Many researchers of "Free energy" are looking for schemes to harvest energy from the Tesla resonant coil. Meanwhile, this scheme has long been known and proposed by Nikola Tesla himself more than a hundred years ago - Fig.1.
Fig.1. The scheme for harvesting energy from a resonant coil, proposed by Nikola Tesla more than a hundred years ago, and its modification from Donald Smith.
The circuit consists of a short excitation coil (inductor) and a long resonant coil. The inductor has spark excitation at the resonant frequency of a long coil. One terminal of a long resonant coil is connected through a spark to a solitary capacitor (plate), to which the earth load is also connected. The second terminal of the resonant coil is free. All together forms asymmetrical transformer. That's the whole scheme - everything is very simple.
Next to the Tesla circuit in Fig.1 is a Donald Smith circuit, in which instead of a solitary capacitor, a conventional one is used consisting of two plates. This does not change the essence of the scheme proposed by Tesla.
Donald Smith, who studied the above Tesla circuit, argued that more energy is produced in the load than was spent on exciting the resonant coil. He also argued that the energy in the load would depend on the frequency and voltage of the resonant coil.
Due to what this was obtained will be considered in this article.
Theories of "Ether Energy" as well as theories of "Divine spark" will not be considered in this article. Everything will be described in the framework of the school physics textbook.
To begin with, we illustrate the dependence of voltage on time, in a simplified form, for resonant coil: without sparks on plate and with sparks on a plate - Fig.2.
Fig.2. Time dependence of voltage on a resonant coil without sparks and with sparks, as well as the voltage distribution along the coil itself with a difference of a half of period.
As can be seen in Fig.2, the spark changes the nature of the voltage distribution on the resonant coil, as well as the form of the oscillations process at resonance. But, the spark does not change the potential difference between the terminals of the coil. That is, if there is sparks or not, the value of the potential difference at the terminals of the coil does not change. This suggests that the spark does not destroy the oscillatory process, although it changes the form of the oscillatory process.
What energy enters the load if the energy of the oscillatory process was not changed during the passage of the spark?
Everyone knows the definition of potential energy from a textbook. It is absolutely correct and does not cause questions.
The essence of potential energy is that if there are two masses in space, than they have mutual potential energy and can do the work - Fig.3.
Fig.3. Two masses spaced in space can do work due to mutual potential energy.
There is nothing surprising in this. As well as the fact that two magnets spaced in space can perform mechanical work also due to the mutual potential energy - Fig.4.
Fig.4. Two magnets spaced in space can do work due to the mutual potential energy.
Which is also quite reasonable and understandable. But, there is one BUT!
If you are the Creator of all things and you can create two masses in different "remote" points of the space of the created World, then you will not spent any efforts to create potential energy. The potential energy will appear as if by itself, as integral part of the World you are creating, simply due to the fact that two masses are separated in space.
If you are an Engineer and can magnetize two magnets at different "remote" points in space, then you will also not spent any efforts on creating potential energy. The potential energy will appear as if by itself, as part of the created World, simply due to the fact that the two magnets are separated in space.
Hence the conclusion: potential energy is the energy, the creation of which does not require additional cost. Hooray! Here it is the long-awaited "Free energy". But, again there is one BUT! You can use this energy only once!!! Further, the two-body system falls into the "potential hole", and it is not possible to get out of it without additional costs. So says modern physics, and we will not argue with her. However, we continue.
In childhood, everyone loved to sled or ski from mountains, turning potential energy into pleasure. At the same time, everyone dreamed of sliding down again and again, without climbing to the top of the mountain. Alas, these are only dreams. But, these dreams can be displayed in the form of a visual illusion, the so-called Penrose staircase - Fig.5.
Fig.5. The illusionary staircase of Penrose: moving along which you constantly rise, or constantly fall - depending on the direction.
It is believed that Penrose staircase belongs to visual illusions and does not have a real practical solution.
However, there is a solution! And it is so paradoxical that is could come to mind only for a true genius like Nikola Tesla. And what is the solution? And the solution is this: after going down, you don't need to go up, you need to turn everything upside down, that is, change the direction of gravity, and move again "down". And repeat it over and over, going "lower" and "lower". And do not spend any energy on changing the direction of gravity. Here is a solution.
You will say that is impossible despite the genius of Tesla, and you will be right. For gravity, this is impossible (for now), but it is already possible today for electric fields, and without additional energy cost! And the resonance will help in this, more precisely electromagnetic oscillations!
The scheme for harvesting energy from a resonant coil proposed by Nikola Tesla - Fig1, is a practical embodiment of the Penrose staircase! Where the return to the beginning of the path is carried out by "turning gravity upside down". However, instead of real gravity, electric fields are used.
Tesla's resonant coil acts as mechanism that turns the "gravitation field" and pulls the system out of the "potential hole" by changing the direction of the electric fields.
At the same time, the energy of the resonance itself is not consumed! To do this, in the Tesla scheme, "descent from the mountain" is "instantaneous" due to an electric spark. And the return to the starting point of the path and the flip of the "gravitational field" (with renewal of potential energy) occurs "very slowly" during the half of period of the oscillations of the coil.
The faster the potential energy is harvested, the less this affects the oscillatory process. The ideal option is the "instantaneous" harvesting of potential energy.
With this approach, the oscillatory process is not destroyed, despite the fact that the system periodically "falls into potential hole". An "indestructible" oscillatory process "pulls it out" in the next half period, by changing the direction of the electric field. Only potential energy will go into the load - Fig.6.
Fig.6. Potential energy does the work, periodically dumping the system into a "potential hole".
Fig.6 shows that after the spark, the charge distribution on the coil changed, and there is no potential difference to ground - a "potential hole" has appeared, from which the "indestructible" oscillatory process will pull the system out after a half of period.
The situation in Fig.6 is shown after many spark discharges, when a charge is formed at one terminal of the coil, and there is no charge at the other terminal of the coil. Without sparking, the charges will be at both terminals of the coil, but of different polarity.
Thus, the task of the oscillatory process is the separation of charges in the coil and the renewal of potential energy relative to the zero level (earth). And, harvesting the energy by the Tesla method is a practical implementation of the Penrose staircase.
What does energy depend on?
Since the harvesting of energy from the resonant coil by Nikola Tesla is a practical implementation of the "impossible" Penrose staircase, it is most logical to illustrate the energy dependencies by looking at this staircase.
First of all, energy will depend on the height of the Penrose stairs. The greater the initial descent height (potential energy), the more energy will be released in one descent. That for a Tesla coil will match the voltage. The greater the voltage across the coil, the more energy will be released in the load per spark.
But, the concept of potential energy also includes mass. The larger the mass will be "lowered" from the initial height, the more energy will be released. That for a Tesla coil will be corresponds to the magnitude of the charge. The large the charge goes into the load, the more energy is release there. The magnitude of the charge itself will be related to the physical dimensions of the coil. The large the dimensions, the more charge it can contain until a spark appears.
The following is the number of "descents from the mountain" per unit time. The more "descents" per unit of time you complete, more the energy will be released in the load per unit of time. Which corresponds to the concept of "frequency".
Thus, the energy released in the load will depend on three main parameters:
Coil oscillation frequency
Law of energy conservation
It should be noted that the law of conservation of energy, like any physical law, has a range of applicability. This area of applicability is determined by Emma Noether's theorem.
A theorem from 1918 by Emma Noether mathematician claims that a certain conservation law corresponds to each continuous symmetry of a physical system: the law of conservation of energy corresponds to the time symmetry, the conservation of momentum corresponds to space symmetry, the conservation of angular momentum corresponds to space isotropy, the conservation of electric charge corresponds to gauge symmetry and so on.
That is, the initial symmetry, and the corresponding conservation law after. If there is no symmetry, then you are outside the scope of applicability of corresponding conservation law. Thus, the law of conservation of energy cannot be violated in principle, since it is a consequence, not a cause. However, one can go beyond the field of its applicability by breaking the corresponding symmetry.
We will be interested in the symmetry of time.
Time symmetry means invariance in the choice of the origin on the time axis. That is, you can choose the origin on the time axis arbitrarily; the result of the experiment should not change from this, unless other conditions have changed.
But with the immutability of the conditions in the Penrose staircase, "not everything is in order". There are points of a "cost free transitions" on the time axis, when the body to the left of them has one potential energy, and to the right of them the other potential energy. That is, the conditions are different on the left and on the right. Thus, it cannot be said that the Penrose staircase will be in the field of applicability of the energy conservation law.
It was shown that taking energy from a resonant coil according to the Nikola Tesla method is a practical implementation of the "impossible" Penrose staircase. In this case, only potential energy is released in the load. The energy of the oscillatory process in the coil remains unchanged, but is used to create this potential energy, as well as its renewal.
So that the energy of the oscillatory process is not destroyed, the harvesting of potential energy occurs "instantly" using a spark. And restoration of potential energy is "very slow" for a half of period of the oscillatory process of the coil.
The energy released in the load depends on the three main parameters:
Coil oscillation frequency
The greater the voltage, size and frequency, the more energy is in the load.
In addition, it should be noted that the devices built on the principle of the Penrose staircase would be outside the scope of applicability of the energy conservation law.
For simplicity of presentation, the article did not address issues: the use of an asymmetrical transformer and spark excitation of resonance. The graphs and drawings were also simplified as much as possible. They should be taken only as illustrations of the described process.
The article does not contain state secrets, as well as the secrets of individuals.