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Colburn 1980
Colburn, D.S. (1980). Electromagnetic Heating of Io. Journal of Geophysical Research 85: doi: 10.1029/JB080i012p07257. issn: 0148-0227.

Electrical-density deposition within Io is a possible mechanism for heating the interior, the source of the electrical current system being the relative motion of Io with respect of Jupiter's magnetic field. The transverse-electric mode currents circulate entirely within Io, with the frequency of Jupiter's rotation rate as observed in the Io frame. Maximum heating for Io is obtained if the electrical conductivity is 0.02 mho m-1, a value spanned by estimates of rock conductivity for hot interiors. Under present conditions, the maximum heating available from the transverse-electric mode is some 3 orders of magnitude less than would be necessary to maintain Io's estimated heat flow. Confinement of Io's field by the external plasma would raise this estimate only moderately. The transverse-magnetic mode is effectively blocked by the cold outer surface layers, the current being bypassed by an alternative current conduction path through the ionosphere, leaving an insignificant amount in the interior. Although the transverse-magnetic heat source can be concentrated at local surface hot spots, the temperature rise is not significant on a time scale appropriate to localized heat sources. It is possible that significant heating was generated in the past by a magnetic field that was larger and had a higher frequency. Heating could have been significant also if Io's ionosphere had not been present.

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Journal of Geophysical Research
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