This is very interesting, and so very important.
The magnet affects the collapsing field in the core. Does this also change the output from the secondary, or only the choke? What if the magnet were placed on the secondary rather than the primary? If the output of the choke is magnetic in some way, will one wire from the choke to a small plate held next to a stream of water deflect the water?
I think I'll try putting a magnet on the bottom of an ignition coil.