The real science of non-Hertzian waves

Broken Links Updated: 15 June, 2018

Updated: 13th August, 2002.

Tesla was at pains to emphasise that his plans for wireless power distribution did not involve Hertzian radiation, and that such radiation could be minimised by a suitably low choice of operating frequency. He maintained that energy would be transferred by means of waves of 'current energy' rather than Hertzian waves, and the term non-Hertzian wave has often been used to label this.

Tesla felt that transmitting energy by forcing currents through the conductive earth was the key to wide area wireless power distribution at high efficiency, and he continued for many years to insist that Hertzian modes of communication were inferior to his alternative schemes.

In this article I shall try to explain why science does not get excited about Tesla's ideas for wireless power distribution using earth currents, and I'll try to clarify the misconceptions made by Tesla in his explanation of how the system would work. To do so I shall describe the character of EM radiation and its interaction with charges, the meaning of the terms near field and far field, and I'll show how these apply to Tesla's schemes. I shall also try to describe the role of the earth and ionosphere in forming a cavity by which Tesla might have hoped to fulfill his dreams.

I hope that these notes will help to clear up some of the misunderstandings and dispose of some of the pseudoscience that collects around this topic.

I have to start with some fairly basic preliminaries, and build up from there. Experts will notice that I've taken a few liberties here and there in order to try to get the general ideas across.

Charges and Fields.

The basic process is this: You take hold of a charge and shake it, and other charges in the universe shake in response. By doing this you have mysteriously transferred energy and momentum to the distant charges. The shaking induced in the distant charges in turn causes your 'source' charge to react and push back against you. It's as if the distant charges are mechanically coupled in some way to your charge. We invent the mathematical concept of an EM field to describe this ability of a charged particle to exchange energy and momentum with another like this. In this model, every charged particle radiates a field which influences all others, and apart from gravity and the nuclear forces, this is the only way that particles can influence each other, at any range, short or long.

It's important to appreciate straight away that you cannot separate the field from the charges. Indeed you cannot draw any real distinction between a charged particle and the EM field that is associated with it, and that it doesn't make much sense to say that energy is either stored in the particle or stored in its field. When you apply energy, it goes into the particle/field system and that's all you can say about it.

What causes a current to flow?

Or in other words - what makes a charge move? If we ignore gravity and the nuclear forces, charged particles have only the EM field through which to exchange energy and momentum. Thus it takes a field to make a charge move, and therefore it takes a field to make a current flow. The only way charged particles can influence one another is via the mechanism of the field.

Incidentally, the converse is also true. Two EM waves approaching each other will simply pass through one other and carry on their separate ways. No transfer of energy or momentum will take place between the two waves unless they impinge together one way or another onto a charged particle. Thus EM waves mediate the transfer of energy and momentum between particles, but from the wave's point of view, the particles mediate energy and momentum between the waves.

To this nice neat picture add another ingredient: an EM wave can sometimes turn into a pair of charged particles, and a pair of particles can combine and convert into an EM wave. If this helps to give the impression that in reality the EM waves are at least as real and substantial as the charged particles, then fine.

Indeed, although we are accustomed to thinking of the charged particles as the real 'stuff' of the universe, and the fields as a kind of abstraction, you can if you like, regard things as though the ripples in the EM field are the real objects of the universe, and the particles are illusive things that mediate between them. There seems likely to be a fundamental symmetry in nature between what we label as forces and particles, and this 'supersymmetry' is one of the important ingredients in the deeper theories at the frontiers of physics.

Does the particle or the wave carry the energy?

I hope the symmetry helps to illustrate that it's futile to try to decide whether the energy stored in the particle/wave system is held in the particles or in their contributions to the EM field. It is important to realise that there is only the one energy 'tank' available for each charged particle. You cannot choose between putting energy into the particle or into its field, you can only feed or draw from the particle/field pair.

So any statements we encounter that indicate the use of currents instead of fields must be viewed with suspicion, or at least carefully interpreted.

Note also that Maxwell's equations are satisfied in the entire volume of space, not just in some 'far-field'. They are satisfied close to the source charges and inside conductors and dielectrics too. That's not to say that all the various terms are always significant, in many cases you can simplify things by ignoring some negligible terms, eg at low frequencies.

So statements which suggest that Maxwell's equations don't apply in some particular case are also suspicious.

How do charges behave in a conductor?

A conductor by definition has a plentiful supply of charges which can move around more or less freely within the body of the material. They will tend to flow with the prevailing field within the conductor, and of course, each charge is adding its own contribution to that field. Much like water finding its own level by falling through a gravity field, our charged particles have no choice but to fall through the EM field until they find their 'own level'. This occurs when the charges have nowhere left to fall, which in electromagnetic terms means that the field within the conductor is zero. Effectively the movable charges flow through the conductor until their own field has cancelled out the prevailing field passing through the conductor from outside.

When the field within the conductor is successfully cancelled out in this way, the result is that the electrical potential is the same throughout the material, just as the surface of a pond is the same height at all points. And just like the surface of a pond, charges will adjust their positions if the external field changes. Tilt the pond and water will flow until it finds a new level with respect to the new angle of the pond. Apply a field to a conductor and its charges will flow until the potential is once again evened out within the material.

Departures from this constant potential are allowed, just like ripples on a pond, and these take the form of EM waves rippling through the space around and within the conductor. The charges redistribute themselves accordingly, which we see as currents.

An electrian would call this process induction of a current in a conductor by a field, whereas a physicist would talk in terms of the prevailing field being scattered by the charges in the conductor. Both these descriptions are valid interpretations of Maxwell's theory.

By the way, this property of conductors to effectively expel an EM field is rather nice. Although we said earlier that Maxwell's equations apply everywhere, we can see that often we don't need to calculate with them for the inside of our conductors. Instead, we can treat conductors as boundaries to the field rather than as materials embedded in the field. Then we only have to calculate for the space surrounding the conductors. This does sometimes lead people to forget that Maxwell applies throughout all space, and it does lead to the mistaken impression that the currents are somehow separate from the fields.

As well as being convenient for calculations, this (apparent) EM field blocking ability of conductors has other profound consequences. As the free charges within the conductor position themselves to level-off the field within the material, the field they create to do so has major consequences in the space beyond the conductor. We'll see some of these in the following sections, but one particularly useful consequence is the tendency of long thin conductors to guide an EM wave along themselves. When an EM field is guided in this way, we call it electricity flowing along a wire, and just as with water flowing downhill along a pipe, we can visualise the charge/field interactions as a flow of an imaginary fluid. For these kind of situations, we can use a very much simplified version of Maxwell's equations, which we call circuit theory. We can also talk as if energy is flowing along the wires carried by the moving charges, whereas in reality it is a consequence of the delicate equilibrium maintained between charges in one part of the wire and charges in another part of the wire - an equilibrium negotiated by their inseparable fields.

How does a cavity work?

A cavity is a space enclosed entirely by conducting walls.

If someone inside a cavity creates a disturbance of the EM field, for example by taking a bar magnet and spinning it so that the poles are swapping ends, this radiates EM waves to infinity. The charges in the the boundary conductors respond to this field by moving, and in their response they radiate their own EM waves. These waves turn out to be just right to exactly cancel the direct waves from the magnet in the universe outside the cavity. The conductor appears to be preventing the field from leaving the cavity, and at the same time, the field radiated from the moving charges within the boundaries makes its own significant contribution to the inside field.

Inside the cavity, the direct waves from the rotating magnet, and the extra waves radiated from the cavity walls, tend to combine supportively to give a more or less strong field (depending on just where you are in the cavity).

This ability of a cavity to contain EM radiation has many useful consequences. Natural cavities can form and we have an example with that of the earth (which roughly speaking is a conductor) and the ionosphere - a set of conductive layers in the earth's atmosphere at several tens of miles altitude. Between them, earth and ionosphere make a rough sort of cavity, more or less a spherical shell. From this comes the speculation by many including Tesla that we could exploit such a cavity for efficient global power distribution.

In practice of course, neither earth nor ionosphere count as perfect conductors, thus the distant field isn't very well cancelled, which means that energy leaks away both to infinity and into the earth's interior. We will look again at this a little later on.

So what are the Hertzian waves?

The vibrations of the EM field are what we call Hertzian waves. Whenever you have an alternating current, or for that matter any disturbance of a charged particle, you therefore have Hertzian waves. You can't say whether the energy is in the current or the associated waves, either would be equally correct. For example, you can measure the power flowing through a wire by multiplying voltage by current, or you can measure power flow by adding up the product of E times H of the EM field associated with the moving charges of the current. Both calculations will give you the same answer for the power flow. This means for example that it is perfectly reasonable to say that the power arriving at a domestic wall socket arrives there as a Hertzian EM wave, guided by the conductors of the domestic wiring and grid network.

Is there a non-Hertzian wave?

Physics doesn't know of any other interaction between charge apart from EM. We have used up all the fundamental degrees of freedom of the particles and photons involved aready, so there are no extra channels of communication between charged particles until you start to consider the other fundamental forces.

However there is a sense in which we can recognise two different types of EM field, and the distinction is meaningful because we can take any EM wave and discern it to be a mixture of the two kinds in some proportion. This concerns the often used phrases 'near-field' and 'far-field'.

When you look at an EM wave a long way from its source, its E and H components tend to have amplitudes close to the ratio E/H = 376.73 in units of ohms. This value, which derives from the electrical properties of empty space, can be thought of as the characteristic impedance of space. Whenever you look at a passing EM wave that's far from its source, it tends towards this value for its E/H ratio, and the further away it is from its source, the nearer it will be to this special value.

Also, at this far distance from the source, E and H oscillate up and down in phase with each other, and therefore represent (by their product) a real flow of energy away from the source. The components E and H each fall off in amplitude in proportion to 1/range and so the power density falls of as 1/(range squared).

Well, that's the long range view.

What happens closer to the source?

Now the field starts to take on some very different characteristics. Maxwell's equations still apply, as they do throughout all space, but the solution they give for the region close to the source has a number of different characteristics. Remember, the source of the field is one way or another down to a charged particle, or a collection of charged particles oscillating in some way - we might call it a radiator or transmitter. We understand that any oscillator is trading energy between its kinetic energy (KE) storage and its potential energy (PE) storage, and this is true of the EM field/particle system too. The H component of the field can be thought of as carrying the KE and the E component can be considered as carrying the PE of the field, and we must consider these to be interchangeable with the KE and PE of the particle, since we are declining to recognise a distinction.

Suppose we have a transmitter, ie a collection of oscillating charge. We force the charge into oscillation by injecting energy into it (which is the same as injecting it into the field). The charge/field begins oscillating, with its stored energy alternating between kinetic and potential at some fixed frequency determined by the overall geometry of the radiator and its surroundings. One way or another a bunch of charge is moving back and forth between one extreme in which it is at maximum PE, so E is peaking, and the other extreme at maximum KE at which H is peaking. In other words, the charge displacements are setting up a sinusoidal E-field and at the same time, the movement of charges between the two stationary extremes is setting up a cosinusoidal H-field.

Thus, unlike the far field situation, the E and H waves are almost 90 degrees apart from one another as they begin their outward journey from the oscillating source. They are also not necessarily in the nice ratio of E/H=377 ohms. The ratio of the two amplitudes when close to the source depends, roughly speaking, on whether you are oscillating a small quantity of charge through a large distance (large E, small H) or a large quantity through a small distance (small E, large H).

Is this an impedance matching thing?

You may begin to see that the process of radiation begins to look a lot like impedance matching of the oscillator to the impedance of free space. That would be one way to look at it.

The moving charge collection launches its field at the E/H impedance ratio determined by its structure (amount of charge and distance oscillated through), and this probably won't be at 377 ohms. The wave oscillation travels outwards and gradually comes up against the impedance of space, to which it is mismatched, and thus it suffers a gradual reflection (from empty space, as it were) back towards the source. Thus we have an oscillating charge and tied to it is an oscillating field into which energy flows with each quarter cycle and out of which much of it flows back on the next quarter cycle.

The region near to the source where E and H are significantly out of phase and mismatched to the ratio E/H=377, we often call the near field, and it is this region that some people may have in mind when they use the term non-Hertzian wave, although it is still a solution of Maxwell's equations. What we have in the near field is a picture of reactive power oscillating between E and H which is synchronised to the oscillatory movement of the charge. E is associated with the charge's displacement from its mean position, and H is associated with the charge's flow between its two extremes of position. The two are almost 90 degrees out of phase. To the electrical circuit which is responsible for driving the oscillation, this phase angle makes the radiator appear to have a capacitive or inductive reactance, depending on whether E or H has the upper hand, respectively.

The near field is characterised by E and H being almost 90 degrees apart (in quadrature) whereas in the far field, E and H are almost in phase. The field can be described as 'reactive' or 'real' on the basis of the phase angle between E and H, just as we do for currents and voltages.

Incidentally, within several wavelengths of the source, the E-field and H-field are roughly proportional to 1/(range squared), so the (slightly reactive) power flux density is now proportional to 1/(range^4). Even closer to the source, at less than wavelength/(2*pi), either the E field or the H field starts to vary as 1/(range cubed), according to whichever component the radiator is predominantly coupling to.

The far field

As opposed to the near field, in which E and H are almost in quadrature, the far field is largely real with E and H almost in phase, and we see a gradual transition taking place between the two. There are a couple of points worth noting here. First, the far field is always present in the near field as well - underneath, so to speak, the larger reactive component. The in-phase (real) portion of the field is present all the way up to the source, and retains its 1/r amplitude and 1/r^2 power density laws. This represents the real power flow away from the source, which is taking place underneath all the reactive two-way ebb and flow of energy. Think of the near field reactive components as being superimposed on top of the inner part of the far field.

Note that the energy and momentum carried to infinity by the far field, although generally irretrievable, in a sense remains associated with the particular charge whose disturbance sent it on its way. We can see this if we look at things from the EM wave's point of view. Long ago, a charged particle in the atmosphere of a distant sun alters its dynamics and emits a ripple of EM - call it a photon. A few billion years later this ancient and battered photon tumbles down through an astronomer's lens and finally hands its energy and momentum over to another charged particle in the instrument. Now from the photon's point of view (which is as equally valid as ours) no time at all has elapsed since it was born. Nor has any distance been travelled. From the photon's point of view, its creation and annihilation take place simultaneously and at the same place. It's as if one charged particle transfers energy and momentum to another using a photon as an intermediary, and it all happens at the same point in the photon's spacetime.

Perhaps this serves to illustrate that although we speak of the far field carrying energy off to infinity, we can still consider it to be associated with its source. To us it appears as if a photon 'remembers' the charged particle from which it was born whereas from the photon's view, it has never really left it. In that sense the energy is never completely detached from its source.

Does that mean that all the energy ever broadcast by a transmitter can be reclaimed, or at least the part of it that's still in the air, so to speak. Well, no. The outgoing radiation is irretrievable unless something reflects it back. This something might a charged particle that our outgoing far field has encountered along the way, stirred into motion by our outgoing far field, it radiates a little EM of its own (from which we obtain the principle of radar).

Does this relate to 'virtual' particles?

At the quantum level, the EM field is often described in terms of a cloud of so-called 'virtual' photons which radiate out from a charged object for some distance before returning. Each virtual photon borrows a little energy and heads out into the world. If it can't convert it to real energy (by finding a load or absorber) it returns its borrowed energy back to the source.

We can see that the quantum description of the process by which a charge influences its neighbours mirrors that of the classical radiation described above. We have a reactive region around the source, containing mostly 'imaginary' or borrowed energy, and this is similar in principle to the cloud of virtual photons surrounding a charged particle. As with the reactive field, the virtual photon can only borrow its energy, and can therefore exist, for a time of around a cycle of its oscillation frequency. You could perhaps think of a virtual photon as a photon with its E and H out of phase, so that it is 'virtual' in the same sense that reactive power is 'imaginary' power, although we would not want to take these mental pictures too literally.

Anyway, enough digression...

What if the radiator is inside a cavity?

The case arises in which we place the source inside a cavity, say the spherical shell cavity of the earth-ionosphere. Now the range is fundamentally limited by the walls of the cavity. Lots of things can happen now. If the wavelength is small compared to the size of the cavity, the waves propagate outwards into the cavity, the reactive components gradually reflecting back and the real components continuing on. If the cavity is lossy, they will continue as far as they can before petering out and the radiator thinks it is in free space. For a less lossy cavity, they will strike the walls and scatter about, ultimately to reflect back upon the source in some phase or another relative to the radiated signal. This appears to the transmitter as an extra reactive component to the load presented by 'space', and the upshot is that the whole cavity can be said to be filled with almost completely reactive EM waves. Under these conditions the reactance seen looking into the antenna terminals is altered from the value it would have in free space. It now represents the reactance due to the total reflection from the cavity. If the driver adjusts (tunes itself) to a conjugate match, we then see the cavity, radiator, and whatever drives the radiator, all oscillating together in a combined resonance.

As objects close to the free space antenna, or anywhere inside the high Q cavity space, begin to absorb energy from the field, this shifts the phase angle of the field a little more towards the 'real' and the antenna sees an increase in the small resistive part of its otherwise largely reactive terminal impedance. Thus energy is drawn from the source via the field to the absorber, and it is the real in-phase component of the field that represents this flow.

Current waves?

Tesla often refers to energy being carried by the currents rather than by Hertian waves. For example, he writes

"From my circuit you can get either electromagnetic waves, 90 percent of electromagnetic waves if you like, and 10 percent in the current energy that passes through the earth. Or, you can reverse the process and get 10 percent of the energy in electromagnetic waves and 90 percent in energy of the current that passes through the earth."

We'll look a bit closer at this misconception later on.

What about reception?

Some people suggest that Tesla intended to draw power from the reactive component of the field, by simply constructing an antenna which responds to the reactive field. Since E dominates, an E field probe (eg a TC electrode) would be resonated with a coil in such a way that a 90 degree phase shift would be given to E. In essence, a system is visualised whereby real power arrives at the transmitter, which is launched into the cavity as a reactive E>>H field, and the receiver simply corrects the power factor by impedance transformation to deliver real power at its terminals.

Does this represent the system envisaged by Tesla? Perhaps. Does it make sense in terms of modern physics? Yes it does, but we have to be careful just how to interpret what's happening. Does it work - in principle? Yes it does, power is transferred from source to load, but we have to look a little more closely to see clearly that there is no new physical principles are involved here and that ordinary EM waves are the energy carrier.

For starters, it would be wrong to say that the reactive field is carrying the power. The power is actually transferred by the far field component, the 'real' bit of the field which remember, is still sitting there underneath the big reactive field. When there are no absorbers in the cavity, the radiator is unable to broadcast a real component to the field at all. However much the radiator pushes on the cavity field, the reaction is always 90 degrees out of phase because 100% of its radiative effort is being reflected back at it. However as soon as something inside the cavity begins to absorb power, the reflection becomes slightly smaller and shifted a little in phase. Now the radiator is able to release a little 'real' radiation. You can go as far as to think of the field as a tank of reactive power, if you like, but it is real power that drains from it, and real power from the radiator that tops it up. So really it is real power that is flowing, as and when an absorber takes it, and the reactive field merely serves to 'seek out' so to speak, these absorbers, much like the cloud of virtual photons around a charged particle seeks out other charged particles with which to interact. Only if they find a load do they convert their imaginary energy and momentum to reality.

I hope this makes it clear that it would be an error to think that reactive power provides an alternative energy channel to that of the real power. We see that it is still real power, with real Hertzian waves, that actually conveys the power.

Does this limit a power radiator to the same performance as a radio antenna?

Yes, it does, ultimately. The two radiators are indistinguishable in principle of operation. A radio antenna will be designed to match to the impedance of free space in order to obtain wide bandwidth and efficient operation. It will have the appropriate length and thickness so that the quantity of charge that's oscillating, and the distance over which it oscillates, is chosen so that E/H will be close to 377. As the design moves away from this ratio, space starts to reflect the power back, and the radiator appears reactive to its driver. Although this reactance can be tuned away, it merely leaves behind the antenna's real radiation resistance, as determined by the impedance at which distant space will accept energy. You can mess with the local reactive field by resonating an antenna in this way, and emphasising either E or H. The reactive field gets stronger but the antenna's ability to radiate real power isn't altered.

If the radiator is placed inside a high Q cavity, a slightly different situation occurs. The cavity fills with the reactive field, which seeks out any absorbers. Absorbers weaken the reflection of the reactive power and this allows real power to enter the field and flow to the absorber. The difference with the cavity is that the free space 377 ohms doesn't have much relevance here. The radiation is never expected to go anywhere, it just bounces back reactively to the source. In this case, it turns out to be the dimensions of the cavity that enforce a particular ratio E/H on the radiation at large within it, and the enforced E/H in general varies from place to place. If real power is to be transferred across the cavity, then the source and absorber antennas must try to match to the particular E/H present in their particular locations within the cavity.

Where else is the near field employed?

In general, if source and destination are sufficiently close, ie well within their near fields, we can transfer energy at whatever E/H ratio we choose to use.

For example, in an AC transformer, we use a very low E/H ratio and we would say that the coupling is via the magnetic field. However, even in the case of a transformer, the real power is transferred by the real part of an alternating E*H, ie a Hertzian or EM wave. In this case we don't care than E/H << 377, in fact this helps to ensure that the transformer doesn't waste much power by sending it off to infinity. Instead the gross impedance mismatch to free space reflects it quickly back. Thus we get the nice strong near field around the windings (which the electrician would call the field due to the magnetising current), and hardly any far field at all.

As mentioned earlier, the near field in this region reduces as 1/(range cubed) for the dominant field component (H for the transformer case) and the other field reduces as 1/(range squared). Thus the coupling coefficient between two windings or between two electrodes would reduce roughly as 1/(range cubed) and the power delivered to a fixed impedance load reduces as 1/(range^5).

Does polarisation come into it?

Since we're still using EM waves, even at short range like in a transformer, polarisation is still important. Any antenna can only receive one polarisation at once, and will not respond to the opposite polarisation. You cannot devise an antenna that will deliver all the energy received at both polarisations simultaneously to a single port. The reverse is true for transmitting - the antenna will only radiate one polarisation, not the opposite. Thus you have to choose a polarisation and ensure that receivers are built to collect that same polarisation.

Do you have a near field or far field?

You can tell if you're in the near field of a source by separately measuring the E and H components. That's easy to do using two antennas, one which couples to the field with E>>H and the other with E<<H, for example a high impedance pair of electrodes, in conjunction with a low impedance loop coil. With care you can measure both at the same time, and compare their phases as well as amplitudes, from which you can work out which direction the energy is flowing in, and where it is coming from. You'll know if you're in the near field because either E/H will not be close to 377 ohms, and/or they will be out of phase with one another.

The field around a Tesla Secondary

By way of an example, I'll present some figures to show the shape and size of the field calculated for a real TC secondary. This system has topload 2 metres high of 60pF capacitance resonating at 75 kHz with a coil of effective inductance 75mH. Let's say that we drive the coil sinusoidally to a top voltage of 500kV with no breakout. If the resonator has a Q-factor of 300, then the power required to reach this steady state is around 12kW. The charge displaced on each half cycle is 30uC and the stored energy is 7.5J.

The TC can be approximated quite well by two Hertzian dipoles, an electric dipole to represent the charge displacement between topload and earth, and a magnetic dipole to represent the effect of the current spiralling through the 75mH inductor. Both dipoles are aligned with the axis of the TC.

The electric dipole has a moment of 60 uC metres and the magnetic dipole, if we assume the 75mH inductor has area 0.2m^2 and 800 turns, has a moment of 7.4 weber metres. Superposition allows us to calculate the effect of each dipole separately and add the results to get the overall field. Each of the two dipoles generates both an E and an H field vector and each field vector will have a horizontal and a vertical component. The table below shows all the four components of each dipole, for the field at various a horizontal distances. Separate figures are given for the reactive (near-field) and real (far-field), so that we can see their respective contributions.

			1 metre	10 metres	100 metres	1 km
Electric dipole	Ev	Near	540kV/m	548 V/m	0.62 V/m	1.4mV/m
		Far	1.33 V/m	0.13 V/m	0.013 V/m	1.3mV/m
	Eh	Near	0	0	0	0
		Far	0	0	0	0
	Hv	Near	0	0	0	0
		Far	0	0	0	0
	Hh	Near	2.25 A/m	0.023 A/m	230 uA/m	2.3uA/m
		Far	0.0035 A/m	350 uA/m	35 uA/m	3.5 uA/m
Magnetic dipole	Ev	Near	0	0	0	0
		Far	0	0	0	0
	Eh	Near	0.59 V/m	0.0059 V/m	59 uV/m	0.59 uV/m
		Far	925 uV/m	92.5 uV/m	9.3 uV/m	0.93 uV/m
	Hv	Near	0.99 A/m	0.001 A/m	1.2uA/m	3 nA/m
		Far	2.5 uA/m	0.2 uA/m	25 nA/m	2.5 nA/m
	Hh	Near	0	0	0	0
		Far	0	0	0	0

Clearly, the electric dipole due to the voltage on the top electrode is the dominant source of radiation, and the magnetic dipole due to the coil current is relatively small. This needn't be the case and the TC could be rearranged so that things were the other way around.

The following points are worth noting.

• The near field of the TC begins to give way to the far field at the 1km range. We see that at this range the near field components are down to about the same size as those of the far field.
• The far field components tend towards the E/H ratio expected from free space.
• E/H close to the TC is around 540000/2.25 = 240 kOhms, so the TC is a very poor match to free space, ie it is a poor radiator.
• The radiated power density from the electric dipole is 0.005 uW/m^2 at 1km range, which amounts to a total radiated power of 63mW. The radiated power from the magnetic dipole is negligible compared to this already small figure.
• With 12kW input and 63mW radiated, the radiating efficiency is 0.0005%.
• The radiation resistance of the resonator, referred to the coil base, is therefore around 0.00016 ohms.

Tesla's Proposals

Tesla's proposals all seem to embody his view that energy would be delivered through the flow of current in the earth, with the Hertzian waves "...being merely an accompanying manifestation [of the current]". In his view, he would eliminate the wasteful EM radiation by operating at a low frequency and by reducing the height of the transmitting electrode. He writes:

"...theoretically, the effect would be dependent upon the quantity of electricity displaced. The quantity of electricity displaced is proportionate to the capacity. Therefore, in order to realize my scheme, it seemed necessary to employ the biggest possible capacities that could be practically constructed;"

This reasoning by Tesla is faulty, and he is mistaken in thinking that this arrangement will transmit power very far. The problem is that the very field which he has suppressed by lowering the height of the transmitter capacity, is the field which is responsible for exciting the earth currents which he hopes will reach his receivers. When the height of the transmitting electrode is lowered, the range of the earth currents is reduced roughly in proportion. We would say that the near field becomes more and more closely confined to the area around the transmitter. As the height is lowered further, the field, and the associated ground currents are confined almost to the area beneath the transmitter sphere. Unfortunately for this scheme, it is the product charge times height which opens out the range of the circulating near field currents, not charge by itself. It is the dipole moment, charge times height, which is creating the field which drives the earth currents. By lowering the transmitter electrode, he is in effect reducing the range to that of the 'fringe field' of a capacitor.

Tesla writes:

"You must not make the antenna give off 90 percent in electromagnetic and 10 percent in current waves, because the electromagnetic waves are lost by the time you are a few arcs around the planet, while the current travels to the uttermost distance of the globe and can be recovered.

He believes that the circulating current entering the earth from his transmitter will uniformly increase the surface charge all over the globe, whereas in fact the earth's movable charges will, as we have seen, flow or displace as necessary in order to cancel out the EM field radiating from the transmitter. As this (dipole) field is largely confined to the vicinity of the transmitter, we find a large circulating current in that area only. The system behaves as if each charged particle pumped into the ground, so to speak, is trying to position itself as close as it can to the place (the top electrode) from which it was drawn. This is what the particle feels is the 'lowest' place in its E-field landscape. The surface charge density (and hence the current available) at any spot on the earth is proportional to the E-field incident at that spot from the dipole radiation (real or reactive) of the transmitter.

Tesla would be entitled, as any electrician is, to say that the energy is carried by the current. But he fails to appreciate that the current will only flow in conjunction with the associated field. The current will not flow without the field, because by definition the field is that thing which applies a force to a particle through the particle's property of charge. Short of proposing a fundamental new interaction involving charge (which he doesn't seem to be doing) Tesla's proposals can only be based on a fairly elementary failure to appreciate just what charges, currents and fields are all about.

This is, indeed, a rather common misconception, and often occurs amongst those trained in electronics and electrical engineering. It is natural (and perfectly reasonable within those domains) to think of the energy as flowing through wires, carried by currents. Voltage is seen as a kind of pressure and current is regarded as a flow of 'electricity', much like a flow of water in a pipe. Fields are regarded as incidental, sometimes a nuisance, and electricians are happy enough with any circuit until the wires reach an antenna, at which point a mysterious thing called radiation happens. The electrician's explanations tend to disolve into handwaving at that point as he struggles to address the question of just where and how is the energy transferred from the circuit to the field.

The physicist sees things differently by viewing nature from a wider perspective - one which isn't constrained by the limited and artificial view of nature given by circuit theory. When looking at an electrical circuit, the physicist sees a complex pattern of E and H fields formed into a rich and marvelously functional 3-D pattern by the boundary conditions imposed by lots of carefully arranged conductors and dielectrics. The technology of arranging those conductors and dielectrics is called electronics. Here and there those conductors might be formed into shapes that allow the fields to spread out in certain useful ways, and the electrician would call one of those bits the antenna.

The physicist's view of an electronic circuit as an intricate pattern of ripples and tensions in the EM field, anchored in place by a beautifully crafted assemblage of materials, is a wonder to behold and helps us to remember that no change in the physics occurs when we move from 'energy in the circuit' to 'energy in the air', and that such a move is merely a convenient change of descriptive language.

By the way, note that it is not necessary for us to say that the current 'causes' the field, or that the field 'causes' the current. There's no cause and effect process in EM interactions at the fundamental level. EM doesn't contain an 'arrow of time'. It is only when thermodynamics steps in, and you start to look at the so called entropy of the system that it becomes meaningful to say that energy flows from A to B. As far as the particle/field is concerned it is just A interacting with B. It is only when you move outside EM and consider the thermodynamic implications of the A-B interaction that you can begin to identify a cause-effect relationship. Only then can you unambiguously declare one to be the 'source' and the other to be the 'load'. The important thing is that charge and field are inseparable, you can't choose between one or the other as a choice of energy transfer mechanism, but you can choose between them as descriptions of the transfer process, and of course, both give the same correct answers.

Can't you 'push' the current with electrical pressure from behind?

Tesla's explanations of the operation of his power transmitter all seem to be based on the faulty notion that you can push a current from A to B, in a sense by simply exerting an electrical pressure at A which forces the charge out to B. He often used a hydraulic analogy to illustrate this. However, to apply this electrical pressure implies that A must extend an E-field as far as B, because it is the potential gradient along the A-B path which is applying force to the charged particles of the earth current.

Well suppose we just increase the amount of charge at A, then its radial E-field component will increase in the same proportions, and free charges in the earth will be attracted or repelled with at worst a 1/range dependancy of the force on distance? This would be called a monopole radiator, which is characterised by a single charge oscillating in magnitude. Unfortunately, such a thing doesn't occur in nature due to conservation of charge.

To increase the charge at A in order to 'raise the pressure' as in the hydraulic analogy, we have to draw that charge from somewhere nearby, which leaves behind a deficit. Therefore wherever we create say a positive charge increase, we also create a nearby negative charge increase too. No matter what we do to shuffle charges around, we can never form a monopole source. Nature only lets us form fields by separating pairs of oppositely charged particles. We have to do real work to separate a pair of charges, and since the particles are unchanged in their internal states by their mutual separation, the physicist likes to say that the energy we've put in has gone 'into the field'.

The loss of the option of making A oscillate its charge in a monopole fashion is a rather serious blow. Hertz must have said to Tesla, something along of the lines of '..but nature does not support a monopolar charge oscillation' and we can only speculate how Tesla might have puzzled over such a statement.

The trouble with the dipole is that the field at B, which we must establish in order to drive any currents or convey energy, is now much weaker than before, because an increase in charge at A is now matched by an increase in the opposing charge at a place close to A. Our field at B is now dependent not on the charge oscillating at A, but on the difference between the field from A and the opposing field radiating from the place where A borrowed its charge from. This cannot be avoided, and the result means that the field at E is proportional to the product of charge displaced times the distance over which it is displaced, a quantity which we call the dipole moment.

Tesla knew he was borrowing charge to force into the earth from his transmitter, and his lending source was a metal terminal fixed above ground. However, he mistakenly thought that he could ignore the field radiating out from his terminal, and that it was a minor side effect that he could minimise and localise to the vicinity of the transmitter by lowering the terminal. He knew the distant field from the low terminal would be very weak, and he thought this was desirable. He just didn't seem to appreciate that it was this rather feeble distant E-field that would drive his earth currents. It's as if he felt that the extra charge he was pumping into the earth would magically distribute itself uniformly across the globe, whereas we know that, as with any other good conductor, it will distribute itself as best it can to prevent the dipole field radiated by the transmitter from entering the earth.

Does a cavity rescue the situation?

Tesla wasn't aware of the existence of an ionosphere, although it soon became clear that radio waves were travelling further around the globe than diffraction around the conductive surface of the earth would account for alone. We now know that the ionosphere does indeed conduct sufficiently to display global resonances of the earth-ionosphere cavity (EIC). If this cavity had a sufficiently high Q factor, then even an inefficient radiator of the kind that Tesla proposed would fill the cavity with a reactive near field. You can say that the TC is sending a field around the globe which induces currents in the ionosphere, or you can say that the TC is inducing currents in the ionosphere that travel around the globe inducing fields as they go. Again it's a case of you choosing the description but nature is using just the one piece of physics.

Now if you suppose an arbitrarily high Q factor for the cavity, then you can in principle use arbitrarily small receivers and transmitters - it is simply a matter of coupling to the E/H ratio prevailing in your neighborhood of the cavity and transforming this impedance, perhaps by resonant devices, to the working impedance of your generators and loads.

In practice, the resonances of the EIC have nowhere near sufficient Q factor to perform this role. We can tell this quite easily, even with low power experiments, in fact without doing much at all other than measuring the background energy rattling around in the earth's field at any one time. The cavity is being constantly filled with energy from sources such as thunderstorms, etc, and this injects a broad band of noise into the cavity. Those noise components that happen to be at a resonant mode of the cavity will rattle around for longer than those that aren't. Simply measuring the background noise from around 1Hz to 30 Hz reveals the enhanced energy at certain frequencies, (this is an experiment that a patient amateur can do), but also demonstrates the hopelessly low Q factors of the resonances.

Information about the so called Schumann resonances of the EIC can be found in http://en.wikipedia.org/wiki/Schumann_resonances and a measured spectrum of the lowest modes can be seen at http://onlinelibrary.wiley.com/doi/10.1029/2005GL023028/full.

Some conclusions and comments.

The reactive region of the field doesn't offer an alternative communication mechanism to the normal radio spectrum. The near field arises as a consequence of the field/source interaction and is therefore part of the normal EM radiation process. Both are part of the solutions to Maxwell's equations, and any real power crossing the near-field region counts as a genuine Hertzian wave, although we've seen that the real power-carrying EM wave doesn't have to have the free space E/H ratio of 377 to achieve efficient operation, providing we provide a high-Q containment for the field.

Some people refer to the reactive near-field as a displacement current field, or as an induction field, according to whether E or H dominates. Fair enough, although strictly speaking all parts of the EM wave, both near and far, involve displacement and induction.

Suggestions that the reactive near-field constitutes some sort of 'scalar' or 'longitudinal' wave which is fundamentally different to the transverse nature of EM are really quite unnecessary. The radiation in both near (reactive) and far (real) fields is always polarised transverse to the direction of propagation. In the reactive near field, the power flux vector still points outwards, although it has a complex rather than real value. E and H remain perpendicular to it. We've used up all the available properties of the photon to explain all known EM phenomena, and there are no genuine anomalies within the energies we can reach at the moment.

It is not really correct to say that Tesla proposed sending power through the earth as opposed to through space. Earth (and ionosphere) are merely providing the boundary currents which contain the EM wave within the cavity.

Tesla's reliance on 'current energy', is not only faulty in principle, it is also poorly named, because his plan to set up an alternating field between the earth's surface and a conductive atmospheric layer would involve the gap between the two spherical shells becoming filled with a reactive near-field which is of the type in with E dominates over H, so that E/H >> 377. Thus the term 'voltage energy' might have been preferable to 'current energy', at least as far as most of the earth's surface is concerned.

I have tried to show here, rather unrigorously I admit, that one way or another electrical energy is always transferred from A to B by the Hertzian or real part of the field (equivalently, real currents and voltages). While we normally use other language to describe these things, transfer of power between the windings of a transformer, or between the plates of a capacitor, or through Tesla's proposed 'World System', or indeed along an ordinary wire conductor, all take place via Hertzian EM waves, just as in a radio communication link. The fundamental difference is the choice of E/H ratio for the exchange, and the extent to which the field is confined and guided to its destination. The rule is, if the field is confined in some way, eg by conductors or magnetic materials, or if the absorber is well within the near field of the source, then we can to some extent choose our own convenient E/H ratio for the energy transfer. If source and absorber are a long way apart and nothing is done to guide the field, then the free space impedance matters, and we have to design antennas to match to this.

Tesla seems to have displayed some rather elementary misunderstandings of the workings of currents and fields, and this would have been very apparent to his peers. This doesn't necessarily mean he was stupid, any more than any modern electronics expert who has a little difficulty grasping the relation between fields and currents is stupid. However, he did abandon the scientific process by not responding to the obvious criticisms of his proposals. If he were to persist with his idea in the proper way, he would have had to explain to a critical expert audience why conservation of charge didn't apply in this instance, and he would have had to explain clearly what alternative force was motivating his earth currents. He would have had to have shown what new laws applied instead of the Maxwell/Lorentz laws, and in which circumstances you apply them. He was able to do none of this, yet he did not interpret this as a problem with his ideas, rather, he felt that electrical engineering was simply ignoring the use of the currents, and concentrating too much on Hertzian phenomena. He failed to appreciate that they are one and the same, but nevertheless he continued to insist to his lay audience that his ideas were correct.

He wrote:

"The Hertz wave theory of wireless transmission may be kept up for a while, but I do not hesitate to say that in a short time it will be recognized as one of the most remarkable and inexplicable aberrations of the scientific mind which has ever been recorded in history."

This apparent irresponsibility has led to generations of enthusiasts trying to produce phenomena in support of Tesla's claims. The naive ideas that he presents find a receptive audience amongst those trained in electronics and electrical engineering, perhaps because those subjects make full use of the approximation which allows us to pretend that energy is flowing 'through the wires'. It is all too easy to carry this too far, and by stretching hydraulic analogies beyond their point of usefulness, electrical engineer and hobbyist alike can both find themselves drawn to a comfortable but wrong understanding of EM and charged particle behaviour.

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