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.