Low-frequency oscillations of the earth's magnetic field recorded by the UCLA magnetometer on board ATS-1, have been examined for the six-month interval, January-June, 1968. The initial interpretation, that these oscillations represent the second harmonic of a standing Alfven wave, has been re-examined, and it is concluded that this hypothesis must be withdrawn. Using evidence from OGO-5 and ATS-5, as well as the data from ATS-1, it is argued that the dominant mode at the synchronous orbit must be the fundamental rather than the second harmonic. From 14 instances when the oscillations of distinctly different periods occurred during the same time interval at ATS-1 it is concluded that higher harmonics can exist. The period ratio in 7 of the 14 cases corresponds to the simultaneous occurrence of the second harmonic with the fundamental, and 4 other cases could be identified as the simultaneous occurrence of the fourth harmonic with the fundamental

Countee, C.

Cummings, W. D.

Lyons, D.

Wiley, W., III

English

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We
PHYSICS
GRAMBLING COLLEGE
~ rambin, Louisiana
(NASA-CR-142030) THE DOMINANT MODE OF N75-16168
STANDING ALFVEN WAVES AT SYNCHRONOUS ORBIT(Grambling State Univ., La.) 16 p HC $3.25
CSCL C8N Unclas
G3/46 07778
https://ntrs.nasa.gov/search.jsp?R=19750008096 2020-03-23T00:59:24+00:00Z
The Dominant Mode of Standing Alfven Waves
at the
Synchronous Orbit
by
W.D. Cummings, Calvin Countee, Donald Lyons
and William Wiley, III
Department of Physics
Grambling State University
Grambling, LA 71245
January 18, 1975
The Dominant Mode of Standing Alfven Waves
at the
Synchronous Orbit
by
W.D. Cummings, Calvin Countee, Donald Lyons
and William Wiley, III
Department of Physics
Grambling State University
Grambling, LA 71245
ABSTRACT
Low-frequency oscillations of the earth's magnetic field recorded by the
UCLA magnetometer on board ATS-1, have been examined for the six-month interval,
January-June, 1968. The initial interpretation, (Cummings et al., 1969) that
these oscillations represent the second harmonic of a standing Alfve/n wave, has
been re-examined, and it is concluded that this hypothesis must be withdrawn.
Using evidence from OGO-5 and ATS-5, as well as the data from ATS-1, we argue
that the dominant mode at the synchronous orbit must be the fundamental rather
than the second harmonic. From 14 instances when the oscillations of distinctly
different periods occurred during the same time interval at ATS-1 we also con-
clude that higher harmonicscan exist. The period ratio in 7 of the 14 cases
corresponds to the simultaneous occurrence of the second harmonic with the fun-
damental, and 4 other cases could be identified as the simultaneous occurrence
of the fourth harmonic with the fundamental.
The Dominant Mode of Standing Alfven Waves
at the
Synchronous Orbit
by
W.D. Cummings, Calvin Countee, Donald Lyons
and William Willey, III
Department of Physics
Grambling State University
Grambling, LA 71245
Lanzerotti and Fukuniski (1974) have recently given a review of experi-
mental and theoretical work related to the modes of magnetospheric Alfvdn waves.
The goal of their review was to raise the question of whether the dominant mode
was odd or even. They conclude from their own conjugate data that near L = 4
the dominant mode is odd.
Lanzerotti and Fukuniski correctly point out that in our initial paper
(Cummings et al., 1969) we assumed that the oscillations observed at ATS-1 were
even mode, primarily because ATS-1 is located on the magnetic equator, and at
least in our idealized model, this position represents a node for standing
Alfven waves of odd mode. It should also be noted that our initial analysis
was based on only 25 events during January, 1968 and that we only studied
oscillations in the period range 50-300 seconds. This latter limitation of the
period range resulted from the fact that we analyzed 15 second averages of the
data. Therefore, our ability to observe oscillations dimished with decreasing
period, and was certainly marginal near a period of 50 seconds.
This limitation turned out to be critical, as it is now apparent from the
present analysis that a dominant period at the synchronous orbit is in the
range 40-90 seconds.
2In a second analysis (Cummings et al., 1972) we analyzed 222 events over a
25-month data interval. However, 15 second averages of the data were also used
in this study, so the limitation at low periods still existed.
The present analysis is based on 273 events that were recorded in the six-
month interval, January-June, 1968. The minimum period recorded was 20.7 secs.
and the maximum period was 410.8 seconds. An artificial oscillation at a
period of 5.12 seconds, the interval of one data sequence, sometimes contami-
nated the data. Therefore, a practical lower limit to the periods we could
observe is approximately 20 seconds, even though we used 0.32 second averages
of the data in the analysis.
ATS-1 was located at 1500 W longitude, which is approximately the inter-
section of the geomagnetic and geographic equatorial planes. The magnetometer
experiment on board ATS-1 has been described in Cummings et al. (1969) and in
Cummings and Coleman (1968). It should be mentioned that the plasma detector
scheduled for ATS-1 failed prior to launch, and the remaining particle detectors
did not provide a complete spectrum of the ambient charged particle population.
It has, therefore, been impossible to determine the ambient total ion number
density from ATS-1 particle data. In this study, we have made use of OGO-5
data and published ATS-5 data to help fill this unfortunate gap in the ATS-1
data.
GENERAL RESULTS
Of the 273 events that occurred during the six-month interval, 25 were
recognized as being similar to those described by Barfield et al., (1972).
That is, they were compressional, usually related to storms or substorms, and
occurred in the dusk sector. We have excluded these events from this analysis.
3The distribution of periods for the remaining 248 events is shown as a
histogram in Figure 1. The most striking feature of the histogram is the peak
in the range 40-90 seconds. The most frequently occurring period is in the
range 60-70 seconds. We cannot rule out an additional peak at periods below 20
seconds, which are unobservable in the ATS-1 data, as explained above. The
average period for the 248 events was Tave = 77.4 seconds.
The distribution of the 248 events in local time is shown in Figure 2. In
the histogram of Figure 2, the ordinate represents the number of hours in which
oscillations occurred in a given local time interval. The peak of the local
time distribution is 1-3 hours past noon, but the distribution is asymmetric,
favoring the morning hours.
This distribution is broadly similar to that observed at 6.25 earth radii
with the DODGE experiment (Dwarkin et al., 1971) in that both distributions show
that the great majority of oscillations occur in the day sector. The local time
distribution in our second analysis (Cummings et al., 1972; Figure 2) was simi-
lar in shape to the present distribution with the peak also shifted slightly
toward the afternoon sector. We note again that the period range in the second
analysis was limited to T )50 seconds because 15 second averages of the data
were used.
In our first analysis (Cummings et al., 1969) we reported that the oscil-
lations were observed predominately on geomagnetically quiet days. It is cer-
tainly true that many of the longer period oscillations are found to occur dur-
ing the quiet recovery phase of magnetic storms. However, it is clear from the
present analysis that one should not associate the more typical oscillations
observed at the synchronous orbit with prolonged periods when the magnetosphere
is quiet. On the contrary, these oscillations seem to be more clearly related
to magnetic storms or periods of magnetic activity.
4To illustrate the above point, we used the hourly values of equatorial Dst
(Sugiura and Poros, 1971) for January-June, 1968, to identify the hours when the
Dst value was at a local minimum. We required the local minimum to be greater,
in absolute value, than 35Y and 50 such instances were found. Next, we compared
this set of times, tmin, to the onset times, tonset, for the oscillations
observed at ATS-1. In particular, for a given tonset we looked for the nearest
tmin and measured Itmin-tonsett. Figure 3 illustrates the result of the study
with a histogram showing the number of events versus the time difference
It mi n-t n s e t . Half of all the events observed at ATS-1 occurred within one day
of one of these local minima.
THE DOMINANT MODE
The most frequently observed period at ATS-1 is in the range 40-90 seconds,
and the average period is Tave = 77.4 seconds. If an oscillation with the aver-
age period corresponds to the second harmonic of a standing Alfven wave, then
according to Table 2 of Cummings et al. (1969), the average number density dur-
ing the oscillations would be in the range 5.6< no < 15.3/cm 3, depending upon
how the plasma is distributed along the ATS-1 field line. Since we know that
the oscillations are associated with periods of magnetic disturbance, when ATS-1
is most likely in the tough region on the dayside of the magnetosphere, these
number densities are unacceptably high. Measurements of the particle density
by detectors aboard ATS-5 (DeForest and McIlwain, 1971) indicate that the maxi-
mum expected density at synchronous orbit on the dayside is no7-2.2/cm3, with a
typical density of no
~
l/cm3.
If on the other hand an oscillation with the average period, Tave = 77.4,
is interpreted as the fundamental mode of a standing Alfven wave, the average
5number density would be in the range 1.4<no 2.2/cm3 . These densities are much
more easily reconcilled with the direct measurements made by ATS-5.
We have already noted that the oscillations observed at ATS-1 seem to occur
preferentially during disturbed times. DeForest and McIlwain (1971) also point
out that intrusions of hot plasma at the synchronous orbit occur during magnetic
substorms. The plasma that supports the oscillations must be composed primarily
of the substorm injected plasma rather than the cold plasma whose source is the
ionosphere. Using OGO-5 cold plasma data, kindly supplied by Dr. C.R. Chappell,
we have tried to compare a few individual cases when OGO-5 was near ATS-l and
oscillations were recorded at ATS-1. In each case, we found that the cold
plasma density was below that required to explain the oscillations even in terms
of the fundamental, much less the second harmonic.
The case of April 17, 1968 is typical of those we studied. 000-5 was in-
bound on its seventeenth orbit and crossed L = 6.6 at approximately 1640 U.T.
near 0900 L.T. ATS-1 passed through 0900 L.T. a little more than two hours
later and oscillations with an average period of 55.7 seconds were recorded.
The density of cold plasma measured by 000-5 was approximately no = 0.4/cm 3
If the oscillations observed at ATS-1 are to be interpreted as the fundamental
mode of a standing Alfven wave, then the total proton number density would have
to be n I /cm3
HIGHER HARMONICS
Of the 248 events under investigation, 28 either overlapped another event
or almost did so. That is, there were 14 cases when oscillations of different
periods were occurring during the same time interval. These events are listed
6in Table 1, which shows the beginning time and ending time for each event, the
average period, and the ratio of the larger period to the smaller period.
There are several interesting features in Table 1. First, note that most
of the overlapping events occur near noon, 2200 U.T. (Recall that ATS-1 is
located at approximately 1500 W longitude. Thus, the local time is ten hours
less than the universal time.) The exceptions are sets Nos. 3, 11, 12, and 14.
Secondly, note that the period ratios cluster around two values, RI'-2.2 and
R2-4.5. The exceptions are sets Nos. 8, 12, and 14. Thirdly, note that for
all the sets that have ratios clustering around R1 the larger period is in the
range 40-90 seconds, which we identify as the dominant mode from the histogram
in Figure 1.
The above observations suggest that these overlapping events represent.
cases when the fundamental and a higher harmonic of the Alfven standing waves
were occurring simultaneously. It is possible to check this hypothesis by using
the simple model of Alfven standing waves that we presented in our initial anal-
ysis (Cummings et al., 1969). Theoretical ratios of the period of the fundamen-
tal and of higher harmonics can be computed using Table 1 in that paper. These
ratios, computed for the toroidal mode, are only weakly dependent on the distri-
bution of plasma along the field lines. The theoretical ratio of the period of
the fundamental to the period of the second harmonic, Tl/T 2 , has a range of
2.0 - 2.6. Six of the seven overlapping sets that cluster around R1 fall within
the above range.
The theoretical ratio of the period of the fundamental 4o the period of the
third harmonic, T1/T3 , has a range of 3.0 - 4.3. None of the fourteen sets of
overlapping events have period ratios that fall within this range.
7The theoretical ratios of the period of the fundamental to the period of
the fourth harmonic, T1/T4, has a range of 4.0 - 5.9. All four of the overlap-
ping sets that cluster around R2 fall within this range.
Two of the three sets that do not have period ratios falling within any of
the above ranges are sets Nos. 12 and 14. Both of these sets occurred in the
dusk sector, where the description of the field as a dipole is probably less
valid than in the noon sector.
Eleven of the fourteen cases when oscillations at two different frequencies
were occurring simultaneously at ATS-1 can be interpreted by our simple model as
either the fundamental and the second harmonic (seven cases) or the fundamental
and the fourth harmonic (four cases). As noted above, for all seven cases that
we interpret as the simultaneous occurrence of the fundamental and the second
harmonic, the larger period is in the range 40-90 seconds. This is the dominant
range of periods observed at ATS-1; more than half of all events recorded have
periods in this range. We thus have added evidence that the dominant mode
observed at ATS-1 is the fundamental mode of a standing Alfven wave.
We also note here from the histogram of Figure 1, that much of the peak in
the period range 20-30 seconds is attributable, to the occurrence of the second
harmonic. In five of the seven cases of the simultaneous occurrence of the fun-
damental and the second harmonic the period of the higher harmonic was in this
range.
SUMMARY AND CONCLUSIONS
The oscillations observed at ATS-1 most frequently occurred with periods
in the range 40-90 seconds. The great majority of the events recorded at ATS-1
occurred on the dayside of the synchronous orbit. The onset of the oscillations
8seems to be associated with a disturbed magnetosphere, rather than a quiet one
as previously supposed. The current best estimates of the total proton number
density on the dayside of the synchronous orbit are consistent with the inter-
pretation of the dominant mode of oscillations observed at ATS-1 as the funda-
mental mode of a standing Alfven wave. From the few cases when oscillations of
distinctly different periods occurred simultaneously, we conclude that the second
and fourth harmonics can also occur.
Acknowledgments
The authors have benefited from helpful discussions with Drs. C.R. Chappell,
R.L. McPheron, and P.J. Coleman, Jr. This research was supported in part by the
National Aeronautics and Space Administration under grant NGR-10-011-007.
9REFERENCES
Barfield, J.N., R.L. McPheron, P.J. Coleman, Jr. and D.T. Southwood, Storm-
Associated Pc5 Micropulsations Events Observed at the Synchronous
Equatorial Orbit, J. Geophys. Res., 77, 143, 1972.
Cummings, W.D., R. Mason and P.J. Coleman, Jr., Some Characteristics of Low-
Frequency Oscillations Observed at ATS-1, J. Geophys. Res., 77, 748, 1972.
Cummings, W.D., R.J. O'Sullivan and P.J. Coleman, Jr., Standing Alfve/n Waves in
the Magnetosphere, J. Geophys. Res., 74, 778, 1969.
DeForest, S.E. and C.E. McIlwain, Plasma Clouds in the Magnetosphere, J. Geo-
phys. Res., 76, 3593, 1971.
Dwarkin, M.L., A.J. Zmuda and W.E. Radford, Hydromagnetic Waves at 6.25 Earth
Radii With Periods Between 3 and 240 Seconds, J. Geophvs. Res., 76, 3668,
1971.
Lanzerotti, L.J. and H. Fukuniski, Modes of Magnetospheric Alfven Waves,
Ae views o-D i - Irc Ics)~J~IV7A4
Sugiura, M and D.J. Poros, Hourly Values of Equatorial Dst for the Years 1957
to 1970, Publication No. 645-71-278, Goddard Space Flight Center, July,
1971.
10
Table I
Overlapping Events at ATS-1
Set Beginning Time (U.T.) Ending Time (U.T.) Average Period Ratio
No. Mon. Day Hr. Min. Mon. Day Hr. Min. of Period
1 Jan. 02 19 06 Jan. 02 22 56 354.3 + 81.3
Jan. 01 18 20 Jan. 02 23 43 80.5 + 12.5
2 Jan. 18 23 09 Jan. 19 01 05 63.9 + 5.4 2.3Jan. 19 00 59 Jan. 19 01 12 28.1 + 1.9
3 Jan. 20 06 28 Jan. 20 10 02 88.4 + 9.3 2.0
Jan. 20 08 15 Jan. 20 08 23 44.8 + 7.1
Jan. 21 17 42 Jan. 22 00 24 52.6 + 5.9 2.2
Jan. 21 18 12 Jan. 22 00 19 24.4 + 2.9
5 Jan. 22 15 22 Jan. 22 18 06 46.2 + 7.4 1.9
Jan. 22 16 09 Jan. 23 01 05 24.4 + 2.2
6 Jan. 23 21 59 Jan. 24 01 12 160.6 + 19.3 5.1
Jan. 23 17 08 Jan. 24 01 54 31.4 + 6.5
7 Mar. 01 21 10 Mar. 02 00 10 285.2 + 45.2 4.6
Mar. 01 20 22 Mar. 01 21 24 61.8 + 3.3
8 Mar. 29 19 52 Mar. 29 22 55 410.8 + 19.3 7.7
Mar. 29 18 20 Mar. 29 22 20 53.4 + 6.3
9 May 12 22 38 May 12 23 10 55.5 + 7.3 2.1
May 12 19 59 May 13 00 15 26.4 + 4.8
10 May 13 20 26 May 14 01 10 76.8 + 9.1 2.5
May 13 19 14 May 13 22 39 30.2 + 4.8
111 Mav 16 00 59 May 16 01 20 59.7 + 8.7 2.2
May 16 00 16 May 16 00 53 26.6 + 0.6
12 June 09 03 25 June 09 04 59 130.5 + 23.8 1.6
June 09 04 11 June 09 04 33 79.8 + 6.2
132 June 11 17 10 June 11 20 22 290.0 + 5.9 4.5
June 11 20 42 June 11 23 23 64.0 + 13.5
14 June 17 00 06 June 17 02 28 101.3 + 6.0 1.2
June 17 00 26 June 17 01 35 82.6 + 2.3
1These two events fail to overlap by 6 minutes.
2These two events fail to overlap by 20 minutes.
FIGURE CAPTIONS
Figure 1 The histogram shows the number of events recorded at ATS-1 with
periods occurring in each ten second interval from 20 to 250 seconds.
As explained in the text, oscillations with periods below about 20
seconds are often obscured by an artificial oscillation, and are,
therefore not included in this study. The data interval for Figures
1, 2, and 3 is January-June, 1968, and compressional storm-related
oscillations are excluded.
Figure 2 The histogram showsthe number of hours in which oscillations were
recorded at ATS-1 for each hour of local time.
Figure 3 The histogram of this figure was constructed in the following way.
The onset time, tonset, for each event was recorded and compared to
the time of the nearest minimum in Dst, tmin. The amplitude of the
excursion in Dst at the minimum point was required to be at least
35 y . The histogram shows the number of events recorded at ATS-1
for each four-hour interval of (t in - tonset). A negative value of
(tmin - ton ) means the onset of the event was prior to the nearest
minimum in st.
35
30
25
No. 20-
of -
Events
15
I0
5-
0 50 100 150 200 250
T.(sec.)
-igure 1
50
40
No.
of 30
Hrs.
20 L
I O
00 06 12 18 24
L.T (hrs.)
20
15
N o.
of
Events
I0-
5
-3 -2 -1 0 2
tmin" tonset (days)
Figure 3


The dominant mode of standing Alfven waves at synchronous orbit

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