Table Of ContentPhysics and Chemistry in Space
Volume 1
Edited by
J. G. Roederer, Denver and J. Zahringer, Heidelberg
Editorial Board:
R. L. F. Boyd, London· H. Elsasser, Heidelberg· G. Elwert,
Tiibingen· L. G. Jacchia, Cambridge, Mass .. J. A. Jacobs,
Edmonton· P. Meyer, Chicago, Ill. . N. F. Ness, Greenbelt,
Md .. W. Nordberg, Greenbelt, Md .. W. Riedler, Kiruna .
J. W. Warwick, Boulder, Colo.
J. A. Jacobs
Geomagnetic Micropulsations
With 81 figures
Springer-Verlag New York Heidelberg Berlin 1970
J.A. Jacobs
Killam Memorial Professor of Science
The University of Alberta, Edmonton, Canada
ISBN-13: 978-3-642-86830-6 e-ISBN-13: 978-3-642-86828-3
DOl: 10.1007/978-3-642-86828-3
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Softcover reprint of the hardcover I st edition 1970
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Title No. 3210.
Preface
The subject of geomagnetic micropulsations has developed extremely
rapidly and it is difficult to know when is an appropriate time to pause
and assess the sum total of our knowledge-both observational and
theoretical. There has in recent years been a tremendous increase in
both the quantity and quality of data and also many theoretical ad
vances in our understanding of the phenomenon. Undoubtedly there
will be further progress in both areas but it seems worthwhile now to
review both our knowledge and our ignorance. This book was essen
tially completed by the end of April 1969 and tries to give a summary
of the subject up to that time.
The Earth is enclosed in the magnetosphere, a hollow carved out of
the solar wind by the Earth's magnetic field. Above the ionosphere
there is a very tenuous thermal plasma of partially ionized hydrogen in
diffusive equilibrium with magnetic and gravitational forces, and ener
getic protons and electrons that constitute the trapped Van Allen ra
diation belts. Throughout this anisotropic and inhomogeneous plasma,
natural and man-made electromagnetic energy propagates in a wide
variety of modes and frequency bands. This book is concerned with
that class of natural signals called geomagnetic micropulsations-short
period (usually of the order of seconds or minutes) fluctuations of the
Earth's magnetic field. They are transitory variations of small amplitude
(usually less than one part in 104 of the Earth's main magnetic field)
and leaye no lasting effects on the Earth's field. One of the most excit
ing aspects of the subject is the very real possibility of using them as
natural probes for remote sensing of the magnetosphere.
In the development and application of plasma physics to micro
pulsations only a cold, two-component plasma will be considered.
Undoubtedly this is inadequate to properly describe conditions in the
magnetosphere. However in our present uncertain state of knowledge,
I do not believe that a more sophisticated detailed treatment of plasma
physics is warranted in a book on micropulsations. I believe that the
time will soon come however when homogeneous models in cosmic
electrodynamics will be inadequate to describe the data, and that the
essential properties of cosmic plasma will only be understood by models
which take into account strong, inhomogeneous small-scale structures.
VI Preface
In this book I have not tried to anticipate this trend and have kept the
mathematics and physical models as simple as possible.
Cgs-Gaussian units are used throughout. Although there is much
in favor of using MKS units, I feel that much would be lost if the units
were not Gauss units.
February 1970 J. A. Jacobs
Contents
The Earth's Magnetic Field . . . . 1
1.1 Introduction. . . . . . . . . I
1.2 Transient Magnetic Variations. 2
1.3 The Magnetosphere 5
1.4 Conjugacy . . . . . . . . . 12
References . . . . . . . . . . . 13
2 The Morphology of Geomagnetic Micropulsations 15
2.1 Introduction. . . . . . . . . . 15
2.2 Classification of Micropulsations. . . . . . 16
2.3 Continuous Pulsations (Pc 1). . . . . . . . 19
2.4 Continuous Pulsations (Pc 2/3, Pc 4, and Pc 5) 33
2.4.1 Continuous Pc 2/3 Oscillations 35
2.4.2 Continuous Pc 4 Oscillations 39
2.4.3 Continuous Pc 5 Oscillations 41
2.5 Pulsations with Irregular Forms 45
2.5.1 Irregular Pulsations Pi 1 . . ,,_ 46
2.5.2 Irregular Pulsations Pi 2 . . 47
2.5.3 Other Forms of Pi Activity. 53
References . . . . . . . . . 60
3 Magneto-Hydrodynamic Waves 64
3.1 Alfven Waves . . . . . . 64
3.2 The Equations of Small Hydromagnetic Oscillations. 65
3.3 The Dispersion Relation . . . . . . . . . . . . 69
3.4 Theories of Pc Oscillations. . . . . . . . . . . . 71
3.5 Transmission of Hydromagnetic Waves Through the Iono-
sphere and Magnetosphere . . . . 74
References . . . . . . . . . . . . . 86
4 Theories of the Origin of Pc 1 Pulsations 88
4.1 Introduction. . . . . . . . . . . 88
4.2 The Structure of the Frequency Spectrum of Pc 1' s 98
4.3 The Cyclotron Instability Process and the Generation of Pc 1' s 100
4.4 Sub Classes of Pc 1' s - Non Linear Theories 109
4.5 Propagation of Pc 1' s to Lower Latitudes 114
References . . . . . . . . . . . . . . . . 122
VIII Contents
5 Theories of Pc 2-5 and Pi Oscillations. 124
5.l Introduction. . . . . . . . . . . 124
5.2 Toroidal Oscillations . . . . . . . 125
5.3 The Excitation Mechanism of Pc 5's 134
5.4 Theories of Pi's . . . . . . . . . 136
References . . . . . . . . . . . . . 145
6 Micropulsations and the Diagnostics of the Magnetosphere 148
6.l Introduction. . . . . . . . . . . . . . . . . .. 148
6.2 Relationship Between Micropulsations, The Solar Wind and
the Dimensions of the Magnetosphere .......... 151
6.3 Plasma Densities in the Magnetosphere Determined from
Micropulsation Measurements. . . . . . . . 160
6.4 Micropulsations Observed in the Magnetosphere 169
References . 174
Subject Index. . . . . . . . . . . . . . . . . . 177
1 The Earth's Magnetic Field
1.1 Introduction
Geomagnetic micropulsations are short period (usually of the order of
seconds or minutes) fluctuations of the Earth's magnetic field. They are
transitory variations of small amplitude (usually less than one part in
104 of the Earth's main field) and leave no permanent effect on the field.
Like longer period disturbances such as magnetic storms they are of
solar origin, in contrast to the Earth's main field and secular variation
which are of internal origin.
At its strongest near the poles the Earth's magnetic field is several
hundred times weaker than that between the poles of a toy horseshoe
magnet-being less than one gauss (r). Thus in geomagnetism we are
measuring extremely small magnetic fields and a more convenient unit
is the gamma (y), defined as 10-5 r. * In 1600 William Gilbert published
the results of his investigations on the variation in direction of the mag
netic force over the surface of a piece of the naturally magnetized mineral
lodestone which he had cut in the shape of a sphere. He found that the
variation of the inclination was in agreement with what was then known
about the Earth's magnetic field, and he came to the conclusion that the
Earth behaved substantially as a uniformly magnetized sphere, its mag
netic field being due to causes within the Earth and not from any external
agency as was supposed at that time. In 1839 Gauss showed by a spherical
harmonic analysis that the field of a uniformly magnetized sphere, which
is the same as that of a geocentric dipole, is an excellent first approxima
tion to the Earth's magnetic field. The geomagnetic poles, i. e. the points
where the axis of the geocentric dipole which best approximates the
Earth's field meets the surface of the Earth, are situated approximately
at 78.8° N, 70.0° W, 78.8° S, 110° E. The geomagnetic axis is thus inclined
at about 11 ° to the Earth's geographical axis.
* Strictly speaking the unit of magnetic field is the oersted, the gauss being
reserved for magnetic induction, and some geophysicists define the gamma in
terms of the oersted. However the distinction is somewhat pedantic in geophysical
applications since the permeability of air is virtually one in cgs units. In accord
with most of the geophysical literature the term gauss has been retained in both
contexts.
1 Jacobs, Micropulsations
2 The Earth's Magnetic Field
1.2 Transient Magnetic Variations
The range of the spectrum of variations in the Earth's magnetic field
is enormous extending from a fraction of a second to more than 30 million
years (see Table 1.1). The causes of the longer period changes such as
the secular variation are internal: fluctuations with periods less than a:
few days are of external origin.
Table 1.1. Spectrum of geomagnetic phenomena
Period
Origin Comments
Seconds I Years
1017 3.109 ? ?
1016
1015 3.107 Internal and Dipolar Dipole Reversals
1014
1013
1012
1011
1010 300
Internal, Non-dipolar Secular variation
109 30
108
107
106 3'10-2 External Magnetic Storms
105 3.10-3 External Diurnal Variation
104
103
102
101 External Micropulsations
100
10-1 External Sub-acoustic
The records from any magnetic observatory show that on some days
all three components exhibit smooth and regular variations, while
on other days they are disturbed and show irregular fluctuations. At each
observatory a figure K between 0 and 9 is assigned to describe the mag
netic conditions for each period of three Greenwich hours 0-3, 3-6,
etc. K indices are a measure, for an interval of 3 hr, of the intensity of
magnetic disturbance as shown on the magnetograms of an observatory.
Thus they incorporate also any local effects such as the systematic diurnal
variations in geomagnetic activity. There is, therefore, a need for an
abstract of the individual K indices to express world-wide features of
geomagnetic disturbances over a 3-hr period. An average of all individual
K indices would not be satisfactory, owing to the inadequate geo
graphical distribution of magnetic observatories. Thus a new index
Transient Magnetic Variations 3
Kp has been designed to measure "planetary" variations in magnetic
activity. It is based on "standardized" indices which have been freed as
far as possible from local features. K indices are given to thirds as follows:
p
The intensity interval 1.5 to 2.5 for example, is divided equally into
three thirds designated as 2 -, 20, and 2 +. This provides 28 grades of
Kp from 00, 0+,1-,10,1 +, ... , 8+,9-,90.
The definition of Kp was chosen so that the whole range of geomag
netic activity from the quietest conditions to the most intense storm
could be expressed by a single digit and an affix. This was achieved by
a quasi-logarithmic relation between the amplitudes of disturbance
in the 3 hr interval and Kp. In order to obtain a linear scale, Kp may
be converted into a 3 hr equivalent planetary amplitude, ap' by means
of Table 1.2. At a standard station in about 50° geomagnetic latitude,
a may be thought of as the range of the most disturbed of the three
p
field components expressed in the unit 2 y, e. g. the range in a 3 hr interval
with K =4+ is 2 x 32, i.e. 64y. The average of the eight a values for
p
a day is called Ap.
In general day to day changes in the intensity of any disturbance
follow a similar pattern over a wide area; similarly, quiet conditions are
usually widespread. Most days show some magnetic disturbance,
but except in periods of very violent activity, it is found that the distur
bance D is superposed on a regular daily variation-called the solar
daily variation S. S is seen in its pure form on quiet days when it is denoted
by Sq. Each magnetic element is affected in a characteristic way by each
of the variations Sand D. For a detailed study of transient magnetic
phenomena results must be obtained from a number of observatories
widely distributed geographically. The type and range of variation also
vary throughout the year, showing a seasonal change and the range
and incidence of D also vary from year to year.
Table 1.2. Relation between Kp and apmagnetic indices
Kp 00 0+ 1- 10 1+ 2- 20 2+ 3- 30 3+ 4- 40 4+
ap 0 2 3 4 5 6 7 9 12 15 18 22 27 32
Kp 5- 50 5+ 6- 60 6+ 7- 70 7+ 8- 80 8+ 9- 90
ap 39 48 56 67 80 94 111 132 154 179 207 236 300 400
It is found that the intensity of magnetic disturbances increases
from low to high latitudes up to about magnetic latitude 65°, the latitude
of the auroral zones. Within these zones the intensity, although con-
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