l.m.d. waves in a tesla coil revised & enlarged

7/31/2019 L.M.D. Waves in a Tesla Coil Revised & Enlarged

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LONGITUDINAL DIELECTRIC WAVES INA TESLA COIL AND QUATERNIONIC

MAXWELLS EQUATIONSRevised and enlarged

Roberto Handwerker (Dr.Eng.)DELTA Ingegneria

- March 2011, Milan, Italy

deltaavalon.com

Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwells equations. 1


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Longitudinal dielectric waves in a Teslacoil and quaternionic Maxwells equations.

Revised and enlarged

Roberto Handwerker (Dr.Eng.)

DELTA Ingegneria- March 2011, Milan, Italy

deltaavalon.com

Abstract

The electrical transformer known as the Tesla Coil with all its peculiar

characteristics has always been officially considered only as an

electrotechnics device, a pure and simple transformer, and as an apparatus

for producing sparks, lightning-like discharges, high voltages and impressiveelectric effects. By closer scientific investigation of the device it is

however possible to throw new light on some aspects of the coil invented by

Nikola Tesla more than a century ago, in particular regarding the emission of

powerful dielectric longitudinal waves.

An analysis supported by a physics/mathematics approach which recalls the

original quaternionic notation of Maxwells equations which involves the

prediction of the existence of dielectric scalar fields and longitudinal waves

and which is also supported by empirical experimentation and research on the

device itself is made. This new point of view discloses some new and striking

facts regarding the coil and the related energy field, which leads to a

completely new and surprising realm.

However, it seems puzzling that the possibility of existence of dielectric

scalar fields and of related dielectric longitudinal waves is still not

accepted by the Academic World, which in turn gives neither sufficientjustification nor proves to support its sceptical position which excludes the

existence of said waves.

In particular, to this revised and enlarged edition is added a general physics

explanation of powerful natural occurring phenomena related to longitudinal

waves: for instance sound, tsunami and seismic waves are briefly illustrated in

order to better understand their common characteristics and the their basic

principles, which are also related to dielectric longitudinal waves.

Last but not least, a few notes about some considerations made by Nikola Tesla

and about his peculiar concepts on radio broadcast and wave propagation through

surrounding media are included, which also allow a brief scientific reflection

about some natural phenomena as seen from a different point of view; this facts

help remember that Gods Creation is vast and there is still a lot to explore.

DISCLAIMER:WARNING ! THE FOLLOWINGEXPERIMENTS AND TESTS MAKE USE OF HIGHFREQUENCY RADIO WAVES AND HIGH VOLTAGE(POSSIBLE EMISSION OF X-RAYS, UV ANDOTHER HARMFUL RAYS): PLEASE DONT TRYTO REPLICATE THESE UNLESS YOU ARE WELL-EXPERIENCED AND SKILLED IN HIGH-TENSIONELECTROTECHNICS AND RADIO-TECHNOLOGY:DANGER OF SERIOUS AND EVEN FATAL

HIGH RADIO

VOLTAGE WAVES

HAZARD HAZARD

INJURIES TO PERSONS, DAMAGE TO PROPERTYBY MISUSE !



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Summary

1.Introduction42.Maxwells equations53. Dielectric induction phenomena and dielectric longitudinal

waves9

4. Transmission of energy through air and related measured values115.Notes on Tesla Coil tuning166. Streams, brushes, discharges and effects in Tesla Coils

lamp bulbs17

7.Analogy between electrotechnics and fluidics188. Conclusion249. Legenda25

Bibliography and references26



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1. IntroductionIt is well known that J.C. Maxwell issued in 1873 his A treatise on

electricity & magnetism[1]where he presented in an elegant form the

results of his studies, writing some 20 E.M. equations; in the

beginning he thought to make use of quaternions[8], whose calculation

was but not quite simple, later Heaviside and Gibbs introduced thevector notation, in order to simplify the equations. It will be

useful to remember that quaternion numbers consist in four terms,

whereas vectors consist only in three terms as in following example:

= a + bi + cj + dk

V= ax + by + cz

The two systems follow different calculation rules, for instance the

former has anticommutative property, the latter on the contrary has

commutative property.

Fi .1 200

210

250

Pri.

Sec.

G

TESLA

COIL

XMTR

50

Fig.1: Tesla coil Transmitter (XMTR) used in laboratory during tests;

the particular design utilized in the investigation is called Extra

Tesla Coil, having cylindrical form and being mainly constituted by a

primary coil (Pri.), a secondary coil (Sec.), top capacitance (bulb)

and a high frequency-high voltage generator (G). Measures are in [mm].

Regarding the existence of longitudinal dielectric waves, there are

two possible explanations about why these do not appear in the well-

known todays Maxwells equations, which are the fundament of modern

electromagnetism:

a) Todays vector notation was introduced, after the death of J.C.

Maxwell, by Heaviside and Gibbs who simplified the original

quaternionic[8] notation proposed by Maxwell; therefore the actual set

of equations would be partially incomplete, thus not including

longitudinal waves.



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b) J.C. Maxwell first issued his set of equations in 1865 including

electromagnetism related phenomena which has been observed or at least

which he reported, that he judged to be fundamental; but N. Tesla

discovered new dielectric induction phenomena only later, in 1892.

nyway, the two above possibilities does not exclude each other.A

2. Maxwells equations

The (Heavisides) commonly adopted vector notation of Maxwells

equation in differential form is following:

. B = 0 (Magnetic flux theorem)

. E = /o (Gausss Law-Dielectric flux)

x E + B/t = 0 (Faradays law)

c2 x B - E/t = J/o (Ampres law)

where: E = dielectric field; B = magnetic field; = charge density; 0 = dielectric constant in vacuum;

/t = time partial derivative; J = current intensity.



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Fig.2: Two flat spiral Tesla coils or pancake coils: a Transmitter

(XMTR) and a Receiver (RCVR) both connected to the ground as described

in Teslas Patent n.649621 from May 1900.

The employ of quaternions by informatics increases computer

calculation speed and allows memory space spare up to 55%, which is a

great advantage for instance in aerospace navigation (typically ininertial platforms)[5]; their application to Maxwells equations

reveals some unexpected elements.

Starting from another point of view it would be possible to write the

Maxwell set of equations by the quaternion notation, which even if it

is more complicated on one hand, on the other hand it leads to some

unexpected and striking results which in particular involve the

prediction of the existence of longitudinal dielectric waves; this

fact was already claimed by other Authors (for example Ignatiev G.F.

& Leus V.A.)[10] and on the basis of some R.F. (= Radio Frequency)

experiments by the employ of transmitting and receiving devices with

ball-shaped antennas even from others. Besides this, if the claimed

possibility by some physics (see appendix: Arbab A. & Satti Z.[6]) of

deriving Maxwells equations from only one wave quaternion vector

potential or:

= (i/c ,A)

where:

2 = o J , J= (ic, J)

by respect of the Lorenz gauge will be considered as accepted, so itwill be possible to take into account an extended result of todays

Maxwells vector form. This imply the existence, besides the well-

known E.M. Transverse waves (T.E.M.= Transverse Electro-Magnetic),

also of Longitudinal waves (L.M.D.= Longitudinal Magneto-Dielectric),

whose scalar potential is related to its dielectric field E byollowing equation:f

E =

This theoretical result was also supported from experimental

laboratory investigation which made use of Tesla Coils which are, asit will be readily seen, not only transformers for high frequency

XMTR RCVR

GNDFi .2

~



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i[mA]200

50

0,5 1 1,5 2 2,5 x[m]Fi .3 Fi .4

L

LEDs

: measure with inductance

: measure with photomultiplier

Fig.3: Diagram shows the relationship between energy field intensity

and distance of the photomultiplier (type 931-A) from the XMTR Tesla

coil as a function of current values read by quantitative measuring

device (M); the dots shows normalised measured values whereas the

dotted line shows the expected quadratic diminishing curve for waves

by increasing distance (x) from the Transmitter.

Fig.4: Small wire loop (L) series connected with two LEDs of different

colour and slightly different sensibility was used as a detector for

resonance frequency and as an auxiliary qualitative measuring device

of the Tesla coil field intensity for tuning purposes.

low voltage into high frequency (= HF) high voltage (= HV) or devices

for creating spectacular lightning-like electric discharges, but are

also a useful means to show the existence of the dielectric

longitudinal field, which is generated by the peculiar design and

construction of the coil itself. In fact, it will be shown the

capability of this kind of field of transmitting electrical energy and

not only weak signal in the surrounding medium, and to drive not only

light bulbs and neon tubes as commonly thought, but even common DC

electric motors under proper conditions (see Fig.17). The

investigation has been conducted by means of empirical observation,

experiments and tests with the help of basic electrotechnics measuring

devices as oscilloscope, analogic multimeter (having more inertia

due to internal coil and indicator, so being less affected by

fluctuations), small pocket AM radio receiver device, brass metal

plates, copper wire loops with LEDs as detectors and other rather

common devices to detect and analyse E.M. (= Electro-Magnetic) fields

and waves: it was avoided the use of complicated systems according to

the keep it simple philosophy also in order to make following

experiments and tests fully replicable, which is of course the main

requirement of scientific investigation and research. For the complete

calculation reference is made to Arbab A. & Satti Z.[6], and it will be

readily shown that according to their work, Maxwells equations could

be simply expressed in the quaternionic form by the following two

equations:

1/c2 2E/t2 - 2E = -1/o ( + 1/c2J/t) (1)

1/c2 2B/t2 - 2B = o ( x J) (2)



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V

Fig.5: Suspended insulated metal plate (P) (dimension: 120x130mm)

series connected to a quantitative measuring device (M) and to ground;

the plate acts as a receiver of energy, which gives rise in the plate

to a comparatively strong current that flows through the device into

the ground; a vacuum tube device (V) type 931-A (see picture) was

then connected to the measuring device (M) instead of the metal plate

(P) in order to further analyse the dielectric field. An iron cored

coil (C) was also connected to device (M) to analyse magnetic field.

The generic scalar field was introduced and consequently alsothe current intensity can be written as J= , the following newgauge transformation can be considered:

'= + 1/c2 /t and J= J- (3) and (4)

it is then noted that the scalar satisfies the wave equation:

1/c2 2 /t2 - 2 = -( .J+ /t) (5)

Further, from the above mentioned work it would descend that thecharge density and the current intensity Jwould travel at the speedof light; so Maxwells equations could be seen as a special case of

equations (1) and (2). Then, this implies that the scalar wave distribution would therefore induce a

charge density:

= -1/c2 /t (6)

and a current intensity:

J= (7)

even if charge and current Jwere not present in a particular zone.This aspect could help explain for example the working principle of an

electric condenser (capacitor), otherwise stated why metal plates

which are separated by a dielectric non-conductive material, thereforenot in direct contact between them, do conduct an electrical current:

it is

Fi .5

XMTR

GND

ELMD

GND

P

i tM

Vx

MEr

C CM



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Fig.6: The two wave components of the energy field known as the T.E.M.

(= Transverse Electro-Magnetic, ETEM) and the L.M.D. (= Longitudinal

Magneto-Dielectric, ELMD) have the same propagation direction (x).

Recalling the hydrodynamic analogy between electrotechnics and

fluidics, sea waves visualize, at least ideally, an example of T.E.M.

(surface waves) and L.M.D. (deep tsunami pressure waves).

then noted that commonly alleged theories of displacement currents

phenomena do not constitute a really convincing explanation, in

particular it is not clear how an electron current could freely pass

or jump through the dielectric according to common theories; an

interesting hint to this is given by Steinmetz C.P.[7] if the

possibility is considered, that by electrostatic (i.e. dielectric)

fields charges are not only confined on the surface of the charged

conductors, but are even present in the surrounding space, just in a

similar way as it happens for magnetic fields.

This is a physical and mathematical approach and also a possible

explanation to the question marked as a) in the introduction.

3. Dielectric induction phenomena and longitudinal dielectric waves

The second question set in the introduction and marked as b)

departs from mere mathematical/physical calculation and is rather

related to the researches and experiments of Dr. N. Tesla, which in

1892 observed what he often used to call curious and striking

phenomena of electricity, which he described in his writings or

during his academic lectures delivered before the Scientific

Community[3],[4], and that made him practically abandon his studies on

high frequency alternating currents and start exploring a new realm.

The phenomena referred to have yet partially been observed for example

in 1872 by Elihu Thomson[9] during a lesson at the Philadelphia High

School, where he was a teacher. By doing a demonstration with a

Ruhmkorff induction coil and willingly to better show the effects to

the students sitting far from the device, he made some changes in the

circuit obtaining, instead of the normally displayed purplish-blueish

sparks, impressive big and white electric discharges, and metal

objects in the room became strangely electrified and kept throwing

sparks in the surrounding space as the device was turned on. This

effect could have been due to a new and peculiar form of dielectric

induction. Tesla realised a number of devices in order to better

investigate the matter and at the end perfected his particular Coil, a

seemingly simple device but hiding many peculiar characteristics as

regards the transmission of energy and signal through the natural

medium, which will not be discussed here, and last but not least, to

ETEM

Fi .6

x L.M.D.

x

luids solids

T.E.M.

ELMDELMD



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N

ELMD

XMTR

AM-RCVR

Fig.7

Fig.7: Neon tube (N) in the XMTRs energy field lit to its full

brightness without any energizing wire connected to it nor other

energy supply; a double copper wire loop (A) antenna series

connected to a small DC electric motor (D) could be tilted up to an

angle = 90 with respect to a horizontal axis without affecting theenergy transmission to the motor.

investigate the existence besides of a Transverse Electro-Magnetic, of

a strong Longitudinal Magneto-Dielectric field in the medium around

it. It is convenient at this point to shortly illustrate the

construction of a typical Tesla transformer by its main components:

1- The generator (H.V. & H.F.)2- The primary (coil) circuit3- The secondary (coil) circuit4- The top spherical inductance (lamp bulb / metal sphere)The generator is designed to provide currents of high frequency and

high voltage to the primary circuit, which is basically constituted by

a coil and a capacitor (which will be called here a condenser as

used by Tesla time) and a spark-gap forming an oscillator; the primary

is coupled to another coil without any iron core, on the top of which

is another condenser, this time of spherical form, together forming

the secondary of the transformer. The secondary coil can be connected

or not to the ground. The above described coils with the related

suitable generator constitute the XMTR (= Transmitter), whereas a

similar device also comprising a primary and a secondary, but without

the generator, constitutes the RCVR (= Receiver). The connection

between the two devices can be made by a single wire, by the ground or

by water, however here will be only discussed the XMTR with respect to

the generation of longitudinal dielectric waves; of course the device

emits also usual T.E.M. waves because of the solenoid form of its

coils. It is to be noted that the capacitance on the top of the

secondary coil has a spherical form; when the generator energizes the

oscillator in the primary, energy transfer occurs to the secondary of

the transformer by dielectric induction without the presence of any

iron core in the coils. The energy of the primary is inducted to the

secondary where the voltage is greatly increased to huge values

depending from the construction parameters of the device as material,

components, dimensions, proportions etc., even if it can be stated

that already a few turns of wire in the secondary coil could give rise

to hundreds and even to millions of Volts without any difficulty as it

should be for well-tuned Tesla Coils. The HF-HV is maximum on the top

of secondary corresponding to the sphere capacitance/condenser (in

this case an argon lamp bulb because of the small dimension of the


A


11/26

Fig.8: A brass metal plate (P) connected by only one wire to an

analogic multimeter and then series to ground was used to analyse the

field around the XMTR; by rotating the plate (P) around its vertical

axis, the received energy varied as shown in diagram of Fig.9.

device) which together with the secondary acts as an antenna; it is

useful to remember again that in Nature waves can exist in the

transverse form, that is having direction perpendicular to the

propagation direction, and in the longitudinal form, that is having

direction parallel to the propagation direction. Transverse waves are,

as is well known, typically generated by antennas such as conducting

dipoles or even in general by AC electrified wires, but in the present

case in addition to the cylindrical solenoid coils (the primary and

the secondary) also a spherical antenna is present which cannot emit

transverse waves because of its form which mathematically annuls the

opposing components of the transverse E.M. waves, therefore only

allowing the emission of longitudinal MD (Magneto-Dielectric) waves.

As already stated, even if components of usual transverse E.M. waves

are also present because of said cylindrical/solenoidal wire coils,

however the latter are not the cause of the effects below described,

which are not magnetic in their nature but dielectric. The term

electric field comprises here both dielectric and magnetic fields,

as referred to by Steinmetz[7]: dielectric will not also encompass

the magnetic part of the E.M. field. According to the hydrodynamic

analogy between fluidics and electrotechnics, as in the former

example of sea surface waves and deep tsunami waves (pressure or

compression waves) are ideally observed, for the analogys

completeness the same should be for electric waves with transverse and

longitudinal components otherwise said analogy would be invalidated.

4. Transmission of energy through air and related measured values

Tests:

in the laboratory several test were performed to investigate the

emission of L.M.D. waves from the Tesla coil transmitter, even if it

was quite not a simple thing to do.

- Qualitative measurements:- First a rather simple and crude but clear test was readily made

by keeping in the hand a common neon (fluorescence) tube withoutany

XMTR

ELMD

GN

PEt

ETEMEr

Fig.8

i t

M



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i[mA]

100

75: measure with metal plate

50

25

Fig.9: Diagram shows the relationship between the angle formed bythe brass plate probe (P) and the propagation direction of the waves

(versor Er): it is noted from the dotted line (a cosine function

curve) that when = 0 (0) (or of course even when = 2 (360)) thatis by versorEr parallel to plate, the measured value of current i

or, in other words, the energy received from the brass plate (P) was

at its minimum, while it was at its maximum by = /2 (90) and =3/2 (180)(by versor Er perpendicular to brass plate), showing thatno transverse E.M. waves components play a relevant role but L.M.D.

waves do. This polarization test measure shows that plate rotation

around its axis in the vertical plane is indifferent to the vertical

T.E.M. Et field, but not to L.M.D. Er field.

connected energizing wires and by simply approaching it to the XMTR

(see Fig.n.7): when the tube was moved to the Tesla coil i.e. it was

set in its energy field, the neon tube amazingly lighted up, at first

only faintly, until it came to its full brightness as it was moved

closer to the coil (note that this result is very difficult if not

impossible to achieve by magnetic fields, but not difficult at all by

dielectric fields of well-tuned Tesla Coils).

- second, in order to exclude any relevant action due to the presenceof magnetic fields, a normal compass has been moved in the energyfield of the transmitter: the compass nail indicator stood still,

never showing any kind of movement; on the contrary, when it was set

on a normal small transformer its indicator immediately started to

move (see Fig.n.10).

- and third, as a further qualitative detector of the fieldintensity of the XMTR was employed a common PVC insulated copper wire

loop (square section: S=2,5mm2, with wire loop diameter D=

100mm,inductance value L= 0,001mH) series connected with two

oppositely paralleled LEDs, by different colours (yellow and blue),

lighting up approximately in the range:

Umin= 0,6 Umax= 2V (t1)

and having a slightly different sensibility; this detecting device was

moved in the Tesla Coil field in the horizontal plane i.e. in an

unfavourable position for T.E.M. waves so to detect mostly L.M.D.

waves. It was also employed for tuning purposes as it readily and

precisely detected the presence of resonance by voltage rise in the

Tesla coil oscillator, therefore indicating when the intensity of theenergy field was greater as the LEDs were at maximum brightness and

beyond, as some of them did burn out due to excessive voltage.


Fi .93/2 0 /2 [rad]


13/26

com ass

s here ca

BTEMELMD

Fig.10: A normal compass was set in the energy field of the Tesla

Coil: its nail indicator (I) showed no movement, on the contrary when

the same compass was approached to a normal E.M. transformer the

indicator immediately started to move, thus detecting a magnetic

field.

The energy field of the transmitter had not only the effect of

lighting up neon tubes and LEDs but was used, always within the near

field, for energizing a small DC electric motor (D) to drive an

electric vehicle (model) in the range of the XMTR, which was of small

power. The receiving antenna was constituted by a double turn of two

coarse copper wire loops, series connected with a small electronic

rectifying circuit and with the DC electric motor in order to

transform the HV and HF received power into DC (rectified) low

voltage; to prove that in the energy transmission no T.E.M. waves were

involved, the double loop antenna was tilted from the vertical plane

to the horizontal: the result was the same, i.e. energy transmission

within said range from XMTR occurred by L.M.D. induction, By T.E.M.

waves as a matter of fact, a receiving antenna must, in order to

achieve maximum efficiency, always stand with its axis perfectly

vertical to the ground just like the direction of (T.E.M.) vector Et.In the present case however, the antenna loop could without any

problem be tilted to the ground that is to the horizontal plane and

still continued to receive energy from the XMTR, proving that T.E.M.

waves were here not mainly involved in driving the DC motor, which

requires of course power and not only weak signal to run.

- A common small pocketAM/FM radio receiver was used to detect R.F.emitted from the Tesla Coil by moving the device away from the coil

axis to a distance, to investigate the field of the XMTR itself, which

generated an audible signal to about the range reported in Fig.n.3.,

so not very far from the AM-RCVR itself.

- Quantitative measurements:- An iron cored inductance (C) (a cylindrical copper wire coil with aferrite core and with its coil terminals connected by two wires to the

multimeter instrument), was employed to detect the magnetic field: the

measurements were taken by moving the inductance away from the Tesla

coil, at first with the iron core inserted in the same coil (having

thereby an inductance of L= 10mH), then without the iron core (thus

having an inductance reduced to L= 6mH): the normalised results of the

test are illustrated in diagram of Fig.3, thus showing that there was

no difference between values measured with or without the iron core

because relevant magnetic induction on the coil was absent, but

evident dielectric induction was present and preponderant.

I TR

Fi .10

nail



14/26

ELMD

s here caP B

Fi .11

Fig.11: A suspended insulated brass metal plate (P) set in the energy

field of the Tesla Coil became dielectrically charged and threw off

sparks to approached objects, for instance to a small metal plate (B).

- Another test with related measurements was made by connecting by a

single wire the analogic multimeter (used as a milliamperometer) to aphotomultiplier vacuum tube (V) type 931-A from R.C.A.-U.S.A (toits pin n.11 - cathode); then by moving the phototube away from the

XMTR axis, the energy field was again measured giving similar results

(normalised values) as regards to inverse square decrease with

distance from the coil axis, once more showing that a dielectric field

was involved (see Fig.n.3). In addition, the phototube device was

rotated around its three axis in different positions but this didnt

affect the results in a relevant way.

- Moreover, a further investigation of the energy field around the

XMTR was made also by use of a suspended insulatedmetal plate made ofbrass, as well-known a non-magnetic material, which was connected in

series by a single wire to a measuring device, in this case an

analogic milliamperometer with a scale range of current i(t) = 0 100

mA, which in turn was connected to ground. The comparison of this

feature with the one described in Teslas patent n.685957 of 1901,

which illustrates an (apparent) puzzling use of a similar insulated

metal plate for utilizing radiant energy also in association with

other auxiliary devices, is remarkable. A quantitative measure of the

(infinitesimal) absorbed power by the plate, i.e. received from the

XMTR, could be made as follows with a plate of dimension S = B x H

(surface=width x height) and the angle between plate and versor Er

dP= dV2/dR (t2)

being R: ohmic resistance in a conductor, so

dR= dx/dS (t3)

where S= surface of brass plate conductor) and being:

dV= Eo cos()dx (t4)

the voltage in the infinitesimal part dx (being dx an

infinitesimal depht element) of the receiving brass plate, so its

infinitesimal absorbed dielectric power is then a function of cosine:



15/26

d d

ELMD

Fig.12: A common condenser (capacitor) (K): an electric current flows

through opposite conducting plates even when separated from a

dielectric; the plates could be separated and moved to a comparatively

considerable distance, however a connected impedance-meter instrument

(M) kept reading an impedance value: the plates felt one another.

and by mathematical integration it comes to the absorbed energy A

from the plate itself:

dP= f((cos2())dx (t5)

so it becomes:

A =f(cos()) (t6)

- At the end of the investigation one more last test, but not least,

was performed: a suspended (by a non-conducting wire) insulated small

(about 120x130mm as before) thin brass metal plate (P) which was set

in the energy field of the Tesla Coil became strongly charged by

dielectric induction from the coil: as a smaller (about 50x50mm) metal

plate (B) was approached to the first plate (P), the (big) brass plate

threw off sparks to the small one and even to an approached hand (see

Fig.n.11).

These experiments and tests could be useful to better understand the

working principle of a common condenser: how an electrical current can

pass or jump through the dielectric non-conducting material

between the opposite metal plates ? According to the accepted theory,

this would be caused by displacement currents on the surfaces of the

plates. Therefore, a simple tests would made by positioning two

parallel opposite condenser plates (square dimension: 40x40mm of very

thin brass) with air as dielectric, each connected to one terminal of

an impedance-meter (type MK5540 from Mitek). At first the plates

were set at a distance of 1mm from one another, then these were moved

apart to more than d= 1m but kept always connected to the impedance-

meter: the instrument read a capacitance value of C=0,040mH for near

plates and of C=0,012mH for far plates. Even if the distance between

opposite condenser plates was increased up to >1000 times, or equal to

>25 times the plate dimension, the instrument did anyway read a value,

so despite of distance the plates felt one another; according to

Fi .12

K

i(t)

M M



16/26

Fig.13: Two flat spiral Tesla coils or pancake coils connected

through the ground; the XMTR with its (H.V., H.F.) generator and the

RCVR with its electric utilities: a neon tube and a DC motor.

C.P.Steinmetz[7] this phenomenon could be better explained as follows:

the dielectric field is not only confined on the surfaces of the

conductors but is also present in the surrounding space in a similar

way as for the magnetic field. The dielectric field issues from the

conductors and the related lines of force pass from one conductor to

the other (see Fig.n.12). The commonly accepted theory of the charge

displacement seems here to be a rather weak explanation with respect

to the dielectric field and related lines of force.

5. Notes on Tesla Coil tuning

All these test were performed in order to investigate nature and

intensity of the energy field around the Tesla coil, which was

stronger when resonance in the device was present or, in other words,

when the coil was well-tuned.

To precisely detect the main frequency fo of the Tesla coil XMTR, a

digital oscilloscope GDS-820-Sseries from GW-Instekwas used and

the related wired probe was placed about d= 2m from the XMTR: the

main resonance frequency was confirmed to be fo= 2,755 MHz with another

main frequency at f= 1,810 MHz; it is noted that the relationship

between said main frequencies is: fo / f= 1,527 MHz (/2)f. As it is:

o= c / fo (where c: speed of light in vacuum) (t8)

said frequency corresponds to a wave length of o= 113,64m or to o/4=28,41m (or quarter wave-length), this means that the tests were

performed in the so-called near field; regarding this aspect it

could be objected that it would invalidate the experiment but, on the

contrary, just by keeping the distance d from the XMTR much smaller

than a quarter wave-length or /4, the T.E.M. components of the wavehad less possibility of influencing the test, thus allowing the L.M.D.

components to mainly play.

RCVRXMTR

Fi .13

G

D

GNDN



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Fig.14: Light streams, brushes and discharge effects in Tesla coils

lamp bulbs (secondary top capacitance); pictures shows streams as

illustrated in (a) and brushes as in (c) respectively.

6. Streams, brushes, discharges and effects in Tesla Coils lamp bulbs

Beyond scientific investigation, well-tuned Tesla Coils shows

curious effects: beautiful light streams or brushes are emitted

when the secondary coil top capacitance is a lamp bulb instead of a

metal sphere, for example an argon gas bulb[11]; when the coil is

running, depending of the driving generator employed, strange light

streams fill the bulb itself varying very much in the form with the

coil design and also with voltage, frequency and a number of other

parameters. For instance, the streams filling the bulb of the Extra

Tesla Coils used by the present investigation looks more like plasma

effects and have different colours among which mainly yellow, orange

pink and violet. When the two Tesla Coils (XMTR and RCVR) are

connected through only one wire or through the earth conductor (or

even water) and they are well-tuned, they both show streams in their

own bulbs. These coils really communicate with one another as it is

fairly clear by just approaching a hand to the XMTR bulb: if its

streams become weaker, on the contrary the streams in the RCVR bulb

become stronger and vice-versa. It is not here a mere question of wave

transmission from the XMTR to the RCVR as it happens for usual so-

called T.E.M. radio broadcasting, whereby the transmitter cannot be

influenced in any way from the receiver, but a peculiar energy

interaction between the two Tesla coils occurs, as true conduction

phenomena were involved. Moreover, the movement of the streams is

peculiar, as these sometimes even show at first a rotation around

their axis, then they stop rotating and tend to establish a rather

stable flux pattern issuing from the lamp filament to the glass

bulb, depending of the adjusting of several parameters, and is also

due to electrostatic or dielectric action according to the definition

given by C.P.Steinmetz[7]; as before stated, brushes or streams may

change very much even in their nature, from smooth and widening

plasma flux spreading to the bulb (see Fig.n.14.a) to soon become a

violent electric discharge (see Fig.n.14.b) when an object is moved

close to the bulb. By higher pressures in the Tesla coil, the streams

can turn into brushes of even strong discharge of blue, purple or of

other colours (see Fig.n.14.c). These remarkable features should be

closer investigated, as the sphere capacitance also emits L.M.D.

waves, which as already stated are dielectric. Fig.n.15 shows two

energized flat spiral pancake Tesla coils with streams in their top

capacitance lamp bulbs; on left is the RCVR drives a small DC motor

with a green LED connected to show it works by energy transmission[12].

a) b)Fi .14

c)



18/26

Fi .15

Fig.15: Two energized flat spiral or pancake Tesla coils showing

yellow/orange streams in the top spherical capacitance lamp bulbs and

the same bulb type being hold in hand showing pink/violet discharges.

By adjusting some parameters in the Tesla coil, curious effect of

repulsion and attraction were then observed[11]: if a hand was

approached to the lamp bulb, under certain conditions, a kind of

pressure was felt by the hand; on the contrary, if a small suspended

metal strip was approached to the same bulb, the conducting material

was attracted to it. This repulsion and attraction effects are

evidently due to dielectric (electrostatic) action.

7. Analogy between electrotechnics and fluidics

As well known there is in physics a nice analogy between electricity

and hydraulics (as well as between mechanics/construction science and

hydraulics), that implies that laws and equations which rules them are

similar or analogous; this fact implies that, so to speak, there is a

parallel of, for instance, tension and pressure, flow of current and

of fluid etc. . To make the similarity more clear it can be stated

that transverse and longitudinal wave forms as observed in ocean water

respectively ideally resemble surface waves and effectively represent

high pressure waves (longitudinal) in the deep, in a similar way

should it be in an electric conductor; as the analogy is yet

accepted from physics, there is no reason to deny the validity of the

similarity for the above mentioned waves: in other words, why

dielectric longitudinal waves should not exist ? In such a case, this

would automatically imply that the analogy referred to would be

incomplete or false. As a matter of fact, the existence of

longitudinal dielectric waves in an electric, typically copper,

conductor is well supported from some wire fragmentation test

conducted by J.Nasilowsky[13] and also other Authors, where wires were

exploded by means of the application of huge electrical currents that

caused the wires to break by stress, which clearly manifested itself

by parallel break stripes perpendicular to wire axis, showing in

addition that no material melting was involved in the process but just

material stress. This stress occurred, as this was evident from the

fragmentation characteristics in wires, in zones of charge density

variation (alternate rarefaction and compression), meaning that a true

pressure waves phenomenon (longitudinal) had taken place in the wire

resulting in excessive tensile stress in the material and its

consequent break due to override of material tensile limit (i.e.

mechanical resistance). Maxwell wrote that the alleged dielectric

longitudinal waves would theoretically only have been possible in

cases of variation of charge density in the direction of



19/26

S-waves

Earth

P-wavesSeismic epicenter

Fi .16

Fig.16: A cross section of earth is showed, where seismic primary

waves pass through core and travel faster than secondary waves,

moreover the latter cannot pass through it as it is partially fluid.

propagation (so not at right angles to it), and therefore concluded

that this condition was not possible to achieve; on the other hand

must be noted that he wrote his Treatise in the 1800s, that is quite

two hundreds years ago: for instance, Maxwell didnt predict neither

laser, nuclear energy, solar panels nor space travel but this

evidently doesnt mean that all these things are not possible at all !

Longitudinal waves are due to alternate compression and expansion

(i.e. density variation of electrical charge) occurring in the same

direction vector of wave propagation, which implies the presence of a

time dependent dielectric scalar field and not of a vectorial one.

To better understand the behaviour of an electrical conductor, for

instance in a copper wire, under action of electric waves, maybe could

help to bring one more example: be it considered a steel spring which

is held between two hands and in which the opposite ends are:

a) alternatively compressed and relaxed in the axis directionb) alternatively bent up and down around a perpendicular axisc) alternatively shifted up and down at right angles to axis

these three situations corresponds to the following type of waves:

a) longitudinal waves (oscillation in the propagation direction)b) standing waves (oscillation at right angles to propagation dir.)c) transverse waves (oscillation at right angles to propagat. dir.)

so these mechanical vibration modes of a spring will help to better

explain and clarify how the different wave types act in a conductor.

Besides tsunami waves in the sea, there are in Nature several otherexamples of longitudinal waves: maybe the most common at all are soundwaves, that is pressure variations in a medium such as a solid, aliquid or a gas; in these various media the propagation speed of these

powerful waves is obviously different, and the related formulae for

sound speed are following in media such as:

solids:

VL = (E/) where E > G (always) (8)

VT = (G/) (9)



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XMTR RCVR

electric motor

Fi .17

Fig.17: A Tesla coil with a spherical antenna as top capacitance on

its secondary can energize in his field not only neon tubes but also

electric motors, for instance to drive a small electric vehicle.

liquids:

VL = (Ea/) where : density (10)

VT = 0 (11)

gases:

VL = (RT/M) where RT/M: gas constant (12)

VT = 0 (13)

It will be then easily noted that in the case of solid media the

value of VL is always greater than the value of VT, as the elasticity

normal modulus E is always greater than the elasticity tangential

modulus G; moreover, it is VT=0 for fluids and gases, which implies

that transverse waves doesnt propagate through them. To give an

indication, the speed of sound in some media is reported in the table:

Sound speed in different materials at 20C

Speed in [m/s]Medium

Air 343

Water 1.480

Glass 5.300

Ether (*) c (**)

(*) according to Dr. Nikola Teslas writings[12]

(**) where c ( 3.108 m/s) is the speed of light.

Other well known longitudinal waves in Nature are earthquake or

seismic waves, that is the so-called primary seismic waves, which areshape compression waves in earth, as secondary seismic waves are shear

waves of the transverse type, in this case acting on earths surface:



21/26

wire L.M.D. waves break attern ( arallel stri es)

x

Fi .18

Fig.18: Electrical conductor wire fragmentation tests: break pattern

clearly showed that wire destruction was due to waves propagated by

alternate compression and expansion, i.e. dielectric longitudinal

waves, therefore not caused by material heat/fusion, but to excessive

tensile (mechanical) stress (see parallel stripes perpendicular to

wire axis).

To recall some general theory about seismic (or earthquake) primary

and secondary waves it will be here sufficient to note that the

respective propagation speeds are given by the following equations:

VP =((k + 4/3)/) (14)

VS = (/) (15)

where k: elast. norm.modulus, : elast. tang.mod, : density of medium

The first equation (14) contains the term k which is due to bulk

elasticity modulus; this term is but not present in the second

equation (15), moreover the term has only factor 1 in equation(14) whereas it has a greater factor 4/3 in equation (15), so that

otherwise stated it must always be:

VP > VS

This relationship implies that seismic/earthquake primary waves

(longitudinal or compression waves) always propagate faster through

the planet that secondary waves (transverse or shear waves), the

latter by the way do not propagate neither through fluids nor gases as

equations (11) and (13) clearly showed, but only through solids as it

is already well known. Seismic phenomena are of course much more

complicated than here described, but the present explanation gives anindication in order to better understand and clarify the matter.

A field where the above equations could for instance also be useful

is electromagnetism and wave propagation through natural media, if

particular reference is made to the writings[2],[12] of Dr. N. Tesla and

to his curious statements regarding electric sound waves[14], as well

as Hertz waves, besides the related opinion held and expressed by

Lord Kelvin as he personally visited N. Tesla in his New York

laboratory in 1897[15]. Nikola Tesla believed that only longitudinal

waves could propagate through the universal gaseous ether medium

just as light would do, but not transverse waves; therefore he also

criticized the principle of the so-called common radio broadcast by

transverse electromagnetic waves (which he named Hertzian waves) and

compared it to an ether whistle[12]. However, this matter would be too

vast and complex indeed to be treated here and would also go



22/26

Fig.19: Hypothetical composition of air as a mixture of gases owing

different atomic mass; proposed according to N. Tesla, D. Mendeleev,

E. Thomson and other great scientists of the time, even the ether

model could be a mixture of different gases having exceedingly small

atomic mass, about one millionth of the one of hydrogen, pervading

everything i.e. from air to outer space. A single gas atom is able to

move and rotate around its axis.

beyond the aim of this writing, taking the reader much too far from

the main argument dealt herein.

At this point it is important to recall the wave equation which

satisfies a generic scalar function u(x,t):

1/v22u/t2 = 2u

where the propagation velocity is:v =(k/)

always keeping in mind the true physical meaning of the scalar

function u(x,t), for example as in the case of sound propagation in

solid and in fluid mediums: sound waves in solid mediums can be o both

transverse and longitudinal type, whereas sound waves in fluids as for

instance gases can only be of the longitudinal type or compression

waves, as it is obvious because in gases no shear phenomena can take

place because of the lack of matter continuity, but just compression

due to pressure variations.

Therefore, if the term etherwas referred to an universal pervading

gaseous medium, a mixture of inert gases having atomic massexceedingly smaller than that of hydrogen (in the order of about one

millionth of its atomic mass, just to give an idea) composed by at

least two gases, if not more, for which D. Mendeleev proposed the two

element names Xand Yand put them before the position of hydrogen

in his periodic table of elements, but subsequently removed them).

The concept of gaseous medium where only longitudinal waves could

propagate was adopted by a number of great scientist during the

Victorian age and beyond (J.C. Maxwell, Nikola Tesla, Elihu Thomson,

Dimitri Mendeleev, Lord Kelvin and others) in their writings by the

end of the 1800s up to the beginning of 1900s, but the concept of

ether as an interstellar gaseous medium seems at present days to

have been forgotten and abandoned from modern science, and only the

following expression still survives, which was used in the early radio

times: transmitting through the ether. The fact that those gases

air

ether



23/26

would be inert is a justification of the fact that they dont react

with other elements. Anyway, after the erasing of the concept of

ether from official science, curiously enough, todays scientists at

a certain point in the last years started seeking for an alleged dark

matter and a dark energy, evidently because they must have begun to

suspect or even maybe they could have recognized that something were

missing: this peculiar fact seems only to be the prelude to a kind ofrediscover of ether under a different name, similarly to what

already happened a number of times with many discoveries of Dr. Nikola

Tesla (see for instance the so-called Schumann resonance, or the

radio emissions from planets and stars as pulsars, or even with some

of his radio circuitry etc.). In other words, when in science such

things occur to happen, it usually means simply that something that

was accepted in previously postulated theories was left unclear or was

incorrect so that, slowly but definitely, confusion grows to the point

that this leads to revision of accepted theories about the matter, as

it often occurred in Science, and introduction of new elements until

correctness is finally reached and occurring problems are at last

clarified.



24/26

8. Conclusion

As expected, because of the comparatively moderated main resonance

frequency of the Tesla coil (XMTR) itself, a limited aerial wave

irradiation was obtained; the coil was in fact originally mainly

designed for other purposes and not specifically to transmit energy

through the air irradiating the surrounding medium with waves. Ofcourse, a different design and construction with an eventual increase

to higher levels of the main resonators frequency would cause even a

bigger amount of radiated energy in the air and a stronger energy

field which however was not, as said, the aim of Nikola Teslas

project, whose ultimate target seemed rather to be the wireless

transmission of energy through the earth/ground (see also his

article[2]). In any case it is useful to remember that any scientific

theory is valid as long as it will not be contradicted by empirical

observation, experiment or research, and this must also be true for

Teslas Wireless System.

The above experiments, tests and measurements performed with the

Extra Tesla Coil XMTR together with other devices clearly showed

that a number of anomalous E.M. phenomena did occur, indicating that

a strong dielectric energy field was present around the coil itself,

which could be ascribed to the action of L.M.D. waves rather than to

T.E.M. waves. Not surprisingly these empirical results could,

according to other Authors, be supported from a physics and

mathematical point of view by the introduction, instead of todays

(Heaviside) vector form, of the (original) quaternionic form of

Maxwells E.M. equations which, as could be clearly seen, do predict

the possibility of the existence of scalar dielectric fields and of

longitudinal dielectric waves besides the well-known transverse E.M.

waves.

From the above illustrated theory it descends that the scalar field

has the form of an electroscalar wave, which does no work to movefree charges, and which has energy flow in the propagation direction,

however without converting E.M. energy into neither mechanic nor heat,

and having no magnetic component. A curious aspect is that said wave has the dimension unit of a magnetic field intensity, or

otherwise stated seems to be a kind of magnetic scalar.

As stated, longitudinal waves belong to the most powerful expressions

of energy among natural phenomena such as sound, seismic, tsunami

waves etc.

So further scientific investigation is needed: the position of the

part of the Academic World who still excludes the existence of L.M.D.waves should also be supported by proves as it has, at the moment,

neither theoretical nor experimental fundament. Anyway, officially at

present everything regarding L.M.D. and ether theory seems only to

belong to the realm of curious physics phenomena.



25/26

9. Legenda:

U or V : tension [Volt]

I : current [A]

P : power [W]

F : force [N]

: angle [rad]

: 2 f [rad/s]

: wave length [m]

x : distance [m]

c : 1/ (oo) speed of light in vacuum [m/s]

v : speed [m/s]

: scalar potential [V/m2]

A: vector potential [A/m2]

: scalar wave [H]

E : dielectric field [V/m]

B : magnetic field [A/m]

: charge density [As/m3]

J: current intensity [A/m2]

0 : dielectric constant in vacuum [As/Vm]

o : magnetic permeability constant [Vs/Am]

: dielectric constant [As/Vm]

: magnetic permeability constant [Vs/Am]

/t : time partial derivative

d/dt : time derivative

d/dx : space derivative

: Nabla operator

: quaternionic vector potential

: quaternionic DAlembertian operator~

(Theboldnotation represents a vector).



26/26

Bibliography and references:

[1] J.C. Maxwell, A treatise on electricity & magnetism, N.Y., 1873.

[2] Nikola Tesla, The True Wireless, Electrical Experimenter, May 1919.

[3] Nikola Tesla, Experiments with alternate currents of very high frequency

and their application to methods of artificial illumination, 1891.[4] Nikola Tesla, On light and other high frequency phenomena, delivered

before the Franklin Institute, Philadelphia, February 1893.

[5] Roberto Handwerker et al.,Rotazione di solidi mediante quaternioni(*),

for Elements of informatics-Faculty of Engineering of Milan Polytechnic,

Milan, 1990 (in italian) (*)

[6] Arbab I.A. & Satti Z.A. On the generalised Maxwell equations and their

prediction of electroscalar waves, Omdurman University, April 2009.

[7] Steinmetz C.P., Electric waves, discharges etc. , N.Y., 1914

[8] W.R. Hamilton, Elements of quaternions, Chelsea, 1866.

[9] Elihu Thomson, On a new connection for the induction coil,

Franklin Institute of Philadelphia, Vol.LXI, n.6, July 1871.

Smithsonian Institution, 1913.

[10] G.F. Ignatiev & V.A. Leus, Instantaneous action at a distance inmodern physics: pro and contra, Hauppage (N.Y.), 1990.

[11] Roberto Handwerker, Tesla and cold electricity, videos on

www.YouTube.com, Milan,2010.

[12] N. Tesla, Nikola Tesla tells of new radio theories, Interview with N.

Tesla in New York Herald Tribune, September 22, 1929

[13] J. Nasilowski: Phenomena connected with the disintegration of

conductors, Przeglad Elektrotechniczny, 1961 (in polnish).

[14] N.Tesla, On dissipation of electrical energy of the Hertz resonator,

The Electrical Engineer, December 21, 1892.

[15] N. Tesla, Famous scientific illusions, Electrical Experimenter,

February 1919.

[16] Prof. D. Mendeleev: An attempt towards a chemical conception of the

ether(trans. from Russian by G. Kamensky (Imperial Mint, St.Petersburg), Longmans, Green & Co. N.Y.,1904.

(*) English translation: Rotation of solids by quaternions

This publication, dedicated to Nucci & Karl, was issued on 03-03-2011

by:

DELTA Ingegneria - all rights reserved.Dr. Eng. Roberto Handwerker

Milan, Italy

e-mail:[email protected]

web:www.deltaavalon.com
http://www.youtube.com/http://www.youtube.com/mailto:[email protected]://www.delta-ingegneria.com/http://www.delta-ingegneria.com/mailto:[email protected]://www.youtube.com/http://www.youtube.com/

l.m.d. waves in a tesla coil revised & enlarged

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