Welcome to Understanding Overunity!!!!!

[TinselKoala]

Hi Watts, thanks for being accepting.
The L1 coil is there, _I think_, so that there remains some relatively high impedance between the battery positive and the mosfets when operating at the design frequency. The drive coil itself is very low impedance usually. With a non-center-tapped drive coil, as in my wireless transmitters, the drive coil isn't center tapped and is _really_ low impedance, so there are 2 "L1" chokes to the positive rail, one on either side of the drive coil. I think this is the case. I had one transmitter fail when one of these chokes failed (got too hot, shorted thru the cheap wire enamel insulation, and actually broke the ferrite core, along with blowing both mosfets.) I'll be interested to see your take on these chokes. I have found that their value isn't too critical; I've used as low as 40 uHy in my transmitters when the schematic calls for 100 uHy. I'm operating at around 800 kHz for the wireless (IIRC, I haven't measured it lately). I've seen some lower frequency  center-tapped versions that call for 1000 uHy here along with big spiral transmitter coils, I haven't played around much with those yet. My best flyback driver (center tapped, one choke) uses about 120 uHy for this choke and works awesomely well.
The Zeners in the drawing I posted, and in the "Hendershot" drawing from Dave, are "gate protection" Zeners which limit the voltage at the mosfet gate by shunting any overvoltage directly to the mosfet source (negative rail, ground.) Most of the mosfets we use have a 20 Volt gate-source limit, some have 30 volt limit. Using 12-volt or 15-volt Zeners here in these circuits is a simple way of allowing the DC input voltage to go higher - 36 volts or more - without taking the chance of exceeding the gate-source limit of the mosfets. If the zeners weren't there you'd be limited on your supply voltage to something that the gate can handle.  There is a _lot_ of reactive power circulating in the coils of these circuits, which is why you need very low Rdss mosfets, because even with true ZVS the mosfets are carrying a lot of peak current when they are on.

In that last circuit of Dave's using the ignition coil to drive the output arrangement (through a spark gap?) those first two diodes are going to have to be capable of handling at least 20 kv PIV, I think.....  so I wonder why not use a modern flyback transformer, whose output is already rectified by its internal HV diodes....

[Dave45]

Finding the best way to explain 
A coils magnetic field resists change not only because of the direction of current through the coil but also the polarity of the current.

[Dave45]

One side needs a pos pulse the other a neg pulse preferably at the same time.
http://jnaudin.free.fr/html/afep01.htm
Naudin using the AV plug
Look at the fwbr and you will see the av plug.

[TinselKoala]

Finding the best way to explain 
A coils magnetic field resists change not only because of the direction of current through the coil but also the polarity of the current.

What is the difference between the "polarity of the current" and the "direction of current" ?

[Dave45]

What is the difference between the "polarity of the current" and the "direction of current" ?

I was trying to spit it out, it came out wrong 

I was thinking on the zvs,
The capacitor sets the frequency that the coils run at, it acts like a spring catching the bemf from both coils.
What happens when we put diodes before the cap, the cap catches the bemf but does not return the energy back into the system, we have freed the coils up to run at their maximum, their only limit would be component speed, wire resistance, core resistance. It would runaway.