  It is well known that when two types of perturbations interact in
cosmological perturbation theory, the interaction may lead to the generation of
a third type. In this article we discuss the generation of magnetic fields from
such interactions. We determine conditions under which the interaction of a
first-order magnetic field with a first-order scalar-or vector-, or
tensor-perturbations would lead to the generation of second order magnetic
field. The analysis is done in a covariant-index-free approach, but could be
done in the standard covariant indexed-approach.
