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13.   The Self-Sustaining Dynamo
in the Earth's Core

Origin of The Earth's Magnetism

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8. Oersted & Ampére

9. The Lodestone

10. Gauss

11. The Magnetic Sun

12. Fluid Dynamos

13. Dynamo in the
    Earth's Core

14. Magnetometers and
    Tobacco Smoking

15. Magnetic Reversals
    & Moving Continents

16. The Magnetosphere

17. Magnetic Planets

    Blackett's Proposal

        It is an uncanny fact that the Earth's magnetic axis is close to its rotation axis--that the magnetic poles, where the magnetic force points straight down, are quite close to the geographical ones. William Gilbert saw it as evidence that rotation and magnetism arose from the same source:

      "Diurnal motion is due to causes which have now to be sought, arising from magnetick vigour and from the confederated bodies."

        Gilbert thus believed the Earth rotated because it was magnetic. P.M. Blackett, who won the 1948 Nobel prize for his work on cosmic rays, seriously considered the opposite possibility--that the Earth was magnetic because it rotated around its axis. Blackett at one time suggested that perhaps a new universal phenomenon existed--that any rotating object was intrinsically magnetized.

        At first this did not seem such a wild idea. Electrons and protons, for instance, do have an intrinsic "spin" giving them properties like those of a rotating solid object, and they also have an intrinsic magnetization, making them tiny magnets, lined-up with their spin axes. In ordinary materials, such atomic magnets point in all possible directions, so that their effects cancel.

    But concerning the Earth, Blackett guessed wrong. Experiments with spinning objects, which by his theory should have produced measurable magnetization, showed none. Later observations also showed that during the last tens of millions of years, the magnetic polarity of the Earth reversed many times, something that Blackett's prediction would never allow.

      The core of the Earth

The Earth's Core

    The way earthquake waves spread tells us that the Earth has at its center a dense liquid core, of about 1/2 the radius of the Earth--and inside that, a solid inner core. It is widely believed this core is made up of molten iron, perhaps mixed with nickel and sulfur. The density seems appropriate, and iron, which among all elements has the most stable nucleus, is abundant in the universe. It concentrated in the Earth's core because it is heavy--the same reason that, when it is extracted from its ores, it sinks to the bottom of the blast furnace.

    Energy is the currency with which most processes in nature must be paid for. The Earth's magnetism is no exception, and its energy seemes to come from fluid motions in the Earth's core, from circulating flows that help get rid of heat produced there. In a similar way, our weather is driven by circulating air flows that help cool the ground, where much of sunlight is absorbed.

    Scientists are still not sure about what provides the heat in the Earth's core. It might come from some of the iron becoming solid and joining the inner core, or perhaps it is generated by radioactivity, like the heat of the Earth's crust. The flows are very slow, and the energy involved is just a tiny part of the total heat energy contained in the core.

    So the molten metal is believed to be circulating. By moving through the existing magnetic field, it creates a system of electric currents, spread out through the core, somewhat like Faraday's disk dynamo, discussed earlier. Currents create a magnetic field--a distribution of magnetic forces--and the essence of the self-sustaining dynamo problem is to find solutions such that the resulting magnetic field is also the input field required for generating the current in the first place.

    Actually, that is only the lowest level of the problem, in which one is free to prescribe the motions. To solve the full problem, we also need information about the heat sources, and these sources must be able to drive motions which also solve the dynamo problem.

    Such problems are not easy. They involve intricate mathematics and are not yet fully solved. Only the roughest ideas in their solutions can be outlined here.

The Sun's Magnetism

One limitation, related to the failure of Blackett's theory, is that any electric circuit rotating like a solid body will not produce "dynamo currents." Even if part of the circuit follows the axis of rotation, and can therefore be viewed as non-rotating, solid rotation will not create any currents. An essential feature of the Faraday disk dynamo is that part of its circuit is outside the disk, not sharing its rotation.

    The rotation of the Sun around its axis, therefore, does not by itself contribute to its magnetism. What is important in this case is that the Sun does not rotate like a solid ball. Its equator has a shorter rotation period than higher latitudes-- about 25 days for the equator, 27 days for latitude 40 degrees (the Earth meanwhile moves some distance around the Sun, so from here the period seems to be 27 and 29 days). If Earth rotated that way, Florida (for instance) would soon pull away from the rest of the US, into the Atlantic Ocean. Such an uneven motion, deforming the surface, can drive a dynamo, and in the Sun's case, it is indeed believed to be the source of sunspot magnetism.

Dynamo Theory

    Before mathematicians tackle a complex problem, they try out simple solutions (joke about a mathematician's model of milk production: "Assume a spherical cow of radius R, uniformly filled with milk... "). No such luck here: early in the game, in 1934, Thomas G. Cowling in England proved that any self-sustaining dynamo in the Earth's core cannot have an axis of symmetry.

Walter Elsasser, at the University of Utah (later at Johns Hopkins) launched in the 1940s a frontal attack on the full 3-dimensional problem. He got nowhere: the equations became more and more intricate and complicated the further one went into the details. Others had similar experiences. Only in 1964 did Stanislaw Braginsky in Russia publish the first valid solutions, by assuming that the field was almost axially symmetric and calculating its small deviations from symmetry.

    The solution of the full problem, including heat flow, is much harder. Not only are we unsure of the source of heat, but any motions caused by it are greatly modified by the Earth's rotation. That modification is a major feature of large-scale motions in the atmosphere, causing hurricanes and storm systems to swirl in their characteristic ways. Eugene Parker in 1955 proposed a mechanism by which such swirling, in the rising flows of the Sun's atmosphere, could create dynamo fields.

    As viewed from above, the swirling direction of storms in the atmosphere is always counterclockwise north of the equator and clockwise south of it. Such asymmetry is also expected in rising flows in the Earth's core, and Steenbeck et al., in Germany, showed in 1966 that thanks to it, disordered convection patterns can indeed produce an average "dynamo field. " That became known as the "alpha effect, " because it involved a mathematical quantity denoted by the Greek letter a (alpha)--but the details are far too complicated to be described here.

    For some current work, simulating the dynamo on a computer, see web site by Gary Glatzmeier and Paul Roberts, here. Glatzmaier and collaborators have conducted some interesting simulations of the dynamo process, with realistic behavior, although limitations of computer speed forced them to simplify the properties of the liquid core.

    A Japanese team of Takahashi et al (Science, 309, p. 459-61, 15 July 2005) has more recently used one of the worlds fastest supercomputers to carry out a similar calculations assuming a much lower fluid viscosity in the core, much closer to the actual one. The behavior seems even closer to the one observed.

Questions from Users:   Inner Core Rotation
        ***         The movie "The Core" (a)
          ***       The movie "The Core" (b)
              ***       Heat sources inside the Earth
                   ***       Technical questions on magnetic energy and heating rate
                    ***     Nuclear reactor at the Earth's center?
                        ***     Currents that Generate the Earth's Magnetism
                            ***     Deriving Dynamo models from Equations?
                                 ***     Earth's core of frozen magnetic oxygen?
                    ;                  ***     Heating the inside of Earth
                    ;      ;                  ***     Magnetism inside the Earth
Next Stop:       14. Magnetometers and Tobacco Smoking

Regarding Dynamos:   15. Magnetic Reversals and Moving Continents

Back to the Master List

Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   earthmag("at" symbol)phy6.org
Last updated 23 February 2008

Above is background material for archival reference only.

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