Author(s)
Lantto, Eric S.
Title
Detailed analysis case studies of trapped plasmas at the earth's magnetic equator
Publisher
Monterey, California. Naval Postgraduate School
Issue Date
1993-06
URL
http://hdl.handle.net/10945/39803
This document was downloaded on May 04, 2015 at 22:10:26
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111I1III
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11
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11l
Illlllll
NAVAL Pu.'1rujiAUATE SCHOOL
Monterey, California
It.
THESIS
Detailed Analysis Case Studies of Trapped
Plasmas at the Earth's Magnetic Equator
by
Eric S. Lantto
June, 1993
Thesis Advisor:
R. C. Olsen
Approved for public release; distribution is unlimited.
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3. REPORT TYPE AND DATES COVERED
Master's Thesis
1993
4. TITLE AND SUBTITLE
S. FUNDING NUMBERS
Detailed Analysis Case Studies of Trapped
Plasmas at the Earth's
Magnetic Equator
6. AUTHOR(S)
Lantto,
Eric S.
7. PERFORMING ORGANIZATION NAME(S) AND ADORESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
Naval Postgraduate School
Monterey, CA 93943-5000
9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/ MONITORING
AGENCY REPORT NUMBER
11. SUPPLEMENTARY NOTES
The views expressed in this thesis are those of the author and do not reflect the
official policy or position nf the Department of Defense or the U.S. Goverruent.
12a. DISTRIBUTION /AVAILABILITY
STATEMENT
12b. DISTRIBUTION CODE
Approved for public release; distribution is
unlimited.
13. ABSTRACT (Maximum 200 words)
A previous statistical
survey of data from the HPCE experiment on the
AMPTE/CCE satellite
established
probability
distributions
for trapped
ions and electrons. An extension of this
survey for ions at
240 and 442
eV and for electrons
at 340 and 770 eV confirmed these distributions.
A further
detailed
analysis of the electron data from 13 individual
data collection
days also showed the trapped electron distribution
to
be concentrated in the dawn to noon region, centered at L=7. These
trapped electron distributions
can be described as a bi-Maxwellian
distribution
function and be characterized reasonably by the criteria
that
the flux has to exceed 5e6 per (sq. cm sec sr), the distribution
has to be within 10 deg. of the magnetic equator, the ratio
of the
perpendicualr temperature to the parallel
temperature exceeds 3.0 and
that
the anisotropy exceeds 2.0 for 150 eV electrons and 4.4 for 340
eV electrons.
14. SUBJECT TERMS
Equatorially
Distributions,
15. NUMBER OF PAGES
17. SECURITY CLASSIFICATION
OF REPORT
UNCLASSIFIED
NSN 7540-01-280-5500
"155
Trapped Plasma, Plasmapause, AMPTE, Ion
Electron Distributions,
Bi-Maxwellian
18.
SECURITY CLASSIFICATION
OF THIS PAGE
UNCLASSIFIED
19. SECURITY CLASSIFICATION
OF ABSTRACT
UNCLASSIFIED
i
20. LIMITATION OF ABSTRACT
UL
Standard Form 298 (Rev 2-89)
Prescribed by ANSI Std. Z39-18
Approved for public release; distribution is unlimited.
Detailed Analysis Case Studies of Trapped
Plasmas at the Earth's Magnetic Equator
by
Eric S. Lantto
Lieutenant Commander, United States Navy
B.S., University of Minnesota
Submitted in partial fulfillment
of the requirements for the degree of
MASTER OF SCIENCE IN PHYSICS
from the
NAVAL POSTGRADUATE SCHOOL
Author:________
Eric S. Lantto
Approved byR. C. Olsen, Thesis Advisor
e"S. Gn
alin
,Se
Reader
K. E. Woehler, Chairman
Department of Physics
ii
ABSTRACT
A previous statistical survey of data from the HPCE experiment on the AMPTE/CCE
satellite established probability distributions for trapped ions and electrons. An extension
of this survey for ions at 240 and 442 eV and fur electrons at 340 and 770 eV confirmed
these distributions. A further detailed analysis of the electron data from 13 individual
data collection days also showed the trapped electron distributions to be concentrated in
the dawn to noon region, centered at L = 7. These trapped electron distributions can be
described as a bi-Maxwellian distribution function and be characterized reabiiably by die
criteria that the flux has to exceed 5x106 (cm' s sr)-', the distribution has to be within 10"
of the magnetic equator, the ratio of the perpendicular temperature to the parallel
temperature is greater than 3 and that the anisotropy is greater than 2.0 for 150 eV
electrons and 4.4 for 340 eV electrons.
Accesion For
NTIS CRA&I
DTIC TAB
Unannounced
'D TT
'•
": :'•:.": .. -.. " ...
Jus
ifiicatiofl
ati n ....
JU~tif
-I
..........................
By .... . .................................... .
Di,.t, ibjtion /
Availoh•jily Co.cs
Dist
in
Av.-Ii
ni/or
TABLE OF CONTENTS
I.
II.
INTRODUCTION
.............
.
BACKGROUND ...................
III.
.
..
1
....................
A.
THE PLASMASPHERE .............
B.
THEORY ...............
1. Plasma Definition
.
4
................
4
....................
12
...............
12
.
2.
Debye Shielding .........
..............
15
3.
Plasma Parameter ........
..............
16
4.
Motion in
5.
Magnetic Mirror .........
6.
Statistical
a Uniform Magnetic Field .....
..............
Distribution ....
..
16
17
..........
21
C.
PREVIOUS OBSERVATIONS ......
.............
23
D.
THE AMPTE/CCE SATELLITE ....
............
40
E.
THE HOT PLASMA COMPOSITION EXPERIMENT
OBSERVATIONS ..............
A.
B.
STATISTICAL SURVEY
(HPCE)
...................
51
................
51
1.
Data.Analysis ..........................
2.
Local Time - McIlwain L Surveys
a.
ION SURVEY ........
b.
ELECTRON SURVEY .......
42
51
......
...............
52
52
............
63
DETAILED ANALYSIS CASE STUDIES .. ........
69
1. Data Analysis ...........
69
iv
...............
2.
3.
4.
Day 84/336 Case Study Trapped Distributions
a.
150 eV .....
b.
340 eV ................
V.
..
.................
80
.................
83
a.
150 eV ............
.................
83
b.
340 eV ............
.................
87
Detailed Analysis
Trapped versus Non-Trapped
90
...............
96
....................
DISCUSSION ...............
..............
96
A.
STATISTICAL SURVEY .........
B.
DETAILED ANALYSIS CASE STUDIES .. ........
CONCLUSIONS ...............
.
STATISTICAL ANALYSIS .......
B.
DETAILED ANALYSIS CASE STUDIES ...
..................
LIST OF REFERENCES .............
INITIAL DISTRIBUTION LIST ........
v
107
.............
(DETAILED ANALYSIS SPECTROGRAMS) ...
...............
97
107
....................
A.
APPENDIX
75
Day 85/002 Case Study Trapped Distributions
Distributions ...........
IV.
75
........
.......
108
111
138
141
LIST OF FIGURES
Figure 1. The Earth's Magnetosphere ........
..........
5
Figure 2.
Plasma Density L Dependance ......
.........
7
Figure 3.
Plasmapause Magnetic Activity Dependance
.
.
8
Figure 4.
Plasma Density L Dependance - Normalized
.
.
10
Figure 5.
The Dusk Bulge
.
.
13
. ..............
Figure 6. Magnetosphere's Electric and Magnetic Fields
14
Figure 7.
Path of Mirroring Particle ...
..
19
Figure 8.
Pitch Angle verses Mirror Latitude
.....
..
22
Trapped
Ion
Figure
9.
Field
Aligned
and
.........
Pancake
Distributions ...............................
Figure 10.
25
Trapped Ion Distribution With Relation to the
Plasmapause ............
....................
Figure 11. Ion Pitch Angle Distribution ...
........
..
26
..
27
..
29
Figure 12.
Electron Pitch Angle Distribution
Figure 13.
Energy Relations of Trapped Plasmas
Figure 14.
Trapped Ion L verses Local Time Dependence .
32
Figure 15.
Flux - Spin Phase/Density Fits .........
33
.....
.
.
..
30
..
Figure 16. Log of Flux verses Pitch Angle - 150 eV and 340
eV Electrons .............
Figure 17.
...................
The AMPTE/CCE Satellite
............
Figure 18. The AMPTE/CCE Payload .....
Figure 19.
Figure
20.
..
41
...........
..
The HPCE Ion-Mass Spectrometer ...........
The
HPCE
Electron
Monitor ..............
Background
......................
vi
39
43
44
Environment
..
46
Figure 21. Trapped Ions (240 eV) - Flux gt 105,
gt
1.5, Maglat gt
Anisotropy
100 .............................
53
Figure 22. Trapped Ions (240 eV) - Flux gt 105, Anisotropy
gt 1.5,
Figure 23.
Maglat gt 100 - Surface Plot .. .......
24.
54
Trapped Ions (240 eV) - Flux gt 105, Anisotropy
gt 1.5, Maglat gt 50
Figure
..
Trapped
.. . . . . . . .. . .. . . . . . . ... . . . . . . .
Ions
(240
eV)
-
Flux
Anisotropy gt 2.0, Maglat gt 50 ...
..........
gt
56
5x105,
57
Figure 25. Trapped Ions (442 eV) - Flux gt 103, Anisotropy
gt
1.5, Maglat gt
50
.............................
58
Figure 26. Trapped Ions (442 eV) - Flux gt 103, Anisotropy
gt 1.5, Maglat gt 50 - Surface Plot ...
Figure
27.
Trapped
Ions
(30-150
eV)
-
Flux
Anisotropy gt 1.5, Maglat gt 100° .......
Figure
28.
Trapped
Ions
Anisotropy gt 1.5,
Figure 29.
(30-150
eV)
-
Flux
Trapped Electrons
(340
eV)
-
Trapped Electrons
(770 eV)
-
Trapped Electrons
(770 eV)
Anisotropy gt 1.5, Maglat gt 100 -
Figure 32.
Trapped Electrons
Anisotropy gt
Figure 33.
1.5,
Maglat gt
Trapped Electrons
Anisotropy gt 1.5,
(150
eV)
100
(150
eV)
.
.
62
64
Flux gt 5x10%,
.........
65
Flux gt 5x106,
.
.
66
Flux gt 5x106 ,
...............
.
67
-
Flux gt 5x106 ,
Maglat gt 100 - Surface Plot
vii
106,
.........
Surface Plot
-
61
Flux gt 5x106 ,
.
o.
-
59
106,
gt
Maglat gt 100 - Surface Plot
Anisotropy gt 1.5, Maglat gt 100.
Figure 31.
gt
.........
Anisotropy gt 1.5, Maglat gt 100° .......
Figure 30.
..
........
.
.
68
Figure
34.
Pitch
84/336,
Angle verses
Time
Eneray 150 eV ......
Spectrogram
-
Day
...............
..
71
..
72
Figure 35.
Electron Pitch Angle Distribution
.....
Figure 36.
Fluxes verses Time - Day 84/336,
Energy 150
eV ...................
Figure
37.
Anisotropies,
Temperatures
eV
.
.
........................
.
.
.
Temperature
verses Time -
Day 84/336,
Ratio
76
and
Energy
150
77
.........................
Figure 38. Average Anisotropy and Temperature Ratio verses
Equator Anisotropy - Day 84/336,
Figure 39.
Fluxes verses Time -
eV .................
Figure
40.
eV .................
Figure
42.
verses
eV .................
Figure 43.
Figure
.
44.
. .
.
. .
Figure 45.
Day 85/002,
Energy 150
85
Day 85/002,
. . .
. .
Ratio
and
Energy 150
86
Day 85/002,
. . .
Energy 340
. . . .
Temperature
verses Time -
eV .................
Energy 340
........................
Anisotropies,
Temperatures
and
82
Temperature
Fluxes verses Time . .
Ratio
........................
Time -
Day 85/002,
. .
Ratio
Energy
. .
88
and
340
........................
Fluxes verses Time - Day 84/336, Energy 150 eV
viii
79
Energy 340
........................
Anisotropies,
Temperatures
eV
Day 84/336,
Fluxes verses Time -
Figure 41.
.
81
Temperature
verses Time -
eV .................
Day 84/336,
.
........................
Anisotropies,
Temperatures
Energy 150 eV
89
(Entire Orbit) ...........
Figure
46.
..................
Anisotropies,
91
Temperature
Temperatures verses Time - Day 84/336,
(Entire Orbit) ...........
Ratio
and
Energy 150 eV
..................
92
Figure 47.
Flux verses Pitch Angle - Various Days
Figure 48.
Detailed Analysis Orbital Coverage
Figure 49.
Equatorially Trapped Electron Distributions
Energy 150 eV ............
.
94
.
......
98
...................
..
Figure 50.
Plasmapause Location ......
Figure 51.
Equatorially Trapped Electron Distributions
Energy 340 eV ............
Figure 52.
............
84/266,
Figure
54.
84/283,
Figure
55.
84/296,
Figure
56.
84/315,
Figure
57.
85/002,
Figure
58.
85/039,
-
..
103
Temperature Ratio verses Equator Anisotropy -
eV .................
53.
99
.. 101
...................
All 13 Detailed Analysis Case Study Days,
Figure
-
Pitch Angle
........................
verses Time
Energy 150 eV .......
Energy 150 eV ........
verses Time
Pitch Angle verses
Energy 150 eV ........
Pitch
Angle verses
Energy 150 eV .......
ix
-
Spectrogram
Spectrogram
Spectrogram
-
-
Spectrogram
Spectrogram
...............
114
Day
.. 115
-
...............
Time
113
Day
..
-
112
Day
..
...............
Time
Day
..
...............
verses Time
Energy 150 eV .......
Spectrogram
...............
Energy 150 eV .......
Pitch Angle
105
...............
Pitch Angle verses Time
Pitch Angle
Energy 150
Day
..
-
116
Day
..
117
Figure
59.
Pitch Angle verses
Time
Spectrogram
-
Day
118
851.27, Energy 150 eV ............................
60.
Pitch Angle verses
85/238,
Energy 150 eV ........
Fj cure
Figure
61.
85/264,
Figure
62.
85/301,
Figure
63.
85/320,
Figure
64.
85/337,
Figure
65.
84/266,
Figure
66.
84/283,
Pitch Angle verses
Energy 150 eV ........
Pitch Angle verses
Energy 150 eV ........
Pitch Angle
verses
Energy 150 eV ........
Pitch Angle
verses
Energy 150 eV ........
Pitch Angle verses
Energy 340 eV ........
Pitch Angle verses
Pitch Angle verses
84/296,
Energy 340 eV ........
Figure
68.
84/315,
Figure
69.
84/336,
Figure
70.
85/002,
Figure
71.
85/039,
Pitch Angle
verses
Energy 340 eV ........
Pitch Angle verses
Time
Spectrogram
Spectrogram
Time
Spectrogram
Time
Spectrogram
verses
Energy 340 eV ........
x
-
Spectrogram
-
Time
-
-
-
125
Spectrogram
-
Spectrogram
Spectrogram
Spectrogram
Spectrogram
...............
Day
.. 126
-
Day
.. 127
-
Day
.. 128
-
...............
Time
Day
...............
...............
Time
Day
.. 124
...............
Time
Day
.. 123
...............
Time
Day
.. 122
...............
Time Spectrogram
Day
.. 121
...............
Time
Day
.. 120
...............
Energy 340 eV ........
Pitch Angle
-
...............
Time
Day
.. 119
...............
Energy 340 eV ........
Pitch Angle verses
-
...............
Energy 340 eV ..............
67.
Figure
Time Spectrogram
Day
.. 129
-
Day
..
130
Figure
72.
85/227,
Figure
73.
85/238,
Figure
74.
85/264,
Figure
75.
85/301,
Figure
76.
85/320,
Figure
77.
85/337,
Pitch
Angle verses
Time
Energy 340 eV ........
Pitch
Angle verses
Angle verses
Time
Spectrogram
Time
Spectrogram
...............
Pitch
Spectrogram
Time
Energy 340 eV ..........
..............
Pitch
Spectrogram
Angle verses
Energy 340 eV ........
Pitch
Angle verses
Energy 340 eV ........
xi
Time
-
-
Spectrogram
...............
134
Day
..
-
?..
33
Day
..
-
132
Day
.
-
131
Day
..
...............
Time
Day
..
...............
Energy 340 eV ..........
Angle verses
-
...............
Energy 340 eV ........
Pitch
Spectrogram
135
Day
..
136
LIST OF TABLES
TABLE
I.
ION
AMPTE/CCE
TABLE
II.
ENERGY
CHANNELS
THE
HPCE
THE
ON
.................................
ELECTRON ENERGY
48
CHANNELS
AM4PTE/CCE ....................
Table III.
IN
IN THE
HPCE ON THE
DETAILED ANALYSIS DATA COLLECTION DAYS
xii
49
.....................
.
.
69
I.
Equatorially
INTRODUCTION
trapped
plasmas
are
ion
distributions trapped within a few degrees
magnetic
equator.
Equatorially
trapped
plasma
distributions were
electron
of the Earth's
plasmas
trapped
distribution
described by a bi-Maxwellian
and
defined
can
These
function.
by
the
be
initial
Ion and electron distributions
observations by Olsen (1981).
peaked at
with highly anisotropic pitch angle distributions,
90 degrees pitch angle, were observed at energies from a few
eV to hundreds of eV, near geosynchronous orbit. These trapped
distributions are of interest as indications of basic wave
particle
interactions,
and
as
an
process
intermediate
in
plasmasphere filling.
The
particle
energy
-
distribution
pitch
indicates
the
wave
interaction aspect of these plasma distributions.
They are indicative of perpendicular acceleration (Tp.rp > Tpar),
and quasi-linear diffusion
(flat diffusion at low energy).
Though
there
not
correspondence
yet
proven,
between
are
equatorially
indications
trapped
of
plasmas
a
and
Bernstein mode waves (equatorial noise) and electron cyclotron
harmonics (Gurnett,
The
1976 and Kurth et al.,
plasmasphere
filling
role
is
1979).
indicated
by
the
correspondence between the plasmapause region and the location
of equatorially trapped ion distributions
1
(Horwitz et al.,
1981).
The variations in pitch angle structure with latitude
also suggests the role (Olsen et al.,
1987).
There have been previous surveys of equatorially trapped
plasmas.
for 0 -
Olsen et al.,
100 eV.
(1987)
surveyed DE 1/RIMS
Sagawa et al.
(ion) data for 0 - 1 keY.
(1987)
(ion) data
surveyed the DE l/EICS
Both surveys of equatorially trapped
plasmas were limited in altitude by the DE 1 orbit, which had
apogee
at
L
=
4.7.
Both
of
these
surveys
also
lacked
complementary electron data.
Braccio (1991) surveyed AMPTE/CCE data for both ions (30 150 eV) and electrons (150 eV) out to 8.8 Earth radii.
The first
purpose of this thesis is to extend the survey done
by Braccio by conducting a statistical survey of the next two
higher energy channels for both the ions and electrons (i.e.
240
and 442
eV for the
ions and
340 and 770 eV
for the
electrons.) The survey will be used to extend the findings in
his paper and to attempt to answer questions he raised, such
as whether
decreased
the higher
probability
energy
from
ions
1200
to
inhabit
1400
the
local
region
time.
of
The
electron survey will ensure that the trapped distribution is
not being under-evaluated and that the location and shape of
the trapped distribution found by Braccio is
accurate.
The second purpose of this thesis is to conduct a detailed
analysis
of
13
individual
days
to
examine
the nature
of
equatorially trapped distributions. The trapped distributions
will be described as bi-Maxwellian distributions, in order to
2
quantify a trapped distribution. In addition, this thesis will
be used to better define the electron distributions,
location of the trapped electron distributions.
3
and the
II.
A.
BACKGROUND
THE PLAKBN&PHERE
A
magnetosphere
is
the
region
around
a
magnetized
planetary body in which that body's magnetic field plays the
dominant role in defining the behavior of charged particles.
It's
outer boundary, the magnetopause,
wind,
and
dominant.
the magnetic
field
in
the
occurs where the solar
solar
wind,
becomes
This boundary occurs on the sunward side of the
Earth at approximately 10 Earth radii (roughly 63,750 km).
location of this boundary is
The
determined by a balance between
the pressure exerted by the solar wind and the obstacle formed
by
the
Earth's
magnetic
field.
During
active
times,
the
magnetopause has been observed as close as 5 geocentric Earth
radii (R;).
The inner boundary of the magnetosphere occurs at
the top of the ionosphere.
This boundary can be taken as
occurring at an altitude of 1000 km or 1.16 RE.
(Parks, p.7)
As can be seen in Figure 1, the Earth's magnetosphere is
highly asymmetric.
While the sunward boundary is
approximately 10 Re,
the Earth's magnetic tail
located at
has been seen
to extend beyond 200 Re on the nightside. The length and shape
of the magnetic tail
again depends on the interaction between
the geomagnetic field and the solar wind.
4
(Parks, pp. 7-8)
I
ID
,.~~
'R2
ii!!
E.-p
V
"''c
E0c
co
Figure 1. The Earth's Magnetosphere.
5
our
For
the
purposes,
the plasmasheet,
magnetosphere are the plasmasphere,
plasmasphere
plasmapause.
The
magnetosphere
that is
the
above
is
the
region
closest to the Earth.
at
ionosphere,
of
components
major
to
low
It
the
and the
of
the
begins just
mid-latitudes.
The
plasmasphere extends in altitude to between 3 and 5 Rk in the
and between +-
equatorial plane,
above the
ionosphere.
600 magnetic latitude just
The plasmasphere
corotates with the
Earth and particles in this region are affected by the Earth's
corotational Electric field.
(Parks,
pp.
11 and 73)
This region contains plasma, ionized atoms and electrons,
cm- 3 .
ion
and
electron energies are on the order of 1 eV at 4.5 RE.
The
with
densities
density
of
of
the
102
-
10i
Characteristic
decreases
plasmasphere
with
altitude.
In
general, the density in this region experiences a gradual drop
proportional to the fourth power of the McIlwain L parameter
(a measure of altitude based on the magnetic field lines that
will be discussed later).
(Chappell et al.,
This is
illustrated
in
Figure 2.
1970)
At approximately 3 to 5 Earth radii,
again depending on
the magnetic activity history, the plasmapause is encountered.
This is
energies
a transition region for the plasma in
sharply
increase
(Parks,
pp.
231
which plasma
and
502)
and
densities drop, generally very sharply, that is used to define
the inner boundary of the plasmapause,
al.,
1970).
6
Figure 3. (Harris et
-.
-.----
2
3
.
.ZJ.:AUGUST 12,1968
~
OUTBOUND PASS
-
4
5
___
...
L
Figure 2. Plasma Density L Dependance
7
7....9
-
#n/2
0D3
JND
OUT
tN
•"*" .
•" 9 L s
z
,
:,"!
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4
Composite of the first four H" ion concentration profiles for the inbound and outýbound paue of OGO 5.
Figure 3.
Plasmapause Magnetic Activity Dependance
8
9
These
aspects
of
the
plasmasphere
can
be
further
illu-trated using (relatively) more modern data from ISEE 1
total electron density measurements obtained from observations
of plasma waves.
Figure 4a shows density versus
solid line at 100 x (L/4.5)" 4 superimposed.
at L = 4.8,
L,
with a
The plasmapause is
1700 local time. The plasma density outside the
plasmapause continues to drop as L 4 . This characteristic of
the plasma density profile can more easily be seen if the data
are normalized by V,
as in Figure 4b.
The plasmasphere
activity.
density is
A large magnetic
(Olsen,
dependent
1992)
on the magnetic
storm can effectively
plasmapause in to less than 3 R..
push the
Figure 3 shows the effects
of magnetic
activity
plasmapause.
Magnetic intensity increases from a low in
upper left
on the
density
and
location
of the
the
panel in the figure to a maximum in the lower right
hand panel.
(Harris et al.,
1970)
The storm-time electric field strips away the plasma at
higher
altitudes,
as
the
plasma
is
convected
to
the
magnetopause. This region is then refilled from the ionosphere
after the storm-time field relaxes. The process, termed polar
wind,
is
driven by ambipolar diffusion
after the electric
field relaxes back to a steady state value of approximately 1
mV/m. This diffusion process calls for electrons to leave the
upper ionosphere,
probably driven by photoemission,
along the geomagnetic
electric field,
field lines.
and move
The resulting ambipolar
caused by the displacement between the
9
22-dt4- 1967
SE.J252.OCEN
II
q4
2
STDT: 82 152
G12
Of 0~ 152
L
B52
a.
£SEE-I
316
100
.32
JUNE 1, 1982
0652-0853
10
3
I
I
2
3
5
4
6
L
b.
Figure 4. Plasma Density L Dependance
10
-Normalized
7
electrons and 0* in the upper atmosphere, causes lighter ions,
such as H÷ and He%, to be dragged up the field lines after the
results in a refilling rate of 1
electrons. This 'polar wind'
to 10 ions/cm3 per dal.
the
On
the
nightside
plasmasheet,
a
(Horwitz,
region
1983)
is
plasmasphere
of
low
hot
density,
by
bounded
plasma
the
(with
densities on the order of 1 cm-3 and characteristic energies
of 1-10 keV).
very
The corresponding plasmapause for this region is
distinct
the
and
from
transition
to
plasmapause
not the case
plasmasheet takes place rather rapidly. This is
for the region that extends from just before dawn until just
on the dayside.
after dusk local time,
(Parks,
pp.
231 and
502)
On the sunward side of the Earth,
region that can be as much as 1
RE
the plasmapause is
a
Additionally,
in width.
usually no sharp distinction corresponding to its
there
is
inner
and
outer boundaries
(Parks, p.231).
Therefore, it
during
this local
time period
is usually a matter of judgement
as to which region you are studying.
The
region
magnetopause is
between
also ill
plasmasheet
encircles
While there
is
the
dayside
defined.
It
plasmapause
and
the
is not clear whether the
the Earth and occupies this region.
no known reason why this should not be the
case, the plasma observed in this region does not display the
characteristics
of
that which
is
found
in
the
nightside
plasmasheet. This has led to questions concerning the plasma
11
filling mechanism for this region as well as to questions of
where the plasma in this region comes from.
In
the dusk region there is
an additional asymmetry as
seen in Figure 5. This dusk bulge is the result of interaction
between the corotational electric field of the plasmasphere
electric field induced by the solar wind.
and the cross tail
The corotational field is the result of the charged particles
rotating with the Earth while trapped in its
and is
tail
geomagnetic field
directed radially inward toward the Earth. The cross
electric field is induced by the solar wind's interaction
with the Earth's magnetic field. This cross tail
the
dawn-dusk
magnetotail.
a series
bulge,
B.
direction
the
equatorial
plane
of
in
the
The sum of these two electric fields results in
contours
of equipotential
Figure 6.
(Parks, pp.
which mirror the
dusk
231-236)
THEORY
1.
Plasma Definition
A plasma
neutral particles,
The
in
field is
physical
is
a collection
of discrete
ionized
and
which has overall electrical neutrality.
dimensions
of
the
plasma
must
be
large
in
comparison with a characteristic length ID called the Debye
12
Sun,
ttt.O
f
ft
@ oi
Vnov11
Obe4oton
Figur
5.
Te
DusuBulg
13
o
ht
She,
IN
COROTATr
ELECTRIC FIELD
UNIFORM COWVECTIOW
ELECTRIC FIELD
pt*
--
att
It
a I
NO
Vt?
141?
-
litv
siIls
TOTAL
ELECTRIC FIELD
utt!
"tt
Nqulpotential contours for the magnetosperc electric field In the
equatorial plane. Upper left: first-order approbimation for the convection electric
field E, as tiniform. The contours are spaced 3 kV apart for E,, = 2.5 x 10-'V
m-.
pper right: the corotallon electric field, contours spaced 3 kV apart. Lowetr
sum of convection and corotation electric fields. The heavy contour separates the
closed and open convection regions. (From Lyons and Williams, 1984)
Figure 6.
Magnetosphere's Electric and Magnetic Fields
14
length. The total number of charges in a sphere with a radius
I, must be much greater than 1.
2.
Deby. Shielding
The electrostatic potential of a point charge q in a
vacuum is given by:
= ----q-_Volts
(l)
where # is the electrostatic potential, t. is the permittivity
constant and r is the distance from the point charge (Halliday
and Resnick,
1988).
If
the charge is
immersed in a plasma,
a
positive charge will attract electrons while repelling ions,
and similarly, a negative charge will attract ions and repel
electrons. The potential then becomes:
q exp M
47ccor
(2)
where
k
is
the
Boltzman
D=()
ne
2
constant,
T,
is
the
electron
temperature, which is a measure of the average kinetic energy,
n is
the equilibrium density of the plasma,
and e
is
the
charge of the electrons. This has the effect of screening out
electric potentials in a plasma.
The electron temperature is
used in the definition of 'D because the electrons are more
mobile than the ions and do most of the shielding by creating
a surplus or deficit of negative charge.
15
(Parks,1991)
3.
Plasma Parameter
In
order for a collection of ionized particles to be
considered a collisionless plasma,
satisfied.
The
Debye
length
dimensions of the plasma.
three conditions must be
must
be
much
less
than
the
The number of particles in a Debye
sphere defined as:
ND-n
(3)
3
must be much greater than 1, that is,
enough
number
of
for
particles
there must be a large
Debye
shielding
to
be
statistically valid. Finally the frequency of collisions of
particles must be low. The plasma parameter g is
defined as:
1
1-
(4)
ND
and for a collisionless plasma g << 1.
(Parks, 1991 and Chen,
1983)
4.
Motion in
a Uniform Magnetic Field
A collisionless plasma will behave as a collection of
individual particles.
move in
The individual charged particles will
trajectories determined by the applied electric and
magnetic fields. For space applications the fields resulting
from the particle motion are often small and may be neglected.
This is particularly true for the magnetic field, less so for
the electric field.
The force acting on a charged particle
moving in a combined E and B field is given by the Lorentz equation:
16
(5s)
E=q (Zyq
where f is the Lorentz force, and v is the particle velocity.
and the magnetic field is
For the case where Z = 0,
a charged
uniform,
simple cyclotron
particle will execute
gyration with a frequency:
md=
(6)
and radius:
Lap--
(7)
mina
Wc
where
m and v are the mass
the pitch
particle and
velocity vector of the
,q!B
IqIB
and velocity
angle a
is
charged
of the
the angle between
charged particle
the
and the magnetic
field. The velocity parallel to the magnetic field line, v,.
= vcos-, is
not affected by the magnetic field. This motion
describes a circular orbit about a guiding center which is
travelling along the magnetic field line with velocity vp..
The trajectory
of this particle is
parallel to the field line.
S.
(Chen,
a helix with it's
axis
1983)
Magnetic Mirror
The Earth's magnetic field lines converge at both the
north
and
increases
additional
south
with
magnetic
altitude.
poles,
and
Because
of
the
this,
field
strength
there
force that acts upon the charged particle.
force can be expressed as:
17
is
an
This
Because the gradient in the
the magnetic moment.
where A is
vý
qE
P
E=-pVB
(8)
magnetic field is parallel to the direction of the field line
directed along the field
can be seen that this force is
it
line.
Since the force is
parallel velocity
directed parallel to the particles
it
component,
will
obviously
particle's velocity. From Lentz's law, it
is
invariant.
(Parks, pp.
Since A is
2
-
V2 par
can be shown that A
89-90)
invariant,
must
Vpep
increase
as
B is
For this to happen vpar must decrease since v 2 perp
increased.
v
affect the
Therefore,
(from conservation of energy).
=
given a
large enough B, there will come a point where vpar = 0. At this
point Vperp will equal v,
Figure 7.
along the field line,
that
the
gyroradius
approaches
the
and the particle will mirror back
also
mirror
(Gladstone,
smaller
gets
point
as
a
as
result
1967).
(Notice
the
particle
of
its
vp.rp
dependence.)
For a particle that mirrors, equation 8 then leads to:
(9)
2
2
Jýrp 0=- *%erpm
qBo
qBm
where subscript o refers to values at the equator and m to
18
MIRLOR
POINT
FIELD
EARTrH/
MIRR•OR
POINT..
Figure 7.
Path of Mirroring Particle
19
those at the mirror point. Rearranging equation 9 gives:
2
vjo_
BO-
(10)
EmV
y
0
2
2
,0
2
Vj~rpz
V0
defining the pitch angle of a particle,
a,
to be the angle
between velocity vector of the particl e and the magnetic field
line gives
vp.,p = v
sin a.
Plugging
this
into equation
10
gives:
(11)
BO_
a2sin
ms
which states that all
particles with a pitch angle so will
mirror at the location defined by B = B,.
so will mirror at lower altitudes.
Particles with a >
(Parks, pp.
111-112)
The magnitude of the Earth's magnetic field is
given
according to:
2
4 -3 cos)L
B=BoE
0
L 3 cos6A
(12)
where Bo, is the magnitude of the Earth's magnetic field on the
Earth's surface at the magnetic equator,
latitude,
A is
and L.is the McIlwain L parameter
the magnetic
(Parks, p.
54).
The McIlwain L parameter is variable, given in units of Earth
radii,
used to label magnetic field lines with relation to
where they cross the plane of the magnetic equator. Its value
is given by:
20
L=--
(13)
cos2A
where r is
the distance from the Earth center,
field line at the magnetic equator.
in k,
to the
(Parks, p. 115)
Substituting equation 12 into equation 11 gives:
sin2 a,=
(14)
COS) M
V4 -3cosz)lm
Therefore,
by
defining
an
equatorially
trapped
plasma
to
mirror at a magnetic latitude of ± 100 or less, this requires
that a charged particle have a pitch angle greater than 690,
at the equator, in order to be equatorially trapped, Figure 8.
It
is
these trapped particles that will be investigated in
this paper.
6.
Statistical Distribution
When dealing with a system which is composed of a very
large number of individual particles it
becomes impractical to
solve the equations of motion for the system.
Instead the
particles may be treated statistically through the use of the
distribution function. Classically the distribution function
gives
the
probability
coordinates
particles in
and momenta
distribution
of
the
of the particles.
coordinate space is
values
of
the
The density of
obtained by integrating the
distribution function over the momentum or velocity space.
21
Pitch Angle vs Magnetic Latitude
"90.000
70.750
67300
A 56.250
45.000
33.750
22500
0.0001
223500
45.000
6700
M~agntic Latitude
Figure 8. Pitch Angle verses Mirror Latitude
22
90.000
That is:
n=ff(x,
) d 3v
1
(15)
where n is
function
the density,
of
position
and f(1,M)
and
is the distribution as a
velocity
integrated
over
three
dimensional velocity space.
The two distribution
thesis are the bi-Maxwellian,
functions of interest in
this
and the Maxwellian or isotropic
distribution function, given by:
(16)
IM
M
f
fbi=
]112 _.E, V12
2=kTp;rjJ 2ckTpaje
13/2
SM
- 2--
2%]F3 / 2e -2
(17)
where T P,-P and Tpar are the characteristic temperatures in the
perpendicular
and parallel
directions
with respect
to the
magnetic field line.
C.
PREVIOUS OBSERVATIONS
Thermal plasma pitch angle distributions seem to have been
first
studied by Horwitz and Chappell (1979)
Horwitz (1980).
to
study
ion
and Comfort and
These authors used electrostatic analyzer data
pitch
angle
distributions
orbit, using ATS 6 data taken in 1974.
at geosynchronous
The surveys dealt with
data taken at 10.50 off the magnetic equator.
23
Comfort and Horwitz (1980)
observed two important aspects
of ion pancake distributions (peak flux near 900 pitch angle) .
The
first
was
the
occurrence
probability
for
the
pancake
component of the ion distribution was local time and energy
dependent. The highest probability of occurrence occurred in
the lowest energy channel (20 - 40 eV) studied and for local
times between 1400 and 1800. Pancake distributions wex,ý seen
42% of the time in this sector for ions of that energy.
The
second
was
that Comfort
and Horwitz
observed
that
field aligned ions and ions with 900 pitch angle seem to be
anti-correlated
at
1700.
Figure
9
shows
that
there
a
is
decrease in the occurrence probability of field aligned ions
when there is a peak in the pancake occurrence probability.
Horwitz et al.
energy
(_-ý 100
eV)
studied pancake distributions in
ion data
obtained
The H"' distributions
spectrometer.
vicinity
(1981)
f rom the
were often
ISEE
low
1 mass
in
found
the
inside
of the plasmapause, Figure 10, and usually just
the plasmapause. Horwitz et al. also observed that the pancake
distribution
was
often
seen
in
the
presence
of
colder,
isotropic plasma.
Olsen (1981) observed a thermal plasma population, trapped
within
electrostatic
a
few
degrees
of
the
magnetic
equator,
analyzer data from the SCATHA satellite.
using
Figure
11 shows the ion count rate, for various ion energies, as a
function of pitch angle. The data for this plot was taken at
the equator at approximately 1000 local time and 5.5 RE.
24
This
FEMWIISCPWUIS
311M
urIn
Total percent occurrence feunIes
for ion pitch angle distributions having
designated components, an functions of local
time.'
Figure 9. Field Aligned and Pancake Trapped Ion Distributions
25
I
I!ii
Figure
10.
Trapped
Ion
Distribution
Plasmapause
26
With
Relation
to
the
EQUATORIAL ION PITCH ANGLE DISTRIBUTIONJ
DAY 179 OF 1979
21:37 TO 21:41 UT
lot
523 eV. CR X f04
TTIME
0
US•
101:
TIME
0
45
10
13Z
130
-
225
270
315
360
PITCH A OLE (oJ
Data are
Ion pitch angle distributions at the equator for day 179 of 1979.
plotted frr the FIX ahd N! detectors at 11, 4?, 193, 523. and 900 eV., Fituges are
Maximum values, '4~th
saeled by increasing facltors to keep them from overlapping.
increasing energ~y are 1150 c/s, 7300 c/s, 4200 c/s, 550 c/s, end 5110 c/S. The 0 -180
0e corresponding[ to loolking south.
rangse corresponds to looking| sunvard, vthlii
Figure li.
Ion Pitch Angle Distribution
27
figure clearly shows a trapped distribution,
and 2700 pitch angle,
to a lesser extent,
centered at 900
for ions of energies 11 to 103 eV and,
for those at 523 eV.
The 900 eV ions do
not show evidence of a trapped distribution. This figure also
shows a well defined loss cone for the three highest energies.
Olsen observed a like distribution in the electron data,
Figure
12.
A source
cone,
centered
at
00
and
1800
pitch
angles, was seen in the 41 eV electron flux concurrent with
the trapped
distribution
speculation
that
(ionospheric)
the
plasma
at higher energies.
field
aligned
source,
and
This
particles
these
led to
were
particles
the
were
subsequently heated in the traverse direction. Note that the
count rates in the last two figures are scaled differently for
different energy levels in order to facilitate presentation of
the data.
Figure 13,
from Scott (1991),
rate versus energy (in
is
eV).
shows a plot of count
The trapped electron distribution
seen to exist in the 50 to 1000 eV range, corresponding to
temperatures of 100 - 200 eV and densities of 1 - 10 cm-3.
trapped
ions show a peak in
the 20 to 200 eV range.
The
This
corresponds to temperatures of 20 to 50 eV and densities of 1
-
10 cm- 3 .
Sagawa
dependence in
the
Dynamics
et
al.
(1987)
observed
a
local
the location of the trapped ions in
Explorer
(DE)
1
satellite.
time
data from
Sagawa
et
al.
additionally saw that the trapped ions were composed primarily
of H÷ ions and that these were in the lowest energy bin (0.01
- 1 keV) of the DE l/EICS summary plots. They reported that
28
EQUATORIAL ELECTRON PITCH ANGLE DI STR IBUITION
DAY 179 OF 1979
HI DETECTOR
II
21:36:20 TO 21:27:35
U
1C1
10•f
'
l
41,ev
Iz.
104
i0m
e
I1
7
i
•
,s
g
10TCH ANGLx
Electron pitch angle distributions
at
the equator for day 179 of 1979.
Data are plotted frown the HI detector at iti, 523, and 11730 eV.
Pitch angle conventions are as in Figure 7.
Figure 12.
Electron Pitch Angle Distribution
29
EQUATORIAL FLUXES
DAY 179 OF 1979
21:37 TO 21:41 UT
too.ooo
LO DETECTOR ELECTRONS
a-9VTO
CR X 2
l o
~•
t,,:.l
io.mo
:.
U
m,|LO
DETECTOR IONS
•
z-"
o
.:.1:1
.---.
I-0MTOOSO
*FIX DETECTOR IONS
//
.•
o
"
* 1
I
ll
II\
,
'I,
/I
10
'
20
650
I0200
(00
I-.."
1.000 2.000
ENERGY ISV)
Ion and electron count rates as a function of energy from the LO detector near 900
pitch angle for day 179 of 1979.
The electron
count rate has been scaled by a factor of 2. The
count rates from the FIX detector dwells were selected at their maxima (900 pitch angle).
The
difference between the LO and FIX ion data reflects degradation of the spiraltrons for the LO
ion detector.
The LO count rate curve has been
traced and moved up to overlap the FIX detector
data (about a factor of 2).
The peak in ion
count rate at 700 eV is a local maximum in the
distribution function as well (see Figure 10).
Figure 13.
Energy Relations of Trapped Plasmas
30
the McIlwain L value was higher,
probability,
for the peak ion occurrence
in the local noon and dusk sectors than it
near local midnight, Figure 14.
Olsen et al.
(1987)
was
also saw
this in their statistical survey. Olsen et al. noted that the
latitudinal extent of the high probability region is
time dependant,
ranging from ± 300
in
local
the early afternoon
region to ± 100 in the early dawn region.
Olsen et al.
(1987) observed, from data collected by DE 1,
that the trapped ion distribution was composed primarily of
H%, but that He+ was seen to have a trapped component,
having
10% the density of the trapped H%, approximately 40% of the
time. In one case, trapped 0 was seen with a relative density
of 0.1% that of H%. Additionally, the trapped distribution was
observed to be very localized about the equator. This is seen
in
the
fact
that
the
ions
change
from
distribution to a trapped distribution
quickly
as the satellite traverses
a
field
aligned
and then back very
the equatorial
Figure 15 illustrates this aspect of the evolution
region.
in
the
pitch angle distributions.
Figures 15a, 15b, and 15c show plots of flux verses pitch
angle
for
the
(approximately),
magnetic
and 3.60 respectively.
ions mirror the H÷ ions,
Figures 15d,
H+ in
latitudes
of
-7.90,
-1.90
In this case, the He+
although at about 3.5% of its
flux.
15e, and 15f show the distribution functions for
these time periods.
Notice the drop in density and the
increase in temperature as the satellite enters the equatorial
31
Occurrence probability of low-energy (0.01-1 keV) H 4
pancake distribution with peak ion flux above 10 5 (cm 2 s sr)-1,
within 5c' of the magnetic equator for active times (Kp2 3-) as a
function of MLT and L shell. L shell bin size AL=0.5.
Figure 14.
Trapped Ion L verses Local Time Dependence
32
DE-I RIMS
FEBRUARY 21. 1982
PITCH4 ANGLE
1900
:n
8c H+ -
T
0.7
na712
eVT
0.7
0n
H
4
BE
H
m3 T - OASeV
-- 16 T2.Ov
10
:~m
100 c
He
4410
2
1900. 190? U T
H
a90
*
4
0
2T
8
He'
191
1
1917 UT
10c0
-90~~f
903 17km/
3o
50
900
90
1
I
L
H+: He+:n
- 7cm-3
219305T - .6 0. 0.7oV
0
I
106
SPNPAS
I*b
*
103
00
xEN+RGYT(eV)
15.
LII
1932 UT
u'90
11H
4
Figur
-
6
10
E~
107
4
Flu
Ft 50
ScnPas/esiy
3305T
OS
6
r
,
region.
(Olsen et al.,
Klumpar
et
al.
trapped plasma in
trapped
ion
interface.
1987)
(1987)
found examples
of
equatorially
the data from the AMPTE/CCE satellite. The
distribution
was
found
near
the
plasmapause
The temperature of these ions were found to be on
the order of 30 - 50 eV. Like Olsen (1981),
they also observed
that the angular distributions of the trapped ion distribution
became narrower for increasing ion energies.
Braccio (1991)
extended the survey of the AMPTE/CCE data
by surveying ions
in
the
30
-
150 eV energy
channel
and
electrons in the 150 eV energy channel out to 8.8 Earth radii.
In
this
survey
Braccio
concluded
equatorially trapped plasmas is
that
the
location
species dependant.
of
The ions
and electrons show a different local time dependance in the
location of their occurrence probability peak. The following
summarizes his conclusions:
Electrons
- display a uniform high probability distribution centered
at 0900 local time and a L value of 6
-display a weak,
if
any,
L dependence on local time
s trapped electrons begin to be seen at dawn leading to
speculation
that
their existence
is
dependent
on
photoelectron emission from the Earth's ionosphere
* the shape of the distribution is basically conical,
however, it drops off more rapidly than it decreases, with
respect to local time
34
Ions
-distribution
shows a strong L dependence on local time
* high trapped ion probability region begins at local dawn,
for L approximately 4, and rises to a maximum at between
1400 and 1500 local time with an L value of 8
*the distribution drops off quickly in altitude after
peaking as local time increases there is a region of
decreased probability in the afternoon sector for his data
that he suggested may be inhabited by higher energy ions.
Part of this thesis will investigate this.
• the overall shape of the high trapped ion probability
region mirrors that of the location of the plasmapause
trapped electrons seem to be excluded from regions of high
trapped ion probabilities and vice versa.
This thesis will further extend the look at the AMPTE data
survey of ions in the 240 eV and
by conducting a statistical
442 eV energy channels and electrons in the 340 eV and 770 eV
energy channels.
There is
not always a clear criteria used to define an
equatorially trapped plasma. Intuitively, the definition seems
to be that the bulk of the plasma
within)
100
of
the
development which
equator.
magnetic
follows
is
confined to
One
an attempt
is
aspect
(mirror
of
to quantify
the
this
concept, and relate the various definitions, tests, and survey
techniques.
study,
Braccio
(1991)
an equatorially
defined,
for the purpose of his
trapped plasma
as having a minimum
(threshold) flux in the 800 to 900 pitch angle bin of 106 (cm2
s sr)-1 for ions and 5 x
106
(CM2
s sr)"1 for electrons with an
anisotropy greater than 1.5 (The anisotropy is defined as the
35
ratio of the fluxes in the 800 to 900 pitch angle bin to those
in
the 600 to 700 pitch angle bin.)
in
the same period.
His
survey generally was restricted to data taken within 100 of
the magnetic equator.
For the
purpose
of
the
statistical
survey in this paper, the anisotropy criterion of 1.5 remains
the same for both ions and electrons and the minimum flux
criterion
for
a
equatorially
trapped
plasma
will
be
as
follows:
Ions
* 240 eV: 105 (cm2 s sr)-1
- 442 eV: i03
(cml s sr)-1
Electrons
o 340 eV and 770: 5x10' (cm2 s sr)-1
The lower flux values for the ions partly accounts for the
lower flux of ions at the higher energy channels.
Another criterion which could be used to characterize a
trapped
distribution
is
the
ratio
of
the
plasma's
characteristic temperatures in the perpendicular and parallel
directions with respect to the magnetic field line; Trp and
Tparl* An equatorially trapped distribution may be described by
a
bi-Maxwellian
distribution
characteristic temperatures
the case studies of this
function
(Scott 1991).
thesis a ratio
with
these
For the purpose of
of Tperp to Tpa r
equal
to three will be used as a lower threshold required for an
36
equatorially trapped distribution to occur.
The relationship
between the above two definitions; flux ratios and temperature
ratios, is
considered next.
Applying the threshold of a temperature
determines the anisotropy
in
ratio of three
flux that must be met for an
electron distribution to be considered
trapped.
Figure
16
shows plots of the log of the flux versus pitch angle for 150
eV and 340 eV.
In each the perpendicular temperature was set
to 75 eV and the parallel to 25 eV; a temperature ratio of
three. These temperatures were selected as representative of
values seen in
the data analyzed.
Scott (1991)
got slightly
larger ratios. The density was set arbitrarily to 1.2 cm-3 as
a
reasonable
value.
The
density
does
not
affect
the
illustration.
In both Figure 16a and 16b there are shown two curves. The
uppermost
is
the
plot
of
the
bi-Maxwellian
distribution
function with the above Tperp and Tpari values at the magnetic
equator.
The lower of the two curves is
a plot of the same
function with the same temperatures, but mapped to a magnetic
latitude of 100.
The peak flux of this curve is
equal to the
magnitude of the flux at the magnetic equator at a pitch angle
of 690.
This is
because a pitch angle of 690 at
maps to a pitch angle of 900 at a magnetic
latitude
the equator
of 100.
With our previous criterion for a trapped distribution being
one that is
limited to within 100 of the magnetic equator this
establishes a lower limit on the pitch angles analyzed at the
37
equator at
690 and a
relevant pitch angle range of 690 to 900
for the analysis of a bi-Maxwellian distribution.
Taking the ratio of the top curve to the bottom curve in
Figures 16a and 16b a differential anisotropy was derived. The
results of this calculation was 1.67 for 150 eV and 3.2 for
340 eV. The survey work done here, and those by Braccio (1991)
use an integral anisotropy calculated by taking the ratios of
the flux in the 800 to 900 pitch angle bin to the flux in the
600 to 700 pitch angle bin.
divided
into pitch
definition
for
Note that the survey files were
angle bins of 100
the
anisotropy
we
in
size.
take
the
Using this
ratio
of
the
integral of the distribution function over pitch angles 800 to
900 to the integral of the distribution function over pitch
angles 600 to 700.
The results
of this
is
an anisotropy of
1.953 for 150 eV and 4.421 for 340 eV. For the purposes of the
detailed analysis
case studies
in
this
thesis the rounded
values of 2.0 and 4.4 will be used for 150 e"I and 340 eV ,
respectively,
Maxwellian
as
and
applied
hence
an
to
a
definition
equatorially
of
being
trapped
bi-
electron
distribution. This will allow for comparison between this work
and previous survey techniques.
calculated
here
is
higher
Note that the integral ratio
than that used
survey.
38
in
the
initial
7.71
'Ratio
7.36
of Peak@ - 1.67
Energy - 150.00 eV
Tperp , 75.00 4V
Tparl 1 25.00 eV
7.02
Density
*,
-
1.20 cm'
6.67
6.32
5.97
0
45
go
pitch angle (dogs)
134
179
a)
7.3
'Ratio
of Peaks - 3.20
Energy - 340.00 eV
Tperp = 75.00 eV
Tporl - 25.00 eV
Density - 1.20 cm'
E 6.55.7
,5.0
c4.2
3.4
0
Figure 16.
45.
90
pitch angle (degs)
b)
134
Log of Flux verses Pitch Angle
Electrons
39
179
-
150 eV and 340 eV
D.
THE AMPTh/CCE SATELLITE
The
(AMPTE)
Active
mission
launched
Magnetospheric
consists
on August
16,
of
1984.
Particle
three
The
Tracer
satellites
Explorers
that
were
purpose of this mission
(Acuba et al., 1985) was to:
1.
investigate the transfer of mass and energy from the
solar wind to the magnetosphere and to study its further
transport and energization within the magnetosphere.
2.
to study the interaction between artificially injected
and natural space plasma.
3.
to establish the elemental and charge composition and
dynamics of the charged population in the magnetosphere
over a broad energy range.
Two of the satellites, the Ion Release Module (IRM)
the
United
Kingdom
Sub-satellite
(UKS),
were
and
concerned
primarily with the introduction of artificially injected ions
into the magnetosphere and will not be discussed further. The
third satellite was the Charged Composition Explorer
Figure 17.
(CCE),
The purpose of this satellite was to measure the
particle distribution of the naturally occurring plasma, with
respect to species,
energy,
and pitch angle,
measure the artificially released ions from IRM.
al., 1985)
The CCE was placed in
as well as to
(Dassoulas et
an elliptical orbit around
the Earth with a period of 15.66 hours and an inclination to
the Earth's equatorial plane of 4.80.
It
had an altitude at
perigee of 1108 km and at apogee of 49,684 km (roughly 1.2 and
8.8 RE respectively).
It
was spin stabilized with a spin rate
40
Figure 17.
The AMPTE/CCE Satellite
41
of 10.25 rev/min (Dassoulas et al.,
collected by this satellite on August 26,
The payload
experiments; 1)
2)
of the CCE,
Figure
Data began to be
1985).
18,
1984.
consisted
Particle Analyzer,
Plasma Wave Experiment
4)
3)
the Magnetometer,
(Dassoulas et al.,
the Medium
and 5)
1985).
the
This paper
indirectly, the
with data from the HPCE (and,
concerns itself
five
the Hot Plasma Composition Experiment (HPCE),
the Charge Energy Mass Spectrometer (CHEM),
Energy
of
Magnetometer).
E.
THE HOT PLASMA COMPOSITION EXPERIMENT (HPCE)
The HPCE consists of the Ion-Mass Spectrometer and the
Electron Background Environment Monitor (EBEM).
The ion-mass
spectrometer,
charge
Figure
19,
provides
mass
per
ion-
composition measurements from very low energies (corresponding
to the spacecraft potential) to approximately 17 keV. The ions
enter the detector through a collimator which
azimuthal and elevation angles of acceptance.
are
ranges
from approximately ±250 for ions at the spacecraft
through
±5.50
to ±7.50
a
accelerated
while
the
elevation
The azimuthal
limits
potential
at
limits both
for those at 17
retarding
potential
through a -2960
keY.
analyzer
V potential.
1985)
42
acceptance
The
ions are
(RPA)
(Shelley
and
et
angle
sent
then
al.,
ILI
I
O£
Figure 18. The AM4PTE/CCE Payload
43
(COA
C
RETA0I1N6 POTNTIAL AIALYZE
-EERY
ON
SLIT 2
(WA)
(EA) IS
ANA IYZER
mL~c!!,,Jm SIT? 5?)
Co
.. ý_lvDTETR(2
,
02)7
ENE06Y DETECTOR (at)
EA IP
s
EA
TOP VIEW
Figure 19.
The HPCE Ion-Mass Spectrometer
44
1
The ions then pass through the object slit
and into the
cylindrical electrostatic energy analyzer. The electrostatic
energy analyzer is programmable in 32 energy per charge steps
from 3 to 20 keV/e. The central portion of the ion flux then
enters the mass analyzer through a second slit,
with a portion
of the spectrum measured by "energy detectors" (ED1 and ED2).
The
mass
analyzer
consists
of
a
second
cylindrical
electrostatic deflection system suspended in a 978 G magnetic
field. The ions that exit this region, through the image slit,
are detected by a high-current electron multiplier (Shelley et
al.,
1985).
until it
This instrument was active from August 26,
failed on April 4,
1985.
The EBEM consisted of eight independenmagnet electron
1984
spectrometers.
Electrons
1800 permanent
entered
the EBEM
through a 50 full angle collimator and were then deflected
through 1800 by a permanent magnet,
focused
onto
an
momentum range,
multiplier.
exit
aperture,
Figure 20. They were then
that
defined
the
allowed
and were then detected by a channel electron
(Shelley et al.,
1985)
Both the ion and electron data for the AMPTE/CCE HPCE were
processed into pool files. These were the data files used for
survey.
These pool
minute bins
files consist
from 0000
of data
to 2400 universal
arranged
time.
in
There
6.5
is
a
separate data file for each day's data and each file contains
both electron and ion data for that day.
1985)
45
(Shelley et al.,
'5.1
RMMATUV
TAIKUL
LINIT
WV
IM6NTIC ELECTRO SFECIWEIfE
Figure 20. The HPCE Electron Background Environment Monitor
46
For this work,
detectors
(ED)
the ion flux measurements from the energy
are used,
since we were
not
interested
differentiating between H÷ and He* for this survey.
data
are
sorted,
by time,
into
18
in
The pool
logarithmically
spaced
energy bins. The lowest four channels use the "RPA" mode data.
The bulk of the data which are available in the pool file have
only
the
fourth
RPA channel,
which
provides
measurement from approximately 30 to 150 eV,
center at 50 to 65 eV.
17keV/e.
an
integral
with a weighted
The remaining channels extend up to
The ion flux is
also sorted by time verses
pitch
angle, with pitch angle bins from 00 to 900 in increments of
100.
(Shelley et al.,
1985)
The electron data is
likewise sorted into 8 energy bins
from 50 eV to 25 keV and by pitch angle from 00 to 900 in
100
increments, each also verses time. The energy channels for the
ion electrostatic energy analyzer and for the EBEM are given
in
TABLE I and II.
Data was also collected for ions species
verses time verses energy and for ion species verses time
verses pitch angle (Shelley et al.,
data was not used in this paper.
47
1985).
This aspect of the
TABLE I.
ION ENERGY CHANNELS IN THE HPCE ON THE AMPTE/CCE
Energy Channel
Energy of Zhannel
Full Energy Width
Center (keV/e)
(keV/e)
1
0.0014
0.0028
2
0.0067
0.0076
3
0.020
0.020
4
0.050
0.125 RPAl
0.052
0.122 RPA2
0.055
0.115 RPA3
0.065
0.095 RPA4
5
0.240
0.216
6
0.442
0.209
7
0.657
0.222
8
0.885
0.235
9
1.127
0.338
10
1.660
0.567
Ii
2.261
0.641
12
2.941
0.724
13
3.709
1.056
14
5.058
1.480
15
6.668
2.143
16
9.339
3.041
17
12.75
3.884
18
17.11
2.600
48
TABLE II.
ELECTRON ENERGY CHANNELS IN THE HPCE ON THE
AMPTE/CCE
Electron Detector
Energy
Center Channel
(keV/e)
Full Energy
(keV/e) Width
CMEA
0.067
0.051
CMEB
0.150
0.126
CMEC
0.340
0.284
CMED
0.770
0.643
CMEE
1.74
1.45
CMEF
3.94
3.28
CMEG
8.89
7.41
CMEH
20.1
11.7
49
50
Ill. OBSERVATIONS
A.
STATISTICAL SURVEY
1.
Data Analysis
Data collected from August 26, 1984 until December 6,
1985 were processed and analyzed. However,
available through April 4,
ion data were only
1985. This was due to the failure
of the ion-mass spectrometer on that day.
The stop date for
the analysis was chosen because the satellite completed one
1984 and
precession around the Earth, starting from August 26,
ending on December 6,
For
spectrograms
data. The first
each
day
1985.
of
were produced
data,
two
different
for both the
types
of
ions and electron
type was an energy channel-time spectrogram,
for pitch angles in the 80-90 degree range.
pitch angle-time spectrogram.
The second was a
The energy channels used were
the ion fifth and sixth channels
(240
and 442 eV)
and the
electron third and fourth channels (340 and 770 eV).
These spectrograms were examined for periods when the
satellite encountered the magnetopause. The spectrograms were
also
inspected to find periods
of very "choppy"
data
and
periods when the instrument was undergoing diagnostic testing.
Data in these periods were then removed from the data fi•
to
ensure that the analysis would not be contaminated by such
artifacts.
51
These edited data files were then surveyed to produce
local time vs McIlwain L probability distribution plots. The
results for ions and electrons were plotted separately then
compared.
2.
Local Time a.
McIlwain L Surveys
ION SURVEY
Figure
21
shows
a
plot
of
the
probability
distribution for equatorially trapped ions using the lowest
criteria from the previous chapter, namely the ion flux in the
800-900
pitch
than
105
ions/(cme s sr),
that the anisotropy be greater than 1.5,
and
that
be
the
the
ions
angle
bin,
at
observed
240
eV,
within
be
100
greater
latitude
from
magnetic equator.
The grey scale for the results runs from 0% to 60%
with zero being white and 60% being black. The coverage plot's
grey scale ranges from 0 to 200 counts and from white to black
respectively.
The
scales
are
allowed
to
saturate
coverage was approximately 600 samples at apogee).
the
1800
to
probability is
2400
local
time
sector's
zero
(peak
Note that
occurrence
due to lack of coverage.
The contents of Figure 21 are alternately presented
as a surface plot in Figure 22.
This plot has x and y axes of
local time and L. The z axis is probability of occurrence,from
0 to 100%.
A contour plot is
also displayed as part of this
figure to facilitate the reading of the surface plot. Again,
the 1800 to 2400 local time sector was not sampled.
52
AMPTE SURVEY
IONS FROM ESA 240 EV
gt
Anisotropy gt 1.5 Flux
1.OOE+05 MagLat It
10.0
PROBABILITY DISTRIBUTION
70
8
-
v.60
:50
40
6
230
20
10
o
4
2~01
0 2 4 6 8 10 1214 1618 2022 24
COVERAGE
10-
200
175
150
8-j
00
075
50
4
25
'~~'
2
~
0 2 4 6 8 10 1214 16 182022 24
Local time
'01
Figure 21. Trapped Ions (240 eV)
1.5, Maglat gt, 100
53
-
Flux gt 105, Anisotropy gt,
o
t
Sb.J
0
(
o
C,-,
C
o
1
...
0.
m
".
..
--- -7
V......
C..
AA
Figure 22. Trapped Ions (240 eV) -Flux
1. 5, Maglat gt 100 - Surface Plot
54
gt 10-1,
I-
Anisotropy 9
The
high probability
(greater than 30%)
region
these ions starts at 0500 local time at an L of 3.5. As local
time increases so does the L value of the peak probability. At
1400 local time the maximum L value,
point the probability
local
time moves
8,
is
reached. At this
appears to drop off sharply in
toward
dusk.
This,
however,
may
L as
be
an
artifact brought about by the low coverage after 1800 local
time.
In
Figures 23 and 24 the results of raising the
selection criteria for a trapped ion distribution are shown.
In Figure 23 the selection criteria are flux greater than 105,
anisotropy greater than 1.5, and measurements within 50 of the
magnetic equator. In Figure 24 the selection criteria are flux
greater
than
5
x
105,
anisotropy
greater
than
2.0,
and
measurements within 50 of the magnetic eemiator. The local time
dependence is
similar in these three figures.
Figure
distribution
for
energy channel
25
shows
a
equatorially
(i.e. 442 eV).
plot
trapped
magnetic
the
ions
for
probability
the
sixth
Here the selection criteria is
2 s sr),
a flux greater than 10' ions/(cm
than 1.5,
of
an anisotropy greater
and a magnetic latitude between within 50 of the
equator.
The grey scales are the same as in
the
previous two figures. Figure 26 is a surface plot of the same
data.
The high probability (greater than 30%)
region for
these ions starts at 0500 local time at an L of 3.5. Again, as
55
AMPTE SURVEY
IONS FROM ESA 240 EV
gt
Anisotropy gt 1.5 Flux
1.OOE+05 Mog Lot It
5.0
PROBABILITY DISTRIBUTION
50
70
60
~50
040
-30
1086 N
101
20
0 2 4 6 8 10 12 14161520 22 24
COVERAGE
10-
200
175
8-
150
~,125
6
~*..C
-.
100
50
4-
24
....
I.
0 2 4 6 8 1012141618202224
Local time
Figure 23.
Trapped Ions (240 eVT)
1.5, Maglat gt
50
56
-Flux
25
0
gt 10', Anisotropy gt
AMPTE SURVEY
IONS FROM ESA 240 EV
Anisotropy 9t 2.0 Flux
gt 5.OOE+05 MagLot It
5.0
PROBABILITY DISTRIBUTION
108- v
80
70
60
6o
40
..
........
0-
4
a.
-20
30
10
2
v
ý . -01I
0 2 4 6 8 10 12 14 16182022 24
COVERAGE
10-
200
175
150
8-
S125
100
6~
075
4250
20
0 2 4 6 8 1012141618202224
Local time
Figure 24. Trapped Ions (240 eV)
gt 2.0, Maglat gt
50
57
-
Flux gt 5x10 5, Anisotropy
AMPTE SURVEY
IONS FROM ESA 442 EV
Anisotropy gt
1 .5 Flux
gt
1 .OOE+O3 MagLat It
5.0
PROBABILITY DISTRIBUTION
10"
80
70
60
8-
~50
40
6c
()30
S0.
20
10 o
4
20
0 2 4 6 8 10 1214 1618 2022 24
COVERAGE
10-
0
8-
175
150
m125
6~
o
0
0
.'~....
4
..
2
100
75
50
25
01
0 2 4 6 8 10 1214 1618 20 2224
Local time
Figure 25. Trapped Ions (442 eV)
1.5, Maglat gt
50
58
-
Flux gt
103
, Anisotropy gt
N
L
CC
Figur) 26
Trpe
Ion
(44
0,Aiorp
eV-lxg
59
as
local time
increases
so does the L value
of the peak
At 1400 local time the maximum L value,
probability.
8,
is
reached and then the probability drops off sharply, probably
due to the lack of data after 1800.
The survey of the additional energy channels for
the ions did not dramatically
Braccio.
change the results found by
Figures 27 and 28 are the probability distribution
plot and surface plot from Braccio
fourth RPA energy channel
flux
in
the
800-900
ions/(cm2 s sr),
(1991)
for ions in
the
(30 - 150 eV) with the criteria of
pitch
angle
bin
be
greater
than
10'
that the anisotropy be greater than 1.5, and
that the measurements be within 10° latitude of the magnetic
is found that the high probability region (greater
equator. It
than 45%)
for the ions started at 0500 local time and in the
area of L = 3.5.
His maximum L value is
on average about 8.0
and occurs generally around 1400 local time. At the maximum
the probability appears to drop off sharply in L as local time
moves toward dusk,
similar to the results above.
The apparent decrease in probability of occurrence
for ions in
Braccio is
the region of 1200 to 1400 local time found by
readily evident in both energy channels surveyed,
which seems to dampen Braccio's hypothesis that the higher
energy ions inhabited this region.
60
AMPTE SURVEY
Ions:
Anisotropy yt
1.5 Flux
gt
1.OOE+06 MagLat It
10.0
PROBABILITY DISTRIBUTION
70
60
8-
4
2
o
S50
040
6
230
O
20
. . . .. . . .. .10
01
2 4 6 B 10 1214 16 182022 24
10'
COVERAGE...20
~
175
150
8c
g~
C
125
:3 100
6
0
0
-~
75
50
4
01
2
0 2 4 6 8 10 12 1416 182022 24
Local time
Figure 27. Trapped Ions (30-150 eV) -Flux gt 106, An~isotropy
gt 1.5, Maglat gt 100
61
If)
00
Figure 28. Trapped Ions (30-150 eV)
gt 1.5, Maglat gt 100
-
Surface Plot
62
-Flux
gt 106, Anisotropy
b.
ELECTRON SURVEY
Figure 29 shows the probability distribution for
trapped
electrons
with
an
energy
of
340
eV meeting
criteria of flux greater than 5 x 106 electrons/(cm'
anisotropy greater than 1.5,
the
s sr),
and measurements within 100 of
the magnetic equator. Figure 30 shows the same type of plot
for 770 eV electrons meeting the same criteria.
presents this 770 eV data as a surface plot.
apparent that the electron distribution is
Figure 31
It
is
readily
vastly different
from that of the ions. There is no obvious L versus local time
trend for the electron probability distribution,
the results found by Braccio,
probability
who also fo,.ind the electron
distribution to be
region of highest probability
similar to
conical
in
shape
being between
with
the
1000 and 1100
local time and for L values around 6.5 - 7.0, as shown in the
probability and surface plots, Figures 32 and 33,
Braccio
(1991).
Here,
106 electrons/ (cm2 s
the criteria is
sr),
taken from
flux greater than 5 x
anisotropy greater than
1.5,
and
measurements within 100 of the magnetic equator.
The
cone
is
probability of occurrence
gradually,
not
completely
symmetrical.
increases to its
as a function of local time,
The
peak value more
than it
decreases.
This characteristic does not seem to alter even when changing
the selection criteria or energy channels and is
that found by Braccio.
the same as
The statistical analysis of the
63
AMPTE SURVEY
ELECTRONS AT 340 EV
Anisotropy
9t
1.5 Flux
gt
5.OOE+06 MogLot It
10.0
PROBABILITY DISTRIBUTION
10 . . . . . . . . . . . .80
70
8-
60
40
6o
0.
20
2
20
0 2 4 6 8 10 121416 18 2022 24
COVERAGE
10
200
175
150
8
S125
M~ 100
6
0
075
50
25
0
4
2
0 2 4 6 8 1012 1416 18 2022 24
Local time
Figure
29.
Trapped
Electrons
Anisotropy gt 1.5, Maglat gt 100
64
(340
eV)
-
Flux
gt
5x10 6,
AMPTE SURVEY
ELECTRONS AT 770EV
Anisotropy 9 t 1.5 Flux
5.OOE+06 Mag Lot It
9t
10.0
PROBABILITY DISTRIBUTION
80
10
.70
....
60
-50
6
40
30
2
10
0
4
2
"1 ,- I, ..........
0 2 4 6 8 1012 1416 18 2022 24
COVERAGE
10
200
175
150
8
-12
CC
13
75
0
50
4
05
2
0 2 4 6 8 10 12 14161820 22 24
Local time
Figure
30.
Trapped
Electrons
Anisotropy gt 1.5, Maglat gt 100
65
(770
eV)
-
Flux
gt
5x10 6 ,
P3*OJw)Y'O )o Ap!fqoqOid
0
-..
a_,
...
---
tDD
0_
0
0
9
0
0'
0
-
4-1wJ
<
E
a-a
r
Figure
31.
Trapped
Electrons
(770
eV)
-Flux
- Surface Plot
Anisotropy gt 1.5, Maglat gt 100
66
gt
5xr0f',
AMPTE SURVEY
Electrons:
Anisotropy gt
1.5 Flux
gt
5.OOE+06 MagLat It
10.0
PROBABILITýY DISTRIBUTION
IV
80
70
8
S
0
60
50
.
40
030
0
4
ý
110
2
01
-
0 2 4 6 8 10 12 14 16182022 24
COVERAGE
10
200
175
150
.~125
8
-
6
100
0
4
75
50
25
2
.
01
0 2 4 6 8 10 12 1416 182022 24
Local time
Figure
32.
Trapped
Electrons
Anisotropy gt 1.5, Maglat gt 100
67
(150
eV)
-
Flux
gt
5x10 6 ,
(.D
to
0+
O'•If)
0
0 C -U
0
--
0L.
Figure
33.
Trapped
An'isotropy gt 1.5,
Electrons
Maglat gt 100
68
(150
-
eV)
-
Flux
Surface Plot
gt
5xi06 ',
coarsely
gridded
survey
files
is
now extended
using
more
detailed looks at the raw data files.
B.
DETAILED ANALYSIS CASE STUDIES
1.
Data Analysis
Detailed analysis of the electron data was conducted,
using data at 150 eV and 340 eV.
Ion data were not readily
available. Data were collected for the days in TABLE III. Only
days 84/336 and 85/002 will be presented in
the thesis. The
days listed in TABLE III were selected from the set of days
where "large" electron events occurred,
Table III.
as found in
DETAILED ANALYSIS DATA COLLECTION DAYS
Local Time
Day
Range
Z•
D~t
84/266
0941-1634
26
-21
84/283
0510-1538
26
-24
84/296
0755-1420
39
-55
84/315
0655-1349
23
-11
84/336
0533-1249
22
-24
85/002
0359-1418
24
-3.2
85/039
0129-0834
28
-24
85/227
1440-1938
20
-21
85/238
1330-2330
22
-10
85/264
2002-2156
29
-19
85/301
1618-2049
7
-17
85/320
1116-1837
19
-18
85/337
1021-1742
17
-31
69
Braccio
(1991) and extended here, to obtain reasonably complete local
time
coverage.
(0600
sector
emphasis was
Special
to
1200
local
time).
given
Each
to the morning
segment
of
data
considered covered the period between plasmapause encounters,
roughly 15 hours of data per day. Also,
listed with the days
and times in TABLE III are the magnetic activity indices,
Ep
and Dt, for the respective time period.
Data were initially considered in one hour increments.
For each hour and each of the energy channels surveyed,
and
340
eV,
generated.
angle
vs
electrons
pitch
a
angle
Figure 34 is
time
vs
time
was
spectrogram
a compilation of the one hour pitch
spectrograms
on day
UT
150
84/336.
in
reduced
for
form
150 eV spectrograms
The
additional days surveyed can be found in
150
eV
for the
the Appendix.
The
grey scale for the spectrogram runs from 7.2 to 9.0 on a log
Pitch angle runs from 00 - 1800 and UT from
scale of the flux.
0000 to 1400. Also, plotted on the x-axis is the corresponding
McIlwain L value and magnetic latitude. Note
local time (LT),
the high flux at 90 degrees from 1000 to 1400 UT. Note how the
equatorially
approaches
trapped
perigee
characteristic
can
fades
distribution
(the
be
plasmapause
seen
in
spectrograms as shown in Appendix.
a
as
at
number
L
the
-
of
satellite
3.9.)
the
This
survey
The data were analyzed by
considering the log of distribution function as a function of
cos 2 a,
Figure 35. This functional form should produce straight
line segments,
if
the data are well represented as a
70
AMPTE
LI
L
&B
23,
56
4.7
84336
150 eV Electrons
7.0
&
7.3
76
L
0.
A
7. 0.6
7.9
7.3
£6
-9-
64
1.
a1.L1&
7.7
41-0-L
M£
T70
UT 301.0
LI 975
L
A
99
£.4
-p
LIT 110
LI
11.5
104A0.
L
5.7
try 11.0
2.2
12.
12&Z..
1030
1125I~
884
5&
23
12.1o
11.0
-!L4
£3
0112
.7S
I
10go5
1091.4
80.7
0V
£3
$e
1231.5
127-
17A
16.7
.
710
4-
AMPTE Survey
I .
-
'
84/336
9 V I 'I 'I '
'. -
150 OV Eleafran
10a
LT
3..
"CO 2
*
*
*
*
0
0
0.0
0.2
0.6
0.4
COS'(a)
Figure 35.
Electron Pitch Angle Distribution
72
0.8
1.0
bi-Maxwellian
Tperp
and
Tparl
(Scott,
can
1991.)
be
From these segments values for
estimated,
obtained. Much of this work is
the data (log f)
and various
flux
ratios
based on consideration of how
vary with pitch angle (cos 2 a).
From this figure a distinct break in the vicinity of
60 degrees can be seen.
At lower pitch angles the isotropic
background dominates the pitch angle distribution. Because of
this effect the data analysis range was limited to between 600
and 900,
a restriction
phenomenon of interest.
that more accurately
This restriction,
considers
however,
the
has the
effect of limiting the data set which can be analyzed. These
equatorial pitch angles
equator.
(600
to 900)
do not map far from the
A restriction of +-60 magnetic latitude was chosen,
which allows a suitable range of (equatorial) pitch angles,
and allows a reasonable range of events.
Fluxes were obtained in three ways:
1. Average Flux (600 - 700): the flux in
the 600 to
700 pitch
angle bin at the location of the satellite.
2.
Average Flux (800 - 900): the flux in
the 800 to 900 pitch
angle bin at the location of the satellite.
3.
Fitted Flux
(600 -
900): the fitted
taking a least squares
fit
flux was derived by
of the data at pitch angles
between 600 and 900 on a plot of the log of the distribution
function versus cos 2 4. This fit
was used to project the
values which would have been obtained at the magnetic
equator, effectively assuming a bi-Maxwellian form.
73
Two different anisotropies were calculated
and are
defined as follows:
1. Average Anisotropy:
the ratio of the average fluxes in
the 800 to 900 pitch angle bin to those in
the 600 to 700
pitch angle bin.
2.
Equator Anisotropy: the fluxes at the latitude of
measurement mapped to the equator and a ratio taken for the
flux at
900 versus the flux at 690.
Two
temperatures
were
calculated
for
each
energy
channel:
1.
Tpe
:
the
characteristic
temperature
in
the
perpendicular direction, with respect to the magnetic field
line, of a bi-Maxwellian distribution. Calculated from the
difference in the log of the distribution functions for 150
eV and 340 eV at a pitch angle of 00. The calculated value
is the same for both energy channels.
2.
TparI : the characteristic temperature in the parallel
direction, with respect to the magnetic field line, of a
bi-Maxwellian distribution. This is based on the calculated
Tperp and the slope of the pitch angle distribution at
the
respective energy. The calculated value is different for
each energy channel, reflecting the non-Maxwellian element
of the energy distribution.
Both temperatures and the density were calculated from
a bi-Maxwellian
form
for
the
distribution
produces valid and well behaved results if
can be characterized as a bi-Maxwellian.
function.
This
the distribution
If
it
is
not well
described as a bi-Maxwellian the results will be invalid and
not well behaved.
The ratio of
data.
Tperp
to Tpari was also calculated for the
This ratio was used to further characterize a trapped
distribution. For the purposes of this paper the ratio had to
74
exceed
three
for
a
equatorially trapped.
factor
distribution
be
characterized
as
This corresponds to a density decrease
of 20% at 100 magnetic
parallel electric fields.
2.
to
latitude
(Scott,
in
the
absence
of
1991)
Day 84/336 Case Study Trapped Distributions
a.
150 eV
Figure 36 shows the plots of the previously defined
fluxes vs UT time at 150 eV. The solid horizontal line plotted
for the flux value
with the fluxes in the bottom two plots is
of 5x106 (cm2 s sr)-' , the minimum threshold established in the
last chapter. Also, plotted on the x-axis are the local time,
McIlwain L and the magnetic latitude.
Figure 37 shows the plots of the previously defined
anisotropies versus time at 150 eV. The solid horizontal line
plotted on each is the anisotropy threshold of 2.0, defined in
the previous chapter
as the minimum anisotropy allowed to
characterize a trapped distribution. Note the periods that the
anisotropies exceed the threshold correspond to the periods of
increased flux. Also, shown in Figure 37 is
vs time, Tpar1 vs time, and the ratio
Tperp
the plots of
Tperp
to Tpari vs time. The
solid horizontal line plotted on the plots for temperature
ratios vs time is
the ratio threshold level of three defined
in the last chapter. At the time the temperature ratio exceeds
three perpendicular temperature is on average 70 eV while the
parallel temperature drops from values of 20 eV to 10 eV. The
peak of the ratio has a value of 6.0. For this day a
75
a-
-h
lIr 7.0
LT 9.1
5.S
L
1 -5.6
-u dip)b Dip W= mm
bwI a1
9.0
9.7
V.
-2.4
Figure 36. Fluxes verses Time
11.0
10.4
7.7
0.6
-
76
13.0
11.5
5.6
2.2
Day 84/336, Energy 150 eV
15.0
15.4
1.8
-2.6
4-
3
-
.
A*I
ka~bcmim
iiM
I. 2-
ii7.0
-
ib A1.
777
qUdWW:5
1m.
15.rO
equatorially trapped electron distribution appears to occur
for a McIlwain L value of about 6 to 7.5. Note that the lower
anisotropy,
1.5 (the dashed line in Figure 37),
statistical
survey would give a wider L extent,
used in
the
from L = 3 to
9. With this lower anisotropy and the corresponding L range as
a
boundary,
for
where
equatorially
distributions exist, a flux value of 5xl0'
trapped
electron
and a temperature
ratio of two can be interpreted as new criterion thresholds
for equatorially trapped electrons,
lines in
as seen by the dashed
the flux and temperature ratio plots of Figures 36
and 37.
Figure 38 shows the plot of the average anisotropy
versus the
equator anisotropy
and the plot of temperature
ratio versus equator anisotropy.
The average anisotropy
is
slightly higher than the fitted equatorial anisotropy as can
be seen when compared to a line of slope one (the line on the
plot.)
In the plot of temperature ratio vs equator anisotropy
the data starts to exceed the ratio criterion threshold of
three at an equator anisotropy of about 2.0,
if
the high end
of
to
support
the
data
points
is
taken.
This
tends
our
definition for an equatorially trapped electron distribution
using flux ratios, and shows that a bi-Maxwellian description
gives comparable results.
Using
the
criteria
electron distributions defined in
for
trapped
the previous chapter of a
minimum flux for 150 eV electrons of
78
equatorially
5x10'
(cm2 s sr)-',
an
:Average
vs Equator Anisotropy
Day: 84/336
Energar.150 eV
3-
:
4-
7
1
2So
Tperp/Tparivs Equator Anisotropy
4
Figure 38. Average Anisotropy and Temperature Ratio
verses
Equator Anisotropy
-
Day 84/336, Energy 150 eV
79
average anisotropy of 2.0,
a measurement within 100 of the
magnetic equator, and the additional criterion for a ratio of
TP.,P Vs Tpri to be greater than three an equatorially trapped
plasma can be seen to start at around 0942 local time at a L
value of 8.7 and at
As L decrease
magnetic latitude of -2.40.
with time all anisotropies increase to a peak at around 1050
local time and a L value of 6.9 and a temperature
ratio of
6.0. All anisotropies decrease with time after that until the
trapped
distribution
ends
at around
1147,
L
of 5.30
and
magnetic latitude of 2.40.
b. 340 eV
Figure 39 shows the plots of the previously defined
fluxes vs UT time at 340 eV. The solid horizontal line plotted
with the fluxes in the bottom two plots is
for the flux value
of 5x10 6 (cm2 s sr)-' , the minimum threshold established in the
previous chapter. Also, plotted on the x-axis are the local
time, McIlwain L and the magnetic latitude.
Figure 40 shows the plots of the previously defined
anisotropies versus time at 340 eV. The solid horizontal line
plotted on each is the anisotropy threshold of 4.4, defined in
the previous
chapter as the minimum anisotropy allowed to
characterize a trapped distribution.
is
to
the plots of Tperp vs time,
Tparl
vs time.
Tpari
Also, shown in Figure 40
vs time, and the ratio
The solid horizontal
plots for temperature ratios vs time is
Tperp
line plotted on the
the ratio threshold
level of three defined in the last chapter. At the time the
80
7-
1
IIIII
3VVmDip
imp)
Ur7.0O
Fig
IfU*b,30
ur
39.
i81
Fluxe
3~
vese
13.0
11.
Tim
-i Da
84/336,
Enry30e
1&0d
Ii
-
A
4-:
lIT~--
282
7I0 9.
1.0130
5.
temperature ratio exceeds three perpendicular temperature is
on average
70 eV while the parallel
values
23
of
eV.
At
this
temperature
energy
a
drops
trapped
to
electron
distribution appears to occur for a more limited McIlwain L
range,
at the higher end of the L range defined by the 150 eV
data.
Using
the
criteria
for
trapped
electron
distributions defined in the previous chapter of a minimum
flux for 340 eV electrons of 5x10 6 (cm' s sr)-',
anisotropy of 4.4,
equator,
an average
a measurement within 100 of the magnetic
and the additional criterion for a ratio of
Tperp
vs
Tparl to be greater than three an equatorially trapped plasma
can be seen to start at around 1031 local time at a L value of
7.5
and
at
a
magnetic
latitude
of
0.80.
The
trapped
distribution does not extend very far ending at 1041 at L
equal to 7.2 and magnetic latitude of 1.20.
A more realistic
anisotropy ratio of
ratio
-
2 and a
temperature
of 2
,
as
shown by the dashed line in both plots of Figure 40 would give
a latitude extent more in
line with respect to the 150 eV
results.
3.
Day 85/002 Case Study Trapped Distributions
a.
150 eV
Figure 41 shows the plots of the 150 eV fluxes vs
time for 85/002.
The solid horizontal line plotted with the
fluxes in the bottom two plots is
(cm2 s sr)-'.
for the flux value of 5x10 6
Also, plotted on the x-axis are the local time,
83
McIlwain
L and the magnetic latitude.
anisotropy suggests
Comparison with the
a flux level of 5x10'
would be a more
accurate indicator on this day, as shown by the dashed line in
the plot.
Figure 42 shows the plots of the previously defined
anisotropies versus time at 150 eV. The solid horizontal line
plotted on each is the anisotropy threshold of 2.0, defined in
the previous chapter
characterize
periods
as the minimum anisotropy allowed to
an equatorially trapped distribution.
that
corresponding
the
anisotropies
to the periods
exceed
the
of increased
flux
Also, shown in Figure 42 are the plots of
time, and the ratio Tperp
Tperp
Note the
threshold
(>
5x10').
vs time, Tparl VS
to Tpari vs time. The solid horizontal
line plotted on the plots for temperature ratios vs time is
the
ratio
threshold
level
of
three.
At
the
time
the
temperature ratio exceeds three perpendicular temperature is
on average
80
eV while the parallel
temperature
drops to
values of 20 eV. For this day a trapped electron distribution
appears to occur for a McIlwain L value of about 5 to 7. Note
the lower anisotropy ratio of 1.5 (the dashed line in Figure
42),
used in
extent,
the statistical
from L = 5 to 8.
survey would give a wider L
With this lower anisotropy and the
corresponding L range as a boundary,
trapped electron distributions exist,
and a temperature
for where equatorially
a flux value of 5x10 7
ratio of two can be interpreted
as new
criterion thresholds for equatorially trapped electrons,
84 -
-W Pi-D
-*
api b'w SAMat&-w
oa
..sp
.~
..
...
....
MW* f".
UT
LT
L
dU-4
im ft qM
it Eauqlw 4
U.
8.0
V.
U.
7.3
U.
1
44-1.0
Figure 41. Fluxes verses Time
10.
V.
7.7
2.0
-
85
12.0
3.8
5V
3.6
Day 85/002, Energy 150 eV
14.0
14.1
2.0
1.2
4-
Amp
-'11 OwOW
atE
=&
ul
SpU
3-
uq~u~
2
O-- - - -- - SPI
i
LOLi9
8.9
-- - -- - 12.0-
7.7
---
Li
2.0-------1.2
FIgue4.AiorpeTmeaueRtoadTmeaue
verses~m
Timeeb Day 85/02
I S OP
-
4--
V.
L7
-1
12-4.
10-0
U~UEu1
Enrg
fo150 eV
bd f ~ l*6Ik OWM
/ MatEN8
1.
2.
as seen by the dashed lines in the flux and temperature ratio
plots of Figures 41 and 42.
Using
the
criteria
for
trapped
electron
distributions def ined in the previous chapter of a minimum
2 s sr) -, an average
flux for 150 eV electrons Of 5XJ06 (cm
anisotropy of 2.0, a measurement within 100 of the magnetic
equator, and the additional criterion for a ratio of Tp,,p vs
Tpari to be greater than three a equatorially trapped plasma
can be seen to start at around 0900 local time at a L value of
7.2
and at
magnetic latitude of 2.60. As L decreases with
time the anisotropies increase to a peak at around 0909 local
time and an L value of 6.9. The anisotropies decrease with
time after that until the trapped distribution ends at around
1003, L of 5.30 and magnetic latitude of 3.60.
b.
340 eV
Figure 43 shows the plots of the fluxes vs time at
340 eV. The solid horizontal line plotted with the fluxes in
the bottom two plots is for the flux value of 5x106 (cm' s
sr)'. Also, plotted on the x-axis are the local time, Mcllwain
L and the magnetic latitude.
Figure 44
shows the
plots of
the
anisotropies
versus time at 340 eV. The solid horizontal line plotted on
each is the anisotropy threshold of 4.4.
Figure 44 are the plots of Tp,,
Also,
shown in
vs time, Tpari vs time,
and
theratio Tperp to Tpari vs time. For the short interval where the
temperature ratio exceeds three the perpendicular temperature
87
I-
.*W
Ft.
05
g* fir OW. W/
d bwg~4O W
Utf 6.0
LT 7.3
8.0
6.0
10
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12.0
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L
U.
8.
7.7
V.
14.1
2.0
-4.4
-1.0
2.0
3i6
1.2
1
Figure 43. Fluxes verses Time
-
88
Day 85/002, Energy 340 eV
14.0
4
Ap*
s1-o
_w
0
/
tSW
------ ------ -----
3-
rO
~=Ib I#
4-
kaldOW
3-
-too-
0-:
50-
uT
6.0
LT 7.3
L
8.9
1 -4.4
6.
V.
-1.0
1.
6.9.8
V.
7.7
2.0
12.0
V.
3.6
14.0
14.1
2.0
12
Figure 44. Ariisotropies, Temperature Ratio and Temperatures
verses Time
-
Day 85/002, Energy 340 eV
89
is
on average 90 eV while the parallel temperature drops to
values of 30 eV. Again, the equatorially trapped distribution
is
its
much more limited in
criterion of a ratio of 4.4 is
the anisotropy
criterion
Indeed the
appearance at 340 eV.
not met.
to 3.0
if
However,
(the dashed
we lower
line
in
the
anisotropy plots of Figure 44) a trapped distribution would be
defined to occur around a McIlwain L value range of 6 to 7.5
at around 0901 local time at a L value of 7.1 and at
The trapped distribution does not extend
latitude of 2.80.
very
ending
far
latitude of 3.40.
magnetic
at
0928
at
L equal
to
and magnetic
6.3
This corresponds to a temperature ratio
2
-
(the dashed line in the temperature ratio plot of Figure 44)
4.
Detailed
Analysis
Trapped
versus
Non-Trapped
Distributions
In
Figure
34
there
was
evidence
of two
The first
trapped electron distributions for day 84/336.
presented
using
Figures
36
through
38,
areas
which
was
of
was
an
equatorially trapped distribution as defined by our criteria.
The other area that presents itself
period
between
0553
and
0700
in Figure 34 is
local
time.
The
the time
broader
distribution seen earlier in the day fail our criteria. Figure
45
and
46
anisotropy,
show
plots
like
previously
of
the
temperatures and temperature ratios,
fluxes,
all verses
time for the entire orbit on 84/336 at 150 eV. Though both
90
MW as M"-i d
IVw
if1~w
W
I04
I2
I
I
5-
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04
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Fluxe
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Time
(Entire Orbit)
91
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neg
15.0e
7-
97
S~
himb a
T
134-
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Figure~
46.
mbp It/ d
~
mIl
isotr
verses Tipme f ay
f=W
Wmi
ii
pis
84/36
Tepeatr
Energ
92
Rati
and Tempeature
150 eVd (EtrObt
time periods show similar increases in
flux the anisotropies
for
exceeds
the
second
time
period
barely
1.3
and
the
temperature ratio never rises above 2.0.
Figure 47 is
a plot of the log1 ,f
versus pitch angle
for 150 eV electrons from different days and hours in
the
detailed analysis. The plot is organized from bottom to top to
show
a
progression
of
non-trapped
to
trapped
electron
distributions. Plot a and b show the pitch angle distribution
for periods when no trapped electron distribution is present.
Plot
c
and
d
distributions.
trapped
show
the
beginnings
of
trapped
electron
Plots e and f show the narrowest equatorially
electron
distributions
observed
in
the
detailed
analysis. Note that as the trapped distribution gets stronger
the peak at 900 gets progressively more pronounced, indicating
that
the
electrons
are
equatorially
trapped.
This
characteristic suggests that the data may be fitted with a biMaxwellian
distribution
function
as
was
performed well and it
was quite evident it
indicating
distribution
that
the
was
distributions.
93
This
did not fit
not
criteria allows us to distinguish between
distributions (e.g., loss c(nes),
done.
trapped.
(simply)
fit
well
This
trapped
versus equatorially trapped
*
1020
I
*
I
I
'
*
I
'
a
-%,
I
'
1) Ow 54/336 10os0ot
10
: ,,*
_ .. m
o..D)
1015
*.a
-r
L
/26M•U.4
|~
d)DW. 08/0= CM
C
.
%J,
11• 3 U6e"
0) De,? "/2"
0
W/6f OWL
1)
mmm
105
90
O030
0
0
0
60
1
1
180
10
150
1
pitch (degrees)
Figure 47.
Flux verses Pitch Angle - Various Days
94
95
IV. DISCUSSION
A.
STATISTICAL SURVEY
The probability
distributions
for equatorially
trapped
ions and electrons show clear localization for regions of high
occurrence probability (>= 50%).
This is particularly true of
electrons. The electron distribution has a very localized peak
at
1000 - 1100 local time,
of the
magnetic
equator.
L = 6.0 - 6.5,
This
is
and within 5 degrees
seen
regardless
of the
selection criteria used in the surveys. This agrees with the
results
found
by
Braccio.
The
survey
also
showed
the
equatorially trapped electrons were primarily located outside
the traditional plasmasphere,
and were primarily confined to
the dawn to noon sector. The peak in the electron distribution
occurred-near geosynchronous orbit.
The results
closely with
for trapped
Braccio's
ion distributions,
results with the
explanation for the decrease
in
also,
exception
agree
of
his
probability between 1200 -
1400. He suggested that the decrease in probability is due to
the average
above
energy of the equatorially
the 150
region.
eV energy
he
surveyed,
trapped ions going
in
this
local
time
Both the 240 eV and 442 eV ions surveyed showed the
same decrease in ion probability distribution for this local
time region.
correct.
It
Sagawa
maybe possible that Braccio's hypothesis is
et al
(1987)
96
did not
show a decrease
in
probability
for the
region
from 1200
to
1500 local
time.
However, Sagawa et al. used summary results from approximately
10 eV to 1 keY,
whereas
Braccio's
survey and this survey
covered 50 to 442 eV. To accurately determine if higher energy
ions
inhabit
this
region
of
decreased
probability
the
additional energy channels of 657, 885 and 1127 eV ought to be
surveyed.
The
ion
survey
reinforces
previous work with ISEE-1 and DE-l,
Braccios'
and
other
with peak ion flux inside
the plasmapause.
B.
DETAILED ANALYSIS CASE STUDIES
In the analysis only 13 days were looked at, therefore a
statistical analysis isn't
coverage,
Figure
48,
appropriate.
of the
days
However,
analyzed was
the orbital
widespread
enough to see patterns or tendencies emerge in the data.
Figure 49 is
a plot of where the 150 eV data from the 13
days that met the criteria to be considered a trapped electron
2
distribution occurred; namely a flux greater than 5.0x106 (cm
s sr)-', an anisotropy greater than 2.0,
a temperature ratio
greater than 3.0 and within 100 of the magnetic equator. The
data is plotted in the x-y plane of the AMPTE satellite orbit.
The trapped distributions start at dawn at a mean L value of
about 3.8 and increase in orbital density and L to a maximum
between 0900 and 1100 local time and an average L of 7.0. The
distributions then drop off rather rapidly with only smaller
occurences of equatorially trapped distributions in
97
E
C-0
cIIi
0
c~cl
w•w
C,,c
C
00
-
-C.4
98-j
0
... . .......
L
"
-0•/
Fiue-4
-o
. Deaie Anlss-ria Cvrg
"0
ci
S
1
Figure 48.
Detailed Analysis Orbital Coverage
98
-¶0
*b
-1----0
Figur49.wdEqatrill
Energ
150
09
Midqi0ght,
2du
Earth
Trpe3lcrn
Lm
10
LNO 0 1
LOW&dMb
itiuin
mid-afternoon at L values in excess of 7.0 and at dusk when
the distributions move back into the smaller L values of 5.0
to 6.5.
Braccio (1991)
in his statistical survey found a similar
general pattern to exist for trapped electron distributions at
the
150
eV
energy
range.
He
found
that
the
electron
distribution had a very localized peak at 0900 local time, L
= 6,
and within
50
of the magnetic equator.
The difference in
the results can be attributed to his survey considering all
days of operation the AMPTE satellite while this thesis only
considered a small portion of the operational life.
The tendency for the trapped electron distributions to
move
out
further
in
L value
starting
at dawn until
late
afternoon and then move back in near dusk can be explained in
terms
of
Williams
plasmapause
et
al.
location.
(1981).
It
Figure
shows
the
plasmapause as a function of local time.
50
is
taken
location
of
from
the
The shape of this
plot mimics the behavior of the trapped electron distributions
in the case studies. Then as the plasmapause moves out during
the day so does the location of the trapped electrons.
Braccio
(1991)
found that trapped electrons seem to be
excluded from regions of high trapped ion probabilities and
vice versa. He,
also, found that the trapped electron
100
30-onU
0
94
;
i-'
*
!
4
ii--
,
U..
dI
t4 lb
to'o
15
%
oft
-
jj
z
Figure 50.
aa
or,
Plasmapause Location
*
lbi-
%a,
distributions probabilities
drop off by local
noon at the
beginning of the peak of the trapped ion probabilities, which
he found to peak between 1400 and 1500 local time at L = 8.
Horowitz et al. (1981) observed that trapped ion distributions
tended to occur along the plasmapause boundary in the dawn to
dusk
region
with
the
majority
just
inside the
boundary.
Therefore Braccio postulated that if trapped ions occur at the
plasmapause, then as the altitude of the plasmapause rises, in
the
course
of
a
day,
the
region
distributions usually occur is
where
trapped
electron
saturated with trapped ions.
This ion saturation seems to, in turn, lead to a disruption in
the process by which the trapped electrons are produced.
This
approach could be used to explain the gap in trapped electron
distributions found in
the case studies,
Figure 49,
between
1200 and 1700 local time inside of L = 7.
Figure 51 is
a plot of the occurrence of 340 eV data in
the 13 days that met the criteria to be considered a trapped
3
6
electron distribution; namely a flux greater than 5.0x10 (cm
s sr)-',
an anisotropy greater than 4.4,
a temperature ratio
greater than 3.0 and within 100 of the magnetic equator.
The
data is plotted in the x-y plane of the AMPTE satellite orbit.
There appears to be no major grouping of trapped electron
distributions
at this
energy
level.
result of the higher anisotropy
This
is
requirement
probably
of 4.4.
the
The
trapped distributions are localized to 0900 to 1100 local time
at L of 7.0 and at dusk from 1700 to 1800 local time at L=5.0.
102
BMbdý sk 340 WV
0Ampte
10
,
,
,
r.m stS=PO
Noon
,
'm
R It 4M
2--
-4-
1
1
-10-8
-6
-10
Midrfight,
-4
-2
0
2
4
6
8
10
Earth Rocai
Figure
51.
Equatorially
Trapped
Energy 340 eV
103
Electron
Distributions
-
A comparison of the two different anisotropies used to
characterize the data found that they tracked reasonably well
with the equator anisotropy being on average 1.075 times the
equator anisotropy in
the dawn to noon region and only 0.59
times the equator anisotropy in the noon to post dusk region.
The difference in anisotropy ratios for the equator anisotropy
between the morning and the afternoon local time could be due
to a lack of samples taken in the afternoon region that were
characterized as trapped.
Over 28,000 samples taken in 13 orbits are summarized in
Figure 52, the plot of
eV electrons.
defining
This figure shows a different technique
anisotropy
distribution
Tprp/Tpa,, vs Equator Anisotropy for 150
and
of
a
suggests
equatorially
that
there
trapped
is
a
for
electron
monotonic
relationship between a temperature ratio greater than 3 and an
anisotropy of 2.0 for 150 eV and 4.42 for 340 eV. For all days
the
threshold of
3
for a temperature
ratio begins
to be
exceeded at the anisotropies of about 2.0 for 150 eV and about
4.42 for 340 eV.
104
5-,
7
I
I
,
i
i '
,
i
I
'
Tperp
Tarl vs Equator Anisotropy
Day: C41/002
7-
Energy: 150 eV
6-
5
* ....-.
.
"1..,....,'--'.'
12
*,
.
vl
, **.
,a
. . ....,:"
.
-;,*..~
•
•
•%
•
,.
.
..
-
,
°•..
3
45
Figure 52. Temperature Ratio verses Equator Anisotropy
13 Detailed Analysis Case Study Days, Energy 150 eV
105
-All
106
V. CONCLUSIONS
STATISTICAL ANALYSIS
A.
The
species dependent.
are
plasmas
The ions and electrons show a different
local time dependence
probability peak.
trapped
of the equatorially
location
in
the location of their occurrence
Electrons show a uniform high probability
distribution centered at 0900 local time and an L value of 6.
The fact that trapped electrons begin to be seen at local dawn
lead to
speculation that their
is
existence
dependent
on
photoelectron emission form the Earth's ionosphere. The shape
of this distribution is basically conical, however,
off more rapidly than it
increases,
it
drops
with respect to local
time.
Ions,
meanwhile,
distribution
have a probability
The high trapped
shows a strong L dependence on local time.
probability region begins at local dawn,
4,
that
for L approximately
and rises to a maximum at between 1400 and 1500 local time
with an L value of 8.
The distribution then drops quickly in
altitude as local time increases.
Additionally,
there is
a
region of decreased probability in the afternoon sector for
this
data
that
was
speculated
by
Braccio
inhabited by higher energy ions, but still
(1991)
to
be
is present for the
higher energies surveyed.
The overall
shape of the high trapped
107
ion probability
region mirrors that of the location of the plasmapause.
suggests that the trapped ion distribution is
plasmapause.
This
would
confirm
observations that 'pancake'
Horwitz
This
linked to the
et
al. 's
(1981)
distributions often occur in the
vicinity of the plasmapause.
Additionally,
seem
to
be
it
has been observed that trapped electrons
excluded
from
regions
probabilities and vice versa. If
occur
at
the
plasmapause,
plasmapause rises,
in
of
high
trapped
ion
the trapped ions actually do
then
as
the
altitude
the course of a day,
of
the
this exclusion
would effectively create a barrier that rest.ricts the trapped
electron distribution to the dawn to noon sector.
B.
DETAILED ANALYSIS CASE STUDIES
The results
of the detailed
analysis
case
studies
in
general agree with the above results found by Braccio (1991).
Trapped electron distributions are concentrated in the dawn to
noon region with a peak around 1000 at an L value of 7. What
trapped distributions occur in the afternoon are generally at
higher L values until late afternoon when they move back into
L values around 5 to 6 at 1800. This follows with the results
found by Braccio,(1991) who found that large trapped electron
distributions
are exclude
from areas
of high trapped
ion
distributions that peak in the 1400 to 1500 local time region.
This also suggests a connection between the plasmapause and
trapped electron distributions.
108
The threshold flux level used in the statistical survey
A higher flux level of 5x107
was too low for 150 eV electrons.
(CM2
s sr) ' could be used for this energy level. The use of an
anisotropy of 1.5 and a temperature
results more in
survey.
ratio of 2.0 produced
keeping with the results of the statistical
The threshold flux level for 340 eV appeared to be
correct.
The use of an average anisotropy at a latitude within 60
of the magnetic equator vice a calculated equator anisotropy
in defining trapped electron distributions is generally pretty
accurate. The average difference is only 7.5% between the two.
It has been shown that equatorially trapped plasmas can be
described by a bi-Maxwellian distribution function. With such
a description the valu2s of the perpendicular and parallel
temperatures can be calculated and their ratio used along with
an anisotropy ratio between the flux in the 800 to 900 pitch
angle range with the flux in the
600 to 700 pitch angle range
to define a electron distribution as equatorially trapped or
not. It was found that a temperature ratio of three along with
anisotropies of 2.0 for 150 eV electrons and 4.4 for 340 eV
electrons
could
distribution
be
along
used
with
to
define
the
a
required
trapped
flux
and
electron
magnetic
latitude requirements.
However,
reliable
the
results
340
than
eV
anisotropy
the
150
eV
of
4.4
produce
anisotropy
with
less
the
theoretical anisotropy and temperature ratios for 340 eV being
109
too
high.
In
this study
Terp
is
calculated
from the
bi-
Maxwellian distribution function and this results in the same
TP.rP for both 150 eV and 340 eV.
available.
However,
underestimate
particles.
This was the only method
the method produces
of the perpendicular
This
suggests
that
a Tperp that is
temperature
the
trapped
for 340 eV
electron
distributions at this energy are not true bi-Maxwellians,
are more like a kappa function.
110
an
but
APPENDIX
(DETAILED ABALYSIS
111
SPECTROGRAIS)
AMPTE
84266
150 eV Electrons
111
107
11.4
LY
07
10.3
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4.0
4.8
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5.5
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7.3
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7.7
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6.0
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10.5
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6.3
-2.5
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zr..K..
0i
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89
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6.9
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266
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84283
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144
556.
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l113
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AMPTE
84296
150 eV Electrons
IS
LT .13A1.
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150 eV Electrons
84315
C
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115
131
4.0
70
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AMPTE
85002
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lb.4
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85039
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AMPTE
85227
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119
AMPTE
85264
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C1043
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1.7
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912
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AMPTE
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8O
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85320
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150 eV Electrons
11-3
145
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Figure 63.
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152
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13.8
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s
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049
1
19.0...
17.0
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100
8
60
5.24.
0.
10.
10.
Pitch Angle verses Time Spectrogram
Energy 150 eV
122
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85/320,
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Figure 64. Pitch Angle verses Time Spectrogram
Energy 150 eV
123
20.1
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7.2
Day 85/337,
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156
Figure 66. Pitch Angle verses Time Spectrogram
Energy 340 eV
125
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84/283,
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w
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Figure 67. Pitch Angle verses Time Spectrogram
Energy 340 eV
126
17.0
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137
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140
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Dr. R. C. Olsen, Code Ph/Os
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CSPAR
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