Construction of Steady-State Hydromagnetic Dynamos. I. Spatially Periodic Fields

摘要

Steady-state hydromagnetic induction in an infinite three-dimensional fluid conductor is studied under the assumption that the velocity field is periodic in space and representable as a finite trigonometric series. It is shown that there exist fields of this type, which include certain perfect fluid motions, such that the corresponding induction equations possess non-trivial regular solutions which vanish at infinity. The conductor thus behaves like a self-excited fluid dynamo, and any such motion is said to constitute a periodic dynamo. (Author)