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 •

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