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Underlying processes of the Jovian decametric radiation / online

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as possible. Figure 8 shows the velocity wave structure at
1 AU during these periods.

In devising a suitable model for the stream interaction
it must be remembered that only large scale effects are of
interest. The microscopic details of the interaction appear
to be very complex and they will be ignored as much as possible
in favor of predicting the macroscopic development of the
density wave. Intuitively, the smaller the amount of inter-
action that takes place before the wave-Jupiter encounter the
less important the microscopic details are.

Input Data

Before proceeding with the development of the models a
discussion of the treatment of the experimental data is in
order. The reduction procedure for the October 1967 - May 1968
apparition and that of the April 1974 - December 1974 apparitions



54



B OUTWARD




SOLAR MAGNETIC SECTORS
OCT. 67 -MAY 68
APR. 74- DEC. 74



Figure 9. Solar magnetic sectors 1967-68 and 1974,



55



differed in some respects. The ultimate goal, however, was
the same.

Figure 10 shows the relative positions of the earth, sun,
and Jupiter for some arbitrary time before opposition. Since
the velocity of the streams is radial, the data of interest are
the velocities as a function of time; at 1 AU on the line
connecting the sun with Jupiter, Since in general no obser-
vations are continuously made at that point, it is necessary
to either interpolate or extrapolate what data are available
to that point.

Despite the radial motion of the stream, the "garden
hose" effect causes the position of the point of intersection
of the stream on the 1 AU orbital circle to rotate with the
sun. Consequently, any projection of measurements made off
the sun- Jupiter radial to the radial involves not only a
projection in space but in time as well. The intersection
point moves in the posigrade sense about 13 •* per day. Conse-
quently, if a measurement is made at a point 13° behind the
radial line, that value becomes an estimator of the velocity
on the radial the following day. If interpolation between two
satellites which straddle the sun-Jupiter radial is employed,
one must assume that any changes that occur are sufficiently
gradual that no inflections lie between the two observations.
If extrapolation from a single point is used, one simply
assumes that the velocity is stable over the period of time
involved.



56



JUPITER




Figure 10. Sun, earth and Jupiter geometry.



57



Gosling and Bame (1972) have shown that if one makes a
prudent choice of apparition the stream structure one full
rotation away — 27 days — may autocorrelate with the current
structure r >0.1. It must be added that such a high
correlation is the exception rather than the rule and thus
the operative phase is "prudent choice." The validity of
assumptions of stability is strengthened if the 27-day auto-
correlation coefficient is reasonably high and one interpo-
lates or extrapolates over periods significantly less than
27 days.

The solar wind data are in the format of a single
average value per day. It is also necessary to point out
that since the Jovicentric solar sector rotation period is
the period of real interest in comparing solar and Jovian
events, the solar rotation periods referred to in the balance
of this study will be the solar magnetic sectors' Jovicentric
synodic rotation period. This period is nominally 25.7
terrestrial solar days.

1967-68 apparition . The velocity information during
this time was that from Pioneers VI and VII. These satellites
were in solar orbit very near 1 AU. They were separated by
about 155° in the ecliptic plane such that they straddled the
sun- Jupiter radial throughout the apparition. Thus, one
satellite or the other was never more than 5 rotation days
from the radial. The table of values for the velocity on the
radial was obtained by a linear interpolation in space of the



58



respective estimators for each day at the radial line. This
is to say, the value of the velocity at each satellite was
projected in time to the radial. The value chosen for the
velocity on the radial for a given day was the average of the
corresponding measurements from each satellite linearly
weighted in favor of the nearer satellite. The autocorrelation
of the 1967-68 period is shown in Figure 11 to have a value of
0.44. This is regarded as quite satisfactory for the
"interpolation. "

1974 apparition . The solar wind velocity data for this
period of time were provided by the IMP 7 and 8 satellites
which were in highly eccentric earth orbits. Unfortunately,
this situation was not as satisfactory as the 1957-68 period
since interpolation was not possible. The only alternative
was to extrapolate the single daily average to the sun-Jupiter
radial line. Figure 12 shows the autocorrelation function for
the 1974 period. The peak in the function after one solar
rotation is 0.81. However, the 1974 data picture may be
overly optimistic. At this writing the only available velocity
data for the 1974 are for the 81-day period from June 25 to
September 14. These data show remarkable repeatability in
the velocity structure. However, this is an inadequate
length of time to permit proper cross-correlation with Jovian
data. Svalgaard (1976), on the other hand, has shown that
the magnetic sector structure was quite stable throughout most
of the year. In order to satisfy the requirements of the
cross-correlation algorithm the June-September data have been



59



CC




-0,5 -



Figure 11. Solar wind velocity autocorrelation function,
1 AU 1967-68.



60



o:




-0.5 -



Figure 12. Solar wind velocity autocorrelation function,
1 AU 1974.



61

used to simulate the 81-day periods immediately preceding
and following the true June-September period. No doubt this
procedure has introduced some errors which may be eliminated
when more complete solar wind data become available.

Magnetic-Field-Free Model

The simplest model for the stream interaction is to
assume there is no interaction. In the absence of a magnetic
field the solar wind is simply a collisionless plasma. Conse-
quently, no interaction between streams occurs. Nevertheless,
this model predicts the buildup of a large scale (length
>0.2 AU) density wave as the fast stream approaches the slow
stream leaving a rarefaction behind. This development of a
density wave from a velocity wave is analogous to the "bunching"
process in a klystron.

The field-free model is applicable in situations where
the initial velocity spread between adjacent streams and their
initial separation in space are such that fast streams do not
often have the opportunity to pass completely through slow
streams before reaching Jupiter. Since the model permits no
stream interaction, at some point in space all of the fast
streams will have passed through the slow streams and the
density wave will decay. In nature, this decay probably does
not occur? consequently, a basic test of the applicability of
the field-free model will be to ascertain whether the model,
given the input velocities for a given apparition, predicts
such a decay before the encounter with Jupiter, (i.e., before



62

about 5.2 AU). If the decay does not occur, the model can be
used. The precise manner of performing this test will be
detailed shortly.

A FORTRAN program designated "Snoplow" (see Appendix)
was developed to generate the modeled values for wind density
and flux as a function of time and space. Starting with the
table of solar wind velocities at 1 AU on the sun-Jupiter
radial, this program extrapolates these values back in time
and space to the sun. Then the model releases groups of par-
ticles from the sun with constant arbitrary density at six-
hour intervals. The four groups for a given day are assigned
the wind velocity extrapolated from the earth for that day.
The progress of each group is tracked for forty days to insure
that even the slowest reaches Jupiter before they are discarded.

Once a day the groups are examined to determine the den-
sity and flux in space at increments of 0.2 AU. Since part of
this program's objective is to permit a view of the wave build-
ing process, the decrease in density caused by the expansion of
the wind (i.e., the 1/r dependence) is deliberately omitted
in this calculation. As a result, the "density" and "flux"
calculated are really the product of the true density or flux,
the square of the radial distance, and some scale factor.
Clearly, for any given radial distance this product is directly
proportional to the true density at that point. Consequently,
the term "density" will frequently be used to denote the product.

The net result of Snoplow is two two-dimensional arrays,
one representing the density, and the other the flux, as



63

functions of time and space out to 6 AU., Figure 13 is an
example of such an array. Prom this one can select a row
corresponding to a given day and see the density or flux as a
function of space, or one can select a column corresponding
to a radial distance and see the density or flux as a function
of time.

Growth test . In order to test the applicability of the
field-free model, a simple auxiliary program examines the
density array. At each increment of radial distance the pro-
gram calculates the average and standard deviation of the den-
sity across the apparition. The program then plots the standard
deviation, expressed in units of the average density, for each
increment in radial distance. This function, then, is merely
the normalized RMS wave amplitude as a function of distance.
If a density wave building process is occurring, the amplitude
will monotonically increase with distance. Conversely, if a
decay is occurring the amplitude will monotonically decrease
with distance. The derivative of the amplitude function may
also be used as an index of growth.

Simple-Field Model

A second model has been developed to handle the case
where the growth test contraindicates the field-free model.
This model implicitly assumes the presence of the interplanetary
magnetic field, but does not attempt to account for the fine
detail of the stream interaction. The model invokes three
assumptions:



64



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51



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65



1. Groups of particles cannot pass through one
another (B 7^ 0) ,

2. The stream collisions are completely inelastic,

3. Momentum is conserved.

These assumptions have been incorporated as a user option in
the program Snoplow outlined in the previous section.

Since Snoplow treats each four hour group of particles
as independent entities rather than as members of a particular
stream, the assumptions are applied at the group level.
Consequently, this model will permit the wave to build up as
an infinitely thin sheet of mass. This is physically un-
realistic because both plasma and magnetic pressure will
limit the compression of the density front. The effect is off-
set somewhat by the coarse scale of the radial distance used
in the density and flux arrays. This insures that the density
wave will never appear smaller than 0.2 AU.

There is another, probably related, effect that the model
does not account for. If one refers back to Figure 7, Wilcox
and Ness show that the peak of the density wave front actually
precedes the peak of the velocity front by about one day at 1 AU.
The forward one-half amplitude point of the density front pre-
cedes the corresponding point on the velocity front by two days.
However, the model will place the density front at the collision
point — the leading edge of the velocity wave. There are no
data available on the phase relationship between velocity and
density fronts at 5.2 AU. However, if the 1 AU characteristic
persists out to Jupiter, the model will consistently



66



overestimate the arrival date of the density fronts at Jupiter
by as much as 2 days.

Model Selection

The first step in the selection of the appropriate model
was to invoke the field-free model for both apparitions. The
growth test routine was then run to plot the density wave
growth for each apparition.

Figure 14 shows the amplitude plot for 1967-68. It
indicates that the RMS density wave amplitude at 1 AU was 0.47,
which is quite consistent with values seen at the earth. The
plot also shows that the principal evolution of the density
fronts took place beyond 1 AU and that the growth arrested at
about 3.4 AU. There is a plateau which is essentially con-
stant through 5.8 AU and then the decay process apparently
begins in earnest. It was decided that, since there was little
decay at 5.4 AU (the location of Jupiter in 1967-68), the field-
free model was an acceptable choice for this apparition.

The field-free amplitude plot for the 1974 apparition
is shown in Figure 15. In contrast to 1967-68, it shows a
much higher growth rate with the amplitude peaking at 2.2 AU
followed by an immediate decay. This characteristic clearly
shows that the field-free model is not satisfactory for the
1974 period.

The accelerated growth of the 1974 density waves, as
compared to the 1967-68 waves, stems directly from the more



67




2 3 4

RADIUS (AU)



Figure 14. Field-free model RMS density wave amplitude,
1967-68.



68




2 3 4
RADIUS (AU)



Figure 15. Field-free model RMS density wave

amplitude, 1974. The inflection at
2.2 AU shows that the model fails
beyond that point.



69



profound peak-to-peak amplitude of the 1974 velocity wave.
Referring back to Figure 8 it is clear that value of the peak-
to-peak velocity averages from cycle to cycle was 130 km/s in
1967-68, but the value in 1974 was 450 km/s. Consequently,
the fast streams overtook the slow ones much faster in 1974.

The simple-field model was then applied to the 1974 data
and a new amplitude plot obtained. The latter is displayed in
Figure 16. The 1 AU value, 0.77, is higher than that usually
observed but not substantially different from the 1 AU field-
free value. The rapid growth evident in the field-free model
is also evident here in the simple-field model. The 1 AU
amplitude value is probably reasonable in that light, though
1974 observational data are not yet available.

The growth process is seen to diminish as it approaches
the Jovian orbit,, suggesting that the interaction process is
nearing completion. This is an expected result for this model.
Once a fast stream has completely accumulated the preceding
slow stream, the only further interaction which can take place
will be between the density fronts themselves. Since they are
widely separated and moving at about the same speed, such
collisions would be very infrequent.

In comparing the two models out to 2.2 AU before the
field-free model breaks down, the two both provide similar
amplitude values. As expected, even in this region, the
simple-field model shows a somewhat higher growth rate. The
accumulated amplitude exceeds that of the field-free model by
34% at 2.2 AU. Nevertheless, it is comforting to see that



70




2 3 4
RADIUS (AU)



Figure 16. Simple-field model RMS density wave amplitude
1974.



71



where they are both valid, these two basically very different
models do not perform differently in any essential way. It is
clear. though that, of the two, the simple-field model would have
to be used for the 197 4 data.



CHAPTER 4
SOLAR-JUPITER CORRELATION

Previous Investigations

The matter of the relationship of solar and geomagnetic
events was discussed at some length in the preceding chapter.
By the time Burke and Franklin published their discovery of
the Jovian decametric emission in 1955> the solar-terrestrial
correlations were already well recognized, even though their
precise nature was not. Since solar events — particularly
solar flares— were seen to produce such dramatic effects as
visible and radio aurora, auroral absorptions (PCAs) and pro-
found geomagnetic disturbances, it was reasonable for early
students of the Jovian radiation to consider the possibility
of solar-Jovian relationships. This natural flow of thought
no doubt was intensified by the timing of the discovery just
prior to the International Geophysical Year, the peak of
solar Cycle 19, and Parker's theoretical insights on the
nature of the solar wind.

Several processes were proposed to explain the emissions
such as Jovian lightning, plasma oscillations excited by
shocks caused by Jovian volcanoes, and atmospheric chemical
activity. In 1958, Carr proposed that the emissions were
triggered by energetic particles of solar origin trapped by



72



73



the Jovian magneto sphere. At about the same time Kraus (1958)
noticed two intense Jovian storms following two large solar
flares and made the same suggestion. The possibility of such
a connection was actively pursued by a number of investigators.

What early observers did not know was that there was a
very powerful and periodic exciter, lo, which was responsible
for much of the activity they were seeing. The influence of
the lo effect was clearly evident in these early observations.
Carr et al . (1958) reported that they had found a very definite
8-day period in their observed activity. (The 8-day period — 7.71
days actually — is nothing but the alias of the second harmonic
of the lo revolution period with the 24-hour sampling period
imposed by the rotation of the earth.) They then suggested
that the period was due to tidal action induced by one of
Jupiter's satellites. Unfortunately this possibility was
not explored more exhaustively at that time. The discovery of
the lo effect would wait for Bigg in 1964.

The presence of the lo modulation would cloud efforts
to detect solar correlations. There was yet another pitfall.
Until Snyder et al . (1953) published their Mariner 2 obser-
vations, the velocity range and the stream structure of the
solar wind were not known. Consequently, there was great
uncertainty as to the appropriate delay time between, say,
an M-region geomagnetic storm and an expected Jovian event.
The only events where the timing might be inferred were
solar flares followed by SCs. In this case the velocity of
the wind disturbance was measurable, at least between the



74



sun and the earth. Since these early investigations took
place near the peak of Cycle 19, flares were in relative
abundance .

Pursuing the search for a solar correlation Carr
et_al. (1960) presented evidence to suggest that there was
an enhancement of Jovian activity 8 days after geomagnetic
disturbances. Warwick (1960) examined solar radio continuum
events and reported increased activity, particularly 1 to 2
days after the cessation of the continuum. More evidence
for an 8-day delay after geomagnetic events was introduced by
Carr et al . (1961).

On the other hand. Six (1962) examined the 8-day delay
and found no clear correlation. Lebo (1964) studied the
delay from flares and geomagnetic storms but extended the
maximum length of delay considered from 15 to 35 days. This
was an important step because the just published Mariner 2
data indicated that the average solar wind velocity was in
the 500 km/s range and the instantaneous values were often
smaller. Thus, the average delay between the earth and
Jupiter was 15 days. In doing so he found indications of
peaks in Jovian activity with delays in 8 to 9 days and 15
to 21 days. Lebo also suggested that future studies be
expanded to cover M-region events as well.

Armed with recognition of the lo effect Sastry (1968)
examined the question anew. He recognized correctly the
complexities imposed by the "artificial" periodicities in



75



the Jovian data on efforts to find time dependent effects,
such as time-of-f light delays. However, he did not attempt
to remove or compensate for the effects. Sastry reexamined
Jovian radio activity from 1958 through 1963 and concluded
that the probability of emission is higher after geomagnetic
activity than before. He cautioned that the correlation might
be an artifact produced by the periodicities.

A paper by Conseil et al . (1971) shows a tanta-
lizing but invalid relationship between the sign of the
derivative of the solar wind velocity and the definition of
"lo-related" activity. They have considered Jovian activity
and solar wind velocity measurements of Pioneers VI and VII in
orbit at 1 AU during 1967-68 — the same period as one of the
two examined in this study. Unfortunately, they explicitly
required that, "propagation effects [in the solar wind] are
not very important." It must be clear that the extent of
these interactions is all- important. However, the effect
they observed may, in fact, be real, but for the wrong reason.

During the 1967-68 apparition, it has been argued here
that the difference between the velocities of high and low
speed streams was such that the field-free or non-interaction
model adequately describes the evolution of the density wave
out to Jupiter. Conseil 's assumption of the unimportance of
the interaction constitutes the invocation of the field-free
model. Their error was in failing to consider the density
wave.



76



Using the satellites' wind velocity data, Conseil and
his colleagues developed a table of solar wind velocities
versus dates at Jupiter. They then examined the Jovian
decametric data for correlations with the velocity table.
What they reported was that the "favored" range of lo phase
(ISC) for source A and source C storms shifted toward lower
angles on days when the wind velocity was increasing and toward
higher angles when the velocity was decreasing. This effect
is shown graphically in Figure 17.

However, it seems very unlikely that the velocity deriva-
tive at 1 AU would be maintained at Jupiter. The derivative
of the velocity is necessarily far more sensitive to stream '
interactions than is the velocity itself. But, it is known
that a positive velocity derivative at 1 AU corresponds to the
leading edge of the fast stream which, in turn, is coincident
with the peak of the density wave. In a similar manner, a


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