain
develop.
4. SCINTfLLAl’IONS DUE TO ROUGHLY ISOTROPIC IRREQULARPHRS
Suppose
of
of phase at the under side of the layer
(1961,~.281)has
irregularities
x, a
isotropic
of the irregularities
in explaining
Although
angle
a total mean square phase fluctuation
the
phenomena
height-ranges
that, in either
the decay spectrum importance
at zenith
(TsecX)/L such irregularities,
of field-aligned
one.
must be recognized.
it is unlikely
producing
could
and LIU,
of roughly
in terms
the outer scales may be different
is
scintillation
scintillation
and
different
In
(cf. WERNIK
irregularities
the relevant
field
field.
the
in terms what
the
not
where
both phenomena
influence
question
and that
the layer
exist in
magnetic
along
BRAMLEY,
should
through
at an
into the lower ionosphere
with
and
The
might
going
The second phenomenon
of the ionosphere
coexist
frequencies, motion
In
radio wave encounters
but would not be likely to extend far
be likely
1974;
of spatial
in the magnetosphere
comparable
at
a presumably
into thermic
into the magnetosphere.
F-region
be created
via
The first phenomenon
the ionosphere might
would
decay
electron
deviation
of
by a typical
(W2 Equations focussing been
averaged
value greater unity.
is
(6) and
+ (AA/A)2 and out.
If
from
(6) and (7) gives,
the
which
(AA/A)2
than unity,
If (Av,)~ calculates
Substitution
include
defocussing,
unity, an extrapolation
(2)
(7)
= (Av)a2. have
effects
of
however
calculates
to
it should be replaced to a value greater
of the theory equation
a by
than
is involved.
(4) into
equations
for the mean square phase and
The role of the mtlgnetosphere in satallite and radio-star scintill&ion
we would then need to have
amplitude fluctuations at ground level,
+-
(Ad2
2(
-
2
L = 100m.
2
1 h see x )
h.BBCx s 2 ( )
1+
1 h BBCx 2 _2( 2 )
set x
1+
(
2
((Afff~Q~j~‘~
)
(10)
\ When set x > Z/h we have
( 11) but when set x < Z/h the formulae become, using equation (5), (Ap)’
+
4r,212(AN)2Lr set x ha 2le(AN)2 - 7 sees x.
(12) (13)
L2
The weak mid-latitude scintillation phenomenon can be explained in terms of these equations by using parameters of the order L =800m,r
=200km,h
-3OOkm
(14)
and using a value of {m}us small oompared with the average ionization density in the F-region. By using & larger value of ((ANa))1/2, let us now attempt to use the same formulae to explain the strong scintillations observed with satellites in equatorial regions (alternative 1 in Section I). In equation (10) the change from the ,X2law in equation (II) to the Eplaw in equation (13) occurs when
that is, when (equ&tion 5) I = (?7L2 COBx)/h.
(18)
1
h set x a *
-
(16)
In order to explain the wavelength dependence for roughly vertical propagation at the Equator, let us assume on the basis of the observations described in Section 2 that the transition-wavelength in equation (16) has the value 10 cm for a value of cos x of the order of unity. Taking h to be 300 km,
(17)
If we now substitute this value into equations (9) and (lo), and use h = 300 km, 7 = 200 km, x = 0, we obtain, for a frequency of 8 GHz,
(9)
4r,“;l”(AN)‘Lr
1093
= I.6 x 10-‘a((AN)“)*~2-
(19)
It follows that, if { ( AN)2)1/2 can be of the order of 1011 mw3, there then would be, at 8 GHz, e phasefluctuation of 0.1 radian and an amplitude fluctuation of 1.6 per cent. It is therefore possible to explain, in accordance with alternative 1 in Section 1, the magnitude of SHF satellite scintillations in terms of irregularities in a 200 km slab in the F-region by using an outer scale of the order of 100 m and an r.m.8. fluctuation of ionization density of the order of 1Oii rne3. Plasma physists would, however, have some difficulty in explaining such behavior in the ionosphere. The needed s&e is comparable with the mean free path of ions in collision with themselves, and the needed fluctuations of ionization density are comparable with the mean ionization density in the F-region, especially at night when scintillations are more common. In addition, roughly isotropic irregularities do not explain the extreme elongation of the field irregularities observed at ground level in equatorial regions in the VHF band. It is appropriate, therefore, to turn attention to alternative 2 in Section 1 and to pay more attention to m~etosphe~~ phenomena. 6. SCDTTILLATIOIiSDUD TO FYELD-ALIWED AGUE
Consider a magnetosphere with field-aligned irregul&rities stretching from the ionosphere in one hemisphere to that in the other. Let T be the outer scale of the irregularities, measured transverse to the Earth’s magnetic field. Allowance should be made for the geometrical variation of T along a particular tube of flux. Allowance also needs to be made for the fact that a, radio wave passing through the magnetosphere is in general propag&ing in a direction making an angle p with the local line of flux of the Earth’s magnetic field. In consequence, the value of L to be used in equations (2), (3) and (4) when handling fieldaligned irregularities is T cosec qa. Furthermore, BOWHILX,(1961, p. 282) has shown that the development of amplitude fluctustions as
H. Q. Booxxn
1094
one moves away from a phase-screen that involves aligned irregularities is appreciably slower than for one that involves isotropic irregularities. As a result, the numerical coefficient a in equation (6) is not rr but lr(8/3)l12. It should also be noted that L in equation (6) is to be replaoed by T, not by T cosec rp. Bowhill also gives a more complicated function to describe the growth of amplitude scintillations in moving away from a phase-screen of aligned irregularities than that applicable for isotropict irregularities. However, to simplify the evaluation of integrals we will preserve the simpler function. We shall now be involved with phase screens stacked over an extended range of height, so that it is necessary to replace the thickness 7 in equations (9) and (10) by an element of height dh and to integrate over all relevant heights. By making all the replacements described, equations (9) and (10) become 1 h set x
l+i-
s Co
4r6212
0
1+
x (AN)2T
2
( 1 ( > h se0 x
2
z
cosec ye set x dh
magnetosphere, ( AN)2 almost oertainly increases with decrease of height. At some height in the magnetosphere, however, (AN)2 must cease to increase as rapidly as N2 because diffusion transverse to the Earth’s magnetic field becomes more important at lower levels. On the other hand, starting from below the magnetosphere, iarv)z for field-aligned irregularities must increase from zero in the lower ionosphere. It follows that, at some level in the plasmasphere, (AN)2 must have a maximum, but there is no present information as to the height at which this maximum occurs. In particular, there is no reason to believe that the maximum of (AN)2 occurs at the height of maximum ionization density in the F-region, or indeed in the ionosphere at all. In the present state of ignorance, let us assume that {(AN)2}r/2 is small compared with the maximumionization density in the F-region, and that it has a constant value between an ionospheric height h, and a magnetospheric height hM. At the height h,, N2 may be assumed to have decreased
z
-
plasmapause in the equatorial plane, (AN)2 may be assumed to be proportional to Nz and even more-or-less equal to N2. Hence, far out in the
(201
to the postulated value of (AN)2. Above the height hM it would be reasonable to assume that (AN)2 decreases with Ns. However, for simplicity of calculation, we will assume that irregularities above the height hM make no important contribution to scintillations and may be neglected.
\
x (AN)2T
cosec ly set x dh.
(21)
We have shown the integral as running from zero
We then have a model in which (AN)2 for fieldaligned irregularities is constant from an ionospheric height h, up to a magnetospheric height hM, and vanishes elsewhere. With the assumptions described, equations (20) and (21) reduce to
to infinity in height, but (AN)2 can be set equal to zero for heights that are not relevant. To simplify evaluation of the integrals in equations (20) and (21) let us confine our attention hdl1 -t 4(h/z)2dh to communication between a stationary satellite (AP)~ = ~v,~A~(A.N)~T hI 1 + (h/-V2 at the Equator and an Earth terminal vertically below it. We may then put x = 0 and y = ?r/2. hdi (h/g)2 dh (23) Furthermore, over the interval of height with = ~T,~A~(AN)~T hl 1 -t (h/Q2 ' which we are likely to be concerned, no pronounced s variation of T is to be expected at the Equator. Evaluating the integrals, we obtain Let us therefore assume that T is independent of height. A more difficult decision has to be made con(h&g) - tan-’ V+)}l (24) cerning the variation of (AN)2 with height, Well out in the magnetosphere, where diffusion transverse to the Earth’s magnetic field is small, there is no objection to assuming that field-aligned z{tan-’ (hN/Z) - tan-‘(hi/Z))]. irregularities are strong. As we come in from the (25)
-s
(22)
The role of the magnetospherein satellite and radio-star scintillation The precise numerical value of h, in equations (24) and (25) is in fact unimportant. If one has integrated through a considerable part of the plasmasphere, it makes little numerical difference whether one stops the integration at a height of 500 km, 150 km or 0 km. We may therefore simplify equations (24) and (25) by putting h, = 0. If at the same time we substitute for the Fresnel distance 2 from equation (5), we obtain 1 + $ tan-’ t
(26) 0
1 - $ tan-‘:
(27) 0
where 1, = ~(8/3)l’~ T2/hM. Since, in equation (27),
l-
!!? tan-l1
I
1 N
10
1 1 2 0 ( 33,
if
1 > 1,
(29)
if
1 Q 1,
(30)
we see that (AA/A)2 is proportional to A2 at long wavelengths and to ;(a at short wavelengths, the break between the two behaviors coming where
where 1, = 5.77 X 10e2 m.
(36)
At a frequency of 8 GHz this gives = 1.0 x 10-11((AN)2)“2 {(AA/A)2}1’2
(37)
x 10-12{(AN)a)1’2.
= 2.5
(38)
We therefore see that the scintillation phenomenon at 8 GHz can be explained in terms of fieldaligned irregularities having an r.m.s. fluctuation of ionization density small compared with the maximum ionization density in the P-region. However, these irregularities need to exist over a few thousand kilometers of height rather than a few hundred kilometers. Using the value 300 m for the transverse scale T of the field-aligned irregularities and the value 8000km for the magnetospheric height hB, to which the irregularities extend, and taking the lower bound of the irregularities to be at a negligibly small height (say, a height in the P-region), the r.m.s. phase fluctuation at ground level in radians calculates, in accordance with equation (34), to the values shown in Fig. 1; the part of the Wavelength, i-2
rz=
1095
rn
I
IO-’
1/3A,
or (equation 28) L = 2d27rT=/hM.
(31)
If, on the basis of the observations described in Section 2, we take this transition wavelength to be 10 cm, and put T = 300m,
(32)
hM = 8000 km.
(33)
we deduce that We are therefore dealing with the part of the plasmasphere extending out more than an Earth’s radius. If we now substitute these values for T and hM into equations (26), (27) and (28), we obtain for the mean square phase and amplitude fluctuations at ground level (A#)2
= 3.82 x 10-20i12(AN)2
I
I
Frequency.
I20 Pan-
12 n0
I
I
I
100
1000
10000
MHz
Fig. 1. The frequency variation of r.m.8. phase fluotuations at ground level for field-aligned irregularities of outer scale 300 m existing in the plasmasphere to a height
of
8000 km.
Vertical
propagation
et
the
Equator is assumed. The portion (A+)2 > 1 is an extrapoletion.
H. G,
1096
BOOKRR
diagram for which (A$)2 > 1 should be viewed with caution. Likewise, on the basis of equation (35), the r.m.s. fluctuation in the fractional amplitude at ground level calculates to the values shown in Fig. 2. These values are in general aocord with the observational facts for scintillation phenomena observednear theEquator using stationarysatellites more-or-less overhead. 0. TEE REWETS AT WHICH SCINTILLATIONS m =OSED To examine the heights in the plasmasphere that are responsible for causing scintillations when the phenomenon is strong we need to plot the integrands in equations (22) and (23) as functions of height. This is done in Fig. 3 for phase scintillations and in Fig. 4 for amplitude scintillations. The ordinates in Fig. 3 and 4 are the coefficients of the expression 29
ile (AN)2 T
I
(39)
in the integramls appearing in equations (22) and (23) respectively. The same parameters have been used as for Figs. 1 and 2. The nerves have not been plotted for heights greater than 8000 km because our crude model of the plasmasphere assnmes that there are no irregularities above this height. Likewise the curves have not been plotted below a ~v~~~gth, -2 K)
10-l
m I
to
I 0
I
I
t
4000
6000
6000
I
2000
Height,
I 10000
km
Fig. 3. The height-weighting in the plasmaspherefor phase tluctuationsat ground level due to field-aligned irregularitiesof outer scale 300 m. Vertical propagation at the Equator is ~~~WTXKL height of 400 km because the field-aligned irregularities presumably do not extend below the a-region. It is olear from Fig. 3 that the whole range of heights up to the assumed cut-off at 8000 km is ~otenti~ly important in causing phase scintillations. On the other hand, Fig, 4 shows that, for amplitude scintillations, irregularities at clistanoes closer to the ground than the Fresnel distanoe 2 tend to be suppressed. The assumption of a uniform value of (alv)z extending from a height of 400 km up to a height of 8000 km is, of course, unlikely to be correct. But the notion that one is concerned at the Equator with the first few thousand kilometers of the plasmasphere, rather than the first few hundred kilometers, should be taken seriously. A more
1000
IO0
MHZ Fig. 2, The frequency variation of T.M.B. fracrtioti amplitude flu&u&one at ground level for &&Migned irregularities of outer so& 300 m existing in the Freawncy ,
plasmasphere to a height of 8000 km. Vertioal propagation at the Equator is assumed.
plausible distribution of (AJJ)2 in the plasmasphere would involve rough uniformity between a height of 400 km and the L shell of 1.3, with smaller values for higher I;-shells, The &-shell of 1.3 intersects the 400 km level at the latitudes f26’, which are the approximate locations where the
The role of the magnetosphere in satellite and radio-star scintillation
1097
Thus, when (A#)2 is large compared with unity, there are about ( A#)2 scatterings in passing through the plasmasphere. On a random walk basis the total mean square scattering angle is then {A/(2nT)}2 (A+)2, leading to an outer scale in the field pattern at the ground of the order of T/(( A+)2}1/2. We may conveniently allow for both the single and mulitple scattering situations by defining the diversity separation transverse to the magnetic meridian as
1
;-~
0
D=
T -. (1 + (A$)2}1’2
If we use the estimates
(40)
of (A#)2 in Fig.
1, we
derive for the diversity separation in equation (40) 2000
4oco
Height,
6000
8000~
10000
km
the estimates shown in Fig. 5. the
Fig. 4. The height-weighting in the plasmasphere for amplitude fluctuations at ground level due to fieldaligned irregularities of outer scale 300 m. Vertical propagation at the Equator is assumed.
diversity
separation
In the SHF
is simply
outer scale of the field-aligned
equal
band to the
irregularities,
this we have assumed to be 300 m.
and
In the VHF
band, however, multiple scattering can reduce the diversity separation substantially.
equatorial
scintillation
phenomenon
is observed
to decrease (CRAPYCand WESTERLUND, 1972). In accordance with equations (20) and (21), useful information about the dependence of ( AN)2 T upon height should be obtainable by measuring the ratio of (AA/A)2 to (A$)2 as a function of frequency at frequencies such that both quantities are less than unity.
It should be noted estimate
of
the
that expression
diversity
separation
(40) is an for
phase
and that, for amplitude fluctuations,
fluctuations,
Wavelength, I
IO-' I
m I I
I
1
7. THE DIVERSITY SEPARATION A point of interest for communications purposes is the minimum distance by which antennas must be separated in order to receive more-or-less uncorrelated fading. For the field-aligned irregularities that we have postulated in the plaamasphere, it is only separation perpendicular to the magnetic meridian that is involved. So long as m < 1, only single scattering is involved and it may be assumed that the diversity sepsxation is given by the outer scale T of the field-aligned irregularities. The scattered waves constitute a fanbeam of half-angle il/(%T) and, as shown by BOOKER et al. (1950), these waves synthesize at ground level to a field pattern having an outer scale T. If, however, s
is appreciably greater then unity, multiple scattering is involved. As a rough guide for experimental purposes, the path may then be divided into sections for each of which (A+)3 is equal to unity. The number of sections is then roughly the number of scatterings involved. 3
RMS. fluctuation in ionization density
I 10000
I
I
I 1000
Frequency,
! loo
MHz
Fig. 6. The frequency variation of an estimated east-west diversity separation for field-aligned irregularities of outer soale 300 m existing in the plasmasphere to a height of 8000 km. Vertical propagation at the Equator is assumed.
H. G. BOOKER
1098
the diversity separation can be greater. Figures 3 and 4 show that, in general, a smaller thickness of the plasmasphere is important for amplitude fluctuations than for phase fluctuations, and in the VHF band this reduces the number of successive scat&rings that are important for amplitude fluotuations. However, the resultingnumerical changes in Fig. 5 are not major. ’ It should also be noted that the value of 300 m that we have used for the transverse outer scale of field-aligned irregularities is in fact bssed on observations that show a spread in the values of the east--west diversity separation extending from 430m down to 50m (KOSTE~, 1966), measured with a stationary satellite at a frequency of 136 MHz. It would not be unreasonableto assume that the transverse scale of the irregularitiesin the plasmasphereis around 430 m and that the smaller
values of diversity separation observed at ground level are associated with various degrees of multiple scattering. This interpretation would increase still further the value of hM derived in equation (33), and make it even more important to considera substantial depth of the plasmaspherein seeking an explanation of equatorial scintillation phenomena. 8. COECLlJsIOEs While weak mid-latitude scintillation is undoubtedly due to roughly isotropic irregularities in the F-region of the ionosphere, the most reasonable explanation for strong scintillations in equatorial regions is in terms of field-aligned irregularitiesin the plasmasphere. Such irregularities appear to be potentially important for scintillation purposesat least up to the magnetospherio L-shell of 1.3, and possibly up to 2 or more.
REFERRECES AARONS J., WHITNEY H. E. and ALLEN R. S. BAILEY D. K., BATEMAN R., BERKNER L. V., BOOKER H. G., MONTGOMERYG. F., PURCELL E. M., SALISB~Y W. W. end WEISWER J. B. BOOKER H. G., RATCLIFFE J. A. and SHINN D. H. BOOKER H. G. and GORDON W. E. BOOKER H. G. BOOKER H. G. BOWHILL S. A. BRAMLEY E. N. BRIQ~S B. H. and PARKIN I. A. GOLD T. HEWISE A. KOSTER J. R. KOSTER J. R. LITTLE C. G. and LOVELL A. C. B. POPE J. H. and FRITZ R. B. RATCLIFFE J. A. RUPENAOH C. L. RUFENAOE C. L. RUFENACH C. L. RYLE M. and HEWISH A. SINGLETON D. G. SmTH F. G. SPENOER M. STOF#ZYL. R. 0. TAUIZ R. R. WERNIK A. W. and LIO C. H.
Referen
1971 1962
Proc. IEEE 59, 169. The PhyaiGd Review 88, 141.
1960 1960 1968 1969 1961 1974 1963 1969 1962 1963 1966 1960 1971 1966 1971 1972 1974 1960 1974 1960 1966 1963 1973a 1974
Tram. Sot. AM!?, 579. Proc. IEEE 58,401.
PTOC.IEEE 46, 293. J. geophys. Res. 64, 2164. J. Res. natA. BUT. Stand. 66D. 276. J. atmoa. terr. Phya. 36, 1603: J. atmoa. terr. Phys. 25, 339. J. geophya. Rea. 64, 1219. Proc. R. SOG.214, 494. J. geophy8. Rea. 68,2679. An& &?ophye. 22. 436. NatUT6, Lo&. 165, 423. Ind. J. Pure Appl. Phye. 9,693. Rep. Progreaa Whys. 19, 183. J. atmoa. tew. Phy8. 85, 1941. J. geophys. Rea. 72, 4761. J. geophye. Reu. 79, 1602. R. Astron. SGG.110,384. J. atmoa. terr. Phys. 36, 113. Nature, Land. 166, 422. PTOG.Phya. SOG.6SB, 493. Phil. Trans. R. SOG. A&6, 113. Cornsat. Tsohn. Rev. 8,146. J. atmos. and terr. Phye. 86,871.
ie a&o made to the following unpublished matwial:
&AFT H. D. and WESTERLUND L. H. CIUluE R. K. SESSIONSW. B.
1972 1974 1972
STEVENS R.
1973
TAG
1973b
R. R.
AIAA 10th AerospaceSciencesMeeting,Paper179. AIAA 12th Aerospace Sciences Meeting, Paper 62. Goddard Spaoe Flight Center, Tech&al Rept. X-810-72-282. Electromagnetic Systems Laboratory, Memorandum 6319. Comsat Leboratories Technical Memorandum CL29-73.