Intro to magnetosphere (Chap. 8)
Homework #3 posted
Reading Chap. 8.1-8.3
1.
Geomagnetic field
a. Basic properties
b. Planetary dynamos
c. Variability
2.
Interaction with solar wind
a. Magnetopause
b. Structure of magnetosphere
Magnetic L-shell
Dipole magnetic field
For coordinates based on magnetic latitude and longitude:
So at the equator on the surface, B~31000 nT
At the pole, B~62000 nT
Equation for field-line:
We define L=shell as the radial distance in
Re where the field line crosses the equator.
Kallenrode, Chap. 8
Invariant latitude:
International Geomagnetic Reference Field: Field Magnitude
International Geomagnetic Reference Field (IGRF): Contours of total
intensity of magnetic field, based on spherical harmonic expansion to 10th
order. Note in particular minimum off South America: “South Atlantic
Anomaly.”
(http://www.geomag.bgs.ac.uk, British Geological Survey,
Lysak, 2010
see alsohttp://www.iugg.org/IAGA/iaga_pages/pubs_prods/igrf.htm)
International Geomagnetic Reference Field: Field Declination
IGRF model showing declination of field (angle with north). This is the angle
between a compass reading and true north. Note declination nearly zero in
Minnesota!
Lysak, 2010
International Geomagnetic Reference Field: Field Inclination
IGRF model showing inclination of field (angle with horizontal). Red
contours give field inclined downward, blue contour upward. Boundary line
gives magnetic equator.
Lysak, 2010
Earth’s magnetic field
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Variability of dipole moment
“Reversals have been documented as far back as 330 million years. During that
time more than 400 reversals have taken place, one roughly every 700,000
years on average. However, the time between reversals is not constant, varying
from less than 100,000 years, to tens of millions of years. In recent geological
times reversals have been occurring on average once every 200,000 years, but
the last reversal occurred 780,000 years ago.”
http://gsc.nrcan.gc.ca/geomag/nmp/reversals_e.php
Kallenrode, Chap. 8
Planetary dynamos
Kallenrode, Chap. 8
•
Same basic physics as we discussed for solar dynamo
•
•
Requires non-axisymmetric convection
To get convection, temperature gradient must exceed adiabatic
500 years before the middle of a magnetic dipole reversal, at the middle of the reversal, and
500 years after the middle
of the reversal.
Glatzmaier-Roberts geodynamo model
Reversal of Earth's Magnetic Field http://www.psc.edu/science/glatzmaier.html
Earth's magnetic field evolving for about 9,000 years before, during and after the simulated reversal. The outer circle indicates
the fluid outer core boundary; the inner circle, the solid inner core. The left hemisphere shows magnetic field contours directed
clockwise (green) and counterclockwise (yellow). The right hemisphere shows contours directed westward (blue) and eastward
(red), out of and into the plane of the paper.
The left hemisphere shows that the field penetrating the inner core is opposed in polarity to the outer core, a feature completely
unanticipated by theory. "The outer core polarity," explains Glatzmaier, "is continually trying to invade the inner core. Only when
the whole field almost decays away, however [middle], does it finally have a chance to diffuse in. Once it does, the opposite
polarity gets established. The inner core polarity is the stabilizing force, like an anchor, the slowest thing that can change."
Magnetic field lines are blue where the field is directed inward and yellow where
directed outward. The rotation axis of the model Earth is vertical and through
the center. A transition occurs at the core-mantle boundary from the intense,
complicated field structure in the fluid core, where the field is generated, to the
smooth, potential field structure outside the core. The field lines are drawn out
to two Earth radii.
http://www.es.ucsc.edu/~glatz/geodynamo.html
http://www.es.ucsc.edu/~glatz/geodynamo.html
Fig.1 A snapshot of the region (yellow) where the
fluid flow is the greatest. The core-mantle boundary is
the blue mesh; the inner core boundary is the red
mesh. Large zonal flows (eastward near the inner
core and westward near the mantle) exist on an
imaginary "tangent cylinder" due to the effects of
large rotation, small fluid viscosity, and the presence
of the solid inner core within spherical shell of the
outer fluid core.
A schematic image
illustrating the superrotation of the inner
core relative to the
Earth's surface (2
and 3 degrees
longitude per year
faster)
Simulated three-dimensional structure of Earth's magnetic field, with inward (blue) and outward (yellow) directed field lines.
Field lines extend two Earth radii from the core. The location of the core-mantle boundary is evident where the structure
becomes complex.
A snapshot of the simulated magnetic field structure within the
core, with lines blue where outside the solid inner core and yellow
where inside.
Convection of inner core determined from changes in the main field at the surface
http://geomag.org/info/coreflow.html
Love, Physics Today, 2008
Location of the north magnetic pole
http://gsc.nrcan.gc.ca/geomag/nmp/long_mvt_nmp_e.php
Prediction based on
observed changes
Have discussed magnetic field generated by convection in
conducting fluids. Where else?
http://geomag.org/info/ocean.html
Have discussed magnetic field generated by convection in
conducting fluids. Where else?
Chapman-Ferraro magnetosphere
(1930)
•
•
•
Trying to explain ‘sudden commencements’
Suggested neutral cloud of electrons and ions
from sun interacted with geomagnetic field
Remembered Maxwell had solved problem of
infinite conducting plane approaching a dipole
magnetic field-just get ‘image dipole’ due to
induced currents
‘Real’ Magnetopause
Simplest model is ‘closed’ magnetosphere
K!u 2 = B 2 /2µ 0
At boundary, current results in B opposed to field sunward of boundary;
doubles field inside boundary.
B = 2BE (RE /rMP ) 3
K!u 2 = [2BE (RE /rMP ) 3 ]2 /2µ 0
rMP = [2BE 2 RE 6 /K!u 2µ 0 ]1/ 6 = RE [2BE 2 /K!u 2µ 0 ]1/ 6
The numbers (assuming K ~ 2) :
rMP = [2x(31x10 !6 T) 2 /(1.3x10 !6 A /m 2 )(1.67x10 !27 kg)(5x10 6 m !3 )(450x10 3 m /s) 2 ]1/ 6 RE
rMP ~ 10RE
Russell et al.,
2011
http://www.phy6.org/Education; Russell, 1990
Discovery of the Magnetopause
Shape?
What happens when theta~90?
First observations of the magnetopause from Explorer 12 by Larry Cahill (UM
Prof!). Note drop in magnetic field magnitude (lowest curve) at about 8 RE.
Otto, Chap. 7
Chapman-Ferraro current
For upper case (charge separation), width is given by
d=
!e !i
For lower case (charge neutralize), width is given by
d= !i
Russell et al., Chap. 12
Russell, The Magnetopause, 1990