The origin of the Earth's magnetic field Author: Stanislav Vrtnik Adviser: prof. dr. Janez Dolinšek March 13, 2007

The origin of the Earth's The origin of the Earth's magnetic fieldmagnetic field

Author: Stanislav VrtnikAuthor: Stanislav VrtnikAdviser: prof. dr. Janez DolinšekAdviser: prof. dr. Janez Dolinšek

March 13, 2007March 13, 2007

OutlineOutline

11 IntroductionIntroduction

2 2 Structure of the EarthStructure of the Earth

3 3 The self-excited dynamoThe self-excited dynamo

4 4 An Earth-like numerical dynamo modelsAn Earth-like numerical dynamo models

5 5 The approaching polarity reversalThe approaching polarity reversal

6 6 ConclusionsConclusions

11 IntroductionIntroduction

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

The mantle: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

2 Structure of the Earth2 Structure of the Earth

Crust

Not to scale

To scale

Upper mantle

Lower mantle

Liquid outer core

Solid inner core

The Crust:The Crust:

5-70 km tick

< 1% Earth’s volume

100 millions years old

Some grains are 4.4 billion years old

Part of the lithosphere divided on tectonic plates

TheThe outer outer corecore::

2180 km tickLiquid

Fe, Ni, some light elements

TheThe inner inner corecore::

Radius of 1220 kmSolid (Fe, Ni)

3 The self-excited dynamo3 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

2rB

22

rBdxxBU

2r

0

FaradFaradaay disk dynamoy disk dynamo

Magnetic flux through the disk:

Induced voltage:

http://en.wikipedia.org/wiki/Image:Larmor.jpg


Permanent magnet → replaced with solenoid

Magnetic flux through the disk:

IM

2

IMU

Induced voltage:

Electrical current is given by:

2

IMIR

dt

dIL

R - electrical resistivity of the complete circuit

Self-excited dynamo


Electrical current is given by:

2

IMIR

dt

dIL

Solution of the differential equation is:

R

2

ML/t

0eII

System becomes unstable when: M

Rc

2

( < 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

A)A)

B)B)

4 4 An Earth-like numerical dynamo modelsAn 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 m4.1 The magnetohydrodynamics Equationsagnetohydrodynamics Equations

Induction equation:

BBvt

B

2)( B

- magnetic field

v

- velocity

0/1 - the magnetic diffusivity interaction diffusion

0v magnetic field decreases exponentially (Earth = 20.000 years)

magnetic field is "frozen" into the conducting fluid

A)A)

B)B)

4.1 The m4.1 The magnetohydrodynamics Equationsagnetohydrodynamics Equations

Navier-Stokes equation:

- mass density

p - scalar pressure

- viscosity

fv)v(p)vvt

v( 2

31

f

- external forces: Lorentz force

gravity forceCoriolis forcebuoyancy force

To simulate the geodynamo we also need equations for: the gravity potentialthe heat flow

Model for geodynamo can have up to 10 equations

4.2 3D simulation of a geomagnetic field4.2 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


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 G.A. Glatzmaier && P.H. Roberts P.H. Roberts


Middle of reversal

•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

G.A. Glatzmaier & P.H. RobertsG.A. Glatzmaier & P.H. Roberts

500 yr before 500 yr after

a) b) c)


•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

G.A. Glatzmaier G.A. Glatzmaier && P.H. Roberts P.H. Roberts, Nature, 377, 203-209 , Nature, 377, 203-209 (1995) (1995)

5000 yr before Middle of reversal 4000 yr after


•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 G.A. Glatzmaier && P.H. Roberts P.H. Roberts, Nature, 377, 203-209 (1995), Nature, 377, 203-209 (1995)


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. RobertsG.A. Glatzmaier & P.H. Roberts

55 The approaching polarity reversal 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


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

•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

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

Direction of the dipole moment:


The magnetic dip poles: NorthNorth SouthSouth

2000

1960

1980

•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

•The northern magnetic dip pole velocity 40 km/year ( last few years)15 km/year (last century)

•The southern magnetic dip pole velocitydecreasing (now 10 km/year)

•The dip pole is simply an ill defined quantity


•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)

The overdue reversal:

6 6 ConclusionsConclusions

•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 youThank you

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The origin of the Earth's magnetic field Author: Stanislav Vrtnik Adviser: prof. dr. Janez Dolinšek March 13, 2007