uml_reinisch_85.511_ch71 ch 6 solar wind interactions. earth’s magnetic field
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UML_reinisch_85.511_Ch7 1
Ch 6 Solar Wind Interactions.Earth’s Magnetic Field
-4
The solar wind interacts with the planets and comets in the solar syatem.
Most planets have a magnetic field (see Table 7.1). Mercury's and and
Mars's fields are tiny, <2x10 of Earth's field. To first order these fields
are dipole fields. Consult Ch 3.8. Fig. 3.11.
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GeomagnetismDipole Magnetic Field
Geomagnetic Coordinates
B-L Coordinate system
L-Shells
Paleomagnetism
External CurrentSystems
Sq and L
Disturbance Variations
Kp, Ap, Dst
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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, wherebymechanical motions of the core materials are converted into electrical currents.
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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 coreiron 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 prominentmagnetic characteristic centers around the magnetic anomalies inIts Southern Hemisphere (see following slides).
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• 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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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:
E 0
E
B 0
B V
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In the current-free zone
Therefore
Combined with another Maxwell equation:
Yields
Laplace’s Equation
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
1 0o
B J
B
V
B 0
2V 0
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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 longitudea = radius of earth (geographic polar coordinates)
ar
n1
gnm cosm hn
m sin m
ar
n
Anm cosm Bn
m sin m
V a Pnmm0
n
n1
cos
n = 1 --> dipolen = 2 --> quadrapole
= 0 for m > n
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“magnetic elements”
(H, D, Z)(F, I, D)(X, Y, Z)
Standard Components and Conventions Relating to the Terrestrial Magnetic Field
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Max
Min.24 G
Surface Magnetic Field Magnitude () IGRF 1980.0
.61 G
.33 G
.67 G
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Surface Magnetic Field H-Component () IGRF 1980.0
.13 G
.33 G
.025 G
.40 G
.025 G
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Surface Magnetic Field Vertical Component IGRF 1980.0
0.0 G
0.0 G0.0 G
.61 G
.68 G
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Surface Magnetic Field Declination IGRF 1980.0
10° 20°0°
0°
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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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Equatorial field intensity in recent millenia, as deduced from measurements on archeological
samples and recent observatory data.
~10 nT/year
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3
3
2 23
ˆˆ, 2sin cos
Values for the diple moments M of the different planets are given
in Table 7.1 of Cravens.
ˆ ˆˆ ˆB , 2sin cos 2sin cos
B , 1 3sin 1 3sin 3.68
:
E
MR
R
MR
R
MR B
R
B r λ
r λ r λ
The dipole field
R
20
0
Using the differential arc lengths in spherical coordinates and the
vector components B and B , one gets the equation of a dipole
field line: cos 3.69
where R is the geocentric distance of the
R R
0
field line at the equator
( =0). One usually writes . ER LR
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2
2 23 3 3 6
2
3 6
2
Then cos , and
B , 1 3sin 1 3sincos
1 3sinB , 3.71
cos
In the next figure shows:
cos for L=2,3,4,...30
, 0.2,0.5, ... 0.001 Orstedt
E
E
E
E
R LR
M ML
R R L
BL
L
RL
R
B R const
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The B-L Coordinate System:Curves of Constant B and L
The curves shown here are the intersection of a magnetic meridianplane with surfaces of constant B and constant L (The difference betweenthe actual field and a dipole field cannot be seen in a figure of this scale.
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2
0
On the dayside at the subsolar point, the thermal pressure in the
magnetosheath just outside the magnetopause (MP) must equal the
magnetic pressure in 2
B
7.2 Location of the Magnetopause for Earth
the magnetosphere just inside the MP. We
approximate here by neglecting the IMF in the magnetosheath,
and the thermal pressure in the magnetosphere. Let us further
assume that the upstream solar wind
2SW
2SW
22
SW0
dynamic pressure
(see Section 4.6.6) gets "deshocked" at the bow shock and converted
into thermal pressure p:
0.85 7.1
For equilibrium: ( )
0.852
SW
SW
MPSW
u
p u
p MSheath p Msphere
Bu
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22
SW0
MP
3
2 23 3
622
SW0
2
0 S
0.852
For a first cut, we consider a dipole field to find the radius R .
1 3sin where 1 3sin .
Then: 0.85 2
2 0.85
MPSW
EMP E E
MP MP E
E ESW
MP
MP E
E
Bu
M R MB B B
R R R
B Ru
R
R B
R
1 6
2W
6 3 27 20 3SW SW
5 2 9 2SW SW
7.6
7 10 1.67 10 10 /
4 10 /
Cha
2 10 /
7.5 at the
pman-Ferra
sub-
ro 1931
solar point.
SW
p
SW
MP E
u
n m m kg kg m
u m s u N m
R R
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Measurements show that 10 , so what is wrong?
Magnetosheath protons and electrons impinging on the "edge" of
Earth's magnetosphere (see Fig. 7.1) are deflected (gyrated) in
opposite direction, for
MP ER R
K 0
ming a . A current
sheet (A/m) has a magnetic field:
1ˆ
2ˆwhere is the normal to the plane of the current
sheet. The current direction is such that it cancels the Earth's dipol
current sheet
K
B K n
n
MP MP
e
field for R > R , and adds to the field for R < R :
UML_reinisch_85.511_Ch7 22
1 3
For : 0 ( cancels outside)
.
For : =2
Then 2 7.5 9.5 . Better!
The magnetic field of a c
How big i
urrent s
s the surface current K
hee
?
MP dipole K K dipole
K dipole
MP dipole K dipole
MP E E
R R B B B B B
B B
R R B B B B
R R R
0
3
40
42
3 70
1t K is .
2
1 for = 0; 0.5 10
2 9.5
2 108 10 /
1000 10 4 10
K
Edipole E E
E
E
B K
RK B B B T
R
BK A m
K 100mA/m
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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).
Sqo
Sqp
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Sqo
Sqp
dusk
dawn
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Sqo
Sq Sqo Sq
p
Solar Quiet Current systems
10,000 Abetweencurrentdensitycontours
UML_reinisch_85.511_Ch7 26 = storm time, time lapsed from SSC
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.):
disturbedfield X = Xobs - Xq
= Dst() + DS()storm-time variation, theaverage of X around acircle of constant latitude
Disturbance local timeinequality (“snapshot” ofthe X variation with longitude at a particularlatitude)
longitude
t=t’
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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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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
Ap apn1
8
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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 occurrenceof days with Ap ≥ 40
Ap and Solar Cycle Variation
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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 andcause damage to the transformer windings
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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.
How Geomagnetic Variations Affect Pipelines
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7.3 Ionospheres THE NEUTRAL ATMOSPHERE
• Temperature and density structure
• Hydrogen escape
• Thermospheric variations and satellite drag
• Mean wind structure
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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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Variation of the density in anatmosphere with constanttemperature (750 K).
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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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Atmospheric Compositions Compared
The atmospheresof Earth, Venus andMars contain manyof the same gases,but in very differentabsolute andrelative abundances.Some values arelower limits only, reflecting the pastescape of gas tospace and otherfactors.
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MarsVenus
Earth
night
day
VenusAverage Temperature Profiles for Earth, Mars & Venus
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At 80-100 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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The most variable parts of the solar spectrum are absorbed above about 100 km
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Formation of Ionospheres
2 2
2 2
Photo ionization: If ( 10 to 20 )
In the terrestrial ionosphere:
(1)
M M
photoelectron
photoelectron
photoelectron
photoelectron
h I I eV
h M M e E
h N N e E
h O O e E
h O O e E
HW : Show that λ < 100nm.
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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:
dP
nmgdh
P + dP
P
PdP Pnmgdh
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Assuming the ideal gas law holds,
Then the previous expression may be written:
where H is called the scale height and
dP
dh nmg
P nkT RT
R R*
m
1
P
dP
dh
1
H
H kT
mg
RT
g
g g(0)RE
2
RE h 2
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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,
P P0e z
z dh
H0
z
T zon n eo T
hH PPeo
h
Hn n eo
hHeo
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17 2 13 2
At top of atmosphere .
sec
The photoabsorption cross section 10 10
exp sec ,
where sec
n n
n
z
n
F F
dF n F ds F n dz
cm m
F z F n dz F e
z n
Exponential decrease of photon flux
λ λ n n
n
HW: (2) Show that for an atmosphere τ z =σ n z H secχ,
where H is the neutral scale height.
z
z dz
isothermal
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2
The production rate at height z is
( ) .
In an isothermal atmosphere, if we assume equilibrium ,
i.e. , and :
1exp 1 sec ,
2
zn n
e d e
e e m
P z n F z F n z e
L k n
n z n z e
e eproduction P = loss L
is the height of maxi
Chapman 1932
mum production ( 1).
m
n
m
z z
H
z
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Absorption of Solar Radiation vs. Height and Species