Download Longitudinal dielectric waves

LONGITUDINAL DIELECTRIC WAVES IN
A TESLA COIL AND QUATERNIONIC
MAXWELL’S EQUATIONS.
Revised 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 Maxwell’s equations.
1
Longitudinal dielectric waves in a Tesla
coil and quaternionic Maxwell’s 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 impressive
electric 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 Maxwell’s 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 sufficient
justification 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 God’s Creation is vast and there is still a lot to explore.
HIGH
VOLTAGE
HAZARD
DISCLAIMER: WARNING ! THE FOLLOWING
EXPERIMENTS AND TESTS MAKE USE OF HIGH
FREQUENCY RADIO WAVES AND HIGH VOLTAGE
(POSSIBLE EMISSION OF X-RAYS, UV AND
OTHER HARMFUL RAYS): PLEASE DON’T TRY
TO REPLICATE THESE UNLESS YOU ARE WELLEXPERIENCED AND SKILLED IN HIGH-TENSION
ELECTROTECHNICS AND RADIO-TECHNOLOGY:
DANGER
OF
SERIOUS
AND
EVEN
FATAL
INJURIES TO PERSONS,DAMAGE TO PROPERTY!
RADIO
WAVES
HAZARD
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
2
Summary
1. Introduction…………………………………………………………………………………………………………………………………………4
2. Maxwell’s equations………………………………………………………………………………………………………………………5
3. Dielectric induction phenomena and dielectric longitudinal ………………
waves…………………………………………………………………………………………………………………………………………………………9
4. Transmission of energy through air and related measured values…11
5. Notes on Tesla Coil tuning…………………………………………………………………………………………………16
6. Streams, brushes, discharges and effects in Tesla Coil’s……………………
lamp bulbs……………………………………………………………………………………………………………………………………………17
7. Analogy between electrotechnics and fluidics…………………………………………………18
8. Conclusion……………………………………………………………………………………………………………………………………………22
9. Legenda……………………………………………………………………………………………………………………………………………………23
Bibliography and references………………………………………………………………………………………………24
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
3
1. Introduction
It 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 the
vector 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:
à = 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.
Ø 50
TESLA
COIL
XMTR
Sec.
210
250
Pri.
G
Fig.1
Ø 200
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 wellknown today’s Maxwell’s equations, which are the fundament of modern
electromagnetism:
a) Today’s 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.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
4
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.
Anyway, the two above possibilities does not exclude each other.
2. Maxwell’s equations
The (Heaviside’s) commonly adopted vector
equation in differential form is following:
c2
notation
of
Maxwell’s
. B = 0
(Magnetic flux theorem)
. E = ρ/εo
(Gauss’s Law-Dielectric flux)
x E + ∂B/∂t = 0
(Faraday’s
x B - ∂E/∂t = J/εo
law)
(Ampére’s law)
where: E = dielectric field;
B = magnetic field;
ρ = charge density;
ε0 = dielectric constant in vacuum;
∂/∂t = time partial derivative; J = current intensity.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
5
XMTR
RCVR
GND
Fig.2
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 Tesla’s 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 in
inertial platforms)[5]; their application to Maxwell’s 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 Maxwell’s equations from only one wave quaternion vector
potential or:
à = (iφ/c , A)
where:
~
□
2
à = μo J
,
J = (icρ, J)
by respect of the Lorenz gauge will be considered as accepted, so it
will be possible to take into account an extended result of today’s
Maxwell’s vector form. This imply the existence, besides the wellknown E.M. Transverse waves (T.E.M.= Transverse Electro-Magnetic),
also of Longitudinal waves (L.M.D.= Longitudinal Magneto-Dielectric),
whose scalar potential “φ” is related to its dielectric field “E” by
following equation:
E =
φ
This theoretical result was also supported from experimental
laboratory investigation which made use of “Tesla Coils” which are, as
it will be readily seen, not only “transformers” for high frequency
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
6
i[mA]
200
: measure with inductance
: measure with photomultiplier
L
LEDs
50
0,5
1
1,5
2
2,5 x[m]
Fig.4
Fig.3
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, Maxwell’s equations could
be simply expressed in the quaternionic form by the following two
equations:
1/c2 ∂2E/∂t2 -
2
E = -1/εo (
1/c2 ∂2B/∂t2 -
2
ρ + 1/c2 ∂J/∂t)
B = μo (
x J)
(1)
(2)
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
7
x
Er
ELMD
XMTR
V
V
M
P
C
i(t)
C
M
M
GND
GND
Fig.5
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 “Σ” was introduced and consequently also
the current intensity can be written as J =
Σ , the following new
gauge transformation can be considered:
ρ'= ρ + 1/c2 ∂Σ/∂t
J’= J -
and
Σ
(3) and (4)
it is then noted that the scalar “Σ” satisfies the wave equation:
1/c2 ∂2Σ /∂t2 -
2
Σ = -(
.J + ∂ρ/∂t)
(5)
Further, from the above mentioned work it would descend that the
charge density ρ and the current intensity J would travel at the speed
of light; so Maxwell’s equations could be seen as a special case of
equations (1) and (2). Then, this implies that the scalar wave Σ
distribution would therefore induce a
charge density:
ρ = -1/c2 ∂Σ/∂t
(6)
and a current intensity:
J =
Σ
(7)
even if charge ρ and current J were 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, therefore
not in direct contact between them, do conduct an electrical current:
it is
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
8
fluids
ELMD
solids
ETEM
x
T.E.M.
x
L.M.D.
ELMD
Fig.6
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
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations.
9
N
ELMD
XMTR
A
α
D
AM-RCVR
Fig.7
Fig.7: Neon tube (N) in the XMTR’s 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 α= 90º with respect to a horizontal axis without affecting the
energy 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:
1234-
The
The
The
The
generator (H.V. & H.F.)
primary (coil) circuit
secondary (coil) circuit
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
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 10
Et
P
XMTR
Er
ELMD
ETEM
i(t)
ψ
M
GND
Fig.8
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
analogy’s
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 without
any
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 11
i[mA]
100
: measure with metal plate
75
50
25
Fig.9
3/2∏
0
∏/2 ψ[rad]
Fig.9: Diagram shows the relationship between the ψ angle formed by
the 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 ψ= 0 (0º) (or of course even when ψ= 2∏ (360º)) that
is by versor Er 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 ψ= ∏/2 (90º) and ψ=
3/2∏ (180º)(by versor Er perpendicular to brass plate), showing that
no 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 presence
of magnetic fields, a normal compass has been moved in the energy
field 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 field
intensity 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 the
energy field was greater as the LEDs were at maximum brightness and
beyond, as some of them did burn out due to excessive voltage.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 12
compass
sphere cap
BTEM
B
ELMD
I
TR
nail
Fig.10
Fig.10: A
Coil: its
the same
indicator
field.
normal compass was set in the energy field of the Tesla
nail indicator (I) showed no movement, on the contrary when
compass was approached to a normal E.M. transformer the
immediately started to move, thus detecting a magnetic
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 pocket AM/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 a
ferrite 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.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 13
ELMD
sphere cap
P
B
Fig.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 a
photomultiplier vacuum tube (V) type “931-A” from “R.C.A.-U.S.A” (to
its 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 didn’t
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 insulated metal plate made of
brass, 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 Tesla’s 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 “ψ” 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(Ψ)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:
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 14
d
d
ELMD
K
i(t)
M
Fig.12
M
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(Ψ))dx
(t5)
so it becomes:
A =f(cos(Ψ))
(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 impedancemeter: 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
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 15
XMTR
RCVR
G
D
GND
Fig.13
N
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-S” series from “GW-Instek” was 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:
λo= c / fo
(where c: speed of light in vacuum)
(t8)
said frequency corresponds to a wave length of λo= 113,64m or to λo/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 “λ/4”, the T.E.M. components of the wave
had less possibility of influencing the test, thus allowing the L.M.D.
components to mainly play.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 16
Fig.14
a)
b)
c)
Fig.14: Light streams, brushes and discharge effects in Tesla coil’s
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 Coil’s 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 socalled 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].
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 17
Fig.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
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 18
S-waves
Earth
P-waves
Seismic epicenter
Fig.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 didn’t predict neither
laser, nuclear energy, solar panels nor space travel but this
evidently doesn’t 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 direction
b) alternatively bent up and down around a perpendicular axis
c) 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 other
examples of longitudinal waves: maybe the most common at all are sound
waves, that is pressure variations in a medium such as a solid, a
liquid 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/ρ)
where E > G (always)
VT = √(G/ρ)
(8)
(9)
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 19
XMTR
rectifier
RCVR
R
electric motor
C
DC
motor
+
M
-
Fig.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. The
RCVR electronic drive circuit on the small car is also shown; the
graphed waveform type only represents a full-wave bridge rectifier.
liquids:
VL = √(Ea/ρ)
where ρ: density
VT = 0
(10)
(11)
gases:
VL = √(γRT/M)
where γRT/M:
gas constant
VT = 0
(12)
(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 doesn’t 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 20°C
Medium
Speed in [m/s]
Air
Water
Glass
Ether (*)
343
1.480
5.300
c (**)
(*) according to Dr. Nikola Tesla’s 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 are
shape compression waves in earth, as secondary seismic waves are shear
waves of the transverse type, in this case acting on earth’s surface:
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 20
wire
L.M.D. waves
break pattern (parallel stripes)
x
Fig.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 + 4/3δ)/ρ)
(14)
VS = √(δ/ρ)
(15)
where k: elast. norm.modulus, δ: elast. tang.mod, ρ: 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 “δ” 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 an
indication 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; he also criticized
called common radio broadcast and called it “ether whistle”[12].
However, this matter would be too vast and complex indeed to be
treated here and would also go beyond the aim of this writing, taking
the reader much too far from the main argument dealt herein.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 21
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. Of
course, a different design and construction with an eventual increase
to higher levels of the main resonator’s 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 Tesla’s
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
Tesla’s “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 today’s
(Heaviside) vector form, of the (original) quaternionic form of
Maxwell’s 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
“Σ” has the form of an electroscalar wave, which does no work to move
free 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 “Σ”
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.
Moreover, the term “ether” referred to an universal pervading gaseous
medium having atomic mass exceedingly smaller than that of hydrogen in
which only longitudinal waves could propagate was used by a number of
great scientist during the Victorian age (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” seems to have been forgotten and abandoned from “modern”
science. Further scientific investigation is needed, and the position
of the part of the Academic World who still excludes the existence of
L.M.D. waves should be supported by proves as it has, at the moment,
neither theoretical nor experimental fundament. Anyway, officially at
present everything regarding L.M.D. seems to belong to the realm of
curious electric phenomena.
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 22
9. Legenda:
U or V : tension [Volt]
I : current [A]
P : power [W]
F : force [N]
α : angle [rad]
ω : 2 ∏ f [rad/s]
λ : wave length [m]
x : distance [m]
c : 1/ √(μoεo) speed of light in vacuum [m/s]
v : speed [m/s]
φ : scalar potential [V/m2]
A : vector potential [A/m2]
Σ
: scalar wave [H]
E : dielectric field [V/m]
B : magnetic field [A/m]
ρ : charge density [As/m3]
J : current intensity [A/m2]
ε0 : dielectric constant in vacuum [As/Vm]
μo : magnetic permeability constant [Vs/Am]
ε : dielectric constant [As/Vm]
μ : magnetic permeability constant [Vs/Am]
∂/∂t : time partial derivative
d/dt : time derivative
d/dx : space derivative
: Nabla operator
à : quaternionic vector potential
~□ : quaternionic D’Alembertian operator
(The bold notation represents a vector).
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 23
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 in
modern 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.
(*) English translation: “Rotation of solids by quaternions”
This publication 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
Roberto Handwerker. Longitudinal dielectric waves in a Tesla coil and quaternionic Maxwell’s equations. 24