How the Tesla Power Transmission Tower worked - its own “investigation”
A few years ago, we - the authors of this material - pretty much rummaging in the patents, diaries and lectures of N. Tesla (fortunately, education allowed) came to the conclusion that the notorious Tesla Tower for energy transfer is not a “fake”, but a completely working construction.
As a result of several years of research, reflection, study of primary sources, data comparison, formation and elimination of hypotheses, etc. - a beautiful and, in fact, simple model appeared that strictly fit into classical physics and was confirmed by numerical simulation in the Ansoft HFSS package. Since the start of the project, we have held a number of discussions in various communities where they demanded that we have an “article for techies” - as a result of this material.
This material is not a rigorous theory (i.e., a theory that takes into account all possible aspects of the operation of the Tesla Tower). Nevertheless, we tried to sufficiently fully illuminate the proposed concept and provide adequate numerical estimates of the main characteristics of the process. So, if you are interested in understanding the model and participating in a constructive discussion, we invite you to familiarize yourself with the materials.
So, in our scientific-pop article the beginning of the concept is stated - in fact, the starting point of research (the formulation of which, by the way, required a fair amount of time).
You can describe the essence of the post in several sentences below, with the note “attention is not for specialists.” Then the essence could be formulated as follows: the Tower creates a resonance of currents and voltages in a long line, where the whole Earth is taken as a long line (a conductor connected at one end to a master oscillator - that is, to the Tower). Earth's resistance is tiny (why - parsed below). Losses from EM radiation also have no dramatic consequences, because “Saves” the ionosphere, from which low-frequency EM radiation is perfectly reflected, and when reflected, it interacts with the Earth, again turning into currents in a long line - the Earth (waveguide model). And there is a stable picture of standing waves of currents – voltages – charges in the earth, accompanied by weak EM – radiation between the earth and the ionosphere.
We started by thoroughly studying the operating mode of the Tesla Tower following its notes and patents. And from this understanding was already born - what physical processes such a device can cause in the planet Earth, and from this understanding - the confidence arose that the transfer of energy by the proposed (and tested) Tesla path is quite possible. At the same time, we are starting from the fact that the Tesla patent contains the entirety of the description and there are no “hidden / hidden" parameters / processes. So the “ideas” actively exaggerated by the yellow press and the media are that Tesla, with the help of his Tower, tried to “pump the energy of the ether”, use “radiant energy”, etc. - we believe are only the fantasies of journalists who are far from physics. In our opinion, the work of the Tower fully fits into the well-known physical laws, does not require the involvement of any new concepts or physical effects, and in this sense our work (and the future planned experiment) is purely applied in nature - and not in the nature of basic research. If the material below is difficult to understand, then you can read the article at the link above (it is written for humanities, and contains a number of inaccuracies bordering on incorrectness, but gives a good qualitative understanding).
For sim, let's get started.
Tesla Tower: Performance Features
If everything impossible is cut off, then the Tesla Tower (excluding the technical nuances that are not essential here) is nothing more than a spiral quarter-wave resonator grounded at one end (characterized by distributed parameters), with an additional capacity at the upper end of the spiral. This resonator is swayed by a master oscillator (sinusoidal signal, frequency below 20 kHz - based on Tesla, US787412 and US1119732 ).
In other words, the circuit diagram of the tower is as follows:
On the left is a physical secluded tank at the top of the tower (additional to the coil’s own capacity), on the right is a conditional equivalent circuit where it is separately emphasized that the tank is secluded, i.e. formally, the capacity between the Tower and infinity, and not between the Tower and the Earth (because otherwise we will get a banal LC-circuit closed through the ground). In order to minimize the parasitic capacitance between the tower and the ground - i.e. closing the LC circuit of the Tower through the ground - obviously, it is necessary to raise the solitary capacity from the ground (a simple assessment shows that it is enough to raise the capacity to a height equal to several average diameters of such a capacity - if this condition is met, the capacity between the Tower and the Earth will decrease to a value comparable to own secluded capacity of the Tower).
As is known from classical electrical engineering, in the resonance mode of such a resonator, the capacitive and inductive resistances mutually cancel each other, so that the generator “sees” only the active resistance of the resonator. A standing wave arises in the spiral - with a voltage node at the point of the generator, and a current antinode there (at the same time, at the end of the resonator, the voltage antinode and current node). A detailed analytical theory of the operation of such a resonator can be seen, for example , here . If the material on this link is difficult to understand, then it can be simplified without loss of essence: a spiral resonator of this kind is nothing more than a quarter-wave long linecoiled - i.e. as in the “elongated” line length, in such a resonator at a resonant frequency there will be a standing wave of current-voltage, with a voltage node at one end of the line, and a current node at the opposite end of the line; A significant difference from the “elongated” long line is only in the enhanced inductive and capacitive coupling between adjacent sections of such a line due to their geometrical proximity in a spiral configuration, which slightly (not at times) changes the resonant frequency and wave propagation velocity along the line.
The figure shows standing waves in a long line. Wave distribution: a - voltage; b - current in a single-conductor line at different points in time (illustration from the site )
In other words, the Tower is a charge buffer - a solitary capacity into which the master power generator “drives” the charge from the earth.
In this case, EM radiation in the sense of radio waves (i.e., a field in the far, wave zone of the Tower) is practically absent for our range of operating parameters. Show it.
In radiophysics, there is the concept of spiral antennas, which, at first glance, can be correlated with such a spiral resonator. However, unlike antennas, the electrical length of the Tower loop is 3-5 orders of magnitude less than the wavelength (i.e., the number of turns is calculated in thousands - despite the fact that the entire length of the winding is approximately equal to a quarter of the wavelength). In this case, most of the currents (current antinode) are concentrated in the lower half of the tower. In other words, in the sense of external EM radiation,such a structure works like an ordinary classical concentrated inductance . Those. ordinary magnetic dipole.
A well-known formula defines the radiation resistance of an electrically short magnetic frame (magnetic dipole) with a wavelength λ ( radiation resistance characterizes the conductor’s losses due to electromagnetic wave emission - i.e., the current energy loss from radiation is considered as a formal active resistance, the losses at which are equal to the losses for radiation):
(formula 4.30 from the link above)Where the equivalent dipole length l e is connected with the radius “a” of the frame by the ratio:
For the case of N turns, the formula is multiplied by the coefficient N 2(for obvious reasons, the radiation energy density is proportional to the square of the amplitude of the field of the frame, i.e., the square of the number of turns in the frame).
Total,
Substituting our parameters (frequency 10 kHz, i.e. wavelength 30,000 m, coil radius - let it be 2 meters, winding length - 10 km, number of turns about 800) we get radiation resistance equal to 390 nanohms. This is negligible compared to the losses on the active resistance of the system (at least a few ohms).
But, in addition to the tangential component of the current in such a resonator, there is also an axial component (resulting vertical current) due to which the Tower gives, among other things, the radiation of an ordinary short electric dipole, for which the radiation resistance is related to the dipole length l and wavelength λ as:
(formula 4.27 from the link above)Thus, the radiation resistance (relative to the current passing through the generator) for the vertical component of the current and for our parameters (tower height of tens of meters - let it be 30 meters for specifics, and frequencies of 10 kHz) can be estimated about 1 milliohm.
As a result, we see that both types of radiation (both from the tangential and axial components of the current) are negligible with respect to losses on the active resistance of the circuit, while these are upper estimates (because for them the current value is assumed to be the same throughout the coil winding , while in reality the current falls along the sine - and at the “hot end” of the coil there is a current node - that is, zero current, and the real radiation will be several times less than the estimates above). So any ideas that the Tower works like an antenna have absolutely no basis (in any case, as long as we follow Tesla’s patents and not engage in fantasies). The tower is not an antenna in the classical sense - its radio emission (i.e. the EM field in the far wave zone) is negligible, and all that it allows you to do is to be an effective accumulator for the charge that the generator starts and removes from the soil at the generator operating frequency. So the “ingenious” objections of the form “you have a normal spiral antenna - the energy transfer efficiency will be lower than the plinth”, and other “arguments” emanating from radio emissions of such a structure - only demonstrate that the opponent does not fully understand the most basic concepts of radiophysics.
With the Tower sorted out, now we go to the Earth
For simplicity, we start with elementary analogies - from which we will gradually move on to the final concept.
Suppose we have an electrically long conductor with a gap at one end, grounded by the second end through an alternating voltage source (electrically long means that the length of the conductor is comparable / greater than the wavelength from the generator, based on the generator frequency and the wave propagation speed - close to the speed light in a vacuum):
In such a long line, if the losses in the line are small, a standing wave of current-voltage arises (i.e., a superposition of incident waves from the generator and waves reflected from the free end of the long line). A typical example of such lines and such waves are ordinary electric vibrators (that is, classic antennas), as shown in the figure below.
Current distribution in symmetrical vibrators of various lengths.The essence of standing waves in a long line is quite simple to understand. You can mentally break the entire conductor into segments at half the wavelength. Each such segment is a capacitance (since the conductor has a capacitance distributed along it) and inductance (similarly). Accordingly, standing waves are nothing more than waves of currents charging such capacities - i.e. the energy in such a standing wave is alternately stored either in the form of a charge distributed along the conductor (along the sine) - at this moment the currents are equal to zero, then in the form of currents distributed along the conductor (also over the sine) - and at this moment the surface density of charges along conductor is zero. Which essentially repeats the operation mode of a conventional LC circuit (an inductance coil connected in series with a capacitor-capacitor), but only taking into account the distributed nature of the capacitance and inductance. The currents in the half-wave “flow” to the center of such a selected segment - creating a voltage antinode (that is, the appearance of a surface charge on the conductor), and in the adjacent segment “flowing” from a similar center - creating a charge of the opposite sign, then this process repeats (in the opposite side - creating opposite charges on the surface of the conductor). Of course, the above refers to an ideal line (without losses) open at the end, in a real line with losses (and / or lines with a load at the end), the processes are somewhat more complicated - but the fundamental essence does not change from this. then this process is repeated (in the opposite direction - creating opposite charges in sign on the surface of the conductor). Of course, the above refers to an ideal line (without losses) open at the end, in a real line with losses (and / or lines with a load at the end), the processes are somewhat more complicated - but the fundamental essence does not change from this. then this process is repeated (in the opposite direction - creating opposite charges in sign on the surface of the conductor). Of course, the above refers to an ideal line (without losses) open at the end, in a real line with losses (and / or lines with a load at the end), the processes are somewhat more complicated - but the fundamental essence does not change from this.
If we turn to elementary mechanical analogies, the closest process will be compression-tension waves in a long spring, which arise when such a spring (lying on a support with zero friction) begins to swing back and forth along the spring axis at one end of the spring - when fixed second end. In this case, the current corresponds to the speed of movement of the corresponding section of the spring, and the voltage corresponds to the compression ratio of the spring. Those. at some point in time, all sections of the spring will have zero speed - and the degree of tension of the spring will vary along the sine along it (such as alternating clumps and discharges) - which corresponds to a zero current in a standing wave and at the same time maximum voltage (i.e. maximum surface charge density on the conductor),
Losses for such a situation as a whole can be divided into 2 components: ohmic losses, and radiation losses.
In the case of a large length of the conductor, and its small ohmic resistance, the main contribution to the loss will come from radiation (i.e., radiation resistance).
It is known that if such a line is surrounded by a grounded conductive shield, then the radiation losses will be leveled, and such a structure is called a coaxial waveguide - and, in our example, the wave in such a coaxial waveguide will exist in the form of a TEM mode (in this case, the excitation port in fact, it is a generator connected through the earth to the internal and external conductors of the waveguide).
In fact, the mode of the TEM mode can be interpreted as the mode of inductive coupling of the internal and external conductors of the waveguide through the field of the near current zone on these conductors (a change in current on the inner core causes respectively an EMF on the external screen, and the current induced on the external screen is directed against the change current in the inner core - that is, in fact, ordinary induction in the near current field), so that the transverse energy fluxes are not just zero in average time (as for the TE or TM modes), but zero at any time. There are no reflections from the boundaries of the waveguide - the energy flux is only longitudinal (i.e., directed along the axis, and accordingly the Poynting vector is also directed strictly parallel to the direction of wave propagation - along the axis of such a coaxial resonator).
Therefore, the TEM mode mode in a coaxial waveguide is characterized by good parameters (relative to the TE or TM mode modes) in terms of energy transfer and in the smallness of the attenuation coefficient of the wave in the waveguide, and if necessary, energy transfer through a coaxial waveguide - as a rule, they tend to use the TEM mode fashion.
However, even if we remove the grounding of the external screen of such a waveguide, along the entire length of the screen except its end sections, the screen will perform its function perfectly.
After all, such a screen is in any case a long line, the quality of the generator for which is the EMF from alternating current on the inner conductor-core. And only at the edges of the screen - due to the very small capacity of such edges, there will be some antinode of voltage, and on the rest of the length of such a screen - will it function normally. This is confirmed by elementary modeling in HFSS.
Further, what will happen if we do not just remove the grounding of the external screen - but “close” the edges as shown in the figure below (so that the external screen becomes a sort of “capsule”)? The answer is quite clear - this situation will not differ from that considered above. The screen will work along its entire length, and at such ends of the external “capsule” there will be antinodes of voltages (and current nodes, respectively).
Further, if the inner and outer conductors are already made in the form of spheres, then we will come to a general model of the proposed experiment (the proportions in the figure, of course, are not met):
As you might guess, the inner conducting sphere is Earth, the outer conducting sphere is upper layers of the atmosphere (mainly the ionosphere). And the general geometry of such a resonator is an ordinary concentric spherical resonator (in which in the strict sense it is impossible to talk about the TEM mode, because only TE and TM modes exist in it), only with a slightly unusual way of exciting the TM mode ( ie, the excitation port - does not interconnect the outer and inner plates, as is done in "classical" electrical engineering).
Although, due to the variable cross section of the internal and external conductors, the amplitudes of standing waves of currents and voltages will decrease with distance from the generator, the general essence remains the same - the TEM mode of the coaxial (or TM mode of a spherical) resonator excited by the corresponding source (Tesla Tower).
At first glance, the idea is strange: it is known that the conductivity of the Earth’s soil, and the ionosphere (on a clear day on the lit side) is about 0.001 S / m (plus or minus the order), while the conductivity of copper, for example, is about 58 000 000 S / m However, let's look at this issue based on numerical estimates, and not on intuitive considerations. And to begin with, we’ll deal with the earth’s soil resistance. The general idea is that from the point of view of the processes of current flow, the division into dielectrics, semiconductors and conductors is rather arbitrary in nature, because with a sufficiently large dielectric cross section, it becomes a very good conductor (i.e., it has a small total resistance).
As you know, with a sufficient thickness of the conductor, the current is significant only at a certain depth, called the depth of the skin layer, which is calculated by the formula :
Where
is the resistivity, 
is the relative magnetic permeability, 
is the frequency. Of course, this is a simplified formula applicable to a conductor, not a dielectric - however, at our ultra-low frequencies, the losses associated with the dielectric constant of the soil are small, so as an estimate, this formula is quite applicable.
For a frequency range of 1-10 kHz, and a conductivity range of 0.001-0.00001 S / m, the depth of the skin layer lies in the range from hundreds of meters to several kilometers. Moreover, the lower the frequency, the greater the thickness of the skin layer, i.e. the lower the ohmic loss in planetary resonance (inversely proportional to the root of the frequency).
Thus, we conclude that, considering the purely active resistance of the Earth (as a sphere made of soil, i.e., a material having a conductivity of 0.01-0.0001 S / m), and implying a frequency range of at least 1 kHz (because . even lower frequencies are not feasible from a practical point of view - based on the required technical parameters of the Tesla Tower) it is necessary to limit oneself to a kilometer layer. We note that Tesla, apparently, was not quite aware of this - and sincerely believed that the currents from his installation go deep into the earth (and not run along the surface thereof), as indicated in our popular science article. According to modern data on electrodynamics, this, of course, cannot be.
The resistance between two rods immersed in a poorly conductive medium (for example, in soil) is given by the formula :
Where
Here L is the length of the rods, D is the distance between them, r1 is the radius of the cross section of the rods,
is the specific conductivity of the medium. It is interesting to note that based on this formula, starting with the distance between the rods being much longer than the length of the rods, the resistance between the rods actually becomes a constant (it stops growing as the distance grows).
So, for example, for two rods 30 m long, 0.2 m in diameter, and soil conductivity of about 0.04 S / m (which is correct for the upper soil layers), the characteristic resistance (between them) lies in the range of 1-3 Ohms - starting from a distance of meters, and further (without limiting the distance of the distance) remains so with any increase in the distance between the rods. So the idea that the Earth is a poor conductor (as an object as a whole) is, of course, an intuitive fallacy, and if so, grounding simply would not make sense.
Also a feature of this formula is the fact that, starting from a certain length of the rods - a further increase in the length of the rod does not lead to a noticeable decrease in the resistance between the rods (i.e., in other words, the total resistance between the receiver and the transmitter depends only slightly on the depth of the skin layer ) What is generally known facts in terms of grounding systems (this characteristic graph is taken from this page ).
Thus, we have every reason for optimism regarding the resistance of the entire Earth's surface.
We now make more rigorous estimates
The attenuation constant characterizing the loss on the walls of the waveguide due to active resistance, for the TEM mode of the coaxial waveguide
(which is close to the larger, the central part of the Earth-resonator as shown in the figure above) is given by the formula (see, for example, here ):
where R s1 and R s2 - surface resistance inner and outer cylinders metal waveguide, which can be defined by the formula:
where mu - is the absolute magnetic permeability (for the overwhelming part of the surface of soil - are respectively a magnetic constant nd ).
Just note that the root is the ratio of frequency and conductivity - i.e. the conductivity lower in comparison with metals is largely compensated by the kilohertz frequency range (while coaxial waveguides are used for frequencies in gigahertz), and the fact that the ratio is under the root sign further “improves” the situation. In total, for our parameters (f = 3 kHz, and σ = 0.01 S / m, we obtain a value of 1.06 Ohms), the characteristic value of the surface resistance (of both the earth and the ionosphere) is of the order of one Ohm, plus or minus the order.
One Ohm is, it would seem, still a rather large value. However, the quality factor of a volume resonator is proportional to its linear dimensions (since the amount of energy in the resonator is proportional to the volume thereof, and the losses are proportional to the area of the cavity walls). What is reflected in the formula in the numerator. The radii D and d in our case are of tremendous importance (D = 6.6 million, m, d = 6,400,000 m), which more than covers the relatively large surface conductivity of the waveguide walls, so the attenuation constant for our parameters can be estimated from formulas above as 10 -8 -10 -9 1 / m.
In reality, most of the planet’s surface is covered with good electrolyte (salt ocean water) - i.e. This rating is the rating from above.
A constant attenuation equal to 10 -9 means that over the entire length of the path “x” of the wave to the opposite point of the globe (approximately 20,000 km), the wave amplitude will fall by
= 2%. What corresponds to the extremely high Q factor of the Earth-Ionosphere resonator (orders of magnitude higher than a hundred) for such a mode, in contrast to the mechanism of propagation of ordinary radio waves through re-reflection from the boundaries of the earth-ionosphere. And even a deterioration in the estimated conductivity by 1-3 orders of magnitude (which makes sense for the ionosphere) does not lead to fatal consequences in terms of the very possibility of the existence of such a resonance.
We were convinced that, in principle, the desired resonance (based on the actual parameters of the resonator) can take place, although the real quality factor of such a resonance can have a plug of about 2-3 orders of magnitude (but even with the worst combination of parameters, it should not be lower than a hundred).
Similar estimates of the possible high Q factor of TM modes in the Earth-ionosphere resonator are given in the work of M.V. Davidovich - “modes of a multilayer concentric spherical resonator”.
If we talk about strict approach, the course should be considered a full concentric resonator in TM-mode (eg, a good overview on this subject can be found at this link , to deepen the theoretical aspects - can recommend here thisand this one ).
The first harmonics of the zero TM mode correspond to the so-called Schumann resonance . However, if we talk about frequencies in the region of several kilohertz, then in addition to the zero mode, the modes following it will also be excited (for 10 kHz, these are mode numbers in the range 0-6).
Indeed, from the formula
for the first mode, the lowest harmonic will have a frequency of about 1.5 kHz, for the second mode - 3 kHz, etc.
Moreover, as follows from the formula for setting the harmonic frequency for each of these modes, starting from the first mode and further on, the “density” of the harmonics along the frequency axis is extremely high (if for the zero mode the harmonics go with a step of the order of 10 Hz, then for the remaining modes falling in the range below 10 kHz - with a step of the order of 0.01-0.1 Hz). So, while exciting the TM modes of such a resonator at frequencies in the range of several kilohertz, it is essentially impossible to talk about any particular mode / harmonic: the final picture of standing waves will correspond to an extremely large number of harmonics, for several modes at once. What fundamentally distinguishes such a resonance from a Schumann resonance.
There is another fundamental difference. As you know (for example, see here - page 8), for a passive resonator, the quality factor of harmonics increases with increasing frequency - approximately in proportion to the root of it. However, the Earth-ionosphere resonator is not passive. In fact, the Earth’s electric machine maintains an approximately constant potential difference between the plates of the planetary capacitor (soil-atmosphere). In the event of a lightning strike, this potential decreases - however, it recovers in a typical time measured in seconds, while the characteristic charge current density is about 0.1-1 amperes(p. 6-8) per square kilometer. In other words, the Earth essentially works as a source of EMF, equalizing (however, very slowly) the potential difference at a certain average level. Obviously, in the case of ultra-low-frequency oscillations corresponding to the Schumann resonance (the first harmonics of the zero TM mode of the resonator), the presence of such an emf source leads to a sharp deterioration in the quality factor of the resonance: if the potential deviates from the average level, this emf source tends to compensate for the deviation, which means the active suppression of the TM mode - and given the planetary scale of the phenomenon, this suppression can be significant. Unfortunately, this factor does not take into account in any of the known resonance models the TM modes in the Earth-ionosphere resonator - and the reasons for this are clear:
Nevertheless, the data on the Q factor of the first harmonics of the zero TM mode of the Earth-ionosphere resonator are known (fresh data - 2011):
It can be seen from these data that with an increase in the harmonic number, the actual Q factor grows faster than the root of the frequency (i.e. . faster than for a passive resonator). Considering the relative “slowness” of the planetary capacitor recharging mechanism, it is precisely for the lower harmonics of the zero mode that this mechanism will have the most strong influence, since with increasing frequency, one can expect an increase in the quality factor of resonance at a significantly higher rate than the root of the frequency.
It is interesting to note that in 2011 (which is reflected in the data from the link above), currents were detected in the ionosphere (corresponding to Schumann resonance) at altitudes (400-800 km), for which all known previous models gave a complete absence of such currents. De facto, the existing ionospheric conductivity models turned out to be incorrect - and they cannot be used to construct TM-mode resonance models in the Earth-Ionosphere resonator.
Thus, there is reason to conduct direct measurements of the quality factor of the final resonance at frequencies of several kilohertz - both based on theoretical assumptions and based on actual results obtained by Tesla. Direct analytical (or numerical) calculation is impossible - the Earth is too complex and poorly known object immediately in a large number of its parameters / characteristics.
The proposed experimental design, in fact, has no relation either to Schumann resonance (fundamentally different Q factors, as well as additional TM modes and resonance harmonics), or to energy transfer by radio waves (i.e., electromagnetic field waves of the far wave zone of ordinary radio emitters) - what Tesla stated bluntly.
Of course, as mentioned above, since the resonator cross section is not constant, the wave resistance (defining the ratio of the voltage in the line to the current in it) will also be variable: the maximum voltage will occur at antinodes near the tower (and the opposite end planet), the minimum is at the “equator” from the Tower, which is confirmed by numerical calculation in HFSS (and the corresponding analytical formulas, for example, for the zero TM mode of such a resonator).
The figure shows the distribution of the amplitudes of the electric E and magnetic B fields for the first 3 harmonics of the zero TM mode of the Earth-ionosphere resonator.
“Grounding” for the Earth-Ionosphere resonator
Where do we get the “grounding” to which the generator is connected to pump such a resonator in the previously shown figure?
The answer is simple - since we had previously analyzed the operation of the Tesla Tower. From the point of view of the generator, the Tesla Tower from a practical point of view is no different from some external earth (connected through the active resistance of the Tower). Because the generator “sees” only the tower’s active resistance, but doesn’t react at all to the amount of charge accumulated on the tower (because capacitive and inductive resistances in resonance mode cancel each other out) - in other words, for the generator the tower is “grounding” through the resistance, equal to the active resistance of the tower.
Of course, as already noted above, such a charge causes a redistribution of charges in the soil in the vicinity of the Tower - but the higher the charge accumulator of the Tower is raised, the less significant this factor (as the capacity of the Tower-Earth decreases). It is enough to raise the charge storage unit to a height noticeably larger than the size of the storage device - for the Tesla Tower to become truly an “external ground” for the master oscillator (that is, it is enough to minimize the capacity between the tower and the ground - so that the tower’s own solitary capacity becomes at least one order with the capacity of the Tower-Earth).
Energy transfer efficiency
After the establishment of standing waves of voltages and currents throughout the planet (in this case, the currents will have an extremely small amplitude - in contrast to voltages), it is possible to effectively remove this energy by a similar system (Tower - but already without a generator). Physical processes during the operation of the receiver are characterized by the creation of a connection between the resonant circuits (tower-receiver), which allows to obtain high transmission efficiency even with an extremely low coupling coefficient of the source and receiver (strictly in accordance with classical electrical engineering).
Consider this issue in more detail.
In the case of the location of the receiver (i.e., a similar circuit) in the antinode of the voltage (and current node) of the resulting standing wave, the surface surface potential will be the source of EMF for the receiver. In this case, a resonance will be excited in the receiver - completely analogous to the resonance in the source, respectively, the receiver will generate a standing wave in the same way as in the source. Moreover, since the receiver is located in the antinode of the voltage (and the current node), the wave it generates will obviously create an additional load on the source - thereby creating a system in the form of the so-called resonant coupled loops (a quick review on this subject can be found here and here) Indeed, in the antinode of the external wave voltage, the receiver has a voltage node (and current antinode), and operates at the same frequency, i.e. in the area of the source location - the receiver will create a voltage antinode (and current node), which the source will “see” as an additional load. What is clearly visible in the video (corresponding to the simulation in HFSS).
In the video, and in the figure above - the source is located in the upper left area, the receiver location area is highlighted in the right near-central part. It can be seen that in the receiver region there is a constant field minimum - which means the effective pumping of energy from planetary resonance. The interference pattern of the waves emitted by the receiver and source is also clearly visible.
For such systems (that is, resonant coupled circuits), the energy transfer efficiency is determined by the product of the coupling coefficient of systems k and their Q factor Q. The coupling coefficient is, roughly speaking, the coefficient that determines which part of the resonance energy of the source circuit “sees” receiver circuit. For example, for closely spaced inductance coils (especially if they are wound on the same core), the coupling coefficient tends to unity, and decreases as the coils are spaced (since, with this spacing, the EMF induced by the coils in each other decreases). A typical graph of the dependence of the efficiency on the product of the coupling coefficient by the Q factor is given below (taken from the document from the link above ):
The physical meaning of this dependence is obvious: even if for one period of oscillations the receiver “picks up” only a small percentage of the source’s energy, but for the same period (due to the high quality factor of the resonance) the energy losses in the total resonance are small - then the transmission efficiency (which determines the ratio of the transmitted and scattered energies) will be high. Those. for high transmission efficiency in the general case, a high coupling coefficient of the loops is not required - a large resonance figure of merit can compensate for the small coupling coefficient.
Let us evaluate the coupling coefficient between the source and the receiver, assuming a high Q factor of the Earth-ionosphere resonator (for which, as mentioned above, there is every reason).
Let the frequency be 10 kHz. This means that the Earth is divided into “rings” 30 km wide, of which about half the perimeter, respectively, is about 700. The capacity of the Earth as a solitary conductor is about 700 microfarads. Let the current in the Tower (source) be 1 kA (this corresponds to a generator power of at least several megawatts). For the long Earth line, our “rings” are parallel capacities. Those. the capacitance per one wavelength in the region of the "equator" from the tower can be estimated at c1 = 1 μF (700 μF / 700 waves). That at a current of 1 kA (going to recharge each of these capacities) it gives a voltage of about 15 kV (according to the standard formula U = I * Rc = I / (c1 * w)). The entire field (for the TM mode) is concentrated approximately at a length equal to half the wavelength (perpendicular to the ground), as follows from modeling in HFSS (and / or from the corresponding analytical formulas referred to above). For 10 kHz it is 15 km.
What does the field strength near the ground mean - only one volt per meter (with the background intensity of the vertical field component - about 130 volts per meter) This is “at the equator”, and in the antinodes closest to the tower (since the capacity is 1-2 orders of magnitude lower) it will be 1-2 orders of magnitude higher, respectively. Those. the receiving tower will “see” a voltage of a hundred kilovolts (and the field strength will be about 10 V / m) - if it is located at a distance of tens of kilometers from the source. In this situation, the variable potential of the soil is large, but the field strength is small, because the field is distributed vertically over a long distance - tens of kilometers (which allows speaking even with gigawatt transmitter power - so as not to go beyond the background level of the field strength near the Earth’s surface) . If we are talking about the "equator", with the indicated parameters, and the resulting resonant voltage in the source, for example, in megavolts (and at the equator, as follows from the estimate above, 10 kilovolts) - the coupling coefficient, respectively, about 1% (and tens of% at a distance of tens of kilometers from the source), because the coupling coefficient can be defined as the ratio of the voltages at the inductance of the receiver (with the receiver open) and the working source (of course, with the same parameters of the receiver and source). Based on the possible quality factor of the resonance in the region of several hundred, such a coupling coefficient means a transmission efficiency of at least tens of% for the equator, and may well give a figure above 90% for a distance of tens of kilometers (which corresponds to the statements made by Tesla on the corresponding experiments) . However, due to problems with modeling and calculating the real quality factor of resonance, trying to make more accurate estimates, in fact, makes no sense (by and large, it all depends on the real quality factor of the resonator-Earth, and the resonator tower - modeling can give errors in orders). So the only adequate option is to set up a full-scale experiment - for which, obviously, it is necessary to build a complete analogue of the Tesla tower. This will allow both to reproduce the “same Tesla Tower” and “the same experiment”, and to place all the “dots above and” in the issue of transmission efficiency for large distances. At the same time, we have no doubt about the high transmission efficiency for the configuration of the experiment corresponding to the parameters of the initial Tesla experiments (i.e., for a distance of a hundred kilometers), which is interesting from a practical point of view in any case. This will allow both to reproduce the “same Tesla Tower” and “the same experiment”, and to place all the “dots above and” in the issue of transmission efficiency for large distances. At the same time, we have no doubt about the high transmission efficiency for the configuration of the experiment corresponding to the parameters of the initial Tesla experiments (i.e., for a distance of a hundred kilometers), which is interesting from a practical point of view in any case. This will allow both to reproduce the “same Tesla Tower” and “the same experiment”, and to place all the “dots above and” in the issue of transmission efficiency for large distances. At the same time, we have no doubt about the high transmission efficiency for the configuration of the experiment corresponding to the parameters of the initial Tesla experiments (i.e., for a distance of a hundred kilometers), which is interesting from a practical point of view in any case.
Additional considerations
In addition to the patents on the Tower itself, Tesla also patented a device for detecting standing waves of stresses in the soil arising from lightning strikes. This device is described in US787412 . The essence of this detector, translating into a modern language, is to organize the so-called synchronous detector (or lock-in amplifier ). Here's what Wikipedia says about this:
The lock-in amplifier is commonly believed to be invented by Princeton University physicist Robert H. Dicke who founded the company Princeton Applied Research (PAR) to market the product. However, in an interview with Martin Harwit, Dicke claims that even though he is often credited with the invention of the device, he believes he read about it in a review of scientific equipment written by Walter C Michels, a professor at Bryn Mawr College. This was probably a 1941 paper by Michels and Curtis, which in turn cites a 1934 paper by CR Cosens.
Obviously, like many other ideas and patents of Tesla on which he objectively had priority - his contemporaries did not understand what and how Tesla did, so priority was not assigned to him and dated by a couple to three decades later. However, a careful analysis of the standing wave detection device used by Tesla leaves no doubt that the priority of the invention of the synchronous detector belongs to Tesla.
In fact, the essence of the device used by Tesla was that at a given frequency (and a given duty cycle - see patent), he created alternating closure of one of the contacts of the capacitor-drive with the ground (at that time the second contact of the capacitor was “in the air”) , purely mechanically - using the sliding contacts on the corresponding drum (F in the figure below).
Thus, provided that the frequency of the standing wave in the ground and the frequency of contact closure in the receiver coincide, the capacitor T gradually accumulates a charge - and then is forcedly discharged through the receiver R (allowing to register the discharge current of such a storage capacitor). Which is explicitly the logic of a synchronous detector. At the same time, since the length of the wires connecting the capacitor to the ground was much shorter than the wavelength, it is not necessary to talk about EM leads to such wires (from lightning strikes) - they will be insignificant.
Here is what Tesla himself wrote about this - and how his path in this area began:
The date I shall never forget - when I obtained the first decisive experimental evidence of a truth of overwhelming importance for the advancement of humanity. A dense mass of strongly charged clouds gathered in the west and towards the evening a violent storm broke loose which, after spending its fury in the mountains, was driven away with great velocity over the plains. Heavy and long persisting arcs formed almost in regular time intervals. My observations were now greatly facilitated and rendered more accurate by the experiences already gained. I was able to handle my instruments quickly and I was prepared. The recording apparatus being properly adjusted, its indications became fainter and fainter with the increasing distance of the storm until they ceased altogether. I was watching in eager expectation. Surely enough, in a little while the indications again began, grew stronger and stronger and, after passing thru a maximum, gradually decreased and ceased once more. Many times, in regularly recurring intervals, the same actions were repeated until the storm, which, as evident from simple computations, was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. grew stronger and stronger and, after passing thru a maximum, gradually decreased and ceased once more. Many times, in regularly recurring intervals, the same actions were repeated until the storm, which, as evident from simple computations, was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. grew stronger and stronger and, after passing thru a maximum, gradually decreased and ceased once more. Many times, in regularly recurring intervals, the same actions were repeated until the storm, which, as evident from simple computations, was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. gradually decreased and ceased once more. Many times, in regularly recurring intervals, the same actions were repeated until the storm, which, as evident from simple computations, was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. gradually decreased and ceased once more. Many times, in regularly recurring intervals, the same actions were repeated until the storm, which, as evident from simple computations, was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. was moving with nearly constant speed, had retreated to a distance of about three hundred kilometers. Not did these strange actions stop then, but continued to manifest themselves with undiminished force. Subsequently, similar observations were also made by my assistant, Mr. Fritz Lowenstein, and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves. and shortly afterwards several admirable opportunities presented themselves which brought out still more forcibly and unmistakably, the true nature of the wonderful phenomenon. No doubt whatever remained: I was observing stationary waves.
Based on the actual design of the detector, there is no doubt that the fact of the operation of such a detector - namely, a periodic sinusoidal change in the amplitude of the energy of the process as the thunderstorm travels and moves away (hundreds of miles) recorded by the detector - unambiguously testified to standing voltage waves at earth's ground, which was for Tesla the starting point of his research.
According to the totality of the information given above, there is every reason for setting up a full-scale experiment with the goal of final confirmation of the operability of the Tesla Tower.
If the material presented is too complicated to understand, then a more “humanitarian” presentation (in some places bordering on incorrectness, but giving a good understanding of what we are going to do in terms of the experiment) can be found, for example, bythis link .
Authors: Sergey Plekhanov, Leonid Plekhanov
FAQ
Below is a list of frequently asked questions, with answers. If you have a question - please, before asking it, make sure that it is not in the list below, or give an argument - why the answer below to such a question is unconvincing.
• If this idea is working, will not currents in the ground kill all living things that are there?
There are no such risks. Just because the current density in the surface layer of the Earth will be scanty (take 2 kiloamperes in the Tower and distribute such a current along the perimeter of 20,000 km long and 100 meters deep; we get a current density of about 1 μA per square meter, which will not no living organism). Those. a large variable external potential from a charge on the ground (kilovolts and above) is combined with very small currents, and at the same time, the vertical component of the electric field near the ground is small (much less than the background value of 130 volts per meter). As the height increases, the field strength (already small) will fall, so that the planes and satellites -) also do not face anything.
• You are making a planetary microwave.
The processes associated with the Tesla Tower have absolutely nothing to do with the mechanism of heating a substance with microwave radiation. Ohmic losses, of course, will be - but even a gigawatt, distributed over the area of the entire planet - is like a warm sea with a match.
• Your model in HFSS is incorrect - you took two metal spheres and of course you got a TM mode.
No, we did not take the sphere from the conductors - we honestly laid the conductivity of the soil and the ionosphere, based on their tabular values. Accordingly, the size of the model is large (so that, due to the cross-sectional area of the dielectric-soil, it can be considered as a conductor).
• It is understood that the TM mode can be excited. But how in practice can a port be forwarded from soil to the ionosphere?
And this does not need to be done - see the article above. It is enough to connect the generator only to the ground, the rest will be automatically induced by alternating currents in the vicinity of the Tower. Those. Formally, it can be considered an antenna - a circular region of soil near a tower, with a radius of the order of the wavelength.
• Earth is a dielectric, so it does not conduct current, and nothing happens.
Soil conducts current perfectly, see above. At the dawn of the railway industry, the Earth served as the return conductor, and it worked quite remarkably as such (without introducing any noticeable resistance). In addition, if the ground as a whole is a poor conductor, ordinary grounding would be useless (i.e. would not work - but practice shows the opposite).
• You have a regular radio antenna, transmission efficiency will be negligible.
As shown above, the Tower has nothing to do with the radio antennas - because in fact, in her practical sense, radio emission is absent (i.e., it is by many orders of magnitude less than the losses due to the ohmic resistance of the Tower).
• How is this all different from Schumann? The usual Schumann resonance, everyone knows this and therefore the idea is not working. And there is nothing new in this.
Schumann’s resonance is not a resonance of a particular mode, but the noise phenomenon at the first harmonics of the zero TM mode, associated with the presence of pulsed pumping of the Earth-Ionosphere resonator at a frequency near the first mode (10 Hz - because on average about 40 50 lightning discharges, of which, according to statistics, only 20% -25% hit the earth), and with the fact that the average frequency of discharges is not uniformly distributed over the planet's surface (with a characteristic scale of the heterogeneity of such a distribution - of the order of the wavelength of the first harmonics). In other words, the Schumann resonance noise is associated with the presence (albeit weak) of the spatiotemporal coherence of lightning strikes. Those. if lightning strikes evenly across the entire surface, there would be no Schumann resonance (i.e. noise at the frequencies of the first harmonics). Or if the average lightning strike frequency were not 10 Hz, but 10 kHz, then the maximum energy would be at completely different harmonics / modes. In addition, only the zero TM mode is excited in the Schumann resonance, and for our frequencies the following modes will actively participate. Thus, although there is an indirect connection with Schumann’s resonance, our case is not Schumann’s resonance. We really do not offer fundamentally new physical effects - everything is strictly within the framework of what has long been known in the relevant sections of physics. We just “glued” the known knowledge to explain the operability of the Tesla Tower. We really do not offer fundamentally new physical effects - everything is strictly within the framework of what has long been known in the relevant sections of physics. We just “glued” the known knowledge to explain the operability of the Tesla Tower. We really do not offer fundamentally new physical effects - everything is strictly within the framework of what has long been known in the relevant sections of physics. We just “glued” the known knowledge to explain the operability of the Tesla Tower.
• The quality factor of the resonance will be low - because you, in fact, have Schumann, so that the standing wave will not work, there will be a traveling wave with a large attenuation.
It’s not true, firstly we do not have Schumann - see questions above, and secondly, even for the first harmonics of the zero TM mode (i.e., for Schumann resonance), the Q factor reaches 10 (see proofs above), which means the decay time of energy in a few tenths of a second - i.e. lots of. And according to actually experimental data, the Q factor with an increase in the harmonic number (i.e., with an increase in frequency) grows, moreover, faster than the root of the frequency. So there will be a standing wave, and the expected quality factor in our frequency range is at least several hundred.
• If there are conductors in the ground that are electrically long with respect to the wavelength, your wave will concentrate and decay on them.
Not true, conductors in the ground (for example, pipes of heating systems, etc.) mean locally improved soil conductivity, which will only lead to an increase in the quality factor of resonance - i.e. increase energy transfer efficiency. Actually, only a conductor of sufficient length that is not in the ground, but is grounded at one end, can work as such a “pulling” conductor. These are not observed (the wires of the power lines, although they are of sufficient length, of course, are not grounded - that is, they do not “see” the variable potential of the soil, and the interference from the external field of the soil will be weak - because the field strength is low, see above) - only the variable potential of the soil itself is great, but not the field from such a potential).
• With this approach, targeted energy delivery is not possible, so there is no point in such a technology - even if it works.
You can go not by targeted delivery, but by controlling delivery. Any receiver will generate a wave that can be elementarily detected. To select an energy flux that is somewhat high in density, a very good grounding and a high-Q receiver (i.e., a fundamental and expensive design) will be required. So to make a fundamental design in order for its functioning to be suppressed the next day is not economically feasible.
• Are you not afraid that you will create a second Tunguska meteorite? Is there any way to protect myself from the field created by the installation?
No, we are not afraid. To seriously talk about it, you need to have a clear model of what the Tunguska meteorite is and how to call it the Tower. We do not have such a model. If there is an acute paranoid desire to protect oneself from the field created by the standing wave, then of course this can be done (for example, by burying an object underground, i.e., essentially just well-grounded its entire external surface - which is simple and inexpensive, or by putting a separate receiver - which removes and removes energy when a certain threshold of energy density is reached).
• You did not take into account possible electrochemistry when current flows in the ground.
Yes of course. As soon as you give us a detailed map (with a resolution of at least a kilometer) of the electrochemical properties of the soil of all the continents of the Earth (to a depth of at least 100 meters), we will certainly take this into account in the model. But in the foreseeable future, such data is not expected.
• You will fit into the range of ADD communications, and / or communications of submarines, and “they will come for you”.
Firstly, a separate pure sine - will not be able to break the connection (i.e. it is filtered completely elementary). Secondly, with a high value of the variable potential of the Earth’s soil, the field strength will be small (due to a sufficiently large region of field distribution in the vertical direction). Thirdly, the experiment, of course, must be carried out under the auspices of one of the research institutes, in which case the corresponding “permissions” for the experiment will not become a problem.
• How will the fact of the operation of several towers / receivers simultaneously affect?
No way. If the frequencies of the towers are the same, then the resulting standing wave will simply be of a slightly more complex shape (as a result of the interference of waves from several towers) than from one Tower - which will not affect the system’s performance in any way. If the frequencies are different, then due to the very high quality factor of the loops (at the source and the receiver), the frequency selectivity of the loops will be huge, i.e. towers essentially simply “will not see” any frequencies other than their own. Those. the total field in the Earth-ionosphere resonator will exist in the form of a frequency beat , but this will not affect the operation of the system.
• Will there be a large step voltage - similar to how it occurs when a dangling end of a power line falls onto the ground?
No, it does not arise. If, for example, we take the amplitude of the variable ground potential in the antinode of the standing wave voltage equal to 15 kilovolts, and a wavelength of 30,000 m (which corresponds to a frequency of 10 kHz, and the source power is much more than a megawatt), then this will give a “step voltage” (t. e. the potential gradient along the surface of the earth) is about 2 volts per meter. Which is completely safe. The main difference from a broken power line wire is that the contact area of the power line wire with the ground is minimal - which gives a very large grounding resistance. As a result, the overwhelming part of the voltage drops in a small (short) neighborhood from the end of the wire, which leads to a high step voltage for this case. In the case of a standing wave from the Tesla Tower, the “localization region” of voltage is very large (half the wavelength — that is, tens of kilometers),
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UPDATE 2017.02.26:
Since the practical implementation of the original idea turned out to be much more complicated than the initial expectations, and in theory and in terms of conducting verification experiments, this project is paused.
We decided to focus on more applied aspects of the application of remote wireless power transmission technology. Two years ago, we became a company in the United States, and during this time we have come a long way in development - establishing business contacts, obtaining investments, agreements on pilot projects, etc. At the moment, we have focused our efforts on the creation and implementation of mass commercial operation of an industrial system for recharging drones on the fly. The essence of the system is the same as in the article above, resonant coupled circuits. Several prototypes were made with a sequential increase in power / efficiency / distance and serious results were achieved. A video of the flight of a large drone fully powered by wireless power transmission can be found here .
To accomplish this (and not only) task, we open an engineering office in Russia (a 100% subsidiary of the parent corporation) and recruit a team of engineers with good practical experience in the field of power pulse circuitry , from design to assembly and debugging of iron. Those. we need hands from the shoulders, a lot of experience and an active position in the project - the willingness to deal with incomprehensible things, and independently formulate / solve non-standard / non-trivial tasks in line with the main direction of the project. An additional plus is the ability to program controllers, knowledge of thermal calculations, experience with electromagnetic compatibility issues, knowledge of state regulation restrictions in the field of radio emission in the range of 10-100 kHz in the USA / Europe, and experience in FCC certification.
Work in the project will be extremely rich and interesting since tasks to be solved are far from areas with well-established solutions. Working hours - full time, in a friendly team, with a competitive salary and good technical support. Disposition - Moscow / near Moscow region.
If you meet the requirements described above and you have a desire to work in such a project, then write in a personal email, we’ll be happy to talk, tell you all the details and learn about your achievements and hobbies. In the comments on this topic I will not answer so that the holivar does not start.