Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos

In the Earth's fluid outer core, a dynamo process converts thermal and gravitational energy into magnetic energy. The power needed to sustain the geomagnetic field is set by the ohmic losses (dissipation due to electrical resistance). Recent estimates of ohmic losses cover a wide range, from 0.1 to 3.5 TW, or roughly 0.3-10% of the Earth's surface heat flow. The energy requirement of the dynamo puts constraints on the thermal budget and evolution of the core through Earth's history. Here we use a set of numerical dynamo models to derive scaling relations between the core's characteristic dissipation time and the core's magnetic and hydrodynamic Reynolds numbers--dimensionless numbers that measure the ratio of advective transport to magnetic and viscous diffusion, respectively. The ohmic dissipation of the Karlsruhe dynamo experiment supports a simple dependence on the magnetic Reynolds number alone, indicating that flow turbulence in the experiment and in the Earth's core has little influence on its characteristic dissipation time. We use these results to predict moderate ohmic dissipation in the range of 0.2-0.5 TW, which removes the need for strong radioactive heating in the core and allows the age of the solid inner core to exceed 2.5 billion years.