Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds
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2017-09-01
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Tyler, Robert H. Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds. NASA (2017). https://ntrs.nasa.gov/citations/20170011279
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This is a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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Abstract
An interesting feature of planetary bodies with hydrospheres is the presence of an electrically conducting shell near the global surface. This conducting shell may typically lie between relatively insulating rock,
ice, or atmosphere, creating a strong constraint on the flow of large-scale electric currents. All or parts of the
shell may be in fluid motion relative to main components of the rotating planetary magnetic field (as well as the
magnetic fields due to external bodies), creating motionally-induced electric currents that would not otherwise
be present. As such, one may expect distinguishing features in the types of electrodynamic processes that occur,
as well as an opportunity for imposing specialized mathematical methods that efficiently address this class of
application. The purpose of this paper is to present and discuss such specialized methods. Specifically, thin-shell
approximations for both the electrodynamics and fluid dynamics are combined to derive simplified mathematical
formulations describing the behavior of these electric currents as well as their associated electric and magnetic
fields. These simplified formulae allow analytical solutions featuring distinct aspects of the thin-shell electrodynamics in idealized cases. A highly efficient numerical method is also presented that is useful for calculations
under inhomogeneous parameter distributions. Finally, the advantages as well as limitations in using this mathematical approach are evaluated. This evaluation is presented primarily for the generic case of bodies with water
worlds or other thin spherical conducting shells. More specific discussion is given for the case of Earth, but also
Europa and other satellites with suspected oceans.