I don't like the naming "artifact". It is an Uind = -L*dI(t)/dt (Lenz's and Faraday's rule). So dI(t)/dt in the coil end up to dB(t)/dt where the magnetic field energy will be converted to heat during the flyback process. This seems the fastest way of killing the B field. The target is contributing to this process more or less.
If the induced voltage is not dissipated through the damping resistor, it will ring and eddy currents will still be produced on the targets (the magnetic field energy will then be dissipated on targets and conductive objects nearby the coil). But we are not taking VLF and PI process to the same level. We have the damping process, which we focus on. And I still state, this is the most important process of a PI, which kicks the target on PI method.
Anyway, we are almost describing the same. We have only different names.

Aziz



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