The origin of the Earth's magnetic field

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The origin of the Earth's magnetic field
Author Stanislav Vrtnik Adviser prof. dr. Janez
Dolinšek March 13, 2007
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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
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1 Introduction
Geomagnetic field is generated in Earths core
Temperatures gt 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 )
Earths 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
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2 Structure of the Earth
Not to scale
The mantle 2900 km thick Silicate rocks (with
Fe, Mg) Solid, but ductile can flow on large
timescale Convection of the material moves
tectonic plates Pressure increase with depth and
change viscosity Lower mantle flow less easily
The Crust 5-70 km tick lt 1 Earths
volume 100 millions years old Some grains are
4.4 billion years old Part of the lithosphere
divided on tectonic plates
The outer core 2180 km tick Liquid Fe, Ni,
some light elements The inner core Radius of
1220 km Solid (Fe, Ni)
Crust
Upper mantle
Lower mantle
Liquid outer core
Solid inner core
To scale
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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
Induced voltage
Faraday disk dynamo
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3 The self-excited dynamo
Permanent magnet ? replaced with solenoid
Magnetic flux through the disk
Induced voltage
Electrical current is given by
Self-excited dynamo
R - electrical resistivity of the complete
circuit
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3 The self-excited dynamo
Electrical current is given by
Solution of the differential equation is
System becomes unstable when
(W lt WC) the resistivity will damp any initial
magnetic perturbation
A)
(W lt WC) the system undergoes a bifurcation ?an
initial perturbation of the field will be
exponentially amplified
B)
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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
Cowlings 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
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4.1 The magnetohydrodynamics Equations
Induction equation
- magnetic field
- velocity
- the magnetic diffusivity
interaction
diffusion
A)
magnetic field decreases exponentially (tEarth
20.000 years)
B)
magnetic field is "frozen" into the conducting
fluid
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4.1 The magnetohydrodynamics Equations
Navier-Stokes equation
- mass density
- external forces
Lorentz force gravity force Coriolis
force buoyancy force
- scalar pressure
- viscosity
To simulate the geodynamo we also need equations
for
the gravity potential the heat flow
Model for geodynamo can have up to 10 equations
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4.2 3D simulation of a geomagnetic field
Glatzmaier-Roberts model with the dimensions,
rotate rate, heat flow and the material
properties of the Earths 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
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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
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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
500 yr after
Middle of reversal
a)
b)
c)
G.A. Glatzmaier P.H. Roberts
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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
4000 yr after
G.A. Glatzmaier P.H. Roberts, Nature, 377,
203-209 (1995)
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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)
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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
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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 Earths 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

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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
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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

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5 The approaching polarity reversal
South
North
The magnetic dip poles
1960

• The two places on Earth
• Horizontal component of the field is zero
• Local objects
• They are affected by all components in a
• spectral expansion
• Move independently of one another

1980

• 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
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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)

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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

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Thank you