The Axisymmetric Self-Exicited Fluid Dynamo.

The behavior of axisymmetric magnetic fields maintained by electric currents in electrically conducting fluids of finite volume executing axisymmetric motion is studied at length. It is shown that the fluid motion cannot indefinitely increase any of the external multipole moments of the field, cannot prevent the decay of the external dipole moment, and cannot lengthen the decay time of the dipole moment by a factor of more than about 4 over its decay time in the absence of fluid motions. It is also shown that a certain weighted space average of the internal magnetic energy decays like the' external dipole moment. When the fluid velocity is very high, an asymptotic expression for the rate of decay of the toroidal field is given. One application of these results is that if the geomagnetic field is maintained by a self-excited dynamo, the absence of axisymmetry of the field is probably essential to its generation and maintenance.