Akula0083 30 Watt Self Running Generator.

[verpies]

@Dave
It is true that you  did not state that the current through a deenergizing inductor reverses but you seem to have implied it.
The voltage (EMF) generated across such deenergizing inductor may appear too reverse if you measure it between two different points in a circuit (e.g. in the Boost Converter circuit).

All EEs and physiciscts understand it very well and there is no need for you to educate us on this part.  We are not sleeping as you have implied.

Also, the fact that a diode has two major ratings (max forward current and max reverse blocking voltage) does not mean that current can be separated from voltage as a concept.

As far as the nature electricity, it is fine to question it.  We do not have a proof that charged electrons are the sole carriers of electric current in solid conductors, although this is often assumed and taught in educational institutions. 
But, for engineering purposes it just does not matter.  The Ohm's law, Faraday's law of induction, etc... are heuristic, empirical laws that were bench proofed for centuries.  Electric circuits really behave according to them even if most of us don't know what goes on under the hood.

[verpies]

Case 1:  When the Stop switch is open-circuit.
When the MOSFET is on, the current flows through L1 and then through the MOSFET to ground.  This is the energizing phase for the magnetic core.  The LEDs may be lit from C3 still discharging from the previous cycle. 

Yes. These load LEDs can also be lit from the turn-on transient when the bootstrap power is first applied to the whole circuit.
L1, C3, R1 and R5 form a series LCR circuit that makes this possible. 
This is boring, of course.  I wrote it only for completeness.

When the MOSFET switches off, the current flow follows the red path.  This is standard Bedini fare like I said before, with the addition of the big C3 decoupling cap to absorb the current spikes and convert them into the voltage that drives the LED array. Not much exciting there.

Yes, it has a high yawn factor. With the L1 circuit alone, it works as a standard Boost Converter.

Case 2:  When the Stop switch is a short circuit.
When the MOSFET switches on, L2 will output a DC EMF that is the duration of the on pulse.  The battery voltage plus the EMF generated by L2 (they add together)

You can't be sure of that because the dot convention on that schematic cannot be trusted.

will then follow the blue DC discharge path on the schematic.  However, there is the 430 kohm resistor R2 in the path.  That's almost like an open circuit.  C4 will pass a tiny puff of AC current flow that will be absorbed by C3.  So there is a very tiny DC current flow and a little puff of AC current flow when the MOSFET first switches on.

Yes, if L2 is really connected so that the battery voltage plus the EMF generated by L2 add together.
It is interesting to consider the motives of the designer here.  Why did he think that R2 and C4 are needed at all?

When the MOSFET switches off, this one might be an unpleasant surprise to some.  The current follows the green path.  There still may be some voltage in C3 that keeps the LEDs barely lit, but this has nothing to do with the green current path.
When you look at the green current path you notice that no energy at all is returned to C11. 

The behavior of the circuit appears different if you look at this simulation with the L2 connection reversed.

There you can actually see the current  returned to C11 (a battery in the simulation).
The D2 - the2^nd diode (the one associated with L2) starts conducting when the voltage across C3 + L2 exceeds the battery voltage.
In this scenario, the effect of D2 seems to be to limit the voltage of C3+L2's EMF to less than battery voltage.  Like an overvoltage non-dissipative clamp of sorts...

It is interesting to note, that the feedback take-off point (junction of R5 & R7) used by the TL494 PWM controller to shorten its output ON pulse width, matters only when its voltage level falls to 0V (or below ground) or when its voltage decrease rate (slew rate of the falling edge) exceeds -6.6V/ms to -18V/ms (see Itsu's experimental video here).

There are very few cases when this TL494 feedback path would be activated.  Why would the author design such rare feedback pulse width limiting condition anyway?

Perhaps that Akula circuit is pure nonsense ...or perhaps when some unconventional magical event happens in the transformer, a very strong pulse is created in L2.  So strong that the feedback point  (junction of R5 & R7)  is quickly taken below ground for a brief time and a huge pulse of energy is returned to the battery (C11) through D2.

I know that, such event is far out, ...but this forum is about keeping our mind open to such possibilities, isn't it?

[Magluvin]

In the sim shown, if you right click on the switch being fed by the timing signal, the ohms of the switch is set at 20ohms(default). 

Im not seeing the inductors/caps nor the switch that cuts off the battery source.  The missing inductors affect efficiency.

Ill see if I can mod the circuit to fit those things.

Mags

[verpies]

I'm not seeing the inductors/caps nor the switch that cuts off the battery source.  The missing inductors affect efficiency.

In the simulation, the battery on the left plays the role of C11.

The bootstrap battery, associated switch and C16 are not included for simplicity.

[Dave45]

Here's a simulation you may find interesting
http://makeagif.com/oud1Sa