Author(s)
Patterson, John Woodward III.; Olsen, Richard C.
Title
Observations of a hydromagnetic wave in the earth's magnetosphere.
Publisher
Issue Date
1987
URL
http://hdl.handle.net/10945/22836
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NAVAL POSTGRADUATE SCHOOL
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THESIS
OBSERVATIONS OF A HYDROMAGNETIC WAVE
IN THE EARTH'S MAGNETOSPHERE
by
John Woodward Patterson III
December 1987
Thesis Advisor:
Richard
C.
Olsen
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OBSERVATIONS OF A HYDROMAGNETIC WAVE IN THE EARTH'S MAGNETOSPHERE
RSONAL AUTHOR(S)
Patterson, John W. Ill
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Alfven Wave, Hydromagnetic Wave, Pc5, SCATHA
STRACT (Continue on reverse
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Measurements of a continuous hydromagnetic micropulsation event, which occurred in
the pre-dawn magnetosphere on July 29, 1979, are reported as observed by wave and
particle instruments onboard the P78-2 (SCATHA) spacecraft. Calculations of the Poynting
vector make it clear that the wave is a traveling Alfven wave guided by the earth's
magnetic field line. Plasma densities are calculated at L = 7. The phase relationship
between the plasma flux and the electromagnetic fields is investigated. A selfconsistent set of particle density and particle velocity data is determined, in order
Current magnetospheric models
to verify the measurement
of the electric field.
predicting Alfven wave speeds, Alfven wave periods and plasma densities are supported
by the study.
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Observations of a Hydromagnetic Wave
in the Earth's Magnetosphere
by
JOHN WOODWARD PATTERSON III
Lieutenant, United States Navy
B.S., PURDUE UNIVERSITY, 1979
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN PHYSICS
from the
NAVAL POSTGRADUATE SCHOOL
December 1987
ABSTRACT
Measurements
pulsation
of
which
event,
wave and particle
instruments
Calculations
clear that the wave is
earth's
magnetic
calculated at
plasma flux
A
L =
a
field
7
.
onboard
P7 8-2
the
(SCATHA)
Poynting vector make it
of the
traveling Alfven wave guided by the
densities
Plasma
line.
are
relationship between the
The phase
data
is
set
of
predicting
particle
determined,
measurement of the electric
models
pre-dawn
the
in
and the electromagnetic fields is investigated.
self-consistent
velocity
occurred
micro-
July 29, 1979, are reported as observed by
magnetosphere on
spacecraft.
hydromagnetic
continuous
a
Alfven
in
field.
density
order
to
and particle
verify
the
Current magnetospheric
wave speeds, Alfven wave periods
and plasma densities are supported by the study.
<
:'•-.
TABLE OF CONTENTS
I.
II.
INTRODUCTION
7
•
A.
GEOMAGNETIC MICROPULSATIONS
7
B.
CONTINUOUS PCS OSCILLATIONS
7
1.
Previous Observations
2.
Theory
8
11
C.
COORDINATE SYSTEMS
12
D.
SCATHA SATELLITE
14
1.
SCATHA Orbit Parameters
14
2.
Instruments
22
OBSERVATIONS
A.
B.
'
25
PARTICLE AND FIELD DATA
25
1.
Magnetic Field Data
25
2.
Electric Field Data
29
3.
Low Energy Ions
35
A CLOSER LOOK, THE D PACKET
36
1.
Field Relationships
36
2.
Particle and Field Relationships
40
3.
Plasma Parameters
43
4.
Electron Density
52
5.
Self Consistency of the Data
55
6.
The Alfven Velocity
57
7.
The Poynting Vector
57
8.
Dependence of the Period on L
60
4
III.
IV.
C.
SOLAR AND MAGNETIC FIELD CONDITIONS
6 3
D.
OTHER OBSERVERS
63
DISCUSSION
65
A.
THE CHARACTER OF THE PCS
65
B.
SPATIAL EXTENT OF THE PC5
66
C.
UNRESOLVED ISSUES
67
D.
RECOMMENDATIONS
67
CONCLUSIONS
69
LIST OF REFERENCES
71
INITIAL DISTRIBUTION LIST
74
ACKNOWLEDGEMENT
The
author
expresses
R.C. Olsen, whose unwavering
led him
his
appreciation to Professor
scholarly advice
patience and
through the obstacles of research, and to Dr. T. L.
NASA Goddard
Aggson, of
theoretical
and
Center, who provided
Space Flight
technical
guidance and support throughout
the research.
The author is also grateful
NASA
Goddard
Space
Flight
to
Dr.
Ledley, of
who was the principal
Center,
investigator for the magnetometer
Brian
data. Dr.
Jack Quinn, of
Lockheed Palo Alto Research Laboratory, who provided the ion
mass spectrometer data and Dr. Richard Johnson, who
principal
investigator
assistance of
who
provided
Dr. Carl
the
UCSD
for
the
particle
spectrometer.
mass
Mcllwain and
was the
The
Dr. Sherman DeForest,
is
also
greatly
Johnson,
also
of NASA
data,
appreciated.
A special thanks to
Goddard Space
Ms.
Judy
Flight Center, who provided data and state of
the art plots which were vital to the
of this study.
successful completion
I.
A.
INTRODUCTION
GEOMAGNETIC MICROPULSATIONS
micropulsations
Geomagnetic
perturbations of
which
internal
of
are
be generated by solar forces.
The gamma, defined
as.
[Ref.
to
extremely
these
gammas
of
tens
1]
ranging
and
into two
main classes.
used when
magnetic
small
fields.
fractions of
from
periods
approximately 0.1 second to 10 minutes.
be divided
geomagnetic
origin,
10"^ Tesla, is commonly
Micropulsations have amplitudes
gammas
main field.
well as magnetic storms, are thought to
micropulsations, as
measuring
They are
to long term variations of the Earth's magnetic
In contrast
field
field.
the Earth's
magnitude of
-when compared to the
frequency
whose amplitude is small
variations
short-lived
generally
magnetic
Earth's
the
low
are
ranging
from
Micropulsations may
Those
with regular or
continuous patterns are called Pc's and those with irregular
patterns
The
Pi's.
system
used
in
this
paper
categorizing continuous pulsations is described in
[Ref.
B.
1.
1]
CONTINUOUS PCS OSCILLATIONS
Micropulsations
with
have amplitudes near 100
have
Table
for
amplitudes
of
the
the
longest
gamma, but
order
7
periods, PcS's, may
generally are
seen to
of ten to twenty gamma.
A
group of Pc5's may
noted
been
have
Pc5's
activity
magnetic
generally occur
10 minutes
last from
They
days.
disturbed
very
on
and
absent on days of very low
be
to
to several hours.
during the recovery periods of several days
which follow moderate magnetic disturbances.
[Ref.
1]
TABLE 1
CONTINUOUS PULSATION CLASSIFICATION
1
Type
Period (sec.
Pel
Pc2
PC 3
PC4
PC5
0.2
--
5
5
--
10
45
150
--
10
45
--
150
600
Previous Observations
.
ground
stations
Stewart observed
disturbance
thousands
at
of
micropulsations.
what
he
described
Observatory
Kew
papers
have
Ground
19th
the
since
been observed
have
micropulsations
Magnetic field
from
--
)
Century.
as
[Ref.
a
great magnetic
Since
2].
published
been
In 1861
concerning
station characteristics of Pc5
were summarized by Barfield and McPherron [Ref. 3].
stations
report
Pc5
'
most
s
frequently
These data indicate that it is common for
degrees of longitude.
conjugate ground
then
'
Ground
at dawn and dusk.
PCS
'
s
to
span 60
Simultaneous observations by magnetic
stations suggested
a
generation mechanism
located near the equator.
With the advent of satellite exploration in the late
1960
's
the
understanding of long period micropulsations was
8
geosynchronous
by
were
correlations
example,
For
orbit.
magnetometers.
satellite
of data taken by spacecraft in
made
were
studies
Several
taken
data
with
furthered
established between micropulsation observations in 1967 from
Applied Technology Satellite
data [Refs.
and
3
magnetospheric
of
(ATS-1)
ground station
and
This analysis showed that the onset
4].
the expansion
occurred during
the events
of 85 percent of
phase
1
suggesting that Pc5
substorms,
'
could be generated by storm enhanced ring currents.
the
early
data
made
In
correlate
energy plasma
showed
of
magnetosphere at
Pc5
scientists
multiple
by
magnetic
resonance
high altitudes [Ref. 5].
mirror instability.
A
is given by Chen [Ref.
on
and high
with ground station
regions
that these resonance regions could be
began to
sensors
data
field
Explorer 45,
data, from
that
plasma
available
Comparison
spacecraft.
data
1970 's
existed
in the
It was suggested
perturbed by
a
drift
good review of plasma instabilities
6].
ATS-6 provided an early example of combined magnetic
field and
plasma flow measurements in 1974 [Ref. 7].
multiple sensors it was
vector using
fields.
possible to
Using
calculate the Poynting
measured magnetic fields and inferred electric
This case study showed the existence
of a standing
Alfven wave.
Multi-sensor observations have become more common in
the past decade.
The addition of mass spectrometers brought
A recent example
to magnetospheric research.
new dimension
1982 [Ref.
is a Pc5 observed by Dynamics Explorer I in July
Using a mass spectrometer, electric field and magnetic
8].
compare simultaneous
field measurements, it was possible to
measurements
the
of
E
B drift velocities and particle
X
derived plasma drift velocities during
plasma
shown
was
perpendicular
rotating
be
to
The
event.
Pc5
a
to
the
Complete analysis of the plasma data showed
magnetic field.
that significant quantities of singly ionized helium, oxygen
and nitrogen, as
plasma, which
well
in the
plasma theory and
in matching
was important
present
were
hydrogen,
as
observations.
GEOS-2 data from
experiment have been reported for Pc5
[Ref.
9].
plasma
'
s
observed during 1979
Observed correlations between
density
were
data
electric field
probe
double
the
wave amplitude and
to support current hydro-
used
magnetic wave period models.
Multi-satellite observations can be
the
spatial
structure
of
data from the SCATHA, GOES
were used
to examine
Pc5 s
'
2,
GOES
Combined magnetic field
.
3
the structure
observed in November 1979 [Ref. 10].
the wave
had an
and GEOS
2
satellites
of a field aligned Pc5
The
study showed that
antisymmetric standing structure along the
field line, and that
the field line.
used to address
the wavelength
was much
shorter than
These are characteristics that have not yet
been explained by existing theories.
10
Analysis
determination
wave
of
leading
observations,
these
of
enhance
propagation characteristics,
characteristics and
growth
modes,
the
to
understanding of
the
basic plasma physics and those processes which determine the
dynamics and structure of the magnetosphere.
Theory
2.
H.
Alfven
showed,
in
propagate
electromagnetic
waves
conductivity in
the presence
[Ref.
can
low
that
1942,
fluids
in
high
of
constant magnetic field
of a
11].
These waves are difficult to observe on
scale.
to
frequency
S.
occur
Lunquist determined that for
between
a
laboratory
strong interaction
a
electromagnetic and hydrodynamic systems
the criterion which must be met is
BLo(y/p)l/2
where B is the
magnetic field,
>>
(1.1)
1
the dimension
L is
conducting fluid, o is the conductivity and
of the
fluid
magnetosphere
[Ref.
Since
12].
are
large,
this
is the density
dimensions
the
type
p
of
of the
of the
interaction
is
possible.
In a Newtonian fluid,
density
p,
of
perfect
conductivity and
small perturbations of the magnetic field, Bq,
will propagate
magnetic field line with velocity
along the
given by
Va
=
co/]c
=
Bq
11
/
(yoP)^^^
(1-2)
which is called the Alfven velocity [Ref. 6].
to the
In 1952, Alfven compared hydromagnetic waves
vibrations
of
its' ends fixed at
with
string
elastic
an
of the
Wilson [Ref. 14].
Sugiura and
given by
analogy is
good summary
A
magnetic field conjugate points [Ref. 13].
The derivation of this analogy is described showing that the
plasma acts
as the
The calculation of
mass of the string.
perturbation modes of these string vibrations, as applied to
the earth's magnetic field, is presented.
Hasegawa and Chen separate the theory of long period
micropulsations into two categories
for each
type [Ref.
One type
15].
resonant Alfven wave excited at
Kelvin-Helmholtz
a
forth
and set
can be explained as a
local
the
second type is interpreted as
an
excitation
Kinetic
Alfven
Wave,
by a
magnetopause.
at
a
line
field
instability
eigenmode,
theory
a
of
a
The
surface
excited by an impulse
energized ring current.
exhibits
Its
paper
this
In
some
source
is
a
event
Pc5
characteristics
believed
to
is
described
which
of a classical Alfven wave.
be
the
current
ring
which
generates a traveling wave along the magnetic field line.
C.
COORDINATE SYSTEMS
The coordinate systems pertinent to this analysis of the
Pc5 data are shown
in Figure
1.
The magnetic
field com-
ponents (Bx,By,B2) are described in topographic coordinates.
X is defined as
North, Y
points East,
12
and
Z
points down,
SOLAR ECLIPTIC
SYSTEM
DUSK
DAWN
SATELLITE SYSTEM
Figure
1.
Coordinate Systems
13
toward the center of the earth, in the radial direction.
The electric
are despun into two components
field data
The X
(Ex and E2) of the solar ecliptic coordinate system.
this system
direction in
is parallel to the earth-sun line
The Y axis
and points in the sunward direction.
is perpen-
The
dicular to the earth-sun line and points toward dusk.
Z
axis is right-hand perpendicular to the X-Y plane.
The satellite coordinate system is a rotating coordinate
system
with
X
pointing
in the direction of the satellite
spin axis, which is essentially held constant throughout the
orbit. The spin axis is nearly anti-parallel to Y (SE)
Y and Z axis rotate through
.
The
perpendicular to the
the plane
spin axis.
D.
SCATHA SATELLITE
The U.
S.
Air Force P78-2 satellite was launched into a
near-geosynchronous orbit in January 1979 as part of a joint
NASA/Department
of
Defense
program
to
Charging At High Altitudes (SCATHA).
SCATHA vehicle is shown in Figure
1.
A
study
Spacecraft
schematic
of the
2
SCATHA Orbit Parameters
The SCATHA orbit is elliptical with a perigee of 5.5
Re and an apogee of 7.7 Re.
7.5 degrees
and the
The inclination of the orbit is
period is
spin period is 59.5 seconds, with
23.5 hours.
a
spin
axis in
plane and perpendicular to the earth-sun line.
17]
14
The satellite
the orbit
[Refs.
16 and
UCSO PLASMA DETECTOR
HSRWARO END
GSFC
MAGNETOMETER
SCATHA SPACE VEHICLE(P78-21
Figure
2.
Schematic of the SCATHA Satellite
15
Figure
the earth's center in earth radii,
Figures
4
and
show the
5
SCATHA's
in
inclination
orbit is
a
hours
7
and longitude
latitude
is
result of the 7.5"
a
variation
The
The
constant.
nearly
remain
in longitude
fact that the orbit is not geosynchronous
The result
continuous
of the
apogee, to 3.74
km/s,
slightly elliptical
wide sector of the
but
change in the satellite's geographic
velocity
SCATHA's
,
slighly inclined elliptical
longitude as well as it's velocity and radial
the earth.
to
4
During the Pc5 event the geographic
orbit.
the
in
reflects the
elliptical.
6378 km), for the
=
geographic latitude
longitude
and
variation
Re
continuous decline in SCATHA's radial distance.
a
during the same period.
latitude
(1
The Pc5 is observed from
24 hours of Day 210.
UT during
distance from
shows the satellite's radial
3
at
varies from
perigee.
distance from
2.55 km/s, at
virtue
The
of this
orbit is that the satellite can sweep a
earth's magnetosphere
while introducing
only small errors in the raw magnetospheric data.
analysis of
In the
lite's location
important in
magnetospheric data, the satel-
relative to
the earth's
the classification
first approximation
of
magnetic field is
of observed
the shape
of the
phenomena.
A
earth's magnetic
field is that of a dipole given by
R = r sin^e
where
r
is
the
distance
from
16
(1.3)
the earth's center to the
SCATHA DAY 210
7.8
7
-
W
6.8
-
<
6.6 H
PERIOD OF
INTEREST
Eh
Q
6.2 H
H
6 H
S
5.8 H
Q
5.6 H
5.4
5.2
O
4.
-r
8
—
—r-
T
12
16
20
HOURS UT
Figure
3.
Radial Location of SCATHA on July 29, 1979
17
24
SCATHA LATITUDE
^
8
7
-
6
-
5
-
W
4
-
Da
cc
3
-
w
Q
2
-
^
1
-
-1
-
E-«
O
C/2
o
PERIOD OF
INTEREST
ca
Q
Z3
E-t
M -2
< -3
U -4
M
X -5
< -6
u -7
o
w
u -8
-
E-t
-
-
1^
I
4
8
12
16
20
HOURS UT
Figure
4.
Geographic Latitude of SCATHA on July 29, 1979
18
24
SCATHA LONGITUDE
< 375
-
370
-
w
O 365
W
P
-
360
-
W
P 355
-
c/3
^
^-—^
/ \
/
/
E-
S 350O
•J
345
-
340
-
U
H
ffi
\
\
<
g 335O
w
O 330 -
\
\
T
\
PERIOD OF /
INTEREST
/
,/
r
'I
!
'
r-
T
12
B
T-
1
,
16
r-
20
i
-
24
HOURS UT
Figure
5.
Geographic Longitude of SCATHA on July 29, 1979
19
the dipole
intersection of
plane.
are
R and
field line.
the polar coordinates of the magnetic
The parameter used to define the location
number of earth radii at which
to the
is equal
of the
the L
magnetic field,
dipole approximation for the
of a
Using the
line is the Mcllwain L [Ref. 18].
magnetic field
field line
with the equatorial
field line
value of L
the field line crosses the equatorial plane. The
at other latitudes is given by
L = Re
/
(1.4)
cos^ej^
where 6^ is the magnetic latitude.
A view of the magnetic field dipole approximation is
shown in Figure
are plotted.
6
where field lines for L
5,
6,
7,
and
8
Scatha's dipole magnetic position between 0400
At
UT and 0700 UT is plotted.
8.03 and
=
descended to
L =
0400 UT
6.59 at
SCATHA was
0700 UT.
at L =
It is during
this period that the Pc5 was observed.
The dipole approximation
field is
most exact
the
earth's magnetic
at dawn and dusk. The approximation is
fairly inexact at noon (where the
poor at
for
midnight (where
field is
compressed) and
the field is extremely elongated).
The distortion of the earth's magnetic field is
to the solar wind.
largely due
A more exact description of the shape of
the magnetic field is given by Hess [Ref. 19].
20
I
O
I
t
I
t
B
2
RE
Figure
6.
A
SCATHA POSITION AT 0700 UT
O
SCATHA POSITION AT 0^00 UT
Mcllwain L and Geomagnetic Latitude of the Pc5
21
2
Instruments
.
spacecraft
The
meters in
approximately 1.75
cylinder
a
length and diameter. The instruments used in this
Goddard Space Flight Center mag-
NASA
the
monitor,
Center electric
Flight
Space
Goddard
NASA
study are the
field
is
netometer and the University of California, San Diego (UCSD)
instruments are shown in Figure
consists
of
two
antennas
The antenna
that
measurable field
50
detector
field
meters in length
are used
as floating
wire is composed of beryllium copper.
electric
ambient
is 0.05
for
the
last
20 meters,
Differential signals between the
the active part.
antennas give the
are
these
of
17]
electric
Each antenna is insulated except
which is
[Ref.
plane which
projecting into the spin
probes.
2.
Goddard
NASA
The
a.
locations
The
experiment.
particle
charged
fields
The minimum
.
time resolution of the
mV/m. The
electric field measurements is limited by the satellite spin
period (59.5 seconds).
SCATHA
data
are
despun
into
the
X
and
components of the solar ecliptic (SE) coordinate system.
this
field
method
(Ejj
the
two
components
and E^), which are
the satellite
spin axis
Z
By
of the measured electric
in the
plane perpendicular to
are known.
It will be shown that
the E2 component of the field data reflects the component of
the Pc5 electric field which is perpendicular to the earth's
magnetic field when the satellite is
22
near local
dawn.
The
transformation
from
measured
the
fields
sunward field to
fields requires the addition of a 0.3 mV/m
account for satellite motion.
The
b.
meter
a 4
[Refs.
form and despun
in raw
16 and 17]
The
c.
particle
charged
UCSD
electrostatic analyzer
are
Data
per second.
vector measurements
with four
three vectors listed of the topographic coordinate
into the
flux.
The resolution is
boom.
from the GSFC magnetometer are used
system.
16 and 17]
is a triaxial flux gate
magnetometer
GSFC
magnetometer mounted on
0.3 gamma
[Refs.
the ambient
to
experiment
is
an
both ion and electron
that measures
Particle data from the electrostatic analyzers (ESAs)
used
to
functions and
the
ion
electron distribution
and
particle density, temperature and
deduce the
The UCSD particle detectors consist of
velocity.
arranged
measure
rotating
two
in
detectors, and
pairs
of
electron
All
ion detector.
one fixed
five ESAs
and
ion
three of the
sensors of this instrument are contained in a single pac]cage
mounted on the forward end of
the satellite.
[Refs.
16 and
17]
One
pairs of rotating detectors covers
the
of
the energy range from
1
The other
E/W detectors)
cover the
pair (the
1
eV
to 81
keV (the
and the fixed detector
eV to 1800 eV energy range.
energy resolution
of 20%
one 64 step energy scan.
(6E/E)
[Refs.
23
N/S detectors).
The analyzers have
and require 16 seconds for
16 and 17]
A more complete
description
of
contained in
the IMS
the
satellite
Source Book
Technical Report [Ref. 21].
24
and
[Ref.
instrumentation
20]
is
and the P78-2
II.
A.
OBSERVATIONS
PARTICLE AND FIELD DATA
During the
morning hours
210 SCATHA recorded a
of Day
disturbance in the earth's magnetic field, beginning at
the spacecraft
7.96, as
of
its
orbit,
micropulsation,
a
approached the maximum inclination
Pc5,
strong
A
degrees.
7.5
L =
field
on each of SCATHA 's
recorded
was
magnetic
sensors
Figure
is an equatorial plane
7
orbit are
The sector
line.
shown with
.
of the orbit, in which the Pc5 event was
recorded from
8
shows
0300 UT
the
SCATHA
to 0800
UT.
magnetic field, Bq, and the three
the field (Bjj,By,B2).
magnetic
field
data
Included are the total
topographic components of
The significant rise in the magnitude
of Bq, the total field, and
earth's
7.
Magnetic Field Data
Figure
due to
the earth sun
respect to
observed, is also indicated in Figure
1
SCATHA 's orbit
The location of the extremes of
on July 29, 1979 (Day 210).
the SCATHA
plot of
Bj^,
the
northerly component, is
the continuous descent of the spacecraft through the
magnetic
field
for
that
period
of
it's orbit.
During that time period, SCATHA 's radial distance diminishes
from 7.3 Re to 5.3 Re, and L decreases from 8.28 to 6.16.
25
SCATHA DAY 210 ORBIT
Z
O
O
z
Z^ = FIRST OBSERVATION OF THE PCS
e+ = MAXIMUM INCLINATION OF THE ORBIT
Z7 = LAST OBSERVATION OF THE PC5
=
s
e- =
s
Q
€
w
Figure
7.
ORBIT CROSSES EQUATOR
PERIGEE
MINIMUM INCLINATION OF THE ORBIT
APOGEE
Equatorial Plane Plot of SCATHA Orbit
26
DAY 210 MAGNETIC FIELDS
220
HOURS UT
Figure
8.
Magnetic Field Data from
27
300 to 0800 UT
EAST-WEST MAGNETIC
5.2
FIELD
(
5.6
HOURS UT
Figure
9
.
The Pc5 in the East-West Component
of the Magnetic Field
28
By
6.8
)
amplitude
The
magnetic field,
B^, varies
from
to 4
1
the
largely due to
of the earth's main magnetic field vector in the
the tilt
The perturbations in B^ are a result of
direction.
component of
the east-west
plot of
small
the field. By,
4:16 UT and continuing until just before dawn,
beginning at
Since the perturbations in
06:56 UT.
a
Z
The Pc5 is observed
component of the Pc5 in that direction.
in the
of
gamma during this
component is
The magnitude of this
period.
component
radial
the
of
are small,
and B^
Bj^
the Pc5 event is largely contained in By.
The By
Figure
expanded in
data are
9
for the time
A charac-
period 0400 to 0700 UT (2:14 to 5:21 local time).
teristic of
which makes it fairly unique, is the
this Pc5,
packetized nature
pulsations.
of the
These packets imply
different regions of hydromagnetic resonance in the magnetosphere.
The packets
labelled
are
A
through
venience
in
follows.
The period of the pulsations decreases
It will
comparison
be shown
the
to
E
for con-
electric field data which
with time.
that the period is a function of L and of
the particle density.
2.
Electric Field Data
Figure 10 is
measured
by
SCATHA
a
plot
from
of
the
electric
300
to
0800 UT.
earlier, the electric field data
is
despun
ponents of
Ej5
the solar
component points in
field data
As mentioned
into
two com-
ecliptic (SE) coordinate system.
the
sunward
29
direction
The
and remains
DAY 210 ELECTRIC FIELDS
HOURS UT
Figure 10.
Electric Field Data from 0300 to 0800 UT
30
almost constant at 1.5 mV/m throughout the event
value of
been added to the
from E^).
separate E^
through
motion
SCATHA's relative
component is
This
in order to
Figure 10,
in
E^,
a
result of the-
plasma,
the
mV/m has
(2
the static
convective electric field, the sunward electric field caused
partial projection
by photoemission [Ref. 17] and a
of the
Pc5 electric field perturbation vector in the X direction.
The
component
E2
to
the solar
This component is nearly equal to the total
ecliptic plane.
electric field
perpendicular
is
component of
the Pc5
A -0.4 3 mV/m offset
.
seen in the data is attributed to error fields and
a
steady
state convective field.
Figure 11a is an expanded plot of E^ from 0400 UT to
The packetized nature
0700 UT.
pulsation
is
venience, the
reflected
the
in
electric field
the magnetic field
seen in
electric field.
data is
resonance packets as listed in Table
For con-
seperated into named
2.
TABLE 2
HYDROMAGNETIC RESONANCE PACKETS
Packet
t
begin
t end
(hours UT)
A
4.41
5.03
5.65
6.10
6.63
B
C
D
E
The
component
of
the
results from a perturbation in By
31
4.90
5.46
6.02
6.40
6.95
electric
field,
Ep, which
(topographic coordinates).
ELECTRIC FIELD
FIG.
2
o
_
1
-4
(
Ez
)
11a
B
n
E-«
O
^-wV/l/VvVi,
>
H
I
ii
ir\Arv
lA
f-VV^i
'^;
»i
H
-2
-
-^
T
T
r
T
^
r
T
r
39.7 eV IONS
Q -
FIG.
S
-1
7
-
lib
CO
Pm
O
O
•J
5
HOURS UT
Figure 11
Measured Electric Field and Low Energy Ion
Distribution Function Showing Modulation
of Ion Flux by the Field
32
should
perpendicular
be
both
to
coordinates) is believed to be
electric
that
there
can
component
no
be
projection of
a
E^
Bq.
(SE
Ep onto the
This is based on the assumption
antenna.
field
and
By
electric field
the
of
sustained in the direction of Bq.
6E
The
electrons
magnetic
in
plasma
a
line
field
Bq =
•
(2.1)
free
are
quickly
and
move along the
to
reduce
potential
any
difference which might be impressed along that direction.
shows the geometry for extracting Ep from
Figure 12
E^.
Here a
is the
angle between
the
B-^
from
geographic
latitude
solar
the
ecliptic
also the
Bq and
and
the radial direction and Ep.
satellite's
inclination
angle between
and
is the sum of
(3
the satellite's
plane.
The angle
^
between E^ and Ep is given by
Table
factors,
UT.
z,
The
3
5
=
90 -
(a + p)
(2.2)
Ep
-
E2
cos
(2.3)
/
these
lists
35
angles
and
the
correction
for calculating Ep for the hours of 0400 to 0700
worst
value
case
correction factor in Table
E
=
|Ep|
-
1
/
IE2I
33
60
percent.
The
is used as follows:
z,
3,
only
is
cos ^
•
Z
(2.4)
a
ANGLE BETWEEN MAGNETIC FIELD LINE AND
Bx
S
INCLINATION OF EARTH AXIS ON DAY ElO (IB.^o)
e
GEOGRAPHIC LATITUDE OF SCATHA SPACECRAFT
a
INCLINATION OF SATELLITE FROM SOLAR ECLIPTIC
a
(e + S)
©
90 - (a
Ep
Figure 12.
AT LOCAL MIDNIGHT
AT LOCAL DAWN
a)
Ez/cos $
Calculation of
34
E.
TABLE 3
CORRECTION FACTORS
FIELD
DATA
ELECTRIC
t
a
(UT)
^
p
(degrees
The factor
which most affects the magnitude of this
correction is the shape of
different locations
projected onto
a,
the E^
antenna.
extremely elongated giving
perpendicular field is
Near midnight the field is
large angle between Bq
a
and thus a small angle between E and the
Z
field,
During
is small.
with
this
a
Bj^,
At dawn
dipole
and so
the analysis of the electric
correction
small
and
antenna.
the magnetic field most closely approaches
this angle
field at
It can be seen in Figure
of the
less
magnetic
earth's
the
in the orbit.
for small
12 that,
1.04
1.08
1.11
1.20
1.29
1.43
1.63
16.4
21.9
25.5
33.5
39.0
45.6
52.1
19.2
18.0
16.7
15.2
13.4
11.5
9.2
54.4
50.1
47.8
41.3
37.6
32.9
28.7
0400
0430
0500
0530
0600
0630
0700
mind,
in
the actual
electric field data will be assumed to represent the perpen-
dicular electric field (E2
3
.
•
Ep)
Low Energy Ions
Figure lib shows
a
plot of the log (base 10)
of the
distribution function of the 39.7 ev ions measured from
7
hours UT.
The Pc5
can
be
seen
in
the
ion
flux.
4
to
A
comparison of
this plot
with the electric field shows that
the
ion
is
39.7
ev
flux
modulated
35
in
phase
with the
This reflects the
the electric field, SE^-
perturbation of
electric field.
convective drift induced in the ions by the
Higher
are also modulated, as
electrons
and
ions
energy
the
of
shown in the expanded presentation
packet which
D
follows
B.
A CLOSER LOOK, THE D PACKET
Since
the
at
6
this time SCATHA is
the
region is
hours UT and ends at 6.4 hours UT.
1
a
=6.97 and
average
The D packet is
orbit.
the
period of 17.23 minutes.
at L
time SCATHA 's
of
was
During this
After
km/sec.
3.25
taking into account the decrease in SCATHA*
s
radial position
appears to span
resonance packet
through this period, this
of this
The center
at 4:21 local time.
velocity
At
recently passed
North, having
at 7.3°
inclination
maximum
observed for
.
This
closer analysis.
amplitude fields, it was chosen for
packet begins
largest
the
exhibits
packet
resonance
D
an arc of 3300 kilometers.
1
.
Field Relationships
Figure
13
shows
versus time for the D packet.
E leads
B by
an average
of spline fitted
plots
Within
of 130°
average period of the pulsations is
are
used
since
the
periods
changing, as if the fields are
or non-harmonic
force.
from 0.62 to 1.8 mV/m.
and
E^;
and By
the resonance region,
±10°,
(-
3tt/4),
224 seconds.
and the
Averages
phases are continuously
driven by
a
multi-frequency
The electric field amplitude varies
The magnetic
36
field amplitude varies
?3
^8
3NndS
Figure 13.
3NndS
Pc5 Electric and Magnetic Fields
(D Packet)
37
from
gamma
6
to
The large amplitudes at the
gamma.
12
resonance in
center of the packet distinguish the center of
this region.
The
perpendicular to
vector of the Pc5 lie in a plane
magnetic
the earth
toward and away from
radial direction
and the
were in
difference of
-tt
would
If
east-west direction.
wave would be propagating in
phase the
will exhibit
The magnetic
direction.
+Z
(SE)
tt/2
line).
magnetic field
the -X direction (south along the
standing wave
direction between the
in a
field vector pulsates in a nearly
the fields
the main
The electric field vector pulsates
line.
field
and the magnetic field
vector
field
electric
difference.
phase
indicate
wave
the
A
A phase
is propagating
northward.
The average
fields in
phase of
This implies that the wave is
not a
Figure 13 is
37t/4.
pure propagating wave.
The continuously changing phase of the fields and the motion
through
of th? spacecraft
different
of resonance
regions
make the phase interpretation somewhat ambiguous
The complexity of the phase relationship is born out
by a phase hodogram plot of 6E2 versus 6By in
Figure 14.
In
a
hodogram
a
the D packet.
propagating wave would give a
diagonal line, and a standing wave a circle (if E
plotted in
that the
nearly
Volts/meter and
wave is
linear.
Tesla).
propagating at
At
other
times
38
and B are
This hodogram implies
times, where
the plot is
it shows the phase of a
Figure 14.
Phase Plot of the Pc5 Electromagnetic Wave
(D Packet)
39
average phase of
3it/4
more circular.
plot becomes
standing wave, where the
The
is reflected in the overall elliptical
nature of the plot.
Hence, the slope of
E and B are related by E = ^^B.
a line,
V(t).
or the inclination of an ellipse, in Figure 14 gives
The slope of the major ellipse
(mv/m)
is 0.15 3
/
(gamma)
which gives a phase velocity of 153 km/sec.
2.
Particle and Field Relationships
analyzers
electrostatic
obtained for
'
measured
were
the
and
by
distribution
energy
energy levels every 16 seconds.
63
versus time
Figure 15 contains plots of the log^g ^
for low
the UCSD
and electron fluxes are
Ion
calculated.
were
functions
rates
count
Particle
energy ions, high energy electrons, and two sets of
high energy ions measured between 6.1
UT and
6.4 UT.
The
data sets chosen were from energy levels which exhibited the
highest particle
count rates.
This
was done
in order to
minimize the statistical error.
A plot
of log
F versus time shows the fluctuations
in the energy of the ions with time.
The main cause
of the
change in the kinetic energy of the low energy ions is the
E X
B force,
which is generated by the Pc5 wave.
packet region the magnetic
mately 140
gamma.
field strength,
Bq,
In the D
is approxi-
Hence, a 2.6 mV/m electric field should
give the plasma an E X B drift velocity equal to
V£)
=
6E2 X Bq
/
|Bo^
40
I
18.6 km/sec
(2.5)
HOURS UT
6.
6.^
1
FIG.
15b
9.3 keV IONS
0.^
Cm
O
O
0.0
FIG.
15c
^.7 keV ELECTRONS
E.O
Figure 15.
Ion and Electron Distribution Functions
41
Table
3
electric field
of the
Here the upper limit
values is used (6E
corrected with
z)
•
If the plasma flow is perturbed by a change in the
fields, then the kinetic energy is given by
U = 1/2 m (V - Vd)2
=
where V
1/2 m (V2 -
particle and
is the
V
2
(2.6)
Vi5
cos
e
+ Vq^)
If V >> v^
the E X B flow.
Vj^
(which is true for 40 ev ions) and, if
9
=
0,
then Equation
(2.7) can be expanded
U = 1/2 m (V - Vd)2
- 1/2
the
If
mv2
particle
-
(2.7)
(m V v^)
distributions
energy
were
Maxwellian, they could be represented by
F = n (m/27TkT)3/2 exp -(U/kT)
(2.8)
and by Equation (2.7)
log F
=
constant + (log
e)
Hence, the plot of log F for 40
tional to
V£).
(mV/kT)
out
plotted).
of
v^
is propor-
ev ions
Comparision of 39.7 ev ions with the electric
field in Figure 15a shows this to be the case.
is
•
phase
with
the
electric
The phase difference with
field
by
the electric
due to the unidirectional counting of the ESA's.
42
The ion flux
tt
(-E^ is
field is
Since they
the positive
are looking in the direction of
the count
induced
the
by
E
X
change in
force.
B
B force,
Thus, the
maximum when 6E2 is negative.
rate is
low energy ion flux is modulated by the
energy
E X
the flow
The higher energy
particles respond primarily to B [Ref. 22].
Figure 15b shows that
modulated
higher energy
in
Hence, the changes in
of course,
velocity
the
9
.
3
ions are effectively
magnetic field data.
the
particles are,
change
small'
with
phase
in
9.3 kev
These
unaffected by the
caused by the E X B force.
kev ion flux reflect the effective
motion of the different magnetic field lines with respect to
the satellite.
like
Figure 15c shows 4.7 kev electrons which, in
show
manner,
flux
modulations
in
with
phase
the
magnetic field.
At higher
begins to
energies the
lag the
magnetic field.
15d where the flux of the
an average
field by
modulation of
of
47.4 kev
tt/2.
the ion flux
This is shown in Figure
ions lags
the magnetic
This difference reflects the
large gyroradius (225 km) of these high energy particles.
These
plasma
is
comparisons
moving
with
illustrate
the
point
that the
the magnetic field lines of force.
Hence, the plasma and the field lines oscillate
together as
if the particles are frozen to the field lines [Ref. 6].
3.
Plasma Parameters
The
can
be
plasma
determined
density,
by
temperature and flow velocity
assuming
43
that
ion
distribution
functions
Maxwellian
nearly
are
Maxwellian
fitting
and
distributions to the data.
Analysis of the ion
population
due
a
multi-species
The distribution
masses.
various
the
to
requires
data
function becomes
=
F
S Fi = S n^
(mi/2TTkT)3/2 exp -(Ui/kT^)
(2.9)
and log F for each population is
=
log F
log
(
=
f(p,T) - (log e
=
f(p,T) + f(T) U
the
begin
To
function of
n (m/2TTkT)3/2
(u/kT) log e
_
process
distribution
the
data is calculated and a plot of log F
the ion
As
Figure 16
an example.
This time was
flux recorded by the N/S detector at 6:12 UT.
selected
because
electric
field.
velocities can
it
It
is
is
be expected
near
here
that
and the
satellite potential shadowing the
amplitude
large
a
shows a
calculated from ion
distribution function
the ion
(2.10)
kT) U
fitting
versus energy is made.
plot of
/
-j
in the
highest
the
drift
effect of the positive
lowest
energy
ions
(H"^)
the smallest.
In this
contain
H"^,
He"*"
assumed, there
fitting process
and
O"*"
ions only.
are three
the plasma
was assumed to
Once the
ion species are
unknowns for
each species in the
distribution function. The temperature, kT, the
44
density, n,
o
0t
I
I
H
I
I
M
»
it t
t
I
t
t
I
I
>
a
m
+
o
o
o
m
>
—
o
o
o
.
+
—
o
o
o
+
1
150.0
°
1
1
o
+
.0
^ >^
+
<<
o
o
/^^
-S^
100.0
t~^
T
i
(
Figure 16.
"
^^
1
1
gWM
/
£S
)
I
J 001
UCSD Ion Distribution Function
(0 - 500) eV
45
0)
flow velocity,
and the
is required.
A self consistent set of values
v.
In particular, consistent
flow velocities are
all ions move together.
One additional free
required since
parameter is the satellite potential.
The temperature,
approximated to
kT, is
be 10 ev.
In a more distinctly separated energy distribution, each ion
species would show a well defined peak and the width
of the
In the present case, the
peak would define the temperature.
curvature of the distribution function is
of both
result
a
temperature and velocity.
Since the
be assumed to be looking
detector cannot
in a direction exactly parallel to
4),
must
the flow,
a
look angle,
The choice of this angle affects the
be included.
calculated density and
velocity.
flow
In
case 10
this
degrees was chosen.
A
peak
in
distribution function determines a
the
velocity, Vp, given by
vp
where Vq
is the
introduced
selection of
in
=
(2U/m)l/2
=
Vq cos
plasma drift
the
calculated
the view
angle is
velocity.
velocity
46
Hence, the error
by
an
erroneous
proportional to cos
error of 15° in the approximation of
in Vp of less than 10 percent.
(2.11)
(t>
<t>,
will cause
<t>.
An
an error
Olsen discusses this process
and shows that the error,
the calculation
introduced in
E, ,
of n is more severe [Ref. 23].
E,
exp -(Vd^
«x
_
vq^
(2.12)
cos2(t))
In Figure 16, the peaks occur at approximately
35 ev and 100 ev.
The lower
due
middle
to
the
H""",
,0"*".
energy peak
An
energy peak.
He"*",
approximation,
Vp,
each population
velocity of
is assumed
energy peak
8
ev,
to be
and the highest
the drift
for
made from the measured
can be
energy peak.
Since
V
=
(2U/m)^/2
Vp H
"39
Vp
-
jjp
km/s
41 km/s
•35
Vp
(2.13)
km/s
In the example. Figure 16, the data are
a
Maxwellian
0"^.
distribution function
for
H"*",
for
He"*"
Consistency requires that the Maxwellian plots
density ratio.
velocity,
a
The
10
ev
values used
for this
temperature,
a
fit are
He"*"
for all
and
0"^.
The results
using UCSD data over the D
35 km/s
look angle equal to 10
degrees, and ion number densities 1.0, 0.5, and
H"*",
and for
have the same drift velocity and a reasonable
three species
for
fitted with
0.3
of this fitting process
packet are listed in Table
47
(cm"-^)
4.
TABLE 4
PLASMA ION NUMBER DENSITY (1-500 ev
(
induced by
1.27 ± .67
0.38 + .05
0.30 ± .10
35 ± 5
35 ± 5
35 ± 5
Total
1.95 ± .73
-
of
The
such a flow
-
the flow
convective
flow
is
It is
1
-
10
state electric field responsible for
steady
(0.2
both
steady background flow.
and the
the PCS
35
contains
km/sec
35
estimated that the background
km/sec.
(km/sec)
cm" 3
H+
He+
0+
velocity
The flow
V
n
Ion
mV/m) is
2.0
electric field instrument.
poorly measured
by the
The remaining, pulsation induced
flow, is approximately 25 km/sec.
From Equation
calculated to
(2.6),
be 18.6
the
km/sec.
flow velocity near 16.4 km/sec.
140 gamma,
is
velocity was
Bq
X
This implies a steady state
Since 6E
=
v^
•
Bq and Bo =
convective electric field as large as 2.3 mV/m
a
implied
6E2
from
throughout the
the
D packet
electric
field
is consistent
Analysis
data.
with this interpre-
tation.
An alternative interpretation is
the value
measured by
that
the floating probe.
6E
is twice
Experience with
the electric field data by the principal investigator, T. L.
Aggson,
has
suggested
problems
48
with the amplitude of the
measured fields.
An aggreement within
this
considered
point,
is
of two, at
factor
a
to be supportive of the direct
measurements of E.
The complete ion distribution is needed to determine
total
the
The
density.
ion
high energy UCSD data were
from the
combined with the high energy ion composition data
Composition Experiment
Energy Ion
SC8 High
determined average ion densities in the
for the
H"*"
density was (1.974 cm~^}, the
(0.089 cm~3} and the
a
-
500
eV)
the total
O"*"
(0
-
80
kev)
ions are part of
The average
density was
He"*"
cm~^).
The SC8
The line plot in Figure 17 is
population.
The low energy
ions are the same population inferred
in Figure
by the fitting process of the UCSD data
UCSD
SC8
21].
32 kev range
to
density was (0.398
O"*"
shown in Figure 17.
plot of log F for
(100 eV
1
period from 0600 to 0700 UT.
one hour
data are
.
[Ref.
ions are shown in Figure 18.
the bulk
of the
The
16.
The 10 keV
plasma sheet population,
while the
47 keV ions are from the tail of the distribution
function.
The SC8 data
with
combined
are
the parameters
obtained from the UCSD experiment and reported in Table
TABLE 5
PLASMA ION DENSITIES (.01
Ion
-
32 KEV)
n
(cm" 3)
H+
He+
0+
TOTAL
3.24
0.47
0.40
4.1
49
±
±
±
±
.68
.15
.17
1.0
5
HIGH ENERGY IONS
32
ENERGY (KEV)
X
Figure 17.
[HE+]
F (PLASMA)
SC8 Ion Distribution Function
(0.1 - 32.0) keV
50
LOG F
(
S^
/
KM^
)
»
I
>
^
o
>
Q)
o
•«
II
I
I
I
*ilitlHI
o
o
m
Figure 18.
UCSD Ion Distribution Function
51
4.
Electron Density
The calculation
on the distribution function
large error
the
of
population being
ion
An error in the look angle can introduce
nearly Maxwellian.
a
ion density depends largely
of the
in
Since
n.
density
number
the
of the
electrons should
be equal to the number- density of the ions
in a plasma, the
value of
check of
a good
Rq is
the ion
density calculations.
All the
members of the electron population have the
same mass, and that
unknowns that
mass
hindered the
useful characteristic of
sections
of
Hence,
ion calculation
magnetospheric
distribution
the
defined slopes
known.
is
is removed
electrons
.
A
is that
plot have clearly
function
which identify
of the
one
different energy populations
of electrons.
In
a
plot
electron distribution function
the
of
versus energy
log Fq
=
log (ng (me/2TTkTe) 3/2^
=
c + b Uq
_
log
e
(1/kTe) Uq
(2.14)
where b is the slope of each section of the distribution
function and c is the
y intercept.
kTe
=
-log
no
=
10^
e
/
/
b
(me /
52
From Equation (2.14)
(2.15)
2tt
kTe)3/2
plot
Figure 19 is a
calculated from
electron distribution
the
of
taken at
UCSD data
Figure 17 are (sec^/km^) versus (keV)
The units of
6:12 UT.
Correcting for units
.
(2.16)
ng
(10^ X 10-24}
=
/
energy sets
In Figure 19 two
slope intercept
By the
shown to have
density of
(9.05 X 10-13
method, the
)3/2
kT (ev)
of electrons
number density
a
/
are identified.
17.5 kev electrons are
of 0.007
The number
cm'^.
the 1.65 kev electrons is shown to be 1.77
cm--^.
By expanding the lower energy section of this data two other
electron groups were identified.
The number densities which
were calculated for each set
electrons
Table
of
reported in
is
6
TABLE 6
ELECTRON NUMBER DENSITY
Energy Range
Temperature
(kev)
(kev)
17.50
1.65
0.71
0.12
15 - 80
1.0 - 15
0.2 - 1.0
0.0 - 0.2
TOTAL
Hence, the
is consistent
n
with
(
cm- 3
0.007
1.77
1.46
0.67
±
±
±
±
.001
3.9
±
.2
.09
.09
.04
calculated ion number density (4.1 cm" 3)
the
independently
density.
53
determined electron
LOG F (S^
/
Km6
)
e
>
O
<
a
Figure 19.
UCSD Electron Distribution Function
(0 - 80) keV
54
5.
Self Consistency of the Data
It
is
now
to determine whether these
important
relationship between n,
numbers represent a self -consistent
B,
Since the plasma acts as
and v.
E
circuit on the electric field antenna,
a
a
parallel resistive
major concern is to
verify the amplitude measurements of E^.
equation to deduce the
the following
Cummings used
density of the ambient plasma from
field and
particle data
measured by the ATS-6 spacecraft in geosynchronous orbit
n = 6b2
where
<m>
is
/
Pq <m>
average
the
relationship is used to
(2.17)
V£)2
particle
investigate the
mass [Ref. 7].
This
consistency of the
ion density calculations.
Assuming that
0"*",
the plasma
is made up of
and using the values from Table 6, the ion
H"^,
He"^
and
mass density
is given by
p = S
=
p =
and
where
=
m^
(2.18)
(3.24(1) + .47(4) + .40(16)} mp
(11.52 mp) kg/cm^
<m> = p
mp
n-j^
/
n
=
2.81 mp
1.672 x 10"^^ kg.
55
Equation (2.17) is then rewritten,
v2 = 5b2
V
Since
|v
<m> n
iJq
6B /
=
(Po P)^^^
|6E / Bq
=
|
/
|
6E = 6B Bq
(6B Bq)
mV/m
units of 6B and Bq are gamma.
In the D packet
Bq
6
Therefore
(2.19)
(Po P)-^^^
6.4 X 10"3
=
where the
/
140 gamma
=
6By
<
12 gamma
<
(2.20)
the magnitude of the electic field inferred by
mass density is
5.4
6E
<
mV/m
(2.21)
^1.8 mV/m
(2.22)
10.8
<
The measured values of 6E2 were
0.62
^
6E2
Taking into account the electric field
correction factor of
1.43, from Table 4, the magnitude of the perturbed
electric field is calculated to be
0.9
These
values
are
Equation (2.21).
a
<
6Ep
<
factor
A factor of
56
2.6 mV/m
of
2
3
(2.23)
lower than predicted by
could
be accounted
for if
the impedance
of the
plasma was comparable to the internal
(this is roughly
impedance of the electric field experiment
the case).
A small error, not larger than a factor of
2,
in
the electric field data is implied by the comparison.
6
The Alfven Velocity
The
velocities.
comparison
same
be
can
made
in
terms
of
The Alfven velocity is
V;^
=
w/k
Bq
=
/
Since
Curl E
=
-dB/dt
then
ik Ep
-
-(-ico)
and
6Ep/By
-
(1-2)
(Po P)^^^
By
= V;^
co/k
(2.24)
Using upper and lower bounds of the field amplitudes
given by Equations (2.20) and (2.23), the Alfven velocity
calculated from measured E is
328 km/sec
<
^p,
<
378 km/sec
(2.25)
Using the ion density relationship
^A
The electric
= ^o /
(^o P)^^^ = 900 km/sec
field data
(2.26)
appears to be low by a factor of
3
in this comparison.
7
The Poynting Vector
The nature of the propagation of the PCS can be seen
by
examining
the
relationship
57
of
SE^
and
6By.
If the
micropulsation was
a
classical plane Alfven wave, then
(1/y) E X B
S =
-
(l/Po)
-
1
(l/Po)
(SEy 5B2 - 6E2 6By)
the Poynting vector
components of
the other
which assumes
5E X 6B
6Ey is not measured, but 5B2 is small, so
are small.
S - 1
In Figure 20 Px
=
(1/yo)
(-5Ez SBy)
(2.27)
X 10"12
(2.28)
(6E2 6By), so
S = -1
(1/yo)
(Px)
watts/m2
The negative values of Px in Figure 20 indicate that
the wave is propagating in the +X direction, northward along
the magnetic
field line.
south of 7° N.
The fact
positive indicates
traveling
wave,
traveling
in
standing
/
The wave must have been generated
that
is
superimposed
southward
the
is,
at
times,
zero or
micropulsation is not a simple
that the
but
Px
on
direction.
a
smaller wave
This is the mixed
propagating nature inferred previously
in Figure
14.
And finally, the magnitude of the Poynting vector is
calculated
Px
=
|S|
(1.8
=
mV/m)
(1/yo)
(-12 gamma)
|Px|
X 10~12
=17.2 yWatts/m2
58
(2.29)
•A
m
m
lO
m
T
1
3W /Sil-YM (^T-O"^ ^
^^Z"!^
^^
xd
Figure 20
The Poynting vector
(Calculated in the D Packet)
59
u^«o
04
1
presumes
This
the
that
measurement
field
is
possible error in 6E, the magnitude of
Given the
correct.
electric
the Poynting vector could be as high as 50 yWatts/m^,
8
Dependence of the Period on L
.
field line
and the
of the wave [Ref. 24].
Alfven velocity
latitude can be
The variation of micropulsation period with
expressed
density.
as
function
a
of
and
L
length of the
on the
The period of the Pc5 depends
n,
the plasma number
[Ref. 25],
L^ Re/Be)
(Po <^> n/Q)l/2
X
=
(2tt
Bg
=
3.12 X 10"^ Tesla
•
(2.30)
Q is proportional to an Alfven wave eigenvalue which is
density gradient, and
calculated for different values of L,
wave type.
In a simpler form this equation corresponds to
X
The SCATHA
data can
the period
of
proportional to
this
=
(m/k)l/2
27T
,
be used to determine the dependence of
Pc5
on
L.
If
the
period,
x,
is
L"^
log
X
=
log C + m log L
(2.31)
where C is a constant.
Figure 21 shows the average micropulsation period in
each
resonance
determined by
packet,
plotted
against
L.
linear regression, is 3.96 ± .07.
60
The slope,
Hence, the
PCS PERIOD VERSUS
L
2.7
2.6
-
THE PERIOD OF A PCS WAVE
IB PROPORTIONAL TO L'*
Q
O
U
2.5
w
CO
2.4.
o
2.3 -
2.2
0.79
1
1
o.ai
T
1
0.85
0.83
LOG
Figure 21.
T
1
1
[
L
1
0.87
]
Pc5 Period Versus Mcllwain L
61
1
1
O.S9
SCATHA data
the theoretical
with
agreement
close
in
is
relationship
Having
(2.30)
verified
the
(2.32)
L^
«
X
dependence of the period. Equation
L
mass density
predict a
is rewritten and utilized to
to compare with the previous measurements.
p =
n <m>
For the values
=
x
(T
=
Be
/
L^ Rg )2 x (Q
2-n
/
\1q)
(2.33)
224 sec (in the D packet)
L = 7.0
Bg
=
3.12 X 10"^ Tesla
n <m>
=
2.514 mp
•
Q
(cm'^)
(2.34)
Orr and Matthew calculate Q for a toroidal mode wave
in plasma density gradients which obey power laws between R^
and r2 [Ref. 25].
3.6
At L
=
(for r4)
these values are
7
<
Q
<
4.2 (for R^
(2.35)
)
The mass density inferred by Equation (2.33) is
9.05 mp
<
The measured mass density
theoretical relationship
n <m>
was
<
10.56 mp
11.52
law of
(cm~-^).
is valid for this Pc5
shown that it is substantively valid
the power
mp
(cm~3)
the period),
62
by the
(2.36)
If the
(it has been
agreement with
then the difference between
predicted particle density and measured density implies that
the mass
a
density has been slightly overestimated.
However,
10 seconds
from the
deviation of the wave period of only
average
used
period,
predicted
density
mass
Equation (2.34), would bring the
in
with
agreement
exact
into
the
measured mass density.
Since
values
the
eigenvalue
theoretical
complete aggreement
study is
not
equation
from
a
wave,
toroidal
the
for
However,
with both
derived
were
results of this
mass density
with the
demanded.
strong agreement
Q
for
comparison shows
this
variables, L and
p.
The plasma
density gradient is the unknown variable.
SOLAR AND MAGNETIC FIELD CONDITIONS
C.
Geomagnetic and Solar Data, published by
Geophysical
Research,
moderately active
substorms
day,
recorded.
indicates
Kp
Forty
event there was a period of
which
a
12 hour
=
to
3
eight
very high
magnetic storm
'
generally
s
occur
during
5,
Day
with
210
was
by
a
no magnetic
hours prior to the Pc5
magnetic activity in
These
occurred [Ref. 26].
conditions support the statement
Pc5
that
the Journal of
Jacobs
recovery
[Ref.
1]
that
periods following
magnetic disturbances.
D.
OTHER OBSERVERS
SCATHA observed the Pc5 at
L =
7.
Magnetograms from
3
31
degrees east longitude on
the National Institute of Polar
63
Iceland (68.2"
39.6° E)
(69.0° S
say
to
These
more.
invariant latitude for L
of this
=
0600 to 0700 UT.
from
station
time resolution of the ground
enough
observed at
indicate that this event was
simultaneously
stations
these
and at Syowa Base, Antarctica
338.3° E)
N
at Leirvogur,
stations
ground
Research from the conjugate
The
7.
located at the
are
stations
not clear
was
data
The
simultaneous observation
imply that the generation was occuring
event would
near the equator.
There is no indication of this observation at Narssarss'
uaq Station,
Greenland (61.2°
Station (47.6°
GOES
2
307.3° E)
N
and GOES
3
magnetic
frequent
correlated
with
geosynchronous
.
314.2° E) or at St. Johns
N
from the NOAA
Magnetograms
satellites were also scanned. They showed
activity,
the
none
These
Pc5.
orbit
but
252°
at
which
satellites
East
and
could
be
were
in
225°
East
respectively.
The lack of Pc5 activity at locations west of the SCATHA
sector indicates a limit on the temporal and
of the
event.
degrees of
spatial extent
The Pc5 appears to have been confined to 45
longitude
in
the
SCATHA.
64
morning
sector
observed by
DISCUSSION
III.
THE CHARACTER OF THE PCS
A.
II, the observable quantities characterizing
In Chapter
focusing on
this Pc5 event were investigated by
at the
temporal and
was shown to
magnetic
be
of the event. The wave
spatial center
traveling
a
data taken
Alfven
wave
by the
guided
line.
The Alfven velocity was nearly 900
kilometers per second.
A calculation of the Foynting vector
field
showed the wave was traveling northward.
The electromagnetic
occuring in a plane
perpendicular
The amplitude of the
measured
The
gamma.
the measured
2
to
3.
and the
(cm~^).
studies.
km/sec is
electric
reached
field
electric field was shown to be low by
The period of the Pc5,
period of
The ion
This
The
also
is
3tt/4.
2.57
By requiring consistency of the data,
at L=7,
factor
a
was 224 seconds
the wave was shown to be proportional to
The plasma density
(gm/cm^).
magnetic field
the
perturbations was near
magnetic field
millivolts per meter.
of
the
was shown to be
magnetic field lagged the electric field by
line. The
12
field perturbation
estimated
was
to
be
1.9
x 10"^-^
number density was determined to be 4.1
with
consistent
calculation
consistent
of
with
65
previous magnetospheric
the
Alfven velocity
previous
studies.
-
900
Most
models of average magnetospheric plasma
recently, empirical
and Fast Mode
and field data were developed to study Alfven
wave
speeds
[Ref.
densities of
and Alfven
3-5
(cm"^),
wave speeds
models
These
27].
predict
plasma temperatures
of 500
-
plasma
of 30-100 ev
1000 km/sec at L = 7.0 in
the morning sector of the magnetosphere.
SPATIAL EXTENT OF THE PCS
B.
The most interesting factor in
packetized nature
of the
this
event
Pc5
is the
micropulsation resonances through
The breadth
this sector of the magnetosphere.
and location
in these regions is presented in Table 7.
TABLE 7
RESONANCE PACKET LOCATION AND SIZE
Width
ID
t
(UT)
(km)
A
4.66
5.25
5.84
6.26
6.80
7.46
The
(°
C
D
E
P
factor,
in
Table
L
N)
7.38
7.50
7.45
7.29
6.96
6.11
5300
5300
4200
3300
3600
5400
B
r
Latitude
7
,
7.8
7.5
7.2
6.9
6.7
6.4
Local
Time
2:45
3:23
3:54
4:21
4:55
5:42
r
0.45
0.50
0.32
1.00
0.72
0.49
is a normalized resonance
strength for each region, which is the ratio of the electric
field amplitude
packet.
in a
region to the electric field in the D
These resonance regions are seperated by sectors of
low resonance which vary in distance from 1200 kilometers to
3600 kilometers.
66
C.
UNRESOLVED ISSUES
A complete understanding of
vector
description
of
this event
There are significant
data.
the
would require a
aspects of the Pc5 which were neglected by this study.
is the
One
effect that the nutation of the spacecraft spin axis
be seen
The nutation effect can
has on the raw data.
as a
small pulsation in each component of the magnetic field data
Another
in Figure 8.
smaller
component
direction, B^.
4
aspect
of
the
the
is
which
Pc5
significance
of the
the
radial
is
in
The B^ component has an average amplitude of
This component has a small effect on the amplitude
gamma.
of the Pc5 magnetic field, but
the rotational
motion of
has a
significant effect on
the field.
A study that included
this component would provide a more realistic description of
the Pc5 event.
A most
difficult aspect,
who follows this study, is
character of
such as
the
separation
of
the spatial
from the temporal description which
the event
this study provides.
which is left for the student
Many of the effects seen in
variation of
the sinusoidal
the data,
the resonance in each
packet, have been described but not explained.
D
RECOMMEND AT I ONS
1.
not be
The spatial
and temporal
determined by SCATHA alone.
known if local dawn was
a
extent of
this Pc5 could
Specifically, it is not
boundary of
the Pc5
or that the
Pc5 ended at all locations at 6:56 UT. The radial boundaries
67
of the event are also left
been
a
SCATHA passed
ended when
the Pc5
coincidence, but it could
major characteristic
available from
the European
resolution
the
a
satellite that was
GEOS-2 satellite)
conjugate
data may be
answer (such
provide an
SCATHA could
of
be a
This may have
6.6.
L =
A correlation with
of this phenomenon.
East of
The observation of
unresolved.
ground
station
.
Better time
data
would
determine the location of the generating mechanism.
2.
Approximate densities
highest
of
resonance,
information made
were calculated in the region
the
available by
wealth
The
packet.
D
SCATHA provides
of
an area for
further study into the magnetospheric plasma profile between
5
.
5
Re
and
7
3.
The theoretical
.
5
models presently available describe
standing and compressional Alfven
Since this event
waves.
provides extensive data from a traveling wave event, further
investigation into this
area
of
micropulsation
theory is
warranted.
4.
Theorists
have
recently
shown
great
interest in
understanding the resonance conditions for Alfven waves.
emphasized
in
this
resonance conditions in the
sphere
is
displayed
the
paper,
packetized
morning sector
vividly
by
the
observations should be used to improve
Alfven wave resonance.
68
As
nature of the
of the magneto-
SCATHA data.
These
the understanding of
CONCLUSIONS
IV.
Observations of
8.0 in
L =
to
Pc5 event occuring between L =
.
6
and
with
kilometers
regions spanning
resonance
Hydromagnetic
5000
6
sector of July 29, 1979, at 7° N,
the pre-dawn
were reported.
3000
a
separated by 2400
centers
kilometers were identified.
shown to
x 10"^-^
be 1.92
resonance region was
the highest
The plasma density in
gm/cm-^
shown to be in phase with the electric
at
kev, and
9
with the
kev
5
magnetic
magnetic field by
Particle data
The
The
shown to be in phase
kev
47
By
from the UCSD electrostatic analyzers was
checking electric
of cross
data was
electric field
comparing
was
shown
to
be
data
this
predictions, the amplitude of
data
lagged the
ions
assumed to be a
projection of the perturbation electric field
antenna.
Ion fluxes
.
radians.
effective means
shown to be an
field data.
tt/2
field
electrons, were
field.
at 40 ev was
Ion flux
.
a
with
measured
the
factor
of
2-3
onto SCATPiA's
density
ion
electric field
too low to be
consistent with the complete set of data (this is considered
to be a small error)
The periods
of the micropulsations, between L
=
6.3 and
7.7, were shown to be proportional to the fourth power of L,
which
supports
present
models
69
of
resonant
Alfven
wave
activity in the magnetosphere. Alfven velocities
were shown
to be nearly 900 kilometers per second within high resonance
regions of the event.
electromagnetic
The
perpendicular to
pulsations
the magnetic
magnetic field lagged
field line.
electric
the
were
field
in
a
In the Pc5
by
plane
,
the
The
3n/4.
Poynting vector was shown to be in the direction of the main
magnetic
field
traveling
Alfven
conjugate
ground
confirming
vector,
Simultaneous
wave.
stations
that
indicated
that
the
wave
was a
observations
by
the generation
could be occurring at the equator.
The
unique
packetized
resonance
regions exhibited by
this PCS as well as the non-classical wave character of this
event
indicates
that
further
data from SCATHA is warranted.
70
theoretical study utilizing
LIST OF REFERENCES
Springer-
1.
Jacobs, J. A., Geomagnetic Micropulsations
Verlag Berlin, 1970.
2.
Stewart, B., "On the Great Magnetic Distrubance which
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Transcripts of the Royal Society of London v 423,
,
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,
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Barfield, J. N. and R. L. McPherron, "Statistical
Characteristics of Storm Associated Pc5 Micropulsations
Observed at the Synchronous Equatorial Orbit,"
Journal of Geophysical Research v. 77, pp. 4720-4733,
,
1972.
4.
Barfield, J. N. R. L. McPherron, P. J. Coleman, Jr. and
D. J. Southwood, "Storm- Associated Pc5 Micropulsation
Observed at the Synchronous Equatorial Orbit," Journal
of Geophysical Research v. 77, pp. 143-158, 1972.
,
,
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Lanzerotti, L. J., H. Fukunishi, C. C. Lin and L. J.
Cahill, "Storm Time Pc5 Magnetic Pulsation at the
Equator in the Magnetosphere and Its Latitude Dependence
as Measured on the Ground," Journal of Geophysical
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6.
Chen, Francis F.
,
Controlled Fusion
,
Introduction to Plasma Physics and
2nd ed. v. 1, pp. 136-140, Plenum
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Cummings W. D., S. E. Deforest and R. L. McPherron,
"Measurements of the Poynting Vector of Standing
Hydromagnetic Waves at Geosynchronous Orbit," Journal
of Geophysical Research v. 83, pp. 697-706, 1978.
,
,
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Waite, J. H.
D. Gallagher, M. Changler, R. Olsen, R.
Comfort, J. Johnson, C. Chappell, W. Peterson, D. Weimer
and S. Shawhan, "Plasma and Field Observations of a Pc 5
Wave Event," Journal of Geophysical Research v. 91,
pp. 11147-11161, 1986.
,
,
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Matthews, John, "Hydromagnetic Wave Activity Detected by
the GEOS 2 Double-Probe Experiment During 1979," Journal
of Geophysical Research v. 92, pp. 7423-7431, 1987.
,
71
10. Takahashi, K., J. F. Fennell, E. Amata and P. R. Higbie,
"Field Aligned Structure of the Storm Time Pc5 Wave of
November 14-15, 1979," Journal of Geophysical Research
V. 92, pp. 5857-5864, 1987.
"On the Existence of ElectromagneticHydromagnetic Waves," Arkiv for Matematik v. 29B No.
11. Alfven, H.
,
,
,
2,
1943.
12. Lundquist,
for Fsyik
S.,
v.
,
13. Alfven, H.
,
"Studies in Magneto-Hydrodynamics," Arkiv
5, pp. 297-347, 1952.
Cosmical Electrodynamics
,
Oxford University
Press, 1950.
14.
Sugiura, M. and C. R. Wilson, "Oscillation of the
Geomagnetic Field Lines and Associated Magnetic
Perturbations at Conjugate Points," Journal of
Geophysical Research v. 69, pp. 1211-1216, 1964.
,
and L. Chen, "Theory of Magnetic
Pulsations," Space Science Reviews v. 16, pp. 347-359,
15. Hasegawa, A.,
,
1974.
C, T. Aggson and B. Ledley, "Observations of
Electric Fields Near Plasmapause at Midnight," Journal
of Geophysical Research v. 91, pp. 12017-12019, 1986.
16. Olsen, R.
,
17.
Craven, P. D., R. Olsen, J. Fennell, D. Croley and T.
Aggson, "Potential Modulation of the SCATHA Spacecraft,"
Journal of Spacecraft v. 24, pp. 150-151, 1987.
,
18. Mcllwain, Carl E.,
Reviews, v. 5, pp.
"Magnetic Coordinates," Space Science
585-598, 1966.
19.
Hess, Wilmot H.
Introduction to Space Science pp. 41Gordon
and
Bresch
Science Publishers, Inc., 1965.
58,
20.
Fennell, J. F.
"Description of the P78-2 (SCATHA)
Satellite and Experiments," The IMS Source Book
American Geophysical Union, pp. 65-81, 1982.
,
,
,
,
21. Air Force Systems Command SAMSO TR-78-24, Description of
the Space Test Program and Payloads , pp. 29-56,
October 31, 1978.
22.
Southwood, David J. and Margaret G. Kivelson, "Charged
Particle Behavior in Low-Frequency Geomagnetic Pulsations; 1. Transverse Waves," Journal of Geophysical
Research v. 86, pp. 5643-5655, 1981.
,
72
23. "Olsen,
Richard Christopher, "Field-Aligned Ion Streams
in the Earth's Midnight Region," Journal of Geophysical
Research , v. 87, pp. 2301-2310, 1982.
24.
Singer, H. J., D. J. Southwood, R. J. Walker and M. G.
Kivelson, "Alfven Wave Resonances in a Realistic
Magnetospheric Field Geometry," Journal of Geophysical
Research v. 86, p. 4593, 1981.
,
"The Variation of
Geomagnetic Micropulsation Periods with Latitude and
the Plasmapause, " Planetary and Space Science v. 19,
25. Orr, David and James A. D. Matthew,
,
p.
26.
899,
1971.
Lincoln, J. Virginia, "Geomagnetic and Solar Data,"
Journal of Geophysical Research v. 84, No. All, 1979.
,
E., and others, "MHD Wave Breaking in the Outer
Plasmasphere, " Geophysical Research Letters v. 14, pp.
1007-1010, 1987.
27. Moore, T.
,
73
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Thesis
P26635
c.l
Patterson
Observations of a hydromagnetic wave in the
earth's magnetosphere.
n
(
Thegis
P26635
c.l
Patterson
Observations of a hydromagnetic wave in the
earth's magnetosphere.