  We consider the evolution of cosmological magnetic fields in FRW models and
outline a geometrical mechanism for their superadiabatic amplification on large
scales. The mechanism operates within standard electromagnetic theory and
applies to FRW universes with open spatial sections. We discuss the general
relativistic nature of the effect and show how it modifies the adiabatic
magnetic evolution. Assuming a universe that is only marginally open today, we
estimate the main features of the superadiabatically amplified residual field.
