Homopolar Generator self-driving by using circumferential field and magnets?

[LeoFreeman]

Can I just throw in an idea to make a Homopolar Generator self-driving? Sorry if this is old-hat.

We can use the generated current to create a circumferential magnetic field around the rim of the copper disk.
This can be done easily with multiple radial loops of wire, as in the attached image.

The wire loop "basket" can be fixed to the surrounds, using brushes to get the current from rim of the rotating disk, and returning it via the axle.

Next, a series of permanent magnets are attached around the rim of the disk. These magnets would move through the wire loops as they interact with the loop's magnetic field.

Now the reason I think this setup might potentially be overunity, is this:

Say it requires a force F to keep the HP generator spinning at a given speed, overcoming friction, while generating a current I which results in circumferential magnetic field B.

Now, for a given circumferential field strength B, the magnetic pushing force f which pushes the rim magnets around is dependent only on the strength of those magnets, and so can be set almost arbitrarily high by selecting very strong magnets.

So if the magnetic pushing force f exceeds the required force F to keep the disk spinning, could we have overunity?

[LeoFreeman]

  Oooops.
That won't work, will it... 
A uniform field inside a toroid can't push a bar magnet around inside parallel to the field.  Is that correct?
But a bar magnet can interact with a shorter length of solenoid field, as in those videos of the "Simplest Electric Train" toy, eg https://www.youtube.com/watch?v=J9b0J29OzAU ?
Perhaps each bar magnet in my proposed machine could make electrical contact with only the loops in its immediate vicinity, as the "train" does.