Outside academia Larmor displayed an equally enigmatic mix of progressive and conservative traits. In his maiden speech as Unionist member of parliament for Cambridge University, a seat he would hold from 1911 to 1922, he vehemently endorsed home rule for Ireland, yet in college politics he was distinctly retrograde, querying the need to install baths as the university had done without them for 400 years. (Nevertheless, once they were in place he took, without fail, a daily walk across the Cam to bathe in the New Court of St. Johns College.)
In 1919 Larmor was working on possible explanations for the magnetic fields of sunspots. One explanation, he suggested, might also relate to the Earth. He had found that when atoms were placed in a magnetic field, their magnetic moments started to revolve about the field direction, rather like the axis of a spinning top about the vertical. The discovery of this motion, now known as “Larmor precession,” would eventually lead to the development of nuclear magnetic resonance, magnetic resonance imaging techniques and indeed the proton precession magnetometer. However, in 1919 Larmor’s preferred explanation for the magnetic fields of sunspots was based not on rotation or precession, but on “an internal cyclic motion [acting] after the manner of the cycle of a self-exciting dynamo.”
Joseph Larmor. While investigating the origin of magnetic fields associated with sunspots, this Irish-born professor of mathematics at Cambridge University came up with the idea that Earth’s magnetic field might originate from a self-sustaining dynamo in the planet’s liquid iron core.
This was a flash of inspiration. Schuster had rejected the idea of electric currents in the Earth because he had been unable to account for their existence. Larmor, on the other hand, had thought back to Michael Faraday’s law of electromagnetic induction and the principle of his disc dynamo. Faraday had shown that when a conductor moved through a magnetic field, a voltage was induced in it. If the conductor formed part of a closed circuit, this resulted in an electric current. If the magnetic field of that current reinforced the original magnetic field, the result was positive feedback and a self-exciting dynamo, which would, as Larmor wrote in a one-page note in Reports of the British Association for the Advancement of Science, “maintain a permanent magnetic field from insignificant beginnings.”
However, nature does not give something for nothing; in fact, as a popular paraphrase of the second law of thermodynamics states, you can’t even break even. As Peregrinus had found— although he did not recognize it as a law of nature and instead blamed his own ineptitude—perpetual motion simply does not occur. Without the continual injection of energy, the process will eventually run down.
Recognizing this problem, Larmor added the rider “at the expense of some of the energy of the internal circulation.” At this point he was still talking about the magnetic fields associated with sunspots and relatively small-scale fluid circulation near the surface of the sun, but at the end of his note he commented that a similar concept would readily account for the “extraordinarily rapid” secular variation of Earth’s magnetic field by “change of internal conducting channels,” although it would require “fluidity and residual circulation in deep-seated regions.”
He was clearly referring to the core of the Earth. Seismologists and geodesists had by now identified the boundary between the core and the mantle, and many were convinced the core was liquid. Furthermore it was heavy, probably metallic, and therefore electrically conductive. As Larmor had realized, only a fluid could move rapidly enough to produce field changes typical of geomagnetic secular variation, features of which move across the globe at tens of kilometers per year.
Could such a self-exciting dynamo really work, either in the sun or in Earth’s core? Over the next few years physicists grappled with the mathematics. This involved combining several theoretical constructs: Maxwell’s equations, which dealt with both the induced electric currents and their associated magnetic fields; Ohm’s Law, from which the energy required to maintain the currents would be determined; and equations describing the fluid dynamics of the core, including the so-called Navier-Stokes equations. These last equations stemmed back to the early nineteenth-century French mathematicians Siméon-Denis Poisson, Claude Navier and Augustin-Louis Cauchy, and to George Gabriel Stokes, another of William Hopkins’ Cambridge senior wranglers.
Once the “magnetohydrodynamic” problem had been formulated mathematically, the task of solving it from first principles was daunting in the extreme. The sheer number of calculations required was so enormous that a full solution would not even be attempted for another seventy years. In the short term, progress could be achieved only by making simplifications—for example, by assuming a simple pattern of fluid flow and seeing whether the equations led to a self-sustaining magnetic field.
The pursuit of a dynamo solution almost stopped in its tracks in 1934, when Thomas Cowling, an English mathematician working on the sun’s magnetic field, proved a dynamo could never result from fluid flowing in a symmetrical pattern about the rotation axis. This discouraging result became known as Cowling’s anti-dynamo theorem.
In the face of this setback, it was not surprising that Schuster’s third idea was revived—particularly when an American astronomer, Horace Babcock, announced that in addition to the local magnetic fields associated with sunspots, the sun also possessed an overall magnetic field, dipolar in form like the Earth’s, and that he had also detected and measured magnetic fields in other stars.
Did this mean that magnetic fields were intrinsic to all massive rotating bodies? The chief proponent of this theory was the renowned professor of physics from Manchester University, Patrick Blackett, who was soon to be awarded a Nobel Prize for his pioneering work on cosmic rays. Blackett thought it was significant that the ratios of rough measurements of magnetic field strength (or, more precisely, dipole moment) and rotational angular momentum came very close to the square root of the gravitational constant— the constant, G, in Newton’s law of gravitation, which had eventually been measured by Henry Cavendish—divided by the speed of light. He built up an elaborate theory around this. For a while this rotating body theory was dubbed the “fundamental theory” and received considerable attention.
Which theory was right? One test would be whether the strength of the magnetic field increased or decreased with depth into the Earth. According to the dynamo theory, the strength of the magnetic field should increase as its source in the core was approached. The rotating body theory suggested it should decrease. Keith Runcorn, then Blackett’s research student, was assigned the task of measuring the magnetic field 1200 meters down the shaft of a disused Lancashire coal mine. The results, reported at a meeting of the Royal Astronomical Society on February 27, 1948, failed to answer the question. Blackett valiantly tried to keep the theory alive but Thomas Cowling, having already poured cold water on the dynamo theory, now criticized the rotating body theory for its “indefinite” basis.
Blackett was not defeated. He now attempted to prove the rotating body theory in a famous experiment designed to detect a magnetic field around a rapidly rotating gold sphere. (The sphere apparently had to be gold to make it heavy enough.) For this experiment he built an incredibly sensitive “astatic” magnetometer— essentially two identical magnets placed in opposite orientations and suspended one above the other on the same wire. Such an arrangement would detect the non-uniform magnetic fields that Blackett hoped to see around his sphere, while eliminating the effect of the prevailing laboratory field.
Unfortunately, although of unprecedented sensitivity, the magnetometer detected nothing, and Blackett finally had to concede victory to the dynamo theorists. His efforts had, however, not been entirely in vain: in the 1950s his magnetometer would become the nucleus from which British paleomagnetism flourished.
At the same 1948 meeting of the Royal Astronomical Society at which Runcorn had reported the results of his coal-shaft experiment, Edward Bullard, a post-doctoral researcher from Cambridge, had presented his new theory about the secular variation. F
irst he described the regional nature of secular variation, with features growing, drifting and decaying in a matter of decades or centuries— much faster than most geological processes. Although these features were distinct from the main field, he reasoned they must also originate in Earth’s fluid core.
He then demonstrated that if fluid near the core–mantle boundary circulated locally, a bit like an eddy, the presence of the main field would cause electromagnetic induction to occur in it, and this would generate local currents and magnetic fields just like those of the secular variation.
This was not a self-exciting dynamo: the main field was an essential ingredient to generate the secular variation. However, it was a major step forward for dynamo theory—that is, until the next speaker took the floor. Imperial College’s John Bruckshaw proceeded to astound the audience by announcing that he and New Zealander Edwin Robertson had found reversely magnetized dykes in the north of England. Until this time the theorists had not taken the possibility of polarity reversals very seriously. If Bruckshaw were correct, the “geodynamo” problem had suddenly become much more challenging.
The Geodynamo
In this way it is possible for the internal cyclic motion to act after the manner of a self–exciting dynamo, and maintain a permanent magnetic field from insignificant beginnings, at the expense of some of the energy of the internal circulation.
—JOSEPH LARMOR, 1919
The ball was now firmly back in the court of the dynamo theorists. The concept was gaining new momentum from the work of two physicists turned geophysicists. Walter Elsasser, born in Germany in 1904, had completed a PhD in the new discipline of quantum physics at the University of Göttingen, before emigrating to the United States and becoming an American citizen in 1940. After the war he took up a series of academic positions at prestigious universities across the country, but it was his geophysical work at the University of Pennsylvania between 1948 and 1958 that would earn him the reputation of father of geodynamo theory.
Edward (Teddy) Bullard, who had used electromagnetic induction to explain secular variation at the 1948 Royal Astronomical Society meeting, had studied nuclear physics under Ernest Rutherford at Cambridge before his interests turned to geophysics. After a year at the University of Toronto, he returned in 1950 to head Britain’s National Physics Laboratory, where he became captivated by the geodynamo problem. He finally returned to Cambridge University in 1956 as head of the Department of Geodesy and Geophysics. He had missed the era of Hospers, Runcorn, Creer and Irving, but would be there in time for Vine and Matthews and the plate-tectonic revolution of the 1960s.
Elsasser and Bullard were both well acquainted with the magnetohydrodynamic equations and their complexity. They agreed that there must be a dynamo or regeneration mechanism, otherwise the field would die away in a matter of a few tens of thousands of years because of electrical resistance. Furthermore, they had both grappled with the problem of the origin of the energy that kept the regeneration process going. Having ruled out astronomical effects such as a difference between the moon’s drag on the core and mantle, or precession or nutation of Earth’s rotation axis, they concluded that only internally driven motion of the core fluid could be the answer. And this, they agreed, would occur only if there were a sufficient difference in temperature between the inner core and the base of the mantle.
With a complete solution of the equations still way beyond their capability, both independently opted to further investigate the mechanical analogue, the disc dynamo. It was easy to see that a simple modification of Faraday’s disc dynamo would transform it into a self-exciting dynamo. Instead of using a separate magnet to provide the magnetic field, the field created by the output current was used; the apparatus merely had to be wired so the magnetic field was in the required direction—essentially a positive feedback effect. In principle, as long as energy was provided to keep the disc rotating, such a system would continue to generate an electric current and produce its own magnetic field. A small “seed” magnetic field was needed to get the dynamo started, but then the seed could be removed and the dynamo’s own magnetic field would stabilize.
Single- and double-disc dynamos. In each case there is an initial magnetic field, Bo, upwards. When each disc is rotated in this field, a current is induced from its center to its rim. This is directed through conducting wires that loop around the axles of the discs as shown. In the single disc dynamo (a), the induced current produces a magnetic field, Bi, that reinforces the initial field Bo, and so sustains the dynamo. In the double-disc dynamo (b), the circuit is arranged so the current induced in one disc provides the auxiliary magnetic field for the other, but they are in opposite directions. In the right-hand disc Bi reinforces Bo, but in the left-hand disc Bi opposes Bo—slowing it until eventually the direction of rotation, and so the polarity of the dynamo, reverses.
Unlike the geodynamo, the disc dynamo could be described mathematically by relatively straightforward, solvable equations. Hence, some of Bullard’s early work drew analogies between his solutions to the mathematics of the disc dynamo problem and what might actually happen in the Earth’s core.
Even so, as soon as Bullard tried to include the tendency of the magnetic field to decay with time, his equations became intractable. To get approximate solutions, he had to resort to a machine at Cambridge University called a differential analyzer. A mechanical forerunner of the electronic digital computer, this machine consisted of systems of rods and gear wheels that, once set, would solve differential equations at the crank of a handle. In this way Bullard was able to show that a disc dynamo produced a roughly dipolar magnetic field that oscillated in strength but maintained a single, stable polarity.
He readily acknowledged that beyond this point the analogy between the mathematics of the disc dynamo and of the geodynamo became “a little precarious.” The rotor, disc and wires of a disc dynamo were a far cry from the Earth’s core, with its large volume of mobile conducting fluid and solid inner part. In the language of the experts, the whole of the conducting core is “simply connected” and the geodynamo is therefore “homogeneous.” Whereas in a disc dynamo (or a power station generator), the rotor is turned mechanically—by hand or by the action of water, wind or expanding pistons—in Earth’s core the driving force had to be convection, the welling up of material from deep in the core towards the boundary between the core and the mantle.
Bullard’s single-disc dynamo could produce a magnetic field in either direction, depending only on the direction of the initial seed field. Once the dynamo was going, the external seed field could be removed and the dynamo would continue to run happily. Oscillations in the strength of the current and the induced field occurred sporadically in some situations, but it turned out that the field’s polarity remained stable: once up and running, the single-disc dynamo never underwent polarity reversals.
To achieve this extra trick, in 1957 Tsuneji Rikitake of the Earthquake Research Institute in Tokyo worked out the effect of a double-disc dynamo. Two discs rotated on parallel axes, but the coil carrying the current induced in the first was wound around the axis of the second and vice versa, so each disc provided the magnetic field for the other. In this way Rikitake tried to simulate the interaction that had to be taking place between different components of the magnetic field in the Earth’s core.
The differential analyzer at Cambridge University’s Mathematics Laboratory, used by Edward Bullard to calculate solutions to the disc dynamo problem in the early 1950s. A mechanical forerunner of today’s digital computers, the analyzer consisted of systems of rods and gear wheels, which, once set, solved differential equations at the turn of a handle.
Amazingly, this simple idea did just what Rikitake had hoped: of its own accord, the magnetic field flipped randomly from one polarity to the other—in what was possibly the first computer-generated example of a chaotic process. Was the double-disc dynamo really mimicking what went on in the Earth’s core? Who knew, but it was an encouraging start.
In the 1960s Frank Lowes and Ian Wilkinson, working alongside Ken Creer in the research group that Keith Runcorn had now established at the University of Newcastle-upon-Tyne, laid to one side the fluid nature and convection of the geodynamo and focused their attention on the magnetic field. The model they built consisted of two cylinders made of an iron-rich alloy. These cylinders were free to rotate in a block of the same alloy, with which they were in good electrical contact via a thin layer of mercury. When the cylinders were made to rotate in a “seed” magnetic field, the currents and magnetic fields induced in each cylinder were found to sustain each other, in a manner similar to Rikitake’s double-disc dynamo. However, there was a difference: Lowes and Wilkinson’s model was a “homogeneous” self-exciting dynamo: there were no wires to channel the currents. A second version, in which the geometry was modified and minor changes made to such things as the materials and rotation speed, even went through the now essential spontaneous polarity reversals.
The next two decades saw the introduction and rapid increase in the use of electronic computers in many areas of research, but this boost in computational power served only to clarify the enormity of the magnetohydrodynamic problem. Geomagnetists were still forced to make assumptions and simplifications in order to run their calculations. One was the so-called “kinematic dynamo,” in which the computer was given an initial pattern of fluid flow and programed to calculate the resultant magnetic field. However, the solutions could only ever be as good as the initial assumptions, and none was yet anywhere near Earthlike.
North Pole, South Pole: The Epic Quest to Solve the Great Mystery of Earth's Magnetism Page 20