1. Ch 6 Solar Wind Interactions. Earth’s Magnetic Field
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2. Geomagnetism Paleomagnetism External Current Dipole Magnetic Field
Systems
Sq and L
Disturbance
Variations
Kp, Ap, Dst
Dipole Magnetic Field
Geomagnetic
Coordinates
B-L Coordinate system
L-Shells
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3. GEOMAGNETISM
According to Ampere’s Law, magnetic fields are produced by electric currents:
Earth's magnetic field is generated by movements of a conducting
"liquid" core, much in the same fashion as a solenoid. The term
"dynamo" or “Geodynamo” is used to refer to this process, whereby
mechanical motions of the core materials are converted into
electrical currents.
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4. The core motions are induced and controlled by
convection and rotation (Coriolis force). However,
the relative importance of the various possible driving
forces for the convection remains unknown:
heating by decay of radioactive elements
latent heat release as the core solidifies
loss of gravitational energy as metals solidify and migrate
inward and lighter materials migrate to outer reaches of
liquid core.
Venus does not have a significant magnetic field although its core
iron content is thought to be similar to that of the Earth.
Venus's rotation period of 243 Earth days is just too slow to produce
the dynamo effect.
Mars may once have had a dynamo field, but now its most prominent
magnetic characteristic centers around the magnetic anomalies in
Its Southern Hemisphere (see following slides).
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5. The main dipole field of the earth is thought to arise from a
single main two-dimensional
circulation.
Non-dipole regional anomalies (deviations from the main field) are thought to arise from various eddy motions in the outer layer of the liquid core (below the mantle).
Anomalies of lesser geographical extent (surface anomalies) are field irregularities caused by deposits of ferromagnetic materials in the crust. [The largest is the Kursk anomaly, 400 km south of Moscow].
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6. Note on ELECTRIC and MAGNETIC DIPOLES
An electrostatic dipole consists of closely-spaced positive and negative point charges, and the resulting electrostatic field is related to the electrostatic potential as follows:
By analogy, if we consider the magnetic field due to a current loop, the mathematical form for the magnetic field looks just like that for the electric field, hence the "magnetic dipole" analogy:
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7. The magnetic field at the surface of the earth is determined
mostly by internal currents with some smaller contribution due
to external currents flowing in the ionosphere and magnetosphere
In the current-free zone
Therefore
Combined with another Maxwell equation:
Yields
Laplace’s Equation
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8. The magnetic scalar potential V can be written as a spherical
harmonic expansion in terms of the Schmidt function, a particular
normalized form of Legendre Polynomial:
internal sources
external sources
r = radial distance = colatitude = east longitude
a = radius of earth (geographic polar coordinates)
= 0 for m > n
n = 1 --> dipole
n = 2 --> quadrapole
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9. Standard Components and Conventions
Relating to the Terrestrial Magnetic Field
“magnetic elements”
(H, D, Z)
(F, I, D)
(X, Y, Z)
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10. Surface Magnetic Field Magnitude (g) IGRF 1980.0
Max
.33 G
Min
.24 G
.67 G
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11. Surface Magnetic Field H-Component (g) IGRF 1980.0
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12. Surface Magnetic Field Vertical Component IGRF 1980.0
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13. Surface Magnetic Field Declination IGRF 1980.00°
20°
10° 0°
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14. Paleomagnetism
Natural remnant magnetism (NRM) of some rocks (and archeological samples) is a measure of the geomagnetic field at the time of their production.
Most reliable -- thermo-remnant magnetization -- locked into sample by cooling after formation at high temperature (i.e., kilns, hearths, lava).
Over the past 500 million years, the field has undergone reversals, the last one occurring about 1 million years ago.
See following figures for some measurements of long-term change in the earth's magnetic field.
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15. Equatorial field intensity in recent millenia, as deduced from measurements on archeological samples and recent observatory data.
~10 nT/year
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18. The B-L Coordinate System: Curves of Constant B and L
The curves shown
here are the
intersection of a
magnetic meridian
plane with surfaces
of constant B and
constant L (The
difference between
the actual field and
a dipole field cannot
be seen in a figure
of this scale. l
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23. External Current Systems
Currents flowing in the ionosphere and magnetosphere also induce magnetic field variations on the ground. These field variations generally fall into the categories of "quiet" and "disturbed". We will discuss the quiet field variations first.
The solar quiet daily variation (Sq) results principally from currents flowing in the electrically-conducting E-layer of the ionosphere.
Sq consists of 2 parts:
due to the dynamo action of tidal winds; and
due to current exhange between the
high-latitude ionosphere and the magnetosphere along field lines (see following figure).
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24. dawn
dusk
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25. Solar Quiet Current systems
between
current
density
contours
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26. DISTURBANCE VARIATIONS
In addition to Sq and L variations, the geomagnetic field often undergoes irregular or disturbance variations connected with solar disturbances. Severe magnetic disturbances are called magnetic storms.
Storms often begin with a sudden storm commencement (SSC), after which a repeatable pattern of behavior ensues.
However, many storms start gradually (no SSC), and sometimes an impulsive change (sudden impulse or SI) occurs, and no storm ensues.
disturbed value of a magnetic element (X, Y, H, etc.):
disturbed
field X = Xobs - Xq
= Dst() + DS()
t=t’
longitude
Disturbance local time
inequality (“snapshot” of
the X variation with
longitude at a particular
latitude)
storm-time variation, the
average of X around a
circle of constant latitude
t = storm time, time
lapsed from SSC
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27. Typical Magnetic Storm
SSC followed by an "initial" or "positive" phase lasting a few hours. During this phase the geomagnetic field is compressed on the dayside by the solar wind, causing a magnetopause current to flow that is reflected in Dst(H) > 0.
During the main phase Dst(H) < 0 and the field remains depressed for a day or two. The Dst(H) < 0 is due to a "westward ring current" around the earth, reaching its maximum value about 24 hours after SSC.
During recovery phase after ~24 hours, Dst slowly returns to ~0 (time scale
~ 24 hours).
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28. The daily Ap index, for a given day, is defined as
Various indices of activity have been defined to describe the degree of magnetic variability.
For any station, the range (highest and lowest deviation from regular daily variation) of X, Y, Z, H, etc. is measured (after Sq and L are removed); the greatest of these is called the "amplitude" for a given station during a 3-hour period. The average of these values for 12 selected observatories is the ap index.
The Kp index is the quasi-logarithmic equivalent of the ap index. The conversion is as follows:
The daily Ap index, for a given day, is defined as
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29. Ap and Solar Cycle Variation
Long-term records of annual sunspot numbers (yellow) show clearly
the ~11 year solar activity cycle
The planetary magnetic activity index Ap (red) shows the occurrence
of days with Ap
≥ 40
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33. cause damage to the transformer windings
Transformer Heating
Saturation of the transformer core produces extra eddy currents in the transformer core and structural supports which heat the transformer. The large thermal mass of a high voltage power transformer means that this heating produces a negligible change in the overall transformer temperature. However,localised hot spots can occur and
cause damage to the transformer windings
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37. How Geomagnetic Variations Affect Pipelines
Time-varying magnetic fields induce time-varying electric
currents in conductors.
Variations of the Earth's magnetic field induce electric currents in long conducting pipelines and surrounding soil. These time varying currents, named "telluric currents" in the pipeline industry, create voltage swings in the pipeline-cathodic protection rectifier system and make it difficult to maintain pipe-to-soil potential in the safe region.
During magnetic storms, these variations can be large enough to keep a pipeline in the unprotected region for some time, which can reduce the lifetime of the pipeline.
See example for the 6-7 April 2000 geomagnetic storm on the following page.
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38. 7.3 Ionospheres THE NEUTRAL ATMOSPHERE Hydrogen escape Thermospheric
Temperature and density structure
Hydrogen escape
Thermospheric
variations and
satellite drag
Mean wind structure
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39. Tropo
(Greek: tropos);
“change”
Lots of weather
Strato
(Latin: stratum);
Layered
Meso
(Greek: messos);
Middle
Thermo
(Greek: thermes);
Heat
Exo
(greek: exo);
outside
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40. Variation of the density in an atmosphere with constant
temperature (750 K).
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41. Vertical distribution of density and temperature for high solar activity (F10.7 = 250) at noon (1)
and midnight (2), and for low solar activity (F10.7 = 75) at noon (3) and midnight (4) according to
the COSPAR International Reference Atmosphere (CIRA) 1965.
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42. Atmospheric Compositions Compared
The atmospheres
of Earth, Venus and
Mars contain many
of the same gases,
but in very different
absolute and
relative abundances.
Some values are
lower limits only,
reflecting the past
escape of gas to
space and other
factors.
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43. Average Temperature Profiles
for Earth, Mars & Venus
Venus
night
day
Venus
Mars
Earth
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44. At km, the time constant for mixing is more efficient than recombination, so mixing due to turbulence and other dynamical processes must be taken into account (i.e., photochemical equilibrium does not hold).
Mixing transports
O down to lower
(denser) levels
where recomb-
ination proceeds
rapidly (the "sink"
for O).
After the O recombines to produce O2, the O2 is transported upward by turbulent diffusion to be photodissociated once again (the "source" for O).
O Concentration
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45. The most variable parts of the solar spectrum are absorbed above about 100 km
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46. Formation of Ionospheres
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47. HYDROSTATIC EQUILIBRIUM
If …..
n = # molecules per unit volume
m = mass of each particle
nm dh = total mass contained in
a cylinder of air (of unit
cross-sectional area)
Then, the force due to gravity on
the cylindrical mass = g nmdh
and the difference in pressure
between the lower and upper
faces of the cylinder balances
the above force in an equilibrium
situation:
P + dP dP P
nmgdh
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48. Assuming the ideal gas law holds,
Then the previous expression may be written:
where H is called the scale height
and
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49. This is the so-called hydrostatic law or barometric law.
Integrating, where
and z is referred to as the "reduced height" and the subscript zero refers to a reference height at h=0.
Similarly,
For an isothermal atmosphere, then,
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52. Absorption of Solar Radiation vs. Height and Species
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