Kinematic dynamo action in a network of screw motions; application to the core of a fast breeder reactor

Abstract

Most of the studies concerning the dynamo effect are motivated by astrophysical and geophysical applications. The dynamo effect is also the subject of some experimental studies in fast breeder reactors (FBR) for they contain liquid sodium in motion with magnetic Reynolds numbers larger than unity. In this paper, we are concerned with the flow of sodium inside the core of an FBR, characterized by a strong helicity. The sodium in the core flows through a network of vertical cylinders. In each cylinder assembly, the flow can be approximated by a smooth upwards helical motion with no-slip conditions at the boundary. As the core contains a large number of assemblies, the global flow is considered to be two-dimensionally periodic. We investigate the self-excitation of a two-dimensionally periodic magnetic field using an instability analysis of the induction equation which leads to an eigenvalue problem. Advantage is taken of the flow symmetries to reduce the size of the problem. The growth rate of the magnetic field is found as a function of the flow pitch, the magnetic Reynolds number (Rm) and the vertical magnetic wavenumber (k). An α-effect is shown to operate for moderate values of Rm, supporting a mean magnetic field. The large-Rm limit is investigated numerically. It is found that α=O(Rm^−2/3), which can be explained through appropriate dynamo mechanisms. Either a smooth Ponomarenko or a Roberts type of dynamo is operating in each periodic cell, depending on k. The standard power regime of an industrial FPBR is found to be subcritical.