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Geomagnetism
© Charles Chandler
 
Figure 1. Earth's magnetic field, courtesy J. Marvin Herndon.
The Earth's magnetic field averages 0.5 Gauss, with its dipole axis tilted about 10° from the rotational axis. It is said that life on Earth depends on this field, because without it, our atmosphere would get whisked away by the solar wind, leaving us dangerously exposed to UV radiation and high-energy particle bombardment. But like many topics in geophysics, that's an idea that was accepted before it was scrutinized. Venus has 82% the mass of Earth, 72% the orbital radius, and 0.1% the magnetic field. With less mass, there is less gravity binding its atmosphere to its surface. Being closer to the Sun, the solar wind is more forceful. And having almost no magnetic field, there should be nothing to prevent the stronger solar wind from liberating the atmosphere from the weaker gravity. Yet the Venusian atmosphere is 51 times denser than the Earth's! Clearly, the role played by planetary magnetic fields needs to be re-evaluated. But first, we need to determine what causes these fields.
 
In ancient times, the Earth was thought to be like a bar magnet, with a frozen-in polarization of unknown origin. We now know from the study of magnetic striping moving away from mid-ocean ridges that the polarity flips every several hundred thousand years on average. So the field can only be generated dynamically, by the motion of charged particles.
 
The most obvious "motion" would be the rotation of the Earth itself.1 (This is consistent with the fact that Venus, whose rotation is the slowest of all of the planets, has the weakest magnetic field.) For rotation to instantiate a dynamo, the Earth would have to have a net charge, because equal quantities of positive and negative charges generate opposing fields that cancel each other out. But this begs the question of how the Earth could maintain a net charge for several hundred thousand years. An alternative is that the planet might be net neutral, but charges within the planet might be separated into charged double-layers.2 Then, the outer layer will travel more distance per revolution, and thus generate a more powerful field. But charged double-layers beg the same question concerning charge separation mechanisms.
 
The first proposed answer was that gravity acts on atomic nuclei more vigorously than on electrons, yielding a net positive charge in the core, and a net negative charge nearer the surface.3 More recent research has shown that electron degeneracy pressure is much more forceful.4 Under extreme pressure, atoms are forced so close together that the outer electron shells fail, and the electrons are expelled, leaving +ions behind. The expelled electrons congregate at a higher altitude, where there is less pressure, and thus there is room between the atoms for extra electrons. So the core is positively charged, while the surface is negatively charged. Since the prime mover is gravity, which is constant, the charge separation is stable, creating current-free double-layers (CFDLs). In other words, there is a charge separation, but even in the absence of sufficient insulation, the charges don't recombine, because the forcing mechanism is still present. Hence the double-layers are current-free.
 
How could the polarity of the net magnetic field from CFDLs invert? The charge configuration must stay the same, since neither the gravity nor the electron degeneracy pressure changes. The only possibility is differential rotation. If the oppositely charged layers are rotating at different rates, the faster one will generate the more powerful field. And indeed, the existence of layers that rotate at different rates has been confirmed by recent research.5 If those layers are oppositely charged, we'll get the effects that are observed. Half of a Gauss isn't actually a very powerful field, especially for charged particles with an equatorial velocity of 465 m/s. The charged particles in an electric motor move only at a couple of micro-meters per second, so the magnetic field from the Earth's rotation should be huge. But if there are two rotating layers, generating opposing magnetic fields, the net field will be generated just by the difference in speed, which might be very slight. And the electric force at the surface will be slight, since most of that field is between the negative surface and the positive interior. In balanced double-layers, the field on the outside is weak.
 
The next question concerns the driving force in the differential rotation. There should be an enormous amount of friction, and over a long period of time, the layers should settle into solid body rotation, where everything rotates at the same rate. But before we jump to conclusions there, the friction might not be as great as we'd otherwise expect. In the next section, reasons are given for there to be electric currents across the boundaries of the charged double-layers, which will generate ohmic heating.6 (In other words, the CFDLs are not entirely current-free.) Thus the transition from the positive mantle to the negative crust might not be solid rock — it might be a supercritical fluid, kept molten by the electric currents, and by the low thermal conductivity of the rock above and below it. As such, the friction might be slight, and an extremely weak force could drive differential rotation. That force might be the magnetic fields themselves. Charged double-layers generate opposing magnetic fields, creating magnetic pressure between them. Each layer would prefer that the other did not rotate at all, so that it wouldn't generate an opposing magnetic field. Yet if one layer was stopped, and the other was rotating twice as fast, there would be a lot more friction. So the differential rotation achieves an equilibrium, accelerated by magnetic pressure, and decelerated by friction.
 
Now we just have to understand what alters the differential rotation, accelerating the slower layer, and decelerating the faster layer, such that the dominant magnetic field flips. That will take a force. One possibility is that the motion of the Earth through the galactic magnetic field generates a Lorentz force that causes the rotation. Here it's interesting to note that all of the planets have prograde orbits around the Sun, and with the exception of Venus, they all rotate around their axes in that same direction. Venus is the exception that proves the rule, because its rotation is rapidly slowing down, suggesting that there is an external force acting on it, and everything else in the solar system, which encourages rotation in the same direction. This also makes sense of the precession of axial rotations, in that precession requires two conflicting forces. Angular momentum is one of them, but what is the other? The rotations within the solar system are roughly aligned to the galactic magnetic field, but the solar system is moving diagonally through that field. The equilibrium among all of those forces is then orbits that are skewed with respect to the galactic field, and planets rotate with precession.
 
 
Figure 2. Solar system relative to the galactic plane, courtesy LeeBee.
 
 
Figure 3. The motion of the solar system through the interstellar medium, along with the orientation of the galactic magnetic field, courtesy IBEX. The bright ring around the heliosphere is the energetic neutral atoms.
 
 
This also suggests what could cause the polarity of the dynamos to flip. If the galactic field changes, its influence could go from an accelerator to a brake. The long-term consequence would be that planetary rotations and orbits would slow down, while the short-term effect would be that the charged double-layers inside planets would reverse roles. The layer that had previously dominated will slow down, and the subordinate layer will speed up.
 
This model is also consistent with the fact that the alternate magnetic stripes are weaker. If the charged layers in the Earth have the same amount of charge, the outer layer will produce a stronger magnetic field, since its angular velocity is greater, and since the strength of an electromagnet is a function of the velocity of the charge. In the Earth, the outer layer (i.e., the crust) is negatively charged, and its rotation produces a field that matches the orientation of the current geomagnetic field. Below the Moho, the mantle is positively charged, from pressure ionization. It has the same amount of net charge as the crust, but its angular velocity is less. So the field from the crust dominates. When the relative velocities oscillate, and the mantle's field is stronger than the crust's, the net field flips, but it isn't as strong.
 
And now we have a model that can answer the original question of what keeps atmospheres bound to planets, if not magnetic shielding. The electric force between the atmosphere and the surface does the work. On Earth, the surface is negatively charged, while the atmosphere is positively charged, with 100 V/m between them. That's a weak force compared to gravity, and the Earth has a thin atmosphere. On the other hand, Venus' atmosphere is highly electrified, with constant lightning. Being closer to the Sun, photo-ionization is more robust. And that atmosphere is very thick, despite the absence of magnetic shielding. So it's the electric field that is responsible for planetary atmospheres, not the magnetic field.

 

References

1. Rowland, H. A. (1878): On the magnetic effect of electric convection. American Journal of Science, 3 (15): 30-38

2. Sutherland, W. (1900): A possible cause of the Earth's magnetism and a theory of its variations. Journal of Terrestrial Magnetism and Atmospheric Electricity, 5: 73-83

3. Rosseland, S. (1924): Electrical state of a star. Monthly Notices of the Royal Astronomical Society, 84: 720-728

4. Chandler, C. (2019): CFDLs Caused by EDP. QDL, 12483

5. Jackson, A.; Livermore, P. W.; Hollerbach, R. (2013): Electromagnetically driven westward drift and inner-core superrotation in Earth's core. Proceedings of the National Academy of Sciences, 201307825

6. Chandler, C. (2020): Tidal Forces. QDL, 9925


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