I don't know how "audio magnetic amplifiers" are related to the original post. Their operation (modulating a DC power source) is obviously quite different from a AC power controller.
Generally speaking, in both cases the actual core and winding data have to put into the calculation.
As I already mentioned, using a single core/single magnetical core for the magnetic amplifier, in constrast to usual transductor or dual core topologies, results in tight, possibly unrealistic requirements for the control circuit, e.g. need for a current source with large voltage compliance. But I presume, this details can be well calculated.