Kinematic-Dynamo Theory

Abstract

The general kinematic-dynamo equations are derived which give the rate of generation of a largescale magnetic field by a random velocity field, with or without large-scale shear. It is demonstrated that under the "short-sudden" approximation for the turbulent flow, the general kinematic-dynamo equations reduce to those previously derived by Parker. Under the "long-slow" approximation, the equations reduce to dynamo equations of the Braginskil type. It is demonstrated that the helicity of the turbulent Lorentx force is the basis for all turbulent-dynamo equations. That part due to helicity in the velocity turbulence was first isolated under the "short-sudden" approximation by Steenbeck, Krause, and Radler as a direct cause of dynamo action on its own (their "a-effect"). We also give a prescription for handling small bulk velocities, and small bulk-velocity shear, occurring in the general kinematic-dynamo equations.