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The origin of the Earth's
magnetic field
Author: Stanislav Vrtnik
Adviser: prof. dr. Janez Dolinšek
March 13, 2007
Outline
1 Introduction
2 Structure of the Earth
3 The self-excited dynamo
4 An Earth-like numerical dynamo models
5 The approaching polarity reversal
6 Conclusions
1 Introduction
Geomagnetic field is generated in Earth’s core
Temperatures > 3000 K;
above Curie point (Tc(Fe) = 1043 K; Tc(Ni) = 627 K )
Magnetic field is generated by electrical current
Unsustained electrical current would dissipate within 20.000 years
Paleomagnetic records (ancient field recorded in sediment and lavas )
Earth’s magnetic field exists millions of years
Mechanism that regenerates electrical currents (self-excited dynamo)
The polarity reversal
Earth will lose magnetic shield for high-energy particles
2 Structure of the Earth
Not to scale
The
The outer
mantle:
Crust:core:
Crust
2180
2900
5-70 km
km tick
thick
Liquid
Silicate
< 1% Earth’s
rocks volume
(with Fe, Mg)
Fe, Ni, some light elements
Solid,
100 millions
but ductile
years old
can inner
flow oncore:
large timescale
The
Some grains are 4.4 billion
Convection
years old
of the
Radius
of 1220
kmmaterial
moves
tectonic
Solid
(Fe,
Ni) plates
Part of the lithosphere
Pressure
dividedincrease
on tectonic
withplates
depth
and change viscosity
Upper mantle
Lower mantle
Liquid outer core
Solid inner core
To scale
Lower mantle flow less easily
3 The self-excited dynamo
Self-excited dynamo model was first proposed by Sir Joseph Larmor in 1919
Magnetic instability
→ (perturbation of the field is exponentially amplified)
Simple experiment with mechanical disk device
Magnetic flux through the disk:
  B r 2
Induced voltage:
r
Faraday disk dynamo
U   B    x dx 
0
  Br2
2
 

2 
3 The self-excited dynamo
Permanent magnet → replaced with solenoid
Magnetic flux through the disk:
  M I
Induced voltage:
M   I
U
2
Electrical current is given by:
L
Self-excited dynamo
dI
M   I
 R I 
dt
2
R - electrical resistivity of the complete circuit
3 The self-excited dynamo
Electrical current is given by:
dI
M   I
L  R I 
dt
2
System becomes unstable when:
A)
B)
Solution of the differential equation is:
I  I0e
 M 

t / L
R 
 2

2  R
  c 
M
( < C) the resistivity will damp any initial magnetic perturbation
( < C) the system undergoes a bifurcation
→an initial perturbation of the field will be exponentially amplified
4 An Earth-like numerical dynamo models
Nonlinear three-dimensional model is needed
Geodynamo operates in ‘strong field’ regime:
nonlinear magnetic Lorentz force ≈ Coriolis force
→ Lorentz force cannot be treated as perturbation
→ nonlinear numerical computation is required
Cowling’s theorem:
self-sustained magnetic field produced by a dynamo cannot be axisymmetric
→ no 2D solution can be sought
→ problem has to be investigated directly in 3D
4.1 The magnetohydrodynamics Equations
Induction equation:


B
 
2
   (v  B )   B
t

B - magnetic field

v - velocity
 1/0 - the magnetic diffusivity
interaction

A) v  0
B)
 
diffusion
magnetic field decreases exponentially (tEarth = 20.000 years)
magnetic field is "frozen" into the conducting fluid
4.1 The magnetohydrodynamics Equations
Navier-Stokes equation:


v  

2
1
 (  v  v )  p  3  (   v )   v  f
t

- mass density
p
- scalar pressure

- viscosity

f - external forces:
To simulate the geodynamo we also need equations for:
Model for geodynamo can have up to 10 equations
Lorentz force
gravity force
Coriolis force
buoyancy force
the gravity potential
the heat flow
4.2 3D simulation of a geomagnetic field
Glatzmaier-Roberts model:
with the dimensions, rotate rate, heat flow and the
material properties of the Earth’s core
Time step: 20 days
Simulation now spans more than 300.000
years
The simulation took several thousand CPU
hours on the Cray C-90 supercomputer
Yellow - where the fluid flow is the
greatest.
The core-mantle boundary - blue
the inner core boundary - red
G.A. Glatzmaier and P.H. Roberts
4.2 3D simulation of a geomagnetic field
Magnetic field is similar to the Earth's field:
•Intensity of the dipole moment
•A dipole dominated structure
•Westward drift of the non-dipolar field at the
surface (0.2° per year)
G.A. Glatzmaier & P.H. Roberts
4.2 3D simulation of a geomagnetic field
•36.000 years into the simulation magnetic dipole underwent polarity reversal
•over a period of a 1000 years.
•the magnetic dipole moment decreases down to 10%
•recovered immediately after
•consistent with the paleomagnetic records
500 yr before
a)
G.A. Glatzmaier & P.H. Roberts
500 yr after
Middle of reversal
b)
c)
4.2 3D simulation of a geomagnetic field
•The longitudinal average of the 3D magnetic field (out to the surface)
•Left – lines of force of the poloidal part of the field
•Right – contours of the toroidal part of the field
•Red (blue) contours – eastward (westward) directed toroidal field
•Green (yellow) lines – clockwise (anticlockwise) poloidal field
5000 yr before
Middle of reversal
G.A. Glatzmaier & P.H. Roberts, Nature, 377, 203-209 (1995)
4000 yr after
4.2 3D simulation of a geomagnetic field
•The radial component of the magnetic field (Hammer projection)
•Upper plots (surface); lower plots (core-mantle boundary)
•Red (blue) contours represent outward (inward) directed field
•Intensity at the surface is multiplied by 10
G.A. Glatzmaier & P.H. Roberts, Nature, 377, 203-209 (1995)
4.2 3D simulation of a geomagnetic field
Rotation of the inner core relative to the surface:
•In simulation rotates 2° to 3° per year faster than at the surface
•Motivated seismologists to search for evidence (0.3° to 0.5° year faster )
•The field couples the inner core to the eastward flowing fluid
•analogous to a synchronous electric motor
G.A. Glatzmaier & P.H. Roberts
5 The approaching polarity reversal
•Study of the geodynamo has received considerable attention in the press
•Concerns of an approaching polarity reversal
•The magnetic field protects Earth’s surface from high-energy particles
•Sun wind, cosmic rays from deep space
•When the field switches polarity, its strength can drop to below 10%
• for few 1000 years.
•with potentially disastrous consequences for: the atmosphere, the
climate and life.
•These concerns are supported by observational facts
5 The approaching polarity reversal
The dipole moment:
•The first term of the spherical harmonic expansion
•It can be recovered in the past (paleomagnetic records)
•Measurements show rapid and steady decrease
of the geomagnetic dipole moment
•Primary motive for pondering the possibility of an
approaching reversal
•The geomagnetic field amplitude is a fluctuating quantity
• The present dipole moment is still significantly
higher than its averaged value
•Over the last polarity interval and the three preceding ones
Date/Period
Dipole moment
In 2005
7.776 x 1022 A m2
In 2000
7.779 x 1022 A m2
Over the last 800.000 years
7.5 ± 1.7 x 1022 A m2
Over 0.8-1.2 million years
5.3 ± 1.5 x 1022 A m2
5 The approaching polarity reversal
Direction of the dipole moment:
•Tilt angle according to the axis of rotation
•The angle is rapidly increasing toward 90°
•Opposite of what is expected for a reversal
5 The approaching polarity reversal
The magnetic dip poles:
•The two places on Earth
North
South
1960
•Horizontal component of the field is zero
•Local objects
•They are affected by all components in a
spectral expansion
1980
•Move independently of one another
•The northern magnetic dip pole velocity
40 km/year ( last few years)
15 km/year (last century)
•The southern magnetic dip pole velocity
decreasing (now 10 km/year)
•The dip pole is simply an ill defined quantity
2000
5 The approaching polarity reversal
The overdue reversal:
•The last reversal dates back some 800.000 years
•7 reversal in last 2 million years
•The reversal rate is not constant
•Average over few million years is 1 per million years
•Maximum value is 6 reversals per million years
•Maximum: Superchrones (10 millions years)
6 Conclusions
•Numerical models are successful but:
restricted to a very remote parameter regime
viscous force is much larger than are in the liquid core
•Experimental fluid dynamos were created (1999 in Latvia and Germany)
the flows were extremely confined
•Dynamo action works on a large variety of natural bodies
planets in the solar system (Venus and Mars excepted)
Sun (reverses with a relatively regular period of 22 years)
galaxies exhibit their own large-scale magnetic field
•Evidence for an imminent reversal remains rather weak
•The typical timescale for a reversal is of the order of 1000 years
Thank you