Art of Transmitting Electrical Energy Through the Natural Mediums

WIRELESS TRANSMISSION THEORY

“By the plan I had conceived, if it was realizable, it was just as easy to telegraph or telephone across the entire globe as it is across this room.”  – Nikola Tesla, 1916

In the late 19th century, shortly after the introduction of AC power, Nikola Tesla began development of a system for the global transmission of electrical energy without interconnecting wires.  Some of his early apparatus took the form of ordinary radio transmitters, much like those used when commercial broadcasting and wireless telecommunications began to take hold in the 1920s.  Others were resonant electrical induction apparatus used in a laboratory setting for electric lighting.  The wireless “electrodynamic inductive” technique lay dormant for some 100 years until 2006, when it was revived before the public’s eyes under the name “Witricity” [1].

Unlike the two methods referred to above, the wireless method that Tesla planned to use at Wardenclyffe depends upon an electrical current flowing through the earth between a Tesla coil transmitter and a Tesla coil receiver.  Both of the prototype transmitter-receiver stations would be built following the same design, with a powerful Tesla coil located inside each of the tower structures.  In the case of Wardenclyffe prototype, the second plant was to be constructed somewhere in Great Britain, perhaps on the west coast of Scotland near Glasgow or to the south in Cornwall.

The atmospheric conduction method depends upon the passage of electrical current through both the earth and the atmosphere.

“The earth is 4,000 miles radius.  Around this conducting earth is an atmosphere.  The earth is a conductor; the atmosphere above is a conductor, only there is a little stratum between the conducting atmosphere and the conducting earth which is insulating. . . . Now, you realize right away that if you set up differences of potential at one point, say, you will create in the media corresponding fluctuations of potential.  But, since the distance from the earth’s surface to the conducting atmosphere is minute, as compared with the distance of the receiver at 4,000 miles, say, you can readily see that the energy cannot travel along this curve and get there, but will be immediately transformed into conduction currents, and these currents will travel like currents over a wire with a return.  The energy will be recovered in the circuit, not by a beam that passes along this curve and is reflected and absorbed, . . . but it will travel by conduction and will be recovered in this way.” [Nikola Tesla On His Work With Alternating Currents and Their Application to Wireless Telegraphy, Telephony, and Transmission of Power, pp. 129-130.]

The electric current through the earth is balanced by an equivalent electrical displacement through the space above it.  This displacement can be achieved by means of electrical conduction through the atmosphere without violating any of the known laws of physics.  With energy transmission by true electrical conduction, a very high voltage on the order of 15 million volts is needed on both of the elevated terminals to break down the insulating air around and above each plant.  The ionization of the atmosphere directly above the elevated terminals is facilitated by a vertical ionizing beam of ultraviolet radiation that leads to the formation of what might be called a plasma high-voltage electrical transmission line.  The upper troposphere between the transmitter and the receiver is available for a conductor by inducing the plasma state within that region. This is the “aurora” effect described by Tesla in the 1916 interview.

“I have constructed and patented a form of apparatus which, with a moderate elevation of a few hundred feet, can break the air stratum down.  You will then see something like an aurora borealis across the sky, and the energy will go to the distant place.” [ibid, p. 110]

The end result is a flow of true conduction currents between the two elevated terminals by a path up to and through the troposphere, and back down to the other facility.  To learn more about this mode of operation read the paper “Nikola Tesla On Wireless Energy Transmission, with additional comments by Henry Bradford and Gary Peterson” located at,

In addition to the atmospheric-conduction method the Tesla coil transmitter design is also adaptable to another method that Tesla had for wireless transmission called “earth resonance.”  Comparing Tesla’s patents covering his wireless system using the earth resonance method and those covering the atmospheric conduction method reveals that both the basic transmitting and receiving apparatus are identical.  Both consist of large Tesla coils connected to the earth and to high-voltage elevated terminals.  (It is important to note that a single earth-resonance Tesla coil transmitter can be made to perform exactly as intended without any additional stations being present.  In this case the earth itself overrides the requirement that one or more additional stations be placed into operation.)

Differences between the two methods are the potential required at the Tesla coil transmitter’s elevated terminal and also the operating frequency.  For atmospheric conduction about 15 to 20 million volts are needed.  For earth resonance Tesla says the elevated terminal has to be charged up to about 100 million volts.  As for frequency, the usable base frequency spectrum is about the same for both methods, about 1,000 to 35,000 cycles per second (1-35 kHz).  An atmospheric conduction system can operate at any arbitrarily selected frequency in this region.  With an earth resonance system it is compulsory that it operate on some harmonic of the fundamental earth-resonance frequency, reported by Tesla as being about 12 Hz.

There is a misconception among some researchers that Tesla intended to transmit electrical energy directly through the Schumann cavity or earth-ionosphere cavity.  While he definitely spoke of exciting a terrestrial resonance mode, he was not talking about the direct excitation of a Schumann resonance. The terrestrial resonance mode that he apparently excited in 1899 at Colorado Springs is referred to by some as an “earth resonance mode,” which are different from the Schumann resonance modes.  Also remember that Tesla made a distinction between electrical energy transmission by atmospheric conduction and electrical energy transmission using earth resonance principles.

     “. . . In one the ionizing of the upper air would make it as good a conductor of electricity as a metal. In the other the power would be transmitted by creating “standing waves” in the earth by charging the earth with a giant electrical oscillator that would make the earth vibrate electrically in the same way a bell vibrates mechanically when it is struck with a hammer. . . .” [“Tesla Cosmic Ray Motor May Transmit Power ‘Round’ Earth,” Brooklyn Eagle, July 10, 1932, John J. A. O’Neill]

One final note, the earth possesses a naturally existing negative charge with respect to the conducting region of the atmosphere beginning at an elevation of about 50 kilometers.  The potential difference between the earth and this region is on the order of 400,000 volts.  Near the earth’s surface there is a ubiquitous downward directed E-field of about 100 V/m. In LIGHTNING PROTECTOR, May 6, 1916, U.S. Patent 1,266,175, May 14, 1918 Tesla referred to this charge as the “electric niveau” or electric level.

     “A point of great importance would be first to know what is the capacity of the earth? and what charge does it contain if electrified?  Though we have no positive evidence of a charged body existing in space without other oppositely electrified bodies being near, there is a fair probability that the earth is such a body, for by whatever process it was separated from other bodies—and this is the accepted view of its origin—it must have retained a charge, as occurs in all processes of mechanical separation.  If it be a charged body insulated in space its capacity should be extremely small, less than one-thousandth of a farad.  But the upper strata of the air are conducting, and so, perhaps, is the medium in free space beyond the atmosphere, and these may contain an opposite charge.  Then the capacity might be incomparably greater.  In any case it is of the greatest importance to get an idea of what quantity of electricity the earth contains.  It is difficult to say whether we shall ever acquire this necessary knowledge, but there is hope that we may, and that is, by means of electrical resonance.  If ever we can ascertain at what period the earth’s charge, when disturbed, oscillates with respect to an oppositely electrified system or known circuit, we shall know a fact possibly of the greatest importance to the welfare of the human race.  I propose to seek for the period by means of an electrical oscillator, or a source of alternating electric currents. . . .” [“On Light and Other High Frequency Phenomena,” Franklin Institute, Philadelphia, February 1893, and National Electric Light Association, St. Louis, March 1893.]

Tesla coil earth resonance transmitters create a local disturbance in the earth’s charge that appear as an annular deviation in the strength of the background electric field.  In operation, successive disturbances move away from the transmitter and diminish in intensity as the distance from the transmitter increases.  A sufficiently powerful transmitter produces electric field distortions that propagate all the way to the antipode at which point the energy is reflected back towards its point of origin.  When properly tuned, constructive interference occurs between the outgoing disturbances and the reflected disturbances returning from the antipode.

The transmission of electrical energy across the entire globe and its reflection all the way back to its source is the basis of Tesla’s earth resonance method.  While the atmospheric conduction method requires that both transmitting and receiving apparatus be placed into operation, a properly tuned and sufficiently powerful earth resonance transmitter, on the other hand, can be made to operate exactly as intended without any man-made Tesla coil receivers being activated.  The earth itself fulfills the requirement that a synchronized receiver be present.

To conclude this section, three fundamental principles behind the operation of Tesla’s global wireless telecommunications system are:

1. Low frequency alternating current can be transmitted through the inhomogeneous earth with low loss due to the fact that the net resistance between antipodes of the earth is considerably less than 1 ohm.  The electrical displacement takes place predominantly by electrical conduction through the more conductive regions.  The electrical energy also propagates through the earth by means of electrostatic induction or displacement current.

2. Low frequency high voltage alternating current can be transmitted through the atmosphere with low loss.  The electrical displacement takes place by a) electrostatic induction, b) electrical conduction, or a combination of these two.

3. The earth possesses a naturally existing negative charge or DC electrostatic potential, on the order of 400,000 volts, with respect to the conducting region of the atmosphere beginning at an elevation of about 50 kilometers, and near the earth’s surface there is a ubiquitous downward directed E-field of about 100 V/m.  The Tesla coil transmitter creates a disturbance in this charge, which may be observed as an annular distortion of the background electric field around it.

Wireless Energy Transmission for the Amateur Tesla Coil Builder (Re: [TCML] Wireless Transmission Theory)

“Since charge is conserved, scalar field S satisfies the homogeneous wave equation, thus one should expect primarily sources of dynamic scalar fields, and not sources of static scalar fields.” – Koen J. van Vlaenderen, 2008

One disagreement yet to be resolved about the Tesla wireless system is whether electrical energy is carried from Tesla coil transmitters to Tesla coil receivers by ordinary radio waves or if some other mechanism is involved.  We are speaking here of scaled-down versions of the system such as might be assembled by the typical Tesla coil experimenter.  The operational power levels involved are assumed to be insufficient to excite earth resonance or result in massive atmospheric ionization in the vicinity of the oscillators.  There are no provisions for the generation of vertical ionizing beams originating at the elevated terminals and projecting up to an elevation of say 8 km where conductivity can more easily be imparted to the air.

Nine Proposed Mechanisms Regarding the transmission of electrical energy from a Tesla coil transmitter to a Tesla coil receiver, six possible mechanisms have been identified that are available according to present electromagnetic field theory. The first three are mutual induction, capacitance, and far-field electromagnetic radiation or ordinary radio waves. The fourth is an alternative mechanism involving ordinary radio waves produced in the far-field zone as a result of ground currents propagating to a great distance from operating Tesla coil transmitters. The fifth model is that of energy transmission by means of a spherical conductor “single-wire” surface wave transmission line. (There may be aspects of the physics behind the single wire transmission line that are not fully understood.)[2] The sixth mechanism is modulation of the natural plasma that exists because of the electrical potential gradient between the earth’s surface and the conducting region of the atmosphere beginning at about 50 kilometers.

The seventh mechanism is what might be called “electrostatic induction.” This explanation exists within a ‘grey area’ of electromagnetic field theory.

The eighth proposed mechanism is propagation by means of an ion-acoustic wave in the intervening space between the two elevated terminals. This is a special case where the operational power levels involved are sufficient to result in massive atmospheric ionization in the vicinity of the two transmission – reception stations, and provisions are made for the generation of vertical ionizing beams originating at the elevated terminals and projecting up to an elevation of say 8 km where conductivity can more easily be imparted to the air. [3]

The ninth proposed mechanism considers the transmitter and receiver as being “self-referencing” by means of virtual electrical grounds, a theoretical concept developed by Eric Dollard and others in the 1980s. This is another special case, that in which the operational power levels involved are sufficient to excite earth resonance. [4]

Mutual induction Energy transmission by “mutual induction” can be excluded because the magnetic field density falls off too rapidly to account for amount of energy received in the far-field zone.  Furthermore, the transfer of energy between a Tesla coil transmitter and the requisite Tesla coil receiving transformer involves electrical conduction between the two respective ground terminals, and this is not taken into account by this model

Capacitive coupling (differential capacitance) The elevated terminal of a Tesla coil transmitter works as a capacitor plate. Opposite to this plate is every other electrically conducting body to which it is connected, including the earth and the receiving transformer’s elevated terminal. The transmitter’s elevated terminal serves two purposes: first, it acts as a charge reservoir in relation to the earth’s surface in the immediate vicinity of the transmitter; second, it is one of two electrodes, the other electrode being the receiving facility’s elevated terminal.

Ed Phillips has observed, “the coupling inferred by Tesla’s use of this figure [below] and the notation of charge which goes with it would be that of mutual capacitance.”

Tesla’s diagram “Explaining the Relation Between the Effective and the Measured Current In the Antenna.” [5]

For distances up to about 1/6-1/2 wavelength the propagation of energy between the respective elevated terminals is a result of displacement current, exactly like the transfer of electrical energy between two closely-spaced plates of a conventional capacitor in a typical AC circuit. This explanation is fine for distances up to about 1/2 wavelength, but the electric field intensity between two capacitor plates, mathematically modeled using a low-voltage DC potential, is a near-field phenomenon.  In other words, at greater distances the standard mathematical capacitive coupling model breaks down.  A.C. de Queiroz, says this:

“Capacitive coupling decreases very fast with distance.  It’s the “local field” of the antenna.  Remember that both coils have capacitance to ground, and this does not change significantly if the coils are moved apart, while the capacitance between the terminals decreases fast.  The capacitance to ground of the receiving coil and the capacitance between the terminals form a capacitive voltage divider of huge ratio for quite small distances. . . .”

Therefore, energy transmission by capacitive coupling would seem to be excluded because when the two elevated terminals are separated by more than about one-half of a wavelength of the applied current they are, in theory, electrically decoupled.

 “. . . If the distance is comparable to the wavelength of the transmitted signal, we have electromagnetic waves, far field.” — A.C. de Queiroz

Far-field electromagnetic radiation or ordinary radio waves Any well-designed Tesla coil transmitter can be shown to be a poor source of radio waves, in both the near field and the far field.  Field strength measurements taken on actual Tesla coil transmitters demonstrate that when these devices are in a higher state of refinement they are very inefficient in terms of the production of electromagnetic radiation, a.k.a. “radio waves.”  There is insufficient signal strength to account for the amount of energy received in the far-field zone.  In light of this, ordinary radio waves can be excluded.

The Bradford Hypothesis The basic idea is that the earth currents and charge-coupled electromagnetic field associated with Tesla coil transmissions gradually decouple from the associated charge carriers and become ordinary radio waves as a function of the distance from the transmitter. Mr. Bradford states, “I do not believe that the theory for it has been worked out, but in principle it is a straightforward application of electromagnetic theory.”

1) The Spherical Conductor “Single-wire” Surface Wave Transmission Line model This explanation, presently being refined by Kenneth and James Corum, et al, is a strong candidate.  A Tesla coil transmitter consisting of a grounded high voltage, pulse-driven, top-loaded helical resonator launches a transmission-line wave or surface wave, in the form of earth currents and a charge-coupled electromagnetic field.  It is somewhat similar to the G-line or Goubau transmission line model promoted by William Beaty.  There is even better agreement with the E-line transmission line model described by Glenn Elmore.  This model is based upon a sometimes overlooked solution to the Maxwell-Heaviside equations that describes a propagating TM₀₀ surface wave on a single conductor.  This “nonradiating surface wave mode . . . exhibits attenuation much lower than coax and a relative propagation velocity of unity. . . . It is very broadband and has practical applications from RF through microwave frequencies and beyond. . . .” (see Elmore, Glenn, “Introduction to the Propagating Wave on a Single Conductor,” 2009 ; http://www.corridor.biz/FullArticle.pdf ).  The terrestrial surface wave or surface plasmon associated with Tesla wireless system apparatus is the result of current flowing between two discrete points of direct electrical connection to the earth’s subsurface, one at the transmitter and the other at the receiver.

2) Modulation of naturally existing plasma model The entire earth possesses a naturally existing negative charge or DC electrostatic potential with respect to the conducting region of the atmosphere beginning at an elevation of about 50 kilometers.  The potential difference between the earth and this region is on the order of 400,000 volts.  Near the earth’s surface there is a ubiquitous downward directed E-field of about 100 V/m.  In operation, a grounded Tesla coil transmitter creates a local disturbance in this charge.  The disturbance manifests itself as an annular distortion of the background electric field around the transmitters ground terminal.  At a point in time when a measurement of the e-field component of the EM field at the ground terminal should show zero volts above the background potential, other measurements should show it rising in intensity until a point 1/4 wavelength (1/4 lambda) away from the ground terminal is reached (axial projection).  From there the e-field should diminish in intensity until, at 1/2 wavelength from the terminal, it again shows zero.  At a measurement point approximately one wavelength away from the ground terminal, an induced e-field once again should begin to emerge above the average background field level, again increasing in intensity until a second maxim is reached at 1 1/4 wavelengths away from the oscillator.  It is possible that measurements would reveal a zero crossing to a relative potential of the opposite sign.  With a sufficiently powerful transmitter this phenomenon would be expected to repeat itself over and over until the antipode is reached, at which point reflection would take place and the transmitted energy would begin to travel back to its point of origin in the reverse direction.  With the proper selection of operating frequency constructive interference with the outgoing wave takes place.

3) “Electrostatic induction” In this model the two distant elevated terminals are electrically coupled together in a manner similar to the transfer of electrical energy between two closely spaced capacitor plates in a typical AC circuit, but at distances greatly exceeding 1/6 – 1/2 wavelength.  The electric field between the two elevated terminals is not homogeneous but has persistent wave properties.  (These persistent structures in the E-field have been called “potential vortices” by Konstantine Meyl, see “Scaling Down Tesla’s Wireless System for Experimentation.”

Tesla used the term electrostatic induction to describe the behavior of capacitors, or more generally, the electrical coupling of two or more conducting surfaces that are separated by one form or another of dielectric. This term appears in Tesla’s SYSTEM OF TRANSMISSION OF ELECTRICAL ENERGY (U.S. Patent No. 645,576, dated March 20, 1900) and elsewhere.

“In some cases when small amounts of energy are required the high elevation of the terminals, and more particularly of the receiving-terminal D’ may not be necessary, since, especially when the frequency of the currents is very high, a sufficient amount of energy may be collected at that terminal by electrostatic induction from the upper air strata, which are rendered conducting by the active terminal of the transmitter or through which the currents from the same are conveyed.”

This model is inconsistent with a basic tenet of mainstream physics related to the scalar derivatives of the electromagnetic potentials, which as of the year 2013 are considered by many to be nonphysical.

Notes: In all cases, with the exceptions of the mutual induction model, it is an absolute requirement that both the Tesla coil transmitter and the terrestrial Tesla coil receiver be well connected to the earth’s subsurface, allowing them to be coupled together by electrical conduction through the earth between their ground terminals.  Also, the transmitter excitation current will typically be ‘mono-polar’ transient in nature, that is to say non-sinusoidal with a rapid rise time and cutoff.

It is quite conceivable that it will be found the best explanation for the long-distance transmission of electrical energy between a Tesla transmitter and receiver is a combination of two or more of the three best-candidate mechanisms listed above.

Yahoo Wireless Energy Transmission Tech Group Message #787

Yahoo Wireless Energy Transmission Tech Group Message #788

In June 2008 Bill Beaty suggested the electrostatic induction that takes place between the ground terminal of a Tesla coil transmitter and the ground terminal of a paired up Tesla coil receiver in the form of “dielectric waves” or “waves of dielectric polarization” might be detected using a deeply buried dipole antenna.

“In Fig. 2 I have shown a device for detecting the presence of the waves such as I have used in a novel method of magnifying feeble effects which I have described in my United States patents Nos. 685,953 and 685,955. It consists of a cylinder of insulating material, which is moved at a uniform rate of speed by clockwork or other suitable motive power and is provided with two metal rings B B, upon which bear brushes a and a’, connected, respectively, to the terminal plates P and P’. . . . The plates P and P’, through which the electrical energy is conveyed to the brushes a and a’, may be at a considerable distance from each other in the ground . . . both plates . . . connected to earth the points of connection . . . selected with reference to the difference of potential which it is desired to secure, the strongest effect being of course obtained when the plates are at a distance equal to half the wave length. . . . by this method a relatively great amount of energy and in a suitable form may be made available for the operation of a receiver. . . .”

An oscilloscope along with a bandpass filter or a spectrum analyzer, and an optional preamplifier [or attenuator] is used in the place of Tesla’s rotating cylindrical switcher-plus-sensitive-device to detect the transmitted electrical energy, i.e., the electrical energy being transmitted through the earth.  The same instrumentation can also be used in conjunction with the Tesla coil receiving transformer.  Coupling to the helical resonator is by means of either an E-field or an H-field probe.

[1] Soljacic, Marin, et al, “Wireless Power Transfer via Strongly Coupled Magnetic Resonances” SCIENCE, vol. 317, July 6, 2007

[2] Electromagnetic space wave radio propagation involves both sky-wave and ground-wave components. In turn, the ground wave has both direct-wave and ground-reflected components. The ground-reflected component reaches the radio wave receiving antenna after being reflected from the earth’s surface.  There is also an induced ground-hugging component called the Norton surface wave.  It is the result of electrical currents induced in the earth by refraction of a portion of the reflected-wave component at the earth-atmosphere interface.  Upon reflection from the earth’s surface the reflected wave undergoes a 180deg phase reversal.  When the transmitting antenna is on or close to the ground, the direct and reflected components tend to cancel out and the resulting field intensity is principally that of this surface wave.  Because part of its energy is absorbed by the ground, the rate of attenuation is much greater than inversely as the distance.  It is the conductivity of the underlying terrain that determines the attenuation of the Norton surface-wave field intensity as a function of distance.  The ground currents of a vertically polarized Norton surface wave do not short-circuit a given electric field but rather serve to restore part of the used energy to the following field.  The better the conducting surface layer, the more energy returned and the less energy absorbed. [Antennas and Radio Propagation, TM 11-666, Dept. of the Army, Feb. 1953, pp. 17-23.]  Sommerfeld describes an electrodynamic wave that is guided along a wire of finite conductivity and Zenneck expands upon this description, asserting that the earth’s surface behaves in a manner similar to a conducting wire.  While the Norton Surface Wave is the result of electrical currents induced in the earth by refraction of a portion of the reflected-wave component of the ground-wave at the earth-atmosphere interface, the Zenneck surface wave associated with Tesla’s apparatus is the result of terrestrial current flowing between discrete points of direct electrical connection to the earth’s subsurface.  When compared with the Norton surface wave it appears the Zenneck surface wave does not diminish as significantly as the distance from the source facility increases.

“With appropriate constitutive parameters, a pure Zenneck wave would seem to hold out the promise of guided propagation with no radiation field to waste energy.” — James Corum

[3] The electrostatic or magneto-hydrodynamic plasma wave model.  In operation a radio-frequency current is applied to each of the two resonators creating, at each location, an oscillating magnetic field.  In turn, the oscillating magnetic field induces an oscillating electric field.  The oscillating electromagnetic field creates a weak to highly ionized plasma in the vicinity of each resonator, depending on the amount of power applied to the oscillation transformer primary.  The volume of the ionized region is proportional to the peak energy of the oscillation.  If the currents in the two resonators have a 180deg phase relationship with each other, then conditions are favorable for interconnection of their respective magnetic fields.  In addition to the inductively coupled discharge created plasma, conditions also exist for the creation of capacitively coupled discharge plasma between the two respective elevated terminals.  These would be either electrostatic waves or more likely magneto-hydrodynamic waves, assuming the presence of inter-connected magnetic field lines.  The transfer of energy between a Tesla coil transmitter and the requisite Tesla coil receiving transformer is by electrical conduction through the earth between the two respective ground terminals, and also through artificially created weakly ionized plasma between the two elevated terminals.  For a high-power system, coupling between the elevated terminals is by electrical conduction through highly ionized plasma.  The two electrodes act as high voltage discharge terminals for the formation of capacitively coupled discharge plasma with the electrical interconnection taking place through the upper level atmosphere.  The ionization of the denser atmosphere directly above the elevated terminals is facilitated by the use of an ionizing beam of high-intensity ultraviolet light to form what might be called a high-voltage plasma transmission line (see Barnes, Jr., Arnold A., Robert O. Berthel, “A Survey of Laser Lightning Rod Techniques,” AD-A239 988, August 21, 1991).

[4] Virtual ground model.  The transmitter and receiver are viewed as being “self-referencing” through the establishment of virtual electrical grounds comprised by the two elevated terminals. The system would use earth resonance to circumvent the Newtonian law of action and reaction.

“In this arrangement energy is continuously bounced back and forth between the earth and the reflecting capacitance at a rate tuned to a natural rate of the earth. This standing wave of energy pulsation is maintained by the energy transformer which delivers electric energy to this standing wave via the coupling transformer. A certain percentage of this energy in the standing wave is refracted thru the earth-transformer reflection point and into the earth. This refracted energy establishes another standing wave in the earth. Hence, a pair of standing waves are produced which communicate energy thru the refraction. The oscillating resonant coil, tuned to an earth harmonic, establishes a virtual ground at one terminal of the coupling transformer thus rendering the earth terminal active from the standpoint relative to the electric conditions surrounding the apparatus. The coil terminal designated as the reflecting capacitance appears active and the earth terminal appears to be neutral, whereas from the earth’s standpoint the earth terminal is active. Thus, the reason for the popular notion that the reflecting capacitance is the output of the apparatus. In light of the virtual ground theory this is obviously not correct.” — Eric Dollard

Alternatively described, circumvention of Newton’s Third Law would be due to electrodynamic force interactions between heavy ions and electrons, known as the anomalous cathode reaction force.

“The work of [Paulo N. Correa & Alexandra N. Correa] began with an investigation of the pulsed abnormal glow discharge that occurs during electron emission from a cold cathode in a vacuum.  At Labofex, the Correas pursued an experimental investigation of the electrodynamics of anomalous cathode reaction forces made manifest when the abnormal glow discharge was conditioned to pulsate autogenously.  External pulsation of the abnormal glow had been previously investigated by Ernesto Manuel, who obtained the 1969 patent for the method used to this day in the plastic coating of soft drink cans!  But the Correas discovered that, under defined physical conditions, the abnormal glow could be made to pulsate ‘autogenously’ by field emission.  Anomalous cathode reaction forces developed by field emission in vacuum-arc discharges had been well known to physicists since the 1930’s, and had led Dr. Harold Aspden of Southampton University, UK, in 1969 to enunciate his principle of an anomalous energy transfer in plasma between electrons and heavy ions, resulting in a vacuum-induced acceleration of electron flow and a progressive increase in electric current.  Dr. Aspden had predicted that in such discharge tubes, the current would increase without limit for a constant applied voltage, and the tube would be destroyed unless some means were taken to limit the current.  Previous electrodynamics experiments of this type in the U.S. and in Russia had ended in failure, apparently because of electrode burn-out.”

[5] Fig. 14. Diagram Explaining the Relation Between the Effective and the Measured Current In the Antenna.

“The actions at a distance cannot be proportionate to the height of the antenna and the current in the same. I shall endeavor to make this clear by reference to diagram in Fig. 14.  The elevated terminal charged to a high potential induces an equal and opposite charge in the earth and there are thus Q lines giving an average current I=4Qn which circulates locally and is useless except that it adds to the momentum.  A relatively small number of lines q however, go off to great distance and to these corresponds a mean current of ie = 4qn to which is due the action at a distance.  The total average current in the antenna is thus Im = 4Qn + 4qn and its intensity is no criterion for the performance.  The electric efficiency of the antenna is q/Q+q and this is often a very small fraction.” — The True Wireless, Electrical Experimenter, May 1919

What is meant by a longitudinal electromagnetic wave?

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I reckon this is most likely a rather obtuse question, but I was wondering what would be meant by a longitudinal electromagnetic wave? Questions such as this one refer to there being ‘no longitudinal electromagnetic waves’, without formally defining what this would be. My issue is that in the case of electromagnetism, we have 4 fields (?) that could be varying: D, E, H and B. I would think that formally, a longitudinal wave would be one for which the direction of the varying field is in the direction of the wave propagation given by the wavevector k. Maxwell’s equations only exclude D and B having a component parallel to k (where there is no free charge present), but clearly in non-isotropic media, E will necessarily therefore have a component parallel to k (and a non-isotropic magnetisable medium ill hae a component of H parallel to k). I have never heard of EM waves in ordinary media being referred to as longitudinal (at least in part). In my lecture notes, the realisation of longitudinal waves was only mentioned briefly in the context of a vaninishing dielectric constant (plasma waves) and when there is a free charge present so that D is not divergenceless…

• electromagnetism
• waves
• electromagnetic-radiation
• dielectric

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edited Dec 28, 2018 at 11:13

Qmechanic♦

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asked Dec 28, 2018 at 9:50

Meep

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  I think, usually people consider EM waves in vacuum where D=E und H=B and both are perpendicular to k (that is, transversal) such that there is no component along k (longitudinal).

  – Photon

  Dec 28, 2018 at 10:02
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  @Photon Thanks for your reply! Though clearly my lecture notes consider non-vacuum cases, (and Wikipedia also mentions longitudinal plasma waves) ad yet the ordinary media case isn’t covered.

  – Meep

  Dec 28, 2018 at 10:29
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  I see. Well, this case is covered by the answer by Vladimir Kalitvianski below.

  – Photon

  Dec 28, 2018 at 10:38

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A wave is longitudinal or transverse depending on thr direction of the field with respect to the propagation vector kk. If the field is parallel, then it is longitudinal, and if it is perpendicular then it is transverse.

In the Fourier representation ∇→ik∇→ik. This means Gauss’ Law becomes  

∇⋅E=4πρ→ik⋅E=4πρ∇⋅E=4πρ→ik⋅E=4πρ

  Since ρρ is exactly zero in vacuum, this means that ik⋅E=0ik⋅E=0 so the electric field is perpendicular to the k-vector and the wave must be transverse. However in a medium, the charge density ρρ is non-zero and so the electric field can have a component parallel to the k-vector (ik⋅E≠0ik⋅E≠0), giving rise to longitudinal waves.

 

 

If you take a charge and start to make it oscillate, next to the charge there will be a longitudinal retarded EMF. Generally, a near field is not transversal, but a superposition of a transversal and a longitudinal waves.

Look at the general solution E⃗ E→ for a radiating charge: it consists of two distinct terms, one being proportional to 1/R21/R2 (the near field) and another one proportional to 1/R1/R (radiated).

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answered Dec 28, 2018 at 10:07

Vladimir Kalitvianski

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  Thank you for your reply. Do you mean to say that a wave should be characterised as transverse or longitudinal based on whether the E field vector at that point is parallel or perpendicular to the k vector at that point?

  – Meep

  Dec 28, 2018 at 13:25
•  
  Vector k⃗ k→ is a variable in the Fourier transform of the field E⃗ (r⃗ )E→(r→). Normally there are many “directions” in a Fourier spectrum. So one may define “transversality” of a harmonic E⃗ k⃗ E→k→ with respect to k⃗ k→ or transversality of the total field E⃗ (r⃗ )E→(r→) with respect to the vector R⃗ R→.

  – Vladimir Kalitvianski

  Dec 28, 2018 at 17:38
•  
  @,21joanna12 yes that’s the definition of longitudinal and transverse.

  – KF Gauss

  May 19, 2019 at 7:52

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An example of a longitudinal electromagnetic mode is a surface plasmon. This requires a corresponding longitudinal charge-density wave, which is how you get this to work with Gauss’ Law. Surface plasmons can be excited at any metal-dielectric interface, or in a conducting material like graphene.

 

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