New Magnetic Motor Principal?

[FatChance!!!]

Ideally, the coil will be energized with a 50% duty cycle  at an RPM that is at a resonant frequency so the dead area at the mid point is not critical.

If you plan any magnet motor where you use 50% duty cycle you can forget about the chance of reaching overunity.
I'm going to make you a little comparison for you to understand the forces somewhat better.

1) The regular 10mm thick N42 NdFeb is similar in electromagnetic strength as an electromagnet wound 11000 turns
and using 1amp of current in super cooled state. This translates to 11000 ampturns. At 2cm it is 22000 ampturns.

2) When your neo enters/passes the electromagnet it induces a voltage. The stronger the electromagnet the
higher the induced voltage. If you need a 10 amp pulse in a e.g 2 ohm electromagnet to run your motor this comes to 200W.
At 50% duty cycle you are using 100W per pulse. But this is without the induced voltage.
If the passing neo induces, let's say, 100V at a certain RPM (the voltage increases by the RPM) then you need to pulse
your electromagnet 10A x 2R = 20V + 100V induced = 120V x 10A = 1200W at 50% = 600W
WOW.....now you need 600W instead of 100W input just because of the induced voltage.

Don't ever think you can get away with less amount of current in your electromagnet.
I have built several and it takes 15000-20000 ampturns to get a reasonable strength and this is still far, far away from any neo.
The electromagnet ampturn = the number of turns times the current passing through.

If you design your EM by using a high number of turns to decrease the current needed you face extremely high inductance to
energize (this takes time and power) not to speak of the induced voltage reaching perhaps 1000V at each passage.

I'm not trying to be rude, tell you lies or fool you in any way. This is pure facts that must be dealt with in all designs.
Most people don't even know about the induced voltage and they get surprised when their motors consumes a lot
more than they ever expected in their ignorant dreams.

[lumen]

Fatchance,

Sure, I understand that, but again you are fighting the field in other designs by attracting or repelling from your coil.
This design should not fight the field at any point along it's path or you are defeating the concept.
I say a 50% duty cycle because that is what you would get at a resonate frequency anyway. Operating at a resonate frequency with a 1/2 wave input would allow it go into a high impedance state that would draw virtually no power!
Because you are not fighting any existing field direction, the coil does not need high current to establish it's magnetic field. Only about the same as if it were operating in open air!

When your coils are applied an increasing frequency, they will eventually reach a resonate point where the current drops to near zero.

[FatChance!!!]

Ok, sounds good.
I wish you the best of luck and progress in your design.