A fuel-efficient geodynamo?

The hunt has been on for a source of extra power to account for the dynamo that generates the Earth's magnetic field. A synthesis of computation and experiment now suggests that the search may not be necessary after all.

The Earth's magnetic field originates in the core, a fluid region almost 3,000 km below our feet of which the main constituent is molten iron. The basic mechanism of field generation is generally accepted — it is a dynamo process, in which the magnetic field is maintained by convection of the highly electrically conducting fluid. But the details are less clear.

For example, how much power is required to drive the geodynamo? With current estimates, the inferred heat flow from the core is not enough to drive a dynamo over most of Earth's history, as is required from measurements of a strong magnetic field recorded in ancient rocks. One possible explanation lies in a re-evaluation of the composition of the core — could it contain more potassium, which would provide an additional heat source from radioactive decay¹? Some geochemists are coming round to this idea, but it remains controversial. On page 169 of this issue², Christensen and Tilgner offer an alternative — they argue that less power than previously estimated is required to drive the geodynamo, and that no additional heat sources are necessary.

The past ten years have seen great progress in understanding the generation of the geomagnetic field, driven primarily by improvements in computing resources that have made numerical models of the dynamo possible. Some dynamo models closely mimic features seen in magnetic-field observations, both historical and over millions of years^3,4. However, because computational resources are inadequate, and are likely to remain so, none of these models can claim to represent the Earth: model viscosity values are orders of magnitude too high for the core, and the rotation speeds are much too slow. As a result, direct quantitative comparison with the Earth is impossible. In fact, we are so far from using true Earth-like parameters that the surprise is not that the models don't always produce fields that look like the Earth's, but that any of them do.

To address this problem, two complementary approaches have emerged. The first is to drive the numerical models as close to Earth-like parameters as possible, often with ‘unphysical’ numerical schemes, and to hope that the resulting models are close enough to realistic conditions. The second has been to consider a suite of dynamos in more computationally accessible regimes and, by varying the parameters involved (viscosity, rotation rate, convection strength), to derive scaling relationships that can then be extrapolated to an Earth-like regime. However, the relationships are derived over little more than one order of magnitude of parameter space, and must then be extrapolated over many more orders of magnitude to reach that regime.

Christensen and Tilgner² demonstrate precisely the pitfalls of such a scheme. They obtain two scaling relations for the power required to drive the dynamo, one a function only of the strength of the flow, and a second additionally a function of fluid viscosity. Both models fit their simulations well; the second model is only weakly dependent on viscosity, but for extrapolation to realistic Earth conditions that dependence is vital. Which model should we believe: the one-parameter model, which allows the geodynamo to be driven without an additional heat source, or the two-parameter model, which requires more power?

Christensen and Tilgner address this issue by recourse to a new and exciting tool for studying the core. Experimental dynamos are being developed by several groups⁵, involving apparatus that contains highly conducting liquids, usually liquid sodium. One such experiment⁶ in Karlsruhe, Germany, has successfully generated a magnetic field by dynamo processes in a parameter regime inaccessible to numerical models (Fig. 1). The results from that experiment are consistent with the simpler, one-parameter scaling relation, but not with the additional viscosity dependence. On this basis, the authors argue for a lower energy requirement to drive the dynamo, so that there is no need for extra potassium in the core.

Figure 1: Core simulations: the innards of the Karlsruhe experimental dynamo.

Forschungszentrum Karlsruhe

Liquid sodium is driven through the 10-cm-diameter pipes, and the flow generates and sustains a magnetic field.

It would be easy to poke holes in this analysis. The conclusion depends crucially on the experimental results. Although the experimental dynamo has a viscosity appropriate for the core, in other ways it is far from Earth-like. For example, rather than being a homogeneous sphere of fluid, it uses a complicated system of pipes to produce a flow geometry suitable for dynamo action. And it is kinematic: that is, the fluid is pumped, and the feedback of the magnetic field on the flow is very limited.

It could therefore be argued that the results have nothing to do with the geodynamo. However, other dynamo experiments are under development, consisting of contained spheres of liquid sodium, that are much closer to Earth's core geometry⁷. As results become available from these experiments, Christensen and Tilgner's approach will become increasingly powerful. We will probably never be able to model the parameter regime of the Earth, either by computation or experiment. But perhaps by combining the two we may be able to ‘sneak up’ on the Earth and make true quantitative predictions for the geodynamo.