On steady kinematic helical dynamos

The equations governing steady kinematic helical dynamos are studied, using the formalism of Benton (1979), when the flow has no radial component (in cylindrical coordinates). It is shown that all solutions must decay exponentially to zero at large distances, s, from the axis of the helix. When the flow depends on s only it is shown that a necessary condition for dynamo action is that the flow possesses components along both the primary and secondary helices. It is also found that periodic motion of one mode along the primary helix cannot support dynamo action even if the field is composed of mean and periodic parts.