Mathematics – Logic
Scientific paper
Nov 1969
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1969moon....1....7s&link_type=abstract
The Moon, Volume 1, Issue 1, pp.7-30
Mathematics
Logic
7
Scientific paper
The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,E o, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 103 mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.
Colburn David S.
Schwartz Kenneth
Sonett Charles P.
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