I need more info to answer that, e.g.:
Are the two mutually-coupled coils "charged" sequentially or simultaneously? 
Is the bifilar winding wound in bucking mode or aiding mode (BTW: this detail should always be specified when using the phrase "bifilar winding") ? 
Does the saturation refer to a soft ferromagnetic core or a hard ferromagnetic core (hard ones exhibit high magnetic remanance after the magnetizing H field is removed) ?

All of it. So we can't miss any possibility to get a surplus of electric energy from somewhere.

These equations are based on centuries of empirical observations, such as voltage measured across inductors when the magnetic field inside them changes or the current that flows in a capacitance/resistance in response to voltage.
To invalidate those equations one of the effects observed by Ampere, Faraday, Lenz, Lorentz, Biot-Savart, Maxwell, Ohm would have to be proved to be wrong or incomplete or nonexistent.  The former two are still possible but require extraordinary experimental proof.

Are the devices of Kapanadze, Stepanov and Marks really not the extraordinary experimental proof? Because to my knowledge not a single observer of these experiments has come forward yet with any solid proof that even one of these experiments is fake.

The second argument that Kapanadze's or Stepanov devices work contrary to these equations is a weak one.  First of all we cannot be sure that they work at all.  Secondly we do not know their operating principle - for example Ampere, Faraday, Lenz, Lorentz, Biot-Savart, Maxwell, Ohm laws might be simply not applicable to their operational principle and the equations, that embody those effects, likewise might not be applicable.

If the laws of Ampere, Faraday, Lenz, Lorentz, Biot-Savart, Maxwell, Ohm are not applicable to the Kapanadze, Stepanov or Marks devices but only to ordinary electric circuits consisting of capacitors, coils and resistors then -as a logical consequence- the Kapanadze, Stepanov or Marks devices cannot be built out of ordinary electric parts. And this then makes the whole subject anything but clearer. Hence what to believe?

By the same token, it is entirely possible that entirely different types of electricity exist (e.g. uncharged electrons, cold electricity,  birotating electrons - Cooper pairs, electron triplets in counterspace) and that these different types do not obey the laws of conventional electricity.

OK, then how do I know for sure that this entirely different type of electricity will not manifest itself in an experiment contrary to all known differential equations because these equations are only valid for conventional electricity? In other words: Even a different type of electricity would need conventional electric parts to manifest itself because we (also most likely Kapanadze, Stepanov and Marks) don't have any unconventional electric parts (whatever that might be).

Lets think about this in a different way. What do you think a body in space is? A capacitance? Each planet in a solar system is one terminal of a capacitor.

Then we should think about this as if we are living between huge charged capacitor plates. Now imagine there is a charged capacitor, one huge plate is to the left of your table and one huge plate is to the right of your table. Which experiment on this table could be suitable to tap into the electric field of this inexhaustible capacitor without touching the plates?

Great philosophical discussions today ...

TK uses radiant energy. I suggest you look it up and formulate new laws of physics to explain it.
Moray used radiant energy.
Bedini uses radiant energy.
Tesla used radiant energy.
Stubblefield used radiant energy.
Some common denominators: RE is cold, also known as cold electricity.
Use batteries or capacitors to convert cold electricity to "normal" electricity.
Capacitors and batteries need conditioning to operate under radiant energy conditions.
Once conditioned, capacitors super charge.
How do I know? I've done the experiments and talked to TK.

I think I do know now the major error in all these differential equations: All these equations are only valid in a closed system. If we measure a circuit then normally we shield it even from the environment in order to get unadulterated results in accordance with the equations written in the textbooks. So if we want energy from the environment then shielding the circuit from it is not the brightest idea. But a differential equation which describes the function of a LC circuit cannot incorporate any perturbations coming from the environment because the specifics of these perturbations are generally unknown. That means we do not know whether the coils recharges the capacitor to -141.4% of the original voltage or to a different value if there is an entry point for radiant energy not considered by these differential equations.

So much for that philosophy.

You could be correct because we are told by Bedini that radiant energy cannot be measured by conventional EE measuring apparatus, so without a new non EE measuring apparatus being developed, its not possible to prove whether radiant energy enters a system. Bedini only believes from his theories that 'cold' radiant is sucked-into a system from the environment and converted into 'hot' energy in capacitors and batteries as he has no method of proving this experimentally. He claims that repeated load testing of a battery charged / conditioned by his energiser system will show the gain but this claim is hotly contested on the grounds that the process of desulfation by HV 'spikes' simply causes an increase in battery capacity through plate cleansing.

As for your comment about no solid proof that TK's devices are faked, there is at least some video evidence that strongly suggests the 'green box' device was faked, so given that a.King21 is still posting occasionally on this thread, I would yet again remind him that we need to see a good quality (original) video of the aqua2 device from his team.

It should be simplified in a way so that a carpenter can come across it by chance while connecting his workshop equipped with disk saws to the grid.
Is there any tangible outcome after all these dozens of pages? If not then obviously something important has been missed here. What could that be?

Maybe that in a parametric (amplification) circuit there should be an entry point for the ambient (radiant) energy in order to excite the oscillations successfully? Just like an audio amplifier which needs a signal on its input in order to amplify.
I think I do know now the major error in all these differential equations: All these equations are only valid in a closed system. If we measure a circuit then normally we shield it even from the environment in order to get unadulterated results in accordance with the equations written in the textbooks. So if we want energy from the environment then shielding the circuit from it is not the brightest idea. But a differential equation which describes the function of a LC circuit cannot incorporate any perturbations coming from the environment because the specifics of these perturbations are generally unknown. That means we do not know whether the coils recharges the capacitor to -141.4% of the original voltage or to a different value if there is an entry point for radiant energy not considered by these differential equations.

So much for that philosophy.

 Well like I said shielding it is to keep the strength and character of the radiant energy pristine. Where you let it be exposed to matter it then converts into real power. Radiant energy when exposed to certain forms of matter also change the character of that conversion as well. All I know is if we expose segmented copper to the field it goes into super current mode. When copper gets energized in this electric field it polarizes and creates a super flow of real current within the coppers structure. Coils define a diode like direction where it resists movement in one direction only. Ie the coils natural ability to fight changes in direction.


 In a bifilar coil This action is amplified and it seems the energy doesn't change in the character but only the amplitude of the excitation. You could think of it as an accelerator of conventional current.


 As Tesla found out with highly charged atoms you can extract huge amounts of real energy if the bifilar coil is used to create a diode like action in the coil. This is also the same premise he used in his liquid valvular diode. I think this item also worked with air and gases. Don't quote me on that one. I seem to remember him working through the concept of diode like action. If Tesla and others would not see this effect then we are trying in vain to find this flow. But they did find ts effect. Tesla found the perfect engine that uses a non compressible fluid (aether or ether), well it doesn't like to be compressed and he could pressurize it much like water. It changes density as it goes through it's pressures and it has an inverted temperature coefficient.


 So as I tried to mention before Tesla created the perfect engine using the electric field. He then devised a way to polarize the flow of that engine and make it harvestable vi matter interaction. You only expose this stuff to matter when you want a reaction from that matter. The bifilar coil is such a diode like device. But not only do you get rectification you get an acceleration of the input which increases the energy associated with the target matter.


 All of these components are very very important.

Even if it sucks ... but I have to quote wikipedia once again:

»Remarkably, if the parameters vary at roughly twice the natural frequency of the oscillator (defined below), the oscillator phase-locks to the parametric variation and absorbs energy at a rate proportional to the energy it already has. Without a compensating energy-loss mechanism provided by beta, the oscillation amplitude grows exponentially.«

The dictionary says: to absorb is equal to soak up, suck up, sponge up. To me that definition means not the source of the energy pushes the energy into the system (like a battery) but the system itself -the parametric oscillator- pulls (sucks, soaks) the energy out of the source. Since our source here is the environment and the environment normally does not push anything in any system, a device that soaks up the energy by itself should be exactly that what we are looking for.

So where does the energy (to be sucked up) enter the parametric oscillatory system in case of Kapanadze, Stepanov and Marks?

The Kapanadze device is connected directly to the ground (soaking 24 amperes). The Stepanov device is connected to a large metallic object, the battery, acting as capacitor plate (soaking 8 amperes). The Marks device is obviously connected to nothing visible. But there is a major difference here: The Marks device operates at a frequency of 6KHz versus 50Hz of the Kapanadze and Stepanov devices. Typically a higher frequency means that all the electronic parts can be kept smaller. So the entry point for the energy can be kept smaller too and therefore it could easily be hidden within the device. The same is true about the yellow suitcase of Dr. Schwartz which has clearly visible a metallic plate in its cover.

Therefore the task would be: How to build a parametric oscillator that works?

And of course the question, which Tesla patent could represent a parametric oscillator?

The Kapanadze device is connected directly to the ground (soaking 24 amperes).

So where is the return?

Same wire but different time. Tesla's single-wire transmission line.

I think you are mistaken in your assumption that a 1-wire power transmission system does not have a separate return path. To my knowledge Tesla's 1-wire experiments (as other 1-wire systems), used a conventional source of energy, with a capacitive linked earth return, using air as the dialectric. In view of this it is highly improbable that TK managed a load current of 24A!! I suggest you do some experiments along these lines to prove this to yourself.

You don't need Earth - just a capacitance. You could use one wire power in space.
Capacitance != typical two-plate capacitor only. It could be any metal object that could hold charge.
Voltage is difference of potential which in turn is caused by charge - as long as you have differently charged plates (even separated by miles) and connect them with wire current will flow.