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Imagine a horse-shoe magnet shaped core, you know, the red painted ACME cartoon magnet shape, made of soft iron, with a soft iron bar that some mechanical arrangement could move to open and close the iron circuit. A toothed soft iron rotor turning at the end of the pole pieces would be a good way to do this.
Now put two windings on the horseshoe. Bias one with a DCcurret, open and close the magnetic path by moving the iron bar, and viola, AC is induced in the secondary winding, as movement of the bar varies the reluctance of the iron circuit, and hence the total flux passing through the secondary.
I doubt that there are any commercial generators based on this principle, but in reverse it is just a variable reluctance motor.
Could this be done with a single iron core, without mechanical movement? Yes, raising the core to the Curie temperature would drop its permeability, maybe all the way down to unity. But heating/cooling a solid core is not going to be very efficient.
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how to vary magnetic reluctance
