Lets start the new year with a bang!

[Hoppy]

Yes , there is certainly some talent on this forum. Hopefully, someone with good knowledge of magnetics will find some suitable core material, read your paper and run with your theory. Thanks for posting.

[pillsbury DOH]

Great stuff Hoppy -- I add this as some had not grasped the magnetic situation I haven grasped the picture aspect of things here .. yet so please use the links or pick it up at energetics

Oh .. please don' t think  I chide you not so .. I want you to clearly understand .. Its far far simpler than gauss and the like ... so don't worry your pretty heads so!
We could form a small chain of nails and paperclips as shown below:

http://www.animatedscience.co.uk/ks5_physics/general/Electricity%20&%20Magnetism/Magnetic%20Fields_files/Image869.gif

You really don't need to make things complicated so dont ! Do you think a fool such as myself could possibly work it out if it was complicated ?  And luckily
'What one fool can do, another can  (ancient simian proverb) quoted by Silvanus P Thomson (a noted FE researcher himself)

http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Silvanus_Thompson_age_25.jpg/200px-Silvanus_Thompson_age_25.jpg

This is so easy you rush by but don't see . You see the Bar magnet holding Iron nails ? If you very gently removed the bar magnet from the top nail why all of the nails would Immediately separate and fall to the floor .... that's because Iron is a 'Soft magnetic material' this is what our four separate  cores are made of .  Soft magnetic material .
The other end of the magnet is Holding paper clips , They are not made of Iron they are made of mild steel  MS is a 'hard magnetic' that means if you carefully remove the magnet all the paper clips will remain stuck together, they will remain magnetised because Mild steel is a very hard magnetic material . Exactly what we do not want . 
Now so you under stand a little better what is occurring picture the particular Iron nail the arrow is pointing at to be one of the four electromagnets I have drawn , (in fact one of the electromagnets supplying the load) what would happen to the poles of that Iron nail if the one above it and the one below it reversed polarity ? Why it would have to instantly reverse poles itself.
Now to take your Imagination just one step further I'm sure most have an Idea how a transformer works ,, or rather how we are taught it works ... now imagine that nail to be the secondary core of a transformer . With windings on it . Each time the flux changes direction .. why It induces a voltage
and the formula for the voltage produced is
http://www.forkosh.com/mathtex.cgi?emf,\;e\;=\;-T\frac{d\phi%20}{dt}

http://www.forkosh.com/mathtex.cgi?emf,\;e\;=\;-T\frac{d\phi }{dt}


                                 .. where T is the number of turns
                                                                               dΦ is the changing magnetic flux 
                                                                    E = -T  ---------------------------------------
                                                                                dt is the time it changes in

For those who hate to tangle with calculus in any shape or form

E = Turns x (Φ1-Φ2)      is quite sufficient where Φ1 and Φ2 are the minimum and maximum flux
                   -------------                     
                     t1 – t2)      whilst t1 and t2 are the times of each cycle

http://www.electrical4u.com/emf-equation-of-transformer-turns-voltage-transformation-ratio-of-transformer/ 
So now do you grasp how simple it really is ? There is no need to get complex .. there is nothing complex or complicated happening here or else I couldn't possibly under stand it I assure you.
Now perhaps you also see why Steve Mark was so busily engaged in working out turns ratio's It is essentially a transformer action.. although much faster than you would normally be used to . Which is why as I say I  am struggling to find suitable core material.  I hope that clears things a little bit for you all. 

[pillsbury DOH]

So another little piece of the jigsaw has slotted into place ! How did Steve mark cut through the toroid ? Well as you know I postulated speaker voice coil core was what he would have used.
However Its years since I pulled a loud speaker apart . The stuff must obviously be very soft (magnetically that is) and obviously capable of huge power handling some of those speakers at rock gigs push well over 1000 watts but I hadn't seen the stuff , when I saw a link not at all what I really expected here it is look]

http://en.wikipedia.org/wiki/Voice_coil

very light pretty frail stuff .. now I can see how Steve Mark could cut the thing in half ... can't you?   scub that stuff doesn't seem magnetic  .... or at least not the one I'm a looking at!

[Cadman]

Non plated #7 shot reportedly makes very good hi frequency cores. Put the shot in a flat pan and spray with polyurethane paint, dry, mix with epoxy and pour into a mold. 10 lbs. Of #7 shot costs about $20 US + shipping.

[Marsing]

hi..  Hoppy, pillsbury DOH and all

any progress ?.