But the collapse of the B field can't provide more than the initial energy, because there's no reason why the work involved in reorienting the dipoles to the rest position should be greater than that involved in orienting them when B is at its maximum
Maybe you did not mean this, but what you have written implies that the energy supplied to magnetize the core occurs after B has reached its maximum value, and that is not the case. The energy is drawn from the source while B is rising due to the dipoles coming into alignment, and the value of B finally reached comes predominantly from the aligned dipoles; the applied current only produces a small contribution to B . Your statement seems to admit that work is involved (energy is consumed) for both the magnetization and the demagnetization phases. You only have to look at the first and second quadrant of a typical BH curve to see that the two energies are not the same, the demagnifying energy consumed in the second quadrant is less than the magnetizing energy in the first quadrant.
The SEMP system does not supply energy to demagnetize, there is some external source doing that. Energy appears in the load resistor as the B field decays. I see no reason why that work output from reorienting the dipoles to the rest position should be linked to that involved in orienting them into alignment when that reorienting field is simply the carrier of energy from the external force to the load resistor. Yes, that external force must supply the extra energy over and above the realignment value.
It's the extra energy needed at the start to reach the final current, i.e. the energy required in addition to that needed to overcome the Joule effect, that represents the magnetizing energy.
You seem to divorce the Joule heating from the magnetizing energy, but the Joule heating of the core is inextricably linked to the BH loop area and the loop only has area if remanent magnetism plays its part, which is very much the case here.
When we apply direct current to a coil, the field created by the electric current reorients the material's magnetic dipoles, and the electrical energy used to work on the dipoles is stored in the B field. The B field models this re-orientation of the dipoles.
That is true only for linear material where there is no remanence. Then the energy stored in the B field is recoverable. In the SEMP system the remanent B field does not directly model the reorientation, it is the time history of the B field that models that energy. The integral of B wrt time yields the voltage that loads the current source, and very conveniently that energy is mapped by the area within the BH loop.
The electric current then serves only to overcome Joule effect losses.
If by Joule losses you mean i2R losses then certainly that is directly linked to the current. But the current is essential for driving the dipole alignment and delivering the energy needed to do that.
When we supply an alternating current to a coil, the alternation corresponding to the current rise is equivalent to the previous case, until we reach the sinusoidal maximum, at which point the additional energy compared to the joule losses will have been stored in the B field. At the alternation corresponding to the fall in current, the collapsing energy of B is returned to the current, so less energy is required from the source. This explains why an LC resonant circuit is able to maintain an oscillation, and all the better if the circuit resistance remains low. Over a whole number of periods, losses aside, we have an energy balance of zero.
Again you are considering a core that has negligible remanence where energy is stored then retrieved, where the quantity of energy stored relates to the B field via the uR of the core material. The small remanence determining the area of the BH loop you have dismissed as Joule losses. This does not apply to the SEMP system.
The idea that demagnetization is linked to a natural phenomenon, for example because we're working near the curie point, or that magnetization/demagnetization takes place slowly or quickly, or that it involves a delay that would allow it to take place after the source current has been cut off, doesn't change the issue at all. Magnetic energy can be recovered in any case.
And what is the quantity of energy to be recovered? In my consideration of a square-loop material, when magnetized the core u
R has dropped to unity when the current is switched off. At that instant the energy stored in the B field with u
R = 1 is far greater than the energy used to magnetize. We have a core that acts like air if we ignore eddy currents. This is already known in magnetic theory where the air space occupied by the core is used to determine the load line applied to the BH curve of permanent magnets. I stick by my view that when some external force is driving the dipole reorientation it is driving the change in M so we can’t then claim M is available to get u
R>>1, we must consider an air core. That yields an output energy that can exceed the original input by quite a margin. The source of that energy is the external force.
Smudge