The electric field produced in the mantle by the dynamo in the core

Details The electric field produced in the mantle by the dynamo in the core The electric field produced in the mantle by the dynamo in the core

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982pepi...28..191b&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 28, Issue 3, p. 191-214.

Physics

30

Scientific paper

A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when r ∂rln σ >> 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ∂V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ∂K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field Er ~ 0 there, while in cases (b) and (c), Er is very large there. Outside the critical layer, Er ~ 0 in all three cases. In no case is the tangential electric field ES small, nearly toroidal, or nearly calculable from the magnetic vector potential A as -∂tAS. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ∂K can be estimated from measurements on ∂V of the magnetic field B and its time derivative ∂tB. A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.
In case (a), it is shown that knowledge of σ in M is unnecessary for estimating ES on ∂K with a relative error r ∂r 1n σ-1from measurements of ES on ∂V and knowledge of ∂tB in M (calculable from ∂tB on ∂V if σ is small). Then, in case (a), u just below ∂K can be estimated as -r×ES/Br. The method is impractical unless the contribution to ES on ∂V from ocean currents can be removed.
The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of r ∂r ln σ-1 a independent questions. It is found that as σ --> 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ --> 0. It is also found that the singular perturbation theory for r ∂r ln σ-1 is a useful tool in the perturbation calculations for σ when both σ and r ∂r ln σ-1 are small.

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