Transcript Ch 6 Solar Wind Interactions - University of Massachusetts

Ch 6 Solar Wind Interactions.
Earth’s Magnetic Field
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, <2x10-4 of Earth's field. To first order these fields
are dipole fields. Consult Ch 3.8. Fig. 3.11.
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Geomagnetism
Paleomagnetism
Dipole Magnetic Field
External Current
Systems
Geomagnetic
Coordinates
Sq and L
B-L Coordinate system
Disturbance
Variations
L-Shells
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, whereby
mechanical 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 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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•
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:
 E  0  E  
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:
 B  0

B  V
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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
B  1 J 0
o
Therefore
B V
Combined with another
Maxwell equation:
B 0
Yields
2
 V 0
Laplace’s Equation
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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:
 n m
V a   Pn cos 
n1m0


= 0 for m > n
n = 1 --> dipole
n = 2 --> quadrapole
an1 m
m
  gn cosm  hn sin m 

 r
n
a 
r 

A cosm  B sin m 

m
n
r = radial distance
a = radius of earth
m
n
internal sources
external sources
= colatitude = east longitude
(geographic polar coordinates)
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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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Surface Magnetic Field Magnitude (g)
IGRF 1980.0
.61 G
Max
.33 G
Min
.24 G
.67 G
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Surface Magnetic Field H-Component (g)
IGRF 1980.0
.025 G
.40 G
.33 G
.13 G
.025 G
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Surface Magnetic Field Vertical Component
IGRF 1980.0
.61 G
0.0 G
0.0 G
0.0 G
.68 G
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Surface Magnetic Field Declination
IGRF 1980.0
10°
0°
20°
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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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The dipole field :


M
B  R,    3 2sin  rˆ  cos  λˆ
R
Values for the diple moments M of the different planets are given
in Table 7.1 of Cravens.



M
B  R,    3 2sin  rˆ  cos  λˆ  2sin  rˆ  cos  λˆ
R
M
B  R,    3 1  3sin 2   BE 1  3sin 2 
 3.68 
R
Using the differential arc lengths in spherical coordinates and the
vector components BR and B , one gets the equation of a dipole
 3.69 
field line: cos 2   R R0
where R 0 is the geocentric distance of the field line at the equator
( =0). One usually writes R0  LRE .
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Then R  LRE cos 2  , and
M
M
2
2
B  L,    3 1  3sin   3 3
1

3sin

6
R
RE L cos 
BE 1  3sin 2 
B  L,    3
L
cos 6 
 3.71
In the next figure shows:
R  
RE
 L cos 2  for L=2,3,4,...30
B  R,    const  0.2,0.5, ... 0.001 Orstedt
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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 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.

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7.2 Location of the Magnetopause for Earth
On the dayside at the subsolar point, the thermal pressure in the
magnetosheath just outside the magnetopause (MP) must equal the
B2
magnetic pressure
in the magnetosphere just inside the MP. We
2 0
approximate here by neglecting the IMF in the magnetosheath,
and the thermal pressure in the magnetosphere. Let us further
2
assume that the upstream solar wind dynamic pressure SW uSW
(see Section 4.6.6) gets "deshocked" at the bow shock and converted
into thermal pressure p:
 7.1
2
p  0.85 SW uSW
For equilibrium: p ( MSheath)  p  Msphere 
0.85  u
2
SW SW
2
BMP

2 0
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2
0.85SW uSW
2
BMP

2 0
For a first cut, we consider a dipole field to find the radius R MP .
3
BMP
 RE 
M
M
2
2
 3 1  3sin   BE 
where
B

1

3sin
.

E
3
RMP
RE
 RMP 
Then: 0.85 u
2
SW SW
B  RE 



20  RMP 
2
E
16

RMP 
B

2 
RE  20  0.85SW uSW

2
E
6
Chapman-Ferraro 1931
 7.6 
SW  nSW m p  7 106  m 3  1.67 1027  kg   1020 kg / m3
2
uSW  4 105 m / s  SW uSW
 2 109 N / m 2
 RMP  7.5 RE at the sub-UML_reinisch_85.511_Ch7
solar point.
20
Measurements show that RMP  10 RE , 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, forming a current sheet. A current
sheet K (A/m) has a magnetic field:
1
B K  0 K  nˆ
2
where nˆ is the normal to the plane of the current
sheet. The current direction is such that it cancels the Earth's dipole
field for R > R MP , and adds to the field for R < R MP :
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For R  RMP :
B  Bdipole  BK  0 (BK cancels Bdipole outside)
 BK  Bdipole .
For R  RMP :
B  Bdipole  BK =2 Bdipole
Then RMP  21 3  7.5 RE  9.5 RE . Better!
How big is the surface current K?
1
The magnetic field of a current sheet K is BK  0 K .
2
3
 RE 
1
4
0 K  Bdipole  BE 
for

=
0;
B

0.5

10
T

E
2
 9.5 RE 
2 BE
104
2
K
 3

8

10
A/ m
7
1000 0 10 4 10
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:
Sqo
Sqp
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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p
Sq
o
Sq
dawn
dusk
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Solar Quiet Current systems
Sqo
Sq  Sqo  Sqp
10,000 A
between
current
density
contours
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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
storm-time variation, the
average of X around a
circle of constant latitude
=
Xobs - Xq
=
Dst(t) + DS(t)
longitude
Disturbance local time
inequality (“snapshot” of
the X variation with
longitude at a particular
latitude)
t = storm time, time
lapsed from SSC
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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
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Ap   ap
n1 28
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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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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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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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 an
atmosphere with constant
temperature (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
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the COSPAR International Reference Atmosphere (CIRA) 1965.
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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Average Temperature Profiles
for Earth, Mars & Venus
Mars
Venus
night
day
Venus
Earth
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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 recombination proceeds
rapidly (the "sink"
for O).
O Concentration
After the O recombines to produce O2, the O2 is transported upward
by turbulent diffusion to be photodissociated once again (the
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"source" for O).
The most variable parts of the solar spectrum are
absorbed above about 100 km
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Formation of Ionospheres
Photo ionization: If h  I M
( I M  10 to 20 eV )
h  M  M   e  E photoelectron
HW : (1) Show that λ <  100nm.
In the terrestrial ionosphere:
h  N 2  N  e  E photoelectron

2
h  O2  O  e  E photoelectron

2
h  O  O  e  E photoelectron

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HYDROSTATIC EQUILIBRIUM
If …..
n = # molecules per unit volume
P + dP
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
dP
nmgdh
P
and the difference in pressure
between the lower and upper
faces of the cylinder balances
the above force in an equilibrium
situation:
P dP  P  nmgdh
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
dP
 nmg
dh
Assuming the ideal gas law holds,
P  nkT  RT
R*
R
m
Then the previous expression may be written:
where H is called the scale height
and
kT
RT
H

mg
g
1 dP
1

P dh
H
R2
E
g  g(0)
RE  h2
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This is the so-called hydrostatic law or barometric law.
Integrating,
PPe
0
z
where
z dh
z
0H
and z is referred to as the "reduced height" and the subscript zero
refers to a reference height at h=0.
 
To  z
nn
e
o T
Similarly,
For an isothermal atmosphere, then,
nn e
o
h
H
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  o e
h
H
49
PPe
o
h
H
Exponential decrease of photon flux
At top of atmosphere F  F .
dF    nn F ds    F nn dz sec 
The photoabsorption cross section   1017 cm 2  1013 m2



F  z   F exp  sec     nn dz   F e t  ,
z



where t   z   sec     nn  z  dz
z
HW: (2) Show that for an isothermal atmosphere τ λ  z  =σ λ n n  z  H n secχ,
where H n is the neutral scale height.
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The production rate at height z is
P ( z )    nn F  z   F  nn  z  e
t   z 
.
In an isothermal atmosphere, if we assume equilibrium ,
i.e. production Pe = loss Le , and Le  kd ne2 :
1

ne  z   ne  zm  exp  1    sec  e    ,
2

z  zm
 
Hn
Chapman 1932
zm is the height of maximum production (t  1).
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Absorption of Solar Radiation vs. Height and Species
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