Homogeneous dynamos and terrestrial magnetism

Abstract

The main object of the paper is to discuss the possibility of a body of homogeneous fluid acting as a self-exciting dynamo. The discussion is for the most part confined to the solution of Maxwell’s equations for a sphere of electrically conducting fluid in which there are specified velocities. Solutions are obtained by expanding the velocity and the fields in spherical harmonics to give a set of simultaneous linear differential equations which are solved by numerical methods. Solutions exist when harmonics up to degree four are included. The convergence of the solutions when more harmonics are included is discussed, but convergence has not been proved. The simultaneous solution of Maxwell’s equations and the hydrodynamic equations has not been attempted, but a velocity system has been chosen that seems reasonable from a dynamical point of view. A parameter in the velocity system has been adjusted to satisfy the conservation of angular momentum in a rough way. Orders of magnitude are derived for a number of quantities connected with the dynamo theory of terrestrial magnetism. It is concluded that the dynamo theory does provide a self-consistent account of the origin of the earth’s magnetic field and raises no insuperable difficulties in other directions.