The Nature of Terrestrial Magnetism1

The hypothesis that regarded the Earth’s magnetic field as the field of a permanent magnet was discarded long ago. It is quite obvious that no reasonable physical explanation can be found for this supposition.

One might try to imagine that the direct effect of the Earth’s motion on the motion of the electrons of atoms is the cause of the existence of the Earth’s magnetic field. However, this effect, in the first place, is small, and in the second, does not explain the deviation of the axis of rotation from the Earth’s magnetic axis, nor the secular variations of the terrestrial field.

Most natural of all is to accept the very widespread hypothesis that the central part of the Earth consists of metal, and to suppose that temperature oscillations within this metallic core, caused by convection, create thermoelectric currents. It is precisely these currents, in the opinion of the author of the paper under review, that create the Earth’s magnetic field.

The fact that the resultant magnetic moment of the system of these currents is not equal to zero is explained by the constant action of the Coriolis force on the convective motion. It is evident that the system of terrestrial currents possesses the corresponding asymmetry (in the symmetric case there would be obtained, on average, no constant circulation of electricity about the Earth’s axis).

A well-known conclusion of potential theory indicates that terrestrial currents, if they exist, flow inside the Earth and not on its surface.

One might suppose that the terrestrial currents are galvanic currents. However, in view of the very slow motion of ions at high pressures, and also because of a number of circumstances, it may be shown that galvanic currents in the Earth must be too weak to explain the existence of the Earth’s magnetic field. The hypothesis of thermoelectric currents leads to currents of the proper strength and,

moreover, is in full agreement with the hypothesis of a metallic core of the earth, distributed among geophysicists.

It is necessary to admit that the metallic core of the earth is nonhomogeneous. Only in this case is the existence of a steady current possible

\[ I=-\sigma \operatorname{grad}\varphi-\operatorname{grad}A-B\operatorname{grad}T, \tag{1} \]

where \(\sigma\) is the conductivity, \(\varphi\) is the electrostatic potential, \(T\) is the temperature, and \(A\) and \(B\) (as well as \(\sigma,\varphi\), and \(T\)) are functions of the coordinates.

Carrying out the calculation in spherical coordinates, the author computes the magnetic moment of the earth

\[ M=\int I_\varphi \cdot r\sin\xi\,dv, \]

expanding the quantities \(B\) and \(T\) in a series in spherical functions. Analysis of the resulting formula shows that the steady magnetic moment is produced by terrestrial currents only when there is simultaneous nonhomogeneity in the material of the earth’s core and in the temperature distribution.

It cannot be assumed that the nonhomogeneity in the mass distribution of the core of the terrestrial sphere is permanent. Elsasser’s theory therefore requires the assumption of the presence within the earth’s core of convective flows of a liquid phase.

A whole series of independent facts shows that, in any case, there are no indications contradicting the hypothesis of a liquid state of the earth’s core. The boundary of the earth’s core is established, though not quite completely, by objective methods. It is known that transverse waves are reflected from the boundary of the earth’s core; longitudinal waves, on the contrary, pass through the earth’s core with imperceptible attenuation. From these data Jeffreys concludes that the behavior of the earth’s core is more characteristic of a liquid body than of a solid one. He also finds that the viscosity of the core does not exceed \(2\cdot10^{9}\) CGS units (the viscosity of the earth’s crust \(\sim10^{22}\)).

Assuming, on the basis of the above considerations, that the earth’s core is in a liquid state, Elsasser considers the equation of motion of a fluid with internal friction

\[ \dot{\mathbf v}+(\mathbf v\operatorname{grad})\mathbf v = 2[\mathbf s,\mathbf v]-\mu\rho^{-1}\Delta\mathbf v-\rho^{-1}\operatorname{grad}p \tag{2} \]

(\(\mathbf v\) is the velocity, \(\rho\) the density, \(\mu\) the viscosity, and \(p\) the pressure, \(\mathbf s\) the angular momentum of the earth).

The velocity entering into the equation is, in Elsasser’s opinion, a quantity of order \(10^{-2}\)—\(10^{-3}\) cm/sec. This figure can be arrived at if one assumes that during the secular change of the earth’s magnetic field (5 centuries) a particle traverses a distance equal to the radius of the earth’s core (\(\sim10^{8}\) cm).

Elsasser uses the simplified equation (2), first, assuming the flow to be stationary (\(\dot{\mathbf v}=0\)); second, discarding the quantity \((\mathbf v\operatorname{grad})\mathbf v\), which is small in comparison with the term \(2[\mathbf s,\mathbf v]\).

The cause of the motion lies in a change of density; in turn, variations of density are explained by temperature fluctuations.

Elsasser calculates that the amount of radioactive substance known to geophysicists to be contained in the terrestrial sphere is sufficient to maintain thermal flows in the metallic core.

The author assumes that, as in other cases of dynamically unstable motions, the motion of the mass of the earth’s core consists in the occurrence of a series of vortices of irregular form.

Estimating the order of magnitude of the quantities appearing in the equation written above, Elsasser comes to the conclusion that the Coriolis force predominates over the other possible dynamic effects.

A further task of the author of the paper was to show that the motion described by a simplified hydrodynamic equation leads to an asymmetry of motion, necessary, as we mentioned at the beginning of the review, for the creation of a magnetic moment of the Earth different from zero.

Under the action of the Coriolis force, perpendicular to the velocity of the moving particle, the mean turbulent motion may have components in all three directions. The author shows that in every vortex (independently of its size and structure) there is an average forward motion in the eastern part and an average backward motion in the western part of the vortex. In other words, the eastern part of the vortex heats up, while the western part cools the surrounding medium. This explains the observed asymmetry of the Earth’s magnetic field.

Asymmetric changes in the thermoelectric constant are caused not only by the mass motion of the core described above. In addition, one must suppose that thermodynamic equilibrium between the phases does not exist within the Earth. Elsasser imagines the following rather nonequilibrium state: large particles of one phase are mixed with another phase having a different density. In such a system there must occur a process analogous to sedimentation. The rate of this process must be comparable with the rate of thermal convection. Such a picture explains the required nonconstancy of the coefficient in equation (1).

On the basis of his theory Elsasser calculates the order of magnitude of the density of terrestrial currents for temperature variations of the order of \(10^\circ\). The value he has computed is

\[ j = 1.5 \cdot 10^{-6}\ \mathrm{A/cm^2}. \]

The magnetic moment of the Earth is, as is known, \(M = 8.2 \cdot 10^{25}\) CGSM. If one assumes that the Earth’s core is continuously and uniformly filled with currents, then, to create a moment of \(8.2 \cdot 10\) CGSM, for a core radius of \(3.5 \cdot 10^8\ \mathrm{cm}\) the current density must be equal to

\[ 2 \cdot 10^{-8}\ \mathrm{A/cm^2}. \]

Elsasser explains the circumstance that the latter figure is about 75 times smaller than the first, besides the roughness of the calculation, by the fact that terrestrial currents are distributed not throughout the whole core, but only in part of it.

A. Kitaigorodsky, Moscow

1. W. M. Elsasser, Phys. Rev., 55, 489, 1939. ↩