Towards a rapidly rotating liquid sodium dynamo experiment

Abstract

The main characteristics of the Earth's dynamo are reviewed. The combined actions of Coriolis and Lorentz forces lead to the so-called \magnetostrophic regime. We derive an estimate of the power needed to sustain the magnetic eld in this regime. We show that an experiment with liquid sodium can be designed to operate in the magnetostrophic regime. Such an experiment would bring most valuable information on the mechanisms of planetary dynamos. In order to prepare this large-scale experiment and explore the magnetostrophic balance, a smaller scale liquid sodium set-up has been designed and is being built. It consists of a rapidly rotating spherical shell lled with liquid sodium, in which motions are set by spinning at a dierent rotation rate an inner core permeated by a strong magnetic eld. We discuss the processes that can be explored with this new device. 1. The magnetic elds in the solar system. Most planets of the solar system have or have had an internal magnetic eld. Recent satellite missions have revealed that Mars probably had a magnetic eld in its early history (1), while two moons of Jupiter, Io and Ganymede (2), show evidence for present magnetic activity. Explaining the origin and behaviour of planetary magnetic elds is a fascinating challenge. As a starting point, one may attempt to build a model of the geodynamo since the Earth's magnetic eld is, by far, the best documented. 2. The Earth's magnetic eld. The characteristics of the magnetic eld of the Earth are known over a wide range of time scales. In historical times, observa- tory records permit to monitor the secular variation of magnetic structures, with typical drift velocities of 0.1 mm/s. Sudden variations of the internal magnetic eld, aecting the entire core surface, have also been discovered in these records, the so-called \jerks, while the total intensity of the eld displays large fluctua- tions and has dropped by more than 30% in the past 2000 years, as recorded in archaeological artefacts.The most striking property of the Earth's magnetic eld, as seen at present, but also in the paleomagnetic records over several hundred of million years, is that it is dominated by a dipole component, whose axis is aligned with the axis of rotation of the Earth. Just as fascinating is the evidence that this dipole has changed polarity many times over the Earth's history, the last inversion having taken place only 780,000 years ago (3). Models of the geodynamo aim at explaining this rich set of behaviours, starting with the dominant dipole character of the eld. 3. The mechanism. Since the pioneer work of Larmor, Bullard and Elsasser, it is widely accepted that the Earth's magnetic eld is created by self-induction in its core. In an electrically conducting liquid, fluid motions in a magnetic eld produce electrical currents, which in turn feed the magnetic eld. When the induc- tion of the magnetic eld overcomes its diusion (i.e., for a large enough magnetic