OK, now this baloney is starting to get somewhere. First: which direction convection should happen in Nature?: (A) up to equator, sinks at poles (B) up to poles, sinks at equator? Answer: I claim B should be Nature's choice. The reason is the nonlinear term for interaction between viscosity and gravity. Specifically, gravity is slightly stronger in the polar direction (no centrifugal counterforce). And it also is effectively stronger when acting on hot stuff, because hotter stuff has lower viscosity. So to enjoy the most effective drive for convection, you want to make the hot stuff rise in the polar direction (enjoying the interaction of strong with strong, giving everything a boost) then the cold stuff sinks from the equator. So this effect should bias things to make sure the convection happens predominantly in style (B). This is good since it agrees with my previous post that (B) is the direction that creates a self-reinforcing dynamo, while (A) would experience negative feedback non-dynamo. Great. (Also note, Venus is almost nonrotating which fits with the observation it has almost no magnetic field.) Second. My model sounded great qualitatively, but was yielding way too small magnetic field strength predictions. But now the solution to that puzzle occurs to me. See http://en.wikipedia.org/wiki/Structure_of_the_Earth Inside the earth is a region called the "outer core" (1220 km < r < 3400 km) believed to consist mainly of liquid metal, mainly iron & nickel. All other regions are mainly solid or semisolid/ductile. (Semisolid still has convection via diffusive atomic rearrangements.) So, this has got to be where the magnetic action is. Since liquid, we should get much faster flow speeds (far lower viscosity, by factor of up to 10^25, versus the Mantle), And since metal, much higher electrical conductivity (by factor of 10^7), and since smaller than the earth (outer core has outer radius half that of the whole planet) everything is more concentrated (smaller distances imply greater fields from same-amp currents). In view of all this, there now is probably no problem at all explaining (at least at the low precision level of my crude estimates) how the Earth can have as large a magnetic field as it does. And in case you are worried I'm now predicting way too LARGE a field, no problem, we can weaken it by postulating there's a lot of funny turbulent motion, which cancels out 99% leaving only 1% uncanceled (or pretty much whatever weakening-factor we want can be postulated in this way). So... I now think, yes, this is the explanation for the Earth's magnetic field. How much of this thinking is original? No idea, but probably not a whole lot.

Warren, you've left out the Coriolis force. It surely plays an important role. Gene

--I find that hard to believe because the flow velocities are very small, and Coriolis force is proportional to velocity.

And I would expect the molten iron to have much higher conductivity than molten silicon rock. But the theory can't just be about fields and rotating conductors, otherwise you could produce a field just by rotation an iron ball.

--A rigidly rotating solid body by itself, can never be a dynamo, as is easy to see. (Also, it would have no way to generate power, vs: convection is continuously powered by radioactive heat.)

The theory must depend on the conductors being carried by the molten convection as well as rotation of the Earth. Brent Meeker

--it indeed does. As I explained in one of my latest posts, molten iron convects up toward poles and down from equator, which is a decidedly non-rigid-body kind of liquid flow, and which IS a dynamo. Furthermore, the rotation of the Earth plays an important role in stabilizing that particular flow configuration as opposed to its time-reverse (which would have been an anti-dynamo featuring negative feedback -- useless). So my current picture, which took a while for me to find, seems to explain a lot plus clearly will produce large enough field numbers: 1. explains why field is normally points parallel or antiparallel to rotation axis 2. explains why Venus no field (not rotating) 3. explains why Mercury<Earth<Saturn<Jupiter in terms of fields 4. explains why Moon has no field (slow rotation, only very small liquid core region) But I would now say I do not understand why Mars has only a tiny field given that Mars is believed to have a liquid metal core and rotates reasonably fast. However, I'm not sure they know a damn thing about Mars' core. Earthquakes and seismic clues tell us what is inside. Moon quakes are not powerful enough to see the Moon's core with the seismic sensors Apollo put on the Moon, and so its presence is less certain. For Mars presumably things are still less certain and I do not think they really know if it has a liquid core, nor do they have any accurate estimate of its size. All they have are models constrained by gravitational measurements, which is not good enough. Both Moon & Mars geo-tectonically dead and hence have only tiny quakes. So it might be that Mars contradicts my picture, but I do not think that will be clear until at least 2016 when they plan to land a seismometer there.

Another problem: What sets the magnetic field value? If there is a fixed velocity field, then induced voltage V is proportional to magnetic field, which via Ohm's law and the law of inductance, means we should approach a current I set by V=I*R where R=resistance, which in turn generates the magnetic field. These equations are linear, so if multiply input magnetic field by X... we multiply output magnetic field by X. There is nothing to set any particular level. And if the output exceeds the input, we would get growth, and what would stop that growth? So something else needs to be put into this picture, some nonlinear effect, which stops the growth and holds the magnetic field at some level. The answer to that is presumably that the input heat-power from radioactive decay, must exceed the Joule power loss I*I*R. But this Joule heat "loss" actually just generates heat which further powers the convection which powers the whole dynamo, so it isn't "loss." So then you realize that the Joule heat is differently distributed than the radioactive heat. So really, this whole thing is a heat-transfer mechanism which allows heat to move out of the Earth's core at a greater rate than convection and conduction alone, sans dynamo, could have done. Plus there is additional "loss" beyond Joule, for example the Earth's magnetic field diverts the solar wind, which effect (exercising your hand to perform "right hand rule" again...) is to diminish the Earth's field and transfer earth-core heat into the solar-wind plasma. This solar-wind loss mechanism must be nonlinear in the magnetic field because there is a volume, the "magnetosphere" which grows the stringer the field is, and outside that volume the Earth;s field is basically canceled out by solar wind effects. The loss is proportional to the field strength times the magnetosphere volume (or surface); and this is clearly growing like a power >1 of the magnetic field. So, CONCLUSION: there is at least one nonlinear loss mechanism preventing huge field growth and which causes the correct qualitative behavior -- self-amplification of small fields, but imposing a ceiling on field strength. So now let us do a numerical estimation to hopefully verify all this. We will compute (a) the earth's heat-generation rate, and compare it with (b) the power loss/transfer from the earth field into the solar wind plasma. (a): wikipedia says Earth internal heat generation rate is 44 to 47 terawatts, although perhaps only 10-20 comes from the core. So say 10^13 watts. (b): view the magnetosphere as bending the solar wind an angle of order 90 degrees. Solar wind properties at 1 AU: speed: 200 to 900 km/sec proton particle energies: 0.2 to 4.2 keV (consequently) proton particle densities: 0.2 to 50 per cm^3 (plus same for electrons) current density of protons (consequently): 6.4*10^(-9) to 3.3*10^(-5) amp/meter^2 The effect then is essentially that the earth is a battery generating order 200-4200 volts at a current of order C*J where J=0.1 nanoamps to 33 microamps/meter^2 is the proton wind proton current (also electron current is same) and C is the cross-sectional area of the Earth magnetosphere which is about pi*r^2 where r=15 to 30 earthradii. proportional to the solar wind. So the current is about 1.8*10^8 to 3.9*10^12 amps. So V*I=power loss to solar wind, is about 3.7*10^11 to 7.7*10^15 watts. This answer (b) is a factor-20000 wide interval (sorry about the crudity) but it does enclose the answer (a) right in the middle (on a log scale), so our picture is not refuted. If this is correct and is really the main thing placing a ceiling on the Earth's magnetic field, then this would predict that if the solar wind were magically turned off, the Earth's field would grow quite a lot larger. And as far as I know from rumors, solar wind variations do indeed cause substantial fluctuations in the Earth's field, suggesting this is indeed the main loss/ceiling-causing mechanism. So back of envelope estimates and simple thinking appear to be successfully getting us quite far.