The shorted coil tries to hold the flux constant (for a reasonable time shorter than the time constant),
No, the coil does not try to hold the current constant. It tries to hold the magnetic flux constant. ,it does not hold the current constant.
Indeed it does not. This is clearly stated in pt.4 of this analysis. So as the ferrite moves towards the coil the current decreases rapidly.
...but the inductance increases rapidly, too. When the ferrite is symmetrically within the coil you have an instantaneous energy balance of (a) energy within the (now increased) inductance of the coil at a much smaller current than the original starting point
Smaller current in higher inductance does not have to amount to lower energy. I think you will find that the sum of those two energies is equal to the original energy stored in the coil at the starting point.
Perhaps, but that expectation is dictated only by the conservation of energy law, which workaround is the purpose of this forum. Perhaps the the Li 2 product stays constant while the ferrite is being attracted and not the sum of EM energy and Kinetic energy. This is what the CARA experiment is designed to check. P.S. Aren't there ways to increase the inductance/permeance without increasing KE, eg.: the Villari effect or magnetocaloric stuff or the ferroelectric methods described in that IEEE article by Konrad & Brudny ? In such systems the coil will also try to hold the flux constant and the current will decrease as the inductance/permeance increases.
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