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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.

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