Editing Earth's magnetic field (section)

=== Earth's core and the geodynamo ===
The Earth's magnetic field is believed to be generated by electric currents in the conductive iron alloys of its core, created by convection currents due to heat escaping from the core.

[[File:Dynamo Theory - Outer core convection and magnetic field geenration.svg|thumb|A schematic illustrating the relationship between motion of conducting fluid, organized into rolls by the Coriolis force, and the magnetic field the motion generates.<ref>{{cite web |title=How does the Earth's core generate a magnetic field? |work=USGS FAQs |publisher=United States Geological Survey |url=http://www.usgs.gov/faq/?q=categories/9782/2738 |access-date=21 October 2013 |url-status=dead |archive-url=https://web.archive.org/web/20150118213104/http://www.usgs.gov/faq/?q=categories%2F9782%2F2738 |archive-date=18 January 2015 }}</ref>]]

The Earth and most of the planets in the Solar System, as well as the Sun and other stars, all generate magnetic fields through the motion of electrically [[Electrical conductor|conducting]] fluids.<ref name="Weiss">{{cite journal |last=Weiss |first=Nigel |title=Dynamos in planets, stars and galaxies |journal=Astronomy and Geophysics |year=2002 |volume=43 |issue=3 |pages=3.09–3.15 |doi=10.1046/j.1468-4004.2002.43309.x|bibcode=2002A&G....43c...9W|doi-access=free }}</ref> The Earth's field originates in its core. This is a region of iron alloys extending to about 3400&nbsp;km (the radius of the Earth is 6370&nbsp;km). It is divided into a solid [[Earth's inner core|inner core]], with a radius of 1220&nbsp;km, and a liquid [[Earth's outer core|outer core]].<ref>{{cite journal  |last=Jordan |first=T. H. |title=Structural Geology of the Earth's Interior |journal=Proceedings of the National Academy of Sciences |year=1979 |volume=76 |issue=9 |pages=4192–4200 |doi=10.1073/pnas.76.9.4192|bibcode=1979PNAS...76.4192J |pmid=16592703 |pmc=411539|doi-access=free }}</ref> The motion of the liquid in the outer core is driven by heat flow from the inner core, which is about {{convert|6000|K}}, to the [[core-mantle boundary]], which is about {{convert|3800|K}}.<ref>{{cite news |title=Earth's Center Is 1,000 Degrees Hotter Than Previously Thought, Synchrotron X-Ray Experiment Shows |date=25 April 2013 |newspaper=ScienceDaily |author=European Synchrotron Radiation Facility |url=https://www.sciencedaily.com/releases/2013/04/130425142355.htm |access-date=21 October 2013}}</ref>  The heat is generated by potential energy released by heavier materials sinking toward the core ([[planetary differentiation]], the [[iron catastrophe]]) as well as decay of [[radioactive]] elements in the interior.  The pattern of flow is organized by the rotation of the Earth and the presence of the solid inner core.<ref name="Buffett2000">{{cite journal |first1=B. A. |last1=Buffett |title=Earth's Core and the Geodynamo |journal=Science |volume=288 |issue=5473 |year=2000 |pages=2007–2012 |doi=10.1126/science.288.5473.2007 |pmid=10856207 |bibcode=2000Sci...288.2007B }}</ref>

The mechanism by which the Earth generates a magnetic field is known as a [[geodynamo]].<ref name="Weiss" /> The magnetic field is generated by a feedback loop: current loops generate magnetic fields ([[Ampère's circuital law]]); a changing magnetic field generates an electric field ([[Faraday's law of induction|Faraday's law]]); and the electric and magnetic fields exert a force on the charges that are flowing in currents (the [[Lorentz force]]).<ref>{{cite book |last=Feynman |first=Richard P. |author-link=Richard Feynman |title=The Feynman lectures on physics |year=2010 |publisher=BasicBooks |location=New York |isbn=978-0-465-02494-0 |pages=13–3, 15–14, 17–2 |edition=New millennium}}</ref> These effects can be combined in a [[partial differential equation]] for the magnetic field called the ''magnetic induction equation'',

<math display="block">\frac{\partial \mathbf{B}}{\partial t} = \eta \nabla^2 \mathbf{B} + \nabla \times (\mathbf{u} \times \mathbf{B}), </math>

where {{math|'''u'''}} is the velocity of the fluid; {{math|'''B'''}} is the magnetic B-field; and {{math|1=''η'' = 1/''σμ''}} is the [[magnetic diffusivity]], which is the [[multiplicative inverse|reciprocal]] of the product of the [[electrical conductivity]] {{math|σ}} and the [[Permeability (electromagnetism)|permeability]] {{math|μ}} .<ref name=MMMch8>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 8}}</ref>  The term {{math|∂'''B'''/∂''t''}} is the [[partial derivative]] of the field with respect to time; {{math|∇<sup>2</sup>}} is the [[Laplace operator]], {{math|∇×}} is the [[curl (mathematics)|curl operator]], and {{math|×}} is the [[vector product]].

The first term on the right hand side of the induction equation is a [[diffusion]] term. In a stationary fluid, the magnetic field declines and any concentrations of field spread out. If the Earth's dynamo shut off, the dipole part would disappear in a few tens of thousands of years.<ref name="MMMch8" />

In a perfect conductor (<math>\sigma = \infty\;</math>), there would be no diffusion. By [[Lenz's law]], any change in the magnetic field would be immediately opposed by currents, so the flux through a given volume of fluid could not change. As the fluid moved, the magnetic field would go with it. The theorem describing this effect is called the ''frozen-in-field theorem''. Even in a fluid with a finite conductivity, new field is generated by stretching field lines as the fluid moves in ways that deform it. This process could go on generating new field indefinitely, were it not that as the magnetic field increases in strength, it resists fluid motion.<ref name="MMMch8" />

The motion of the fluid is sustained by [[convection]], motion driven by [[buoyancy]]. The temperature increases towards the center of the Earth, and the higher temperature of the fluid lower down makes it buoyant. This buoyancy is enhanced by chemical separation: As the core cools, some of the molten iron solidifies and is plated to the inner core. In the process, lighter elements are left behind in the fluid, making it lighter. This is called ''compositional convection''. A [[Coriolis effect]], caused by the overall planetary rotation, tends to organize the flow into rolls aligned along the north–south polar axis.<ref name="Buffett2000" /><ref name="MMMch8" />

A dynamo can amplify a magnetic field, but it needs a "seed" field to get it started.<ref name="MMMch8" /> For the Earth, this could have been an external magnetic field. Early in its history the Sun went through a [[T Tauri star|T-Tauri phase]] in which the solar wind would have had a magnetic field orders of magnitude larger than the present solar wind.<ref name=MMMch10>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 10}}</ref> However, much of the field may have been screened out by the Earth's mantle. An alternative source is currents in the core-mantle boundary driven by chemical reactions or variations in thermal or electric conductivity. Such effects may still provide a small bias that are part of the boundary conditions for the geodynamo.<ref name=MMMch11>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 11}}</ref>

The average magnetic field in the Earth's outer core was calculated to be 25 gauss, 50 times stronger than the field at the surface.<ref>{{cite journal |first1=Bruce A. |last1=Buffett |title=Tidal dissipation and the strength of the Earth's internal magnetic field |journal=[[Nature (journal)|Nature]] |volume=468 |pages=952–954 |year=2010 |bibcode=2010Natur.468..952B |doi=10.1038/nature09643 |issue=7326 |pmid=21164483 |s2cid=4431270}}
*{{cite web |date=December 17, 2010 |title=First Measurement Of Magnetic Field Inside Earth's Core |website=Science 20 |url=http://www.science20.com/news_articles/first_measurement_magnetic_field_inside_earths_core}}</ref>

==== Numerical models ====
Simulating the geodynamo by computer requires numerically solving a set of nonlinear partial differential equations for the [[magnetohydrodynamics]] (MHD) of the Earth's interior. Simulation of the MHD equations is performed on a 3D grid of points and the fineness of the grid, which in part determines the realism of the solutions, is limited mainly by computer power. For decades, theorists were confined to creating ''kinematic dynamo'' computer models in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. Kinematic dynamo theory was mainly a matter of trying different flow geometries and testing whether such geometries could sustain a dynamo.<ref name=Kono2002>{{cite journal |last1=Kono |first1=Masaru |last2=Roberts |first2=Paul H. |s2cid=29432436 |title=Recent geodynamo simulations and observations of the geomagnetic field |journal=[[Reviews of Geophysics]] |year=2002 |volume=40 |issue=4 |pages=1–53 |doi=10.1029/2000RG000102 |bibcode=2002RvGeo..40.1013K |doi-access=free }}</ref>

The first ''self-consistent'' dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan<ref>{{cite journal |last1=Kageyama |first1=Akira |last2=Sato |first2=Tetsuya |author3=the Complexity Simulation Group |title=Computer simulation of a magnetohydrodynamic dynamo. II |journal=Physics of Plasmas |date=1 January 1995 |volume=2 |issue=5 |pages=1421–1431 |doi=10.1063/1.871485 |bibcode=1995PhPl....2.1421K }}</ref> and one in the United States.<ref name="selfconsistent">{{cite journal |last1=Glatzmaier |first1=Gary A. |last2=Roberts |first2=Paul H. |title=A three-dimensional self-consistent computer simulation of a geomagnetic field reversal |journal=Nature |year=1995 |volume=377 |issue=6546 |pages=203–209 |doi=10.1038/377203a0 |bibcode=1995Natur.377..203G |s2cid=4265765 }}</ref><ref>{{cite journal |last1=Glatzmaier |first1=Gary A. |last2=Roberts |first2=Paul H. |title=A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle |journal=Physics of the Earth and Planetary Interiors |year=1995 |volume=91 |issue=1–3 |pages=63–75 |doi=10.1016/0031-9201(95)03049-3 |bibcode=1995PEPI...91...63G}}</ref> The latter received attention because it successfully reproduced some of the characteristics of the Earth's field, including geomagnetic reversals.<ref name="Kono2002" />