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Rediscovering the Zenneck Surface Wave

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From Feed Line No. 4

by Gary Peterson

In 1916 while speaking of his system for global transmission, Tesla cited an analysis of mathematician Arnold N. Sommerfeld as validation of his explanations of observed radio surface wave phenomena.  Tesla was referring to his wireless system in which, he claimed, 90% to 95% of the electrical energy was manifested at the transmitters output as "current waves" with the remainder existing as dissipating electromagnetic radiation (see Antenna Theory).  In 1907 another investigator by the name of Johann Zenneck, while working to explain Marconi's trans-oceanic results, had shown that a unique type of surface wave could travel along the interface between the ground and the air.  In the words of Dr. James Corum,

"The distinguishing feature of the Zenneck wave was that the propagating energy didn't spread like radiation, but was concentrated near the guiding surface.  Sommerfeld had shown that an electromagnetic wave could be guided along a wire of finite conductivity, and Zenneck conceived that the earth's surface would perform in a manner similar to a single conducting wire." [see "Operating Principles of the Wardenclyffe Apparatus"]

In commenting on Sommerfeld's analysis of the surface wave, James R. Wait stated that "The field amplitude varies inversely as the square root of the horizontal distance from the source. . . ."  It's interesting to note that Sommerfeld made a point of distinguishing between the "electrodynamic" surface wave and its Hertzian counterpart the space wave, believing that both components could be present in varying proportion in the wave complex.  It was Tesla's assertion that the exact composition of the emissions was dependent upon the design of the transmitter launching structure.

Geometry for Zenneck wave propagation.

According to Dr. Corum's mathematical analysis of the Zenneck wave,

"The resulting wave is a surface guided (single conductor) transmission line mode which attenuates exponentially along the guide. . . .  There is no inverse square spreading or diffraction, as with Hertzian waves. . . .  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."

As the study of radio propagation progressed, and through the misinterpretation of certain mathematical analyses, some doubt as to the physical existence of Zenneck surface waves began to develop.  In 1937 limited support was given to these misgivings after tests showed simple antennas driven at 150 MHz produced 100 times lower field strength than predicted.  More recent investigations show evidence that Zenneck waves can, indeed, be generated.  The lower the frequency, the lower are the propagation losses.  It is also apparent that they are not a major contributor to the field produced by an electric dipole or a quarter wave radiator, however they might be excited by an energetic quarter wave resonator.  To quote Hill and Wait,

"As it turns out, the Zenneck wave is generally difficult to excite with a realistic source because it has a rather slow decay with height above the earth's surface.  But there is still an open question whether other types of sources may not be more favorable. . . . An infinite vertical aperture with height variation corresponding to that of the Zenneck wave will excite only the Zenneck surface wave with no radiation field. . . ." [Hill, D. and J.R. Wait, "Excitation of the Zenneck Surface Wave by a vertical Aperture," Radio Science, Vol. 13, No. 6, November-December, 1978, pp. 969-977.]

And to once again quote Dr. Corum,

"The 1978 analysis provided by Hill and Wait examined the fields produced by a vertical sheet of horizontally directed magnetic current with an exponential variation in an 'infinite Zenneck" aperture. . . . The analysis . . . showed that this field has no intrinsic merit at 1 to 10 MHz, and we certainly agree.  One wonders, however (and this is pure conjecture at this point), if the disposition of Tesla's Colorado Springs high voltage (10-20 Mv) VLF resonator did, in fact, possess an effective vertical distribution of magnetic current which could launch a similar Zenneck Surface Wave. . . ."

Plots of field strength vs. frequency indicate that a Zenneck wave propagates best at ELF and VLF frequencies up to about 35 kHz and begins to lose its advantage as frequency rises above this point.

Predicted Zenneck wave field strength decrease for around-the-world propagation as a function of frequency in kHz.

The complex longitudinal propagation phase constant along the Earth's surface for the Zenneck surface wave.

The Zenneck Surface Wave vs. the Norton Ground Wave

A 1/2-wave dipole antenna in free space--the Hertz antenna--approaches an ideal source of electromagnetic radiation emitted in the form of space waves.  These space waves can reach the receiver either by sky-wave propagation or by ground-wave propagation, the latter being the portion of the radiated space wave that propagates close to the earth's surface.  The ground wave has both direct-wave and ground-reflected components, and under certain conditions a tropospheric ducting component.  The direct-wave is limited only by the distance to the horizon from the transmitter plus a small distance added by atmospheric diffraction around the curvature of the earth.  The ground-reflected portion of the radiated wave reaches the receiving antenna after being reflected from the earth's surface.

There is also an induced earth-hugging component known as the Norton ground wave.  This wave is the result of electrical currents induced in the ground 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 both transmitting and receiving antennas are on, or close to, the ground, and the distance between them becomes great, the direct and reflected components tend to cancel out, and the resulting field intensity is principally that of this loosely coupled wave.  Because part of its energy is absorbed by the ground, its electrical intensity being attenuated at a much greater rate than inversely as the distance.  It is the conductivity of the underlying terrain that determines the attenuation of the field intensity as a function of distance.  The ground currents of a vertically polarized Norton 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.]

It is useful here to consider two additional forms of wireless telecommunications antennas or launching structures, the Marconi antenna, a vertical 1/4-wave monopole antenna element and the 'Tesla antenna,' a vertical high aspect-ratio 1/4-wave helical resonator with sufficient capacitive top loading to prevent electrical discharge, and small overall height compared to the electrical 1/4 wavelength.  In both cases the structure is base fed, and a ground connection is used.

The Marconi antenna is a modified 1/2-wave Hertz antenna adapted to the real-world conditions encountered in the construction of medium and low frequency transmitters.  These adaptations are imposed by the long wavelength involved and the resulting physical dimensions required of the antenna.  The dipole antenna is modified in that its lower half, 1/4 wavelength in length, exists only as a mirror image of its upper counterpart.  The resulting 1/4-wave vertical monopole antenna takes advantage of the fact that at lower frequencies the ground acts as a mirror for the radiated energy.  The ground reflects a large amount of the energy that is radiated downward from the antenna mounted over it.  In the physical construction of the ground connection is important to have as high a conductivity as possible.   The object is to provide the best possible reflecting surface for the energy radiated downward from the antenna.  The ground might consist of a number of bare conductors arranged radially and connected, 1/2 wavelength long, buried a short distance beneath the earth's surface.  In practice these conductors may act as part of the reflecting surface as well as making the connection to ground itself.   An alternative type of ground is the counterpoise.   It is a wire structure erected a short distance above the ground, and insulated from the ground.  Not unlike the Hertz antenna, the Marconi antenna is a source electromagnetic radiation in the form of radio space waves.

The Tesla antenna is a form of wireless antenna or wave launching structure developed by Tesla in which the transmitted energy propagates or is carried to the receiver by a combination of electrical current flowing through the earth and a charge-coupled electric field directly above it.  It can be viewed as an electric dipole source, consisting of an elevated isotropic capacitance, a helical resonator and a ground charge terminal electrode in direct relation to Earth itself.  The above-ground structure is not intended as a source of electromagnetic radiation, rather, it is designed to minimize the production of electromagnetic radiation.  In operation, the Tesla launching structure induces a dynamic electrical current in the earth between the transmitting and receiving stations, along with a guided surface wave, that propagate the transmitted energy. 

(In an earlier application of the design, a second conducting path would, in theory, be established through the rarified upper level atmosphere between the transmitting and receiving stations' elevated high voltage terminals, leading Tesla to coin the term "disturbed charge of ground and air method."  In this case the conducting media are the earth and also the upper atmosphere beyond about 5 miles elevation above sea level.  While this region extending up to the ionosphere is not an ohmic conductor, the density or pressure is sufficiently reduced to so that, according to Tesla, the atmosphere's insulating properties can be easily impaired allowing an electric current to flow.  His theory further asserts that the conducting region is developed through the process of atmospheric ionization, shifting the effected portions thereof to a plasma state.  A magnetic field is developed by each plant's helical resonator, meaning that an embedded magnetic field might also be involved.  The atmosphere below 5 miles is also viewed as a propagating medium for a portion of the above ground circuit, and being an insulator, electrostatic induction or 'displacement current' would be involved rather than true electrical conduction.  Tesla felt that with a sufficiently high electrical potential on the elevated terminal the practical limitation imposed upon its height could be overcome.  He speculated that a pair of highly energetic transmitters could charge their elevated terminals to a point where the entire path above them would break down and become ionized, leading to a flow of true conduction currents between the two terminals through the troposphere path connection.)

Now, Sommerfeld described an electrodynamic wave that is guided along a wire of finite conductivity and Zenneck expanded upon this description, asserting that the earth's surface performs in a manner similar to a conducting wire.  And, while the Norton 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 surface wave associated with Tesla's apparatus is the result of electrical ground currents flowing between two discrete points on the earth's surfaceUnlike the lossy Norton wave that is excited by a conventional AM radio transmitter it would seem that Tesla's low-frequency surface wave would not diminish quite as significantly as the distance from the source facility increases.  [See "A Comparison of the Tesla and Marconi LF Wireless Systems"]

[This piece is derived in part from "The Zenneck Surface Wave," Appendix II of the paper entitled "Nikola Tesla, Lightning Observations and Stationary Waves" by K. L. Corum and J. F. Corum, Ph.D. 1994., presented at the 1994 Colorado Springs Tesla Symposium.  This and other related papers are available through PV Scientific Instruments' Tesla Reprint PageSee also The Purpose of the Wardenclyffe Tower.]

Revised: 04/26/2019

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