The low-frequency oscillations observed at ATS-1 are the result of an attempt by the magnetospheric plasma to conserve its angular momentum as it convects through the magnetosphere

Cummings, W. D.

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SA-CR-138797) STUDY OF LO FPBEQUE Y
=• _) 13 p BC $4.000
CSCL 08 Unclas 02
DEPARTMENT OF
PHYSICS
GRAMBLING COLLEGE
Grambling, Loeisiam
https://ntrs.nasa.gov/search.jsp?R=19740019689 2020-03-23T08:02:25+00:00Z
Semi-Annual Status Report
for a
STUDY OF LOW FREQUENCY HYDROMAGNETIC WAVES
USING ATS-1 DATA
(NGR-19-011-007)
by
W. D. Cummings
Department of Physics
Grambling College
December 19, 1973
SEMI-ANNUAL STATUS REPORT:
SUBMITTED TO: NASA Scientific and Technical
Information Facility
P. 0. Box 33
College Park, Maryland 20740
REFERENCE NUMBER: NGR-19-011-007
Supplement No. 2
INSTITUTION: Grambling College
Grambling, Louisiana 71245
TITLE: A Proposal to Continue Studying
Low Frequency Hydromagnetic
Waves Using ATS-1 Data
PRINCIPAL INVESTIGATOR: W. D. Cummings, Professor
Department of Physics
DURATION:
(Original Grant) One (1) Year
(Supplement No. 1) One (1) Year
(Supplement No. 2) One (1) Year
SUM GRANTED BY NASA:
(Original Grant) $11,421
(Supplement No. 1) $11,987
(Supplement No. 2) $11,997
DATE:
(Original Grant) December 1, 1970
(Supplement No. 1) December 1, 1971
(Supplement No. 2) December 1, 1972
(This Report) December 19, 1973
SIGNATURE:
Principal Investigator 
__
W. D. Cummings
)' Department of Physics
Grambling College
Grambling, Louisiana 71245
Semi-Annual Status Report
for a
STUDY OF LOW FREQUENCY HYDROMAGNETIC WAVES
USING ATS-1 DATA
(NGR-19-011-007)
by
W. D. Cummings
Department of Physics
Grambling College
Introduction:
I would like to devote this report to a discussion of a research
problem that Calvin Countee (a student) is pursuing. The idea behind
the problem is that perhaps the low-frequency oscillations observed at
ATS-1 are the result of an attempt by the magnetospheric plasma to con-
serve its angular momentum as it convects through the magnetosphere.
Discussion:
Let's consider a particle that mirrors in the equatorial plane.
The conservation of the first adiabatic invariant means that
wi/B = const. =
or
lmv2 = v
The angular momentum of the particle about its guiding center is
1 = mvr
2But r is the gyroradius given by
r = mv/qB.
Hence
1 = m2v 2 /qB
or
1 = 2n/q = const.
Thus the angular momentum of the particle about its guiding center
is constant, if the first adiabatic invariant is conserved.
The next thing to consider is the angular momentum associated with
the convective flow of the plasma through the magnetosphere. Following
Kavanagh et al. (1968) we suppose the convective flow of the plasma is
due to crossed electric and magnetic fields, where the electric field
consists of a co-rotating component and to a solar wind component.
Ecr = -wBRer
Esw = C1y,
where w is the angular frequency of rotation of the earth, B is the
magnetic field at the position of the particle, and R is the geocentric
distance to the particle. We will use a coordinate system where the
Z axis is perpendicular to the geomagnetic equatorial plane of the
earth, the X axis is in the solar meridian. Then assuming a dipole
magnetic field, we have
% 3
Ecr = -BoREC -- i-- (8x x +gyy)
3Esw = Cey
xB -BoE - 3 -wy) x + x ey
Now the angular momentum associated with a bulk equatorial flow
velocity V is
L = r x mV = m(x Vy - y Vx )
If L is to be constant, we must have
X Vy = y Vx + Const
For the convective flow above, we have
X2 CR3 .y2 + Const
or
wR2 Z YCR3  + Const.
BoRE3
Remaining Questions:
We are still seeking answers to the following questions:
(1) Do the convective flow contours for the plasma correspond to
contours of constant angular momentum?
(2) Should the angular momentum of the convecting plasma be con-
served, i.e., is there a torque on this plasma?
(3) Does the elliptical polarization of the hydromagnetic waves
that we observe at ATS-1 correspond to a similar motion of
the plasma? If so, can the plasma carry angular momentum in
the form of these oscillations?
We are working on computer codes that will help give answers to
these questions. Most of the codes are complete, but we still have a
few bugs.
Other Matters:
We are enclosing a copy of the catalog of low frequency oscillations
for January, 1968. It is incomplete, as we received some additional
rolls of microfilm after the catalog was completed. We are revising the
catalog now.
Catalog of Low-Frequency Oscillations
of the
Earth's Magnetic Field as Observed at ATS-1
.During January, 1968
W. D. Cummings and D. Lyons
Department of Physics
Grambling College
Grambling, LA 71245
October 31, 1973
Catalog of Low-Frequency Oscillations
of the
Earth's Magnetic Field as Observed at ATS-1
During January, 1968
W. D. Cummings and D. Lyons
Department of Physics
Grambling College
Grambling, LA 71245
Introduction
The attached catalog of events has been prepared to facilitate a comparison
of ATS-1 data with other ground and satellite magnetometer data. We have begun
the catalog in March, 1968, when the ATS-1 data begins to overlap data from the
DODGE satellite. We hope to eventually catalog all our data for 1967, 1968, and
1969.
Explanation of the Catalog
In this catalog an event is defined as an oscillation of the magnetic field
with a duration of at least ten minutes, and a frequency that remains roughly
constant, Events are distinguished on the basis of the frequency of the oscil-
lation, e.g., when a high frequency oscillation is superimposed upon a lower
frequency oscillation, two events are identified.
The oscillations of an event usually occur in bursts that are typically one
hour in duration. In a burst the amplitude of the oscillation begins at a low
level, grows to a maximum, and then decreases to a low level again. Because the
oscillation begins with a low amplitude, it is often difficult to exactly specify
the beginning time of the event.
The beginning time is given in Universal Time. ATS-1 is stationed in the
geographic equatorial plane at a geocentric distance of 6.6 RE and at 1500 W
longitude. One can easily arrive at the Local Time for the beginning of the
event by subtracting 10 hours from the Universal Time (or by adding 14 hours if
the hour of the beginning time (U.T.) is less than 10).
Gaps of as much as an hour may occur between bursts in a given event. How-
ever, we defind the duration of an event as the time interval between the begin-
ning of the first burst and the end of the last burst,
We have used microfilm copies of the data at 0.32 second averages to measure
the time interval between successive peaks. We tried to make at least ten such
measurements during an event to determine the average period. In a few cases we
were unable to make ten measurements, but in all cases we made at least five,
The error figure associated with the average period is the standard deviation of
the individual measurements of the period. This error figure is more a measure
of the real variability of the time interval between successive peaks than it is
of uncertainty in determining that time interval.
The average frequency was determined by inverting each individual measure-
ment of the time interval between successive peaks and then averaging these
individual measurements of the frequency. The error figure associated with the
average frequency is the standard deviation of the individual measurements of the
frequency.
Acknowledgements
Our work is supported by the National Aeronautics and Space Administration
through grant NGR-19-011-007.
Low Frequency Oscillations in the Earth's Magnetic Field
Observed at ATS-1
January, 1968
Event Beginning Time (U.T.) Duration Average Period Average Frequency
No. Day Hour Min. (Min.) T (Sec.) f (milli-Hz)
01 Jan 01 00 57 126 100.0 ± 12.0 10.1 ± 1.3
02 01 20 00 113 59.5 + 9.8 17.2 + 2.8
03 02 00 30 136 72.6 + 5.2 13,8 + 1.1
04 02 03 34 60 56.8 + 9.3 18.1 + 3.1
05a  02 04 45 99 44.0 + 5.1 23.0 + 2.7
06 02 12 19 86 66.2 + 8.1 15.3 + 1.7
07 02 15 49 51 83.3 + 6.5 12.1 + 1.0
08 02 18 20 323 80.5 + 12.5 12.7 + 2.0
09 02 19 06 230 354.3 + 81.3 2,9 + 0.6
10 03 02 35 70 97.2 + 11.9 10.4 + 1.4
11 03 19 20 335 65.8 + 7.0 15.4 + 1,7
12 04 02 09 139 88.3 + 8.2 11.4 + 1.1
13 04 09 19 44 117,8 + 8.4 8.5 + 0.6
14 04 19 52 38 77.5 + 7,6 13.0 + 1.3
15 04 21 45 292 133.0 + 16,2 7,6 + 0,9
16 05 07 30 25 46.7 + 3.2 21,5 + 1.3
17 05 10 52 17 78.9 + 3.9 12,7 + 0,6
18 06 02 19 99 83.6 + 20.4 12.6 + 3.0
19 06 07 30 85 104.0 + 11.2 9.7 + 1.1
20 06 16 29 206 28.8 + 3.0 35.2 + 4.1
21 06 21 22 12 68.3 + 12.4 15.0 + 2.5
Event Beginning Time (U.T.) Duration Average Period Average Frequency
No. Day Hour Min. (Min) T (Sec) f (milli-Hz)
22 06 22 57 62 32.2 + 2.1 31.2 + 1.9
23 07 01 40 39 32.0 + 3.7 31.6 + 3.9
24 07 18 28 167 27.1 + 1.6 37.5 + 2.2
25 08 18 48 250 56,9 + 6.3 17.8 + 2.3
26 09 20 54 136 158,4 + 15,2 6.4 + 0,7
27 10 20 40 10 31,9 + 2.6 31,5 + 2,7
28 10 23 36 14 32.1 + 3.8 31.5 + 3.8
29 12 22 52 53 37.9 + 4.5 26,7 + 3.4
30 a  13 05 42 15 55.4 + 11,2 18,6 + 3.7
31 13 17 47 119 29.3 + 3.1 34.2 + 2.5
32 14 23 02 93 69.5 + 10,2 14,7 + 2.7
33 15 01 30 37 121.8 + 17.3 8.4 + 1,2
34 15 08 31 37 49.4 + 2,4 20.3 + 1.0
35 16 00 35 151 142.8 + 13.4 7.1 + 0.6
36 16 20 50 61 20.7 + 3.8 49.8 + 8.6
37 16 22 36 383 75.9 + 13.4 13.6 + 2.9
38 17 12 27 68 67.0 + 4.8 15,0 + 1.1
39 17 14 56 242 28,6 + 6.0 36.3 + 6.9
40 17 20 15 289 24.0 + 6.0 44.1 + 10.3
41 18 02 50 90 112.3 + 18.3 9.1 + 1.4
42 18 05 25 87 49,1 + 6,6 20.7 + 2.7
43 18 23 09 116 63.9 + 5.4 15.8 + 1.3
44 19 00 59 13 28.1 + 1.9 35.8 + 2.3
45 19 11 05 90 46.8 + 1.8 21.4 + 0.8
46 19 16 16 564 25.8 + 2.9 39.2 + 3.9
Event Beginning Time (U.T.) Duration Average Period Average Frequency
No. Day Hour Min. (Min.) T (Sec) f (milli-Hz)
47 20 06 28 214 88.4 + 9.3 11.4 + 1.3
48 20 08 15 18 44,8 + 7.1 22.9 + 4.5
49 20 16 28 228 26.1 + 2.4 38.7 + 3.7
50 21 04 15 16 66.3 + 1.2 15.1 + 0.3
51 21 23 22 63 57.5 + 1,9 17,4 + 0.6
52 23 21 57 203 167.8 + 12,1 6.0 + 0.5
53a 27 03 55 175 195.4 + 63.3 5,6 + 1.8
54a 29 00 38 24 66,4 + 16.0 15.8 + 3.4
55 29 02 40 124 117.0 + 81.0 12.6 + 7.8
56 29 23 45 185 82,5 + 17,0 12.6 + 2.5
57 30 04 46 14 174.3 + 2.2 5,7 + 0.1
58 30 11 02 82 80.7 + 6.6 12.5 + 1.1
59 30 20 02 378 69.8 + 4.4 14.9 + 4.9
aMeasurements made on Bz only.
High resolution data not available from January 21, Hr. 00 to January 27, Hr. 03.


Study of low frequency hydromagnetic waves using ATS-1 data

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