1 - Fundamentals of Dynamo Theory

Summary

INTRODUCTION

Cosmic Dynamos

Many stars, planets and galaxies possess magnetic fields whose origins are not easily explained. Even the ‘solid’ planets cannot be sufficiently ferromagnetic to account for their magnetism, for the bulk of their interiors are above the Curie temperature at which permanent magnetism disappears; obviously the stars and galaxies cannot be ferromagnetic at all. Nor are the magnetic fields transient phenomena that just happen to be present today. Palaeomagnetism, the study of magnetic fields ‘fossilized’ in rocks at the time of their formation in the remote geological past, shows that Earth's magnetic field has existed at much its present strength for the past 3 x 10⁹ years, at least. But, unless they contain sources of electric current, conducting bodies of spatial dimension, L, can retain their magnetic fields only for times of the order of the electromagnetic diffusion time τ_η = L₂/η, where η is the magnetic diffusivity of their constituents; η = l/μ₀σ, where σ is their electrical conductivity and μ₀ is the permeability of free space. (SI units are used throughout.) Being proportional to L², this time may be very considerable, but is as nothing compared with the ages of the bodies concerned. For example, Earth contains a highly conducting region, its core, of radius about L = 3.48 x 10⁰ m, and its conductivity is about 4 x 10⁵ S/m. This gives η ≍ 2 m²/s and τ_η ≍ 200,000 years. Similarly, it is thought that the magnetic fields of other planets cannot be fossil relicts of their birth. A mechanism is required to maintain them.