The screw dynamo is one of the simplest examples of a conducting fluid flow in which magnetic field can be self-excited provided the magnetic Reynolds number is sufficiently large (see, e.g., Roberts 1993). Such a flow can be encountered in some astrophysical objects and also in such technological devices as breeder reactors. For example, jet outflows in active galaxies and near young stars can be swirling. A flow of this type is used for modelling the dynamo effects in laboratory conditions (Gailitis 1993). The generation of magnetic fields by a laminar flow with helical streamlines was discussed by Lortz (1968), Ponomarenko (1973), Gailitis & Freiberg (1976), Gilbert (1988), Ruzmaikin et al. (1988) and other authors as an eigenvalue problem. Below we use the results of the asymptotic analysis of this problem for large Rm by Ruzmaikin et al.

We introduce an axisymmetric velocity field whose cylindrical polar components are (0, rω(r), v2(r)), with (r, φ, z) the cylindrical coordinates. We

consider smooth functions v2(r) and ω(r) vanishing as r → ∞. Both v2 (0) and ω(0) are assumed to be of order unity.

For Rm ≫ 1, an eigenmode of the screw dynamo represents a dynamo wave concentrated in a cylindrical shell of thickness ≃Rm−1/4 a certain radius r0.