Kinematic Dynamo Problem

The properties of the dynamo equation are discussed to show that the dynamo equation is self-adjoint for a curl-free velocity under a suitable restriction. The impossibility of a steady dynamo by a motion having only a radial velocity component which vanishes at the boundary surface is proved, and an attempt has been made to verify the possibility of an oscillating toroidal field dynamo. Also it is shown that any poloidal magnetic field cannot be amplified by a uniform stellar contraction, while quasi-steady toroidal fields can be maintained by a homologous contraction.