  The generation of large-scale magnetic field in the kinematic regime in the
absence of an alpha-effect is investigated by following two different
approaches, namely the test-field method and multiscale stability theory
relying on the homogenisation technique. We show analytically that the former,
applied for the evaluation of magnetic eddy diffusivities, yields results that
fully agree with the latter. Our computations of the magnetic eddy diffusivity
tensor for the specific instances of the parity-invariant flow-IV of G.O.
Roberts and the modified Taylor-Green flow in a suitable range of parameter
values confirm the findings of previous studies, and also explain some of their
apparent contradictions. The two flows have large symmetry groups; this is used
to considerably simplify the eddy diffusivity tensor. Finally, a new analytic
result is presented: upon expressing the eddy diffusivity tensor in terms of
solutions to auxiliary problems for the adjoint operator, we derive relations
between magnetic eddy diffusivity tensors that arise for opposite small-scale
flows v(x) and -v(x).
