Fast dynamo action in a steady flow

The existence of fast dynamos caused by steady motion of an electrically conducting fluid is demonstrated by considering a two-dimensional spatially periodic flow in which the velocity is finite and continuous everywhere, and in which the vorticity is infinite at the X-type stagnation points. A mean-field model is developed using boundary-layer methods, and the magnetic field is confined to sheets with width of order R exp -1/2. The mean magnetic field is uniform on horizontal lines, and its alternating directions give it a rope-like structure within the sheets. Two sources of alpha-effect are found whose relative strength for a given flow is a function of R and the vertical stretched wavenumber beta. When the vorticity is finite everywhere and beta is much less than 1, it is shown that the dynamo is almost fast, with growth rates of order 1/ln R.