Title: Power Requirements for the Earth's Magnetic Field
Bruce Buffett, University of Chicago

Abstract: Paleomagnetic measurements show that the Earth has possessed a magnetic field for at least 3 billion years. The persistence of the field requires continual regeneration because ohmic losses would otherwise dissipate the field in less than 105 years. The precise nature of the dynamo process is poorly understood, although it is probably driven by vigorous convection in the electrically conducting, liquid outer core. A supply of energy is needed to power the dynamo, and the most important sources are usually associated with cooling and solidification of the core. Some of the energy available to the dynamo arises through latent-heat release on solidification and through the associated generation of compositional buoyancy by exclusion of light elements from the iron-rich solid inner core. Other possible sources of energy include the thermal energy associated with cooling and radioactive heat sources.

The power required to operate the dynamo places tight constraints on the heat flow from the core. If the heat flow is too low, thermal convection is shut off and the rate of generation of compositional buoyancy by solidification becomes too low to drive the dynamo. Conversely, a high heat flow causes rapid growth of the inner core, so that convection prior to the appearance of the inner core must be sustained by thermal buoyancy alone. The attendant requirements on primordial heat become more severe as the age of the inner core decreases. Present-day estimates of heat flow from the core satisfy the power requirements for the dynamo. However, the resulting thermal histories predict implausibly hot conditions in the early Earth.

One way to reduce the high temperatures at early times is to add radioactive heat sources to the core. Additional heat sources slow the rate of cooling of the core, which lowers the core temperature as we extrapolate back in time. For example, a potassium concentration of several hundred parts per million (by weight) provides enough heat from the decay of 40K to eliminate the problems with the thermal histories. Another way to reduce the high temperature at early time is to lower the heat flow from the core. This can be accomplished without a substantial revision of the current core temperature by accumulating heat-producing elements in a layer immediately above the core (e.g. the D" region). Limits on the concentration of heat-producing elements in such a layer are set by the minimum heat flow needed to run the dynamo. Given the uncertainty in the power consumption of the dynamo, it is possible to find reasonable thermal histories that rely entirely on the presence on heat-producing elements in a layer above the core.