The idea that the Moon would have a liquid interior, carrying a net current, which by dynamo effect would generate the current creating the magnetic field, looks rather implausible. This proposal has problems also in the case of Earth. The problem is that the current creating the magnetic field should have dissipated a long time ago. The magnetic field of Earth however stubbornly continues to exist. The same problem is encountered with magnetic fields in cosmic scales: they should not exist since in standard cosmology the currents would be short ranged.
At microscopic level, TGD replaces magnetic fields with magnetic flux quanta, flux tubes and flux sheets. The flux tubes can be monopole flux tubes in which case they are stable and no current is needed to preserve the field. This is crucial. The cross section of the flux tube is closed 2-surface, which requires non-trivial space-time topology. Second kind of flux tubes have vanishing flux and correspond to Maxwellian magnetic fields requiring current.
In the case of Earth, a good guess for the strength of monopole contribution would be about .2 Gauss, roughly 2BE/5 from experiments of Blackman et al leading to the notion of the dark matter as heff>h phases at magnetic flux tubes. This field would play a key role in TGD inspired quantum biology but this value would not be the only value possible.
This leads to a model for the maintenance of BE. When the non-monopole part of BE becomes weak enough, the magnetic body (MB) of Earth turns, and induced currents re-creating the induced part (see this).
Could the monopole part of the magnetic field at monopole flux tubes play a role analogous to field H induces a magnetization M cancelling the total field B= H+M in the case of diamagnets? H and M would be at different space-time sheets but their effects on test particles touching all sheets would sum up and at QFT limit B would be the detected effective field and vanish for dia-magnets.
Superconductors are diamagnetic. This is usually explained in terms of the Meissner effect. TGD however leads to a model of superconductivity in which supra currents are heff>h phases at flux tubes, presumably monopole flux tubes. Could magnetic fields actually penetrate to super-conductors as monopole flux tubes (or sheets) with quantized flux inducing a magnetization cancelling the total effective field at quantum field theory limit, which is the sum over fields at different space-time sheets as far as its effects are considered (see this).
Venus is in many aspects twin of Earth but does not have a detectable magnetic field. Also Mars seems to have no global magnetic field but has auroras and local magnetic fields. This inspires crazy questions. Could Venus be a diamagnet. Could the magnetic bodies of Venus, Mars and also Moon be superconductors in the scale of the entire object? But why would the MB of Earth not be able to cancel the total field? Could the rotating liquid core induce an additional field, which prevents this?
For a summary of earlier postings see Latest progress in TGD.