This
Captured
Lightning® sculpture
was created by injecting a block of clear acrylic with an electron beam
from a 5 million electron volt (MeV) particle accelerator.
Electrons were first injected from the left side, the specimen was then
rotated 180
degrees,
and electrons injected into the opposite side. This
created two
independent, highly-charged layers deep inside the specimen. The
charge layer on the right was then manually discharged, creating a
miniature "lightning storm" within the layer immediately above.
Additional discharges then grew between the right and left charge
layers, forming a beautifully interconnected 3D discharge structure.
The
entire event occurred in less than 100 billionths of a second! The
sculpture above is illuminated from below by
blue
light emitting diodes (LED's). Each of our Captured Lightning®
sculptures
contain a unique, incredibly detailed, fractal discharge
pattern. Unlike laser art, no two sculptures are identical. As they
branch, the discharge channels become increasingly finer and
hair-like, ultimately disappearing at the tips. The
smallest discharges are thought to extend to the molecular level. See our Captured Lightning Frequently Asked Questions (FAQ) for a quick overview.
(Actual sculpture size: 3" x 3" x 2")
What are Lichtenberg figures?
Our Captured Lightning® sculptures are actually "Lichtenberg figures".
Lichtenberg figures are branching, tree-like or fern-like patterns that
are created by high voltage discharges along the surface, or within,
electrical insulating materials (dielectrics).
The first Lichtenberg figures were actually 2-dimensional patterns
formed in dust on the surface of electrostatically charged resin plates
in the laboratory of their discoverer, German physicist Georg Christoph Lichtenberg
(1742-1799). Professor Lichtenberg made this observation in the late
1700's, demonstrating the phenomenon to his physics students and peers, and he reported his findings in
his memoir: Super nova methodo naturam ac motum fluidi electrici investigandi (Göttinger
Novi Commentarii, Göttingen, 1777). The basic principles involved
in forming these electrostatic figures evolved
to become modern xerography and the science of plasma physics.
Dr.
Lichtenberg used electrostatic devices to charge the surfaces
of various insulating materials such as resin, glass, or ebonite (hard
rubber). He then sprinkled a mixture of finely powdered sulfur and red
lead (lead tetroxide) onto the surface. The powdered sulfur (being
slightly negatively charged through friction) was attracted to the
positively charged regions, and the red lead was preferentially
attracted to the negative regions. This made previously hidden
regions of trapped surface charge clearly visible. Lichtenberg noted
that the shapes of the positively and negatively charged figures were
significantly different. Positive
figures tended to be star-like with long branches, while
negative figures tend to be shorter, rounded, and fan-like. By
carefully pressing a piece of paper onto the dusted surface, he was
able to transfer these images onto the paper, demonstrating what was
later to become the process of xerography. Drawings of positive and
negative figures that Lichtenberg made are shown below.
Positive Lichtenberg figure
Negative Lichtenberg figure
Notable 19th and 20th century Lichtenberg figure researchers included Gaston Planté (mid-1850's), French artist and scientist Etienne Leopold Trouvelot and Thomas Burton Kinraide (late 1800's), and Carl Edward Magnusson, Maximilien Toepler, and Arthur Von Hippel
(1920's-30's). Many of these researchers used photographic film to directly
capture the faint light emitted by positive or negative high voltage
discharges along dielectric surfaces. Von Hippel discovered that
Lichtenberg figures were actually created through complex interactions
between ionized gas (corona, or
small electrical sparks called streamers) and the
dielectric surface below. It was also found that increasing the applied
voltage, or reducing the surrounding gas pressure, caused the length of
the figures to increase.
The relationship between Lichtenberg figure length versus voltage was utilized in various recording instruments, such as klydonographs,
that
photographically recorded the size
and shape of Lichtenberg figures that appeared during abnormal
electrical surges on power lines. Klydonographs and related instruments
allowed lightning
researchers and power system designers in the 1930's and 1940's to
estimate the peak voltage and
polarity of abnormal voltage transients when lightning
struck power lines. These measurements provided critical
information about the electrical characteristics of lightning strikes.
They helped power engineers to develop and test the effectiveness of
various lightning protection techniques. Lightning protection is now a
key element in all modern electrical
transmission and distribution systems. A schematic diagram of the main
parts of a
klydonograph is shown on the leftmost drawing below, along with
examples of "klydonograms" from equal magnitude positive and negative
high voltage transients.
Schematic view of a klydonograph showing the position of the
photographic film and HV electrode. Light from high voltage
discharges creates a permanent photographic record of the event.
From W.W. Lewis, "The Protection of Transmission Systems
Against Lightning", John Wiley & Sons, 1950
Lichtenberg figures are now known to occur during electrical breakdown processes
within most gases, insulating liquids, and solid dielectrics. Lichtenberg figures may be created very quickly (tens of nanoseconds) when dielectrics are heavily overstressed, or they can grow very slowly, through a series of low-energy partial discharges, evolving into partially conductive surface patterns or 3D "electrical trees".
Electrical
trees often form on contaminated insulator surfaces or within
dielectrics due to internal defects or voids, or at points where an
insulator has been physically damaged. Since they can eventually cause
a
flashover and complete electrical failure of the insulator, preventing
their formation and growth is critical to the long-term reliability of
high voltage equipment.
The first Lichtenberg figures were created inside clear plastic by physicists Arno Brasch and Fritz Lange in the late 1940's. By using a newly-invented particle accelerator, they injected electrons inside plastic specimens, causing electrical breakdown and the formation of internal Lichtenberg Figures. Electrons
are tiny, negatively charged particles that orbit the nucleus of the atoms that make up all condensed matter. At
their laboratory at AEG (Berlin, Germany), they used high voltage pulses from a 2.4 million volt Marx Generator
to drive a pulsed electron beam accelerator. An
article about their research and their accelerator (which they called a
"Capacitron") appeared in the March 10, 1947 issue of LIFE Magazine.
The Capacitron could deliver a 3 million volt pulse, and could generate a powerful beam of electrons with a peak current of
up to 100,000 amperes! The glowing region of ionized air created by the exiting high-current
beam of electrons resembled a bluish-violet rocket engine flame. A complete set of previously unpublished B&W pictures,
including Lichtenberg figures inside a clear block of plastic, has
recently become available online, as has another article with color pictures from the April, 1951 issue of Popular Mechanics.
Formal research on the detailed
behavior of charge storage and movement within dielectrics was first conducted by Dr.
Bernhard Gross in the early 1950's. Gross confirmed that internal Lichtenberg figures could be created within a variety of polymers and glasses by injecting them with high-energy electrons using a linear accelerator (LINAC).
The techniques that we use to make our sculptures build upon
the theoretical work and techniques originally developed by Gross,
Brasch, and Lange. The resulting Lichtenberg figures are also
called electrical
trees, electron trees, or beam trees - we call ours Captured Lightning® sculptures.
How do we create Captured Lightning® sculptures?
Over many years, we have refined irradiation and fabrication
techniques to create a truly unique line of beautiful 2D and 3D
sculptures.
We start with specially cut and polished specimens of a clear polymer, polymethylmethacrylate (or PMMA).
This material is commonly known as "acrylic", and is sold under various trade names such as
Lucite, Plexiglas, or Perspex. PMMA has a unique combination of
high optical clarity and superior electrical
and mechanical properties, and it is actually clearer than glass. Other clear polymers, such as polycarbonate
(PC), polystyrene (PS) , polyethylene terephthalate (PET), and polyvinyl
chloride (PVC) also work to varying degrees. However, most of
these materials form dark gray or black trees instead of the sparkling
mirror-like fractures seen within acrylic.
Most
of
our Lichtenberg figures were produced
by
injecting specimens with high-energy electrons from a 150 kW linear accelerator (LINAC) called a Dynamitron. The
Dynamitron
is four-stories high, and the heart of the device is a large evacuated
"vacuum tube". Electrons
are emitted by a small tungsten filament at the top of the tube. The
filament is also connected to a large negative voltage source, while
the other end of the
tube is connected to ground (or 0 volts). The high voltage causes the
electrons emitted by the filament to be accelerated to very
high velocities as they "fall" though the large potential difference.
The energy of the
electrons that exit the accelerator is measured in millions of electron volts (or MeV). Most of our specimens were created using electron energies of between 2 - 5 MeV. At these energies, electrons exiting the accelerator are traveling at relativistic velocities - between 98.5% and 99.6% of the speed of light. When an acrylic specimen is irradiated by relativistic electrons, the electrons are driven deep inside the acrylic. The depth of penetration is
determined by the energy of the electron beam, the target material's
dielectric properties, and its atomic density.
The higher the energy of the electron beam, the deeper the electrons will penetrate before coming to a stop.
As
the specimen is irradiated, huge numbers of electrons accumulate
inside, creating a cloud-like
layer of excess negative electrical charge called a space charge.
Since
acrylic is an excellent electrical insulator, the injected electrons become temporarily trapped inside, forming a
plane of accumulating negative space charge deep inside the specimen. By passing
specimens through the beam in two or more passes, or by rotating them
while they're being
irradiated, complex 3-dimensional space charge regions can be produced.
As the space charge builds, the internal electrical field increases dramatically. Eventually, the immense electrical stress overcomes the
dielectric strength of the acrylic, and some of the chemical
bonds that hold the acrylic molecules together are ripped apart. This strips away additional free electrons in a process
called ionization.
These newly-freed electrons are also accelerated by the
electric field, ionizing even more acrylic molecules, and creating
additional free electrons in a runaway process known as avalanche breakdown.
Within billionths of a
second, thin electrically conductive channels form within the acrylic, and the
material suddenly undergoes dielectric breakdown.
As breakdown occurs, the previously trapped charges suddenly rush out.
Thousands of electrically conductive branches feed their current into
the main "lightning
bolt" channel that exits the acrylic with a brilliant flash and a loud
BANG. Although the "Tree of Fire" discharge appears as though we're injecting high
voltage into the block, in reality we are removing excess
charge that was previously trapped within the block. Dielectric
breakdown occurs within an incredibly short interval. For example, the electrical discharges
within a 2 inch square specimen last for less than 60
billionths of a second! The following image shows a 4x4 inch specimen at the instant of discharge:
(Photo courtesy of Theodore Gray)
The
miniature lightning bolts blast permanent trails in the acrylic,
forming a complex, branching "lightning fossil" within. The current
within the electrical discharge is typically hundreds, or even thousands, of
amperes. The hot plasma within the discharge causes the acrylic to melt and fracture along each path, and higher
current "roots" may slightly char the acrylic. The exit point of the discharge appears as a small crater on the surface of
the acrylic. The discharge point is typically located at a surface defect, or where a
point of external mechanical stress
has weakened the dielectric. A defect concentrates
the electric field, creating a small region where the breakdown process
can begin. Although we inject a huge amount of negative charge into our
specimens, electrical breakdown actually originates from points which
are more electrically positive (versus the space charge layer), so our
Captured Lightning® sculptures are
actually "positive" Lichtenberg figures! The resulting sculptures are completely
safe - they have been electrically discharged and they retain no trace
of radioactivity or X-rays.
Video clip of a huge 18 Inch figure being created:
Following
is
a short video clip of an 18" x 18" x 1" specimen being discharged.
Prior to discharge, the estimated potential of the internal charge
plane was about 2.2
million volts. Because of its size, this specimen had
considerably more
stored electrostatic energy, and the discharge was quite loud and
extremely
bright! The actual discharge, although very brief, temporarily
overloaded the
video camera's image sensor. A multitude of secondary discharges can
also be observed after
the main discharge. (Video courtesy of Terry Blake. Specimen
was owned, and discharged, by Jeff Larson.)
The rounded, crystalline flakes that make up the Lichtenberg Figure are actually chains of hollow tubules and tiny conchoidal
fractures. The shell-shaped fractures are characteristic of the way glassy (amorphous) materials
fracture when stressed beyond their breaking point. The countless
fractures behave like tiny mirrors, so illuminating a
figure through an edge causes the entire Lichtenberg figure to glow brilliantly
with the reflected color(s) of the external light source.
Lichtenberg figures are fractals
Lichtenberg figures exhibit branching patterns which look
similar at various scales of magnification. This self-similar property
suggests that Lichtenberg figures might be mathematically described using a branch of mathematics called Fractal Geometry. Self similarity is a key property of fractals.
Fractal objects do not have an integral (2D or 3D) dimension, but
instead are characterized by fractional dimensions. Our
regularly-branched 2D Lichtenberg figures have a typical fractal
dimension of 1.5 - 1.7. Lichtenberg figures also show a range of fractal behavior and dimension depending upon
the magnitude of charge injected into the acrylic and when the
specimens are discharged. Branching figures are technically called
"dendritic" or "arborescent" (i.e., tree-like). If a large amount
of electrical charge is injected into the specimens and it is then
immediately discharged, a very dense dendritic discharge is
created, such as Figure 1 below.
These dense discharges are quite similar in appearance to ferns or moss
agate. If the level of charge is reduced and the specimen manually
discharged, a more classical, lightning-like or tree-like discharge
results as Figure 2 below. If premature breakdown occurs while we are
actively irradiating a specimen, densely tangled "chaotic" discharges occur, as in Figure 3.
Some specimens contain a fascinating and complex combination of these basic patterns.
Figure 3. Chaotic Discharges
(prematurely discharged
while being irradiated)
Self
similarity can easily be seen in the following sequence of zooms
from a 12" x 12" Lichtenberg Figure with nominal dendritic discharges.
The branches become finer and
hairlike, ultimately disappearing. Similar fractal patterns are seen in
aerial views of some rivers and their tributaries, and organic structures such as branching tree
limbs, and arteries, veins, and capillaries within your body.
Lichtenberg figures were first modeled using a process called "Diffusion Limited Aggregation" (DLA). An enhanced model that combines an electric field with DLA is called the Dielectric Breakdown Model (DBM).
The DBM appears to fairly accurately describe the macroscopic branching
forms of electrical breakdown that occur within solid, liquid, and
gaseous insulators.
Solarization, fluorescence, birefringence, dead zone
When acrylic is irradiated by high-energy electrons, it glows brightly with a blue-white
color. Although radiation chemistry studies suggest that this may be a combination of luminescence, x-ray fluorescence, and Cherenkov radiation, the precise light-emitting mechanisms are not completely understood. You may also notice a
discharge-free "dead zone" along all of the outside edges. This is because
acrylic is not a perfect insulator, and some of
the internal charge "leaks away" to the outside surfaces along the
perimeter of each specimen. This reduces the stored charge along
the
perimeter to the point where the internal electrical field is no longer
sufficient to break down the
acrylic, resulting in a discharge-free zone along the perimeter.
Newer specimens often have a layer with an amber tint. This coloration is called solarization, and is thought to be caused by material defects from energetic electron
collisions and high energy x-rays, and from electrons temporary trapped within the molecular structure of
the acrylic. Solarization usually occurs in the region between the surface that was
irradiated by the electron beam and the discharge layer. During irradiation, electrons are initially traveling at
about 99% of the speed of light. As they penetrate the specimen, they collide with the acrylic molecules, rapidly coming to a stop within a fraction
of an inch. The electrons in the beam have a tremendous
amount of kinetic
energy, and as they suddenly brake to a stop,
they release this energy in the form of heat and powerful X-radiation.
The electrons and x-rays stimulate chemical and physical reactions that alter the physical and optical
properties of the acrylic. Some of these changes are temporary, while others appear to be permanent. Although
the specific causes of solarization are not completely understood, there
is evidence that irradiation creates unstable, longer-lived
"metastable" compounds that preferentially absorb light at the blue end of
the spectrum (250 - 400 nm). This causes portions of the acrylic to turn green, brownish, or amber.Some electrons may remain trapped for months, or even years, creating color centers which also contribute to solarization.
Most
irradiated
specimens initially turn a bright lime green color. This gradually
fades to an amber color over a few minutes to a few hours, and the
solarized region may
take months, or even years, to eventually fade away.
Fading
can usually be accelerated by gently heating the block in the
presence of oxygen, or by leaving the specimen in bright light for an
extended period of time. It has been determined that atmospheric oxygen
also plays a role in the fading process. As oxygen diffuses into the
acrylic from the
outside surfaces and the discharge layer, it slowly bleaches the
solarized region,
causing the solarized layer to gradually become thinner and thinner,
eventually
disappearing altogether. Most
older Lichtenberg figures are completely bleached. Although they no
longer show any solarization, some specimens continue to show slight
residual
"fogging" due to permanent radiation damage in the acrylic. Some
specimens
exhibit little
initial
solarization, while a small number of specimens permanently retain
their amber color. We recently discovered that fully-charged
specimens will retain their green color and stored electrical charge indefinitely
if kept at dry
ice temperatures. This suggests that the initial green color may be due
to a high density of trapped charge. If these specimens are then
discharged weeks
later, they quickly change to the longer-term amber color. Clearly,
a number of different processes appear to be
associated with solarization.
Recently, it has also been discovered that the solarization layer is sometimes quite fluorescent.
An amateur scientist from Australia, Daniel Rutter, discovered that monochromatic light from a green laser pointer changes color
when passed through the solarized layer of a Lichtenberg figure. More
recently, we have discovered that the light from a near-ultraviolet
source (such as a Blu-ray laser or even bright blue LED's) cam cause
the solarized region to glow with a brilliant yellow-green
fluorescence. This occurs on some specimens but not others, and as the
solarization fades over time, so does the fluorescence.
Most specimens also exhibit
slight changes in refractive index close to the Lichtenberg discharge layer. This is
thought to be due to residual mechanical stresses near discharge fractures. Residual
stresses near the Lichtenberg figures can easily be seen as
multicolored regions
near the discharge plane when a sculpture is illuminated by polarized
light and then viewed through a second polarizing filter (crossed
polarizers). When physically stressed, acrylic exhibits a property called birefringence.
When viewed through cross polarizers, stress-induced
birefringence causes changes in color that are directly related to the amount
and distribution of otherwise hidden stresses.
Discharge current measurements... and a paradox During
our
2007
and 2009 production runs, we measured and recorded discharge
current waveforms for a number of 4" x 4" x
3/4" specimens. We designed a special
holding
fixture with copper foil plates that made physical contact
with the large surfaces of a
charged acrylic specimen. A heavily insulated wire connected the pair
of foil
plates to a pointed discharge tool, and the wire was also passed
through the center of a wideband Current Transformer (CT). When the
specimen was discharged, the main current pulse flowed through the wire
and was measured via the CT. The CT
transformed the discharge
current pulse
that flowed through the wire into a voltage pulse that could then be
captured and stored within a high speed
Tektronix digital storage oscilloscope. One of the digitized waveforms
is shown below. We
found that, for this 4" x 4" specimen, the discharge
lasted for less than 120 billionths of a second (120 ns), the
peak current reached almost 600 amperes, and the waveform contained
four
discrete current peaks. Other specimens showed between three and seven
current peaks.
This
suggests that propagating electrical trees may progress via a series of
advancing breakdown waves. Each current peak reflected a surge of newly
conducting channels ("streamers" and "leaders") as they tapped into new sources of stored charge. Newer channels
apparently blasted
their way into previously untapped reservoirs of
charge within the acrylic, paused briefly, then surged again, etc. The
average discharge velocity was between 8.5 x 105 and
1.3 x 106 meters/second (526 and 790 miles/second, or around 0.3% the speed of
light). However, pauses between successive current surges suggest that the peak discharge
velocity during propagating phases was significantly faster. Surprisingly,
the average velocity within the specimen was actually 10-100 times faster
than the velocity of positive lightning leaders in air. This is thought to be
due to the extremely high electrical field (estimated to be in the range of 10 - 20+
million volts/cm) at the tips of the propagating discharges within the
acrylic.
However,
these high streamer velocities create a paradox, since the
measured breakdown velocity is over 800 times the speed of
sound within PMMA. This is inconsistent with Griffith's theory of crack propagation within solids,
which predicts that the maximum crack propagation speed within a solid
is limited to the speed of sound within the material or 1.614
km/second for PMMA. The current waveform
clearly demonstrates that the breakdown process (the complete formation of chains of cracks
and gas channels across the specimen) for our Lichtenberg
figures occurred at a minimum speed that was almost three orders of magnitude
FASTER than the maximum speed predicted by classical materials
theory!
Some
insight
into
this problem may come from the work of a Russian
researcher, Yu N. Vershinin. Vershinin
explored electrostatic energy storage in regions of solid dielectrics
where space charge has been slowly injected (called "charge trapping"), and
its rapid release
("charge detrapping") as the dielectric undergoes
partial or complete electrical
breakdown. Vershinin proposed
that, when a dielectric contains significant trapped space charge,
the potential
energy stored within the electrical field around the trapped charges
may be rapidly liberated, contributing to the formation and growth of
crack tips. As chemical bonds in the surrounding material are ruptured,
high pressure gases are liberated, expanding the channels behind the
propagating crack tips. Vershinin speculated (and experimentally
verified) that for very high internal fields, the potential energy
initially stored within the electrical field was rapidly converted into
kinetic and thermal energy that drove crack
propagation at hypersonic velocities. Vershinin called this process
"electronic detonation" since it was similar to the supersonic chemical reaction wave (shock wave)
that propagates through a high explosive when it detonates. However,
electronic
detonation is often hundreds of times faster than the shock waves that propagate through even the fastest chemical explosives.
Because of the large amount of electrostatic energy stored within our
specimens, and the extremely short discharge intervals, the
instantaneous power liberated during a Captured Lightning discharge can
exceed a gigawatt (109 watts)! Not
surprisingly,
the
discharge
creates
a satisfyingly loud BANG(!), as the brilliant, blue-white
lightning-like sparks wreak havoc inside the acrylic, creating
countless permanent fractures and tubules within the space charge
layers. Charge detrapping is now known to be an important degradation
and breakdown mechanism
within dielectrics that are subjected to long-term high voltage
stresses, sudden voltage changes, or abrupt polarity reversals. In some
respects, sudden charge detrapping within a solid dielectric is similar
to a destructive high voltage capacitor discharge within the insulating material itself.
After
the
main discharge, hundreds of smaller
secondary electrical discharges continue to occur throughout the
specimen as small pockets of residual stranded charge redistribute
themselves. Large figures sparkle and sizzle, making a sound similar to
frying bacon, and intermittent
sparking has been seen over 30 minutes after the main discharge.
Secondary discharges often sting our fingers when we handle
recently-discharged
specimens. Click on the following image to see some high
resolution video captured during our 2007 production run that shows
primary and secondary
discharges.
(Photo and video courtesy of Mike Walker and Theodore Gray) Click on the Above image to see a video clip
of many Lichtenberg figures being discharged
Natural Lichtenberg figures - fulgurites and lightning tattoos
Occasionally, nature also creates "fossilized lightning". Called fulgurites,
these
are hollow and sometimes branching tubes that are formed when the powerful
electrical
current from a lightning strike creates underground discharge channels within poorly conducting sandy or sandy-clay soils. These hollow channels were formed as the intensely hot channels from the lightning arc fused surrounding sand
and soil particles which then cooled to form a solid glassy tube. Some
fulgurites also exhibit fractal characteristics as they split into
smaller diameter root-like branches at further distances from the site
of the main strike.
Lichtenberg figures, sometimes called "lightning flowers" or "skin feathering",
are sometimes formed
beneath the skin of unfortunate humans who have been struck by lightning. The victim will often have one
or more reddish radiating feathery patterns that branch outward from
the entry
and
exit points of the strike:
From "Lichtenberg Figures Due to a Lightning Strike" by Yves Domart, MD, and Emmanuel Garet, MD,
New England Journal of Medicine, Volume 343:1536, November 23, 2000
Medical
terms for this phenomenon include arborescent lightning burn, arborescent erythema, keraunographic markings or ferning
patterns. Although the exact causes are subject to
some debate,
they appear to be the result
of physical damage to small capillaries under the skin, perhaps caused by the
flow of electrical current, or by shock wave bruising from external flashovers
just
above
the skin. The arborescent (tree-like)
reddish marks fade away over a
period of
hours
or days. They are recognized by forensic pathologists as clear evidence
that a victim has been struck by lightning. The patient above survived
with no permanent injuries, and the lightning flowers completely faded
within two days. A small Lichtenberg figure
has
also been observed at the entry point
where a high voltage spark penetrated the skin of an unfortunate (but
surviving) local electrical experimenter who was accidentally zapped by a
homemade 60,000 volt Marx Generator.
A similar phenomenon is sometimes seen when
lightning
hits a grassy field, as in this picture where lightning struck a
flagpole, leaving this beautiful 25 foot Lichtenberg figure on the
green of a golf course:
(From "Lightning and Lichtenberg Figures" by Cherington, Olson and Yarnell, Injury, Volume 34, Issue 5, May 2003)
Note the similarity between the figure above and the Lichtenberg figure below (illuminated by blue LED's):
High voltage discharges to the surface of water can also create Lichtenberg figures. Some very beautiful examples
of
both positive and negative Lichtenberg figures on water surfaces can be seen on Dr. Colin
Pounder's Lichtenberg figures web site.
Natural lightning sometimes creates transient "Lichtenberg figures" in the sky. Air is an excellent dielectric and, although the physical breakdown
mechanisms
for air and PMMA are considerably different, the appearance of the
branching
discharges is quite similar. So it should not be surprising
that the
branching forms of lightning also have fractal
characteristics. This similarity can clearly be observed during "anvil crawler" and horizontal "spider lightning".
Spider lightning follows a thin, positively charged cloud layer, and the
slowly propagating discharges can crawl across the sky for 30-40 miles
- literally spanning from horizon to horizon. On a much smaller scale, transient Lichtenberg figures
(often mistakenly called St. Elmo's Fire) often appear on the outer
surface of cockpit windows of airplanes as they fly within thunderstorms.
Similar
branching fractal patterns also occur when thunderstorms generate electrically conductive leaders that
propagate downward from a charged cloud to the ground below. When one
of these leaders connects with an unfortunate object on the ground, a high current pulse (called the return stroke) surges back upward through the completed path, resulting in a Cloud-to-Ground (CG) lightning
strike.
Exceptional examples of downward propagating positive leaders have been captured by South Dakota lightning
researcher, Tom Warner. Using high speed video imaging equipment, he
was able to capture the downward progression of leaders and the return
stroke from a positive lightning bolt. Positive lightning
is a significantly rarer, and considerably more dangerous, form of lightning than negative lightning. The
"slow motion" video (below) shows the air breaking down, forming
glowing conductive plasma paths (called leaders) that fan
downward from the huge reserve of positive charge within the cloud
above. The brightly glowing tips of the positive leaders smoothly propagate,
unlike
negative leaders
which propagate in a series of discrete jumps (called stepped leaders). The
first descending leader to finally connect with the Earth below
completes the circuit, resulting in a powerful
Positive Cloud-to-Ground (+CG) lightning discharge.
The video clip
below was captured at 7200 frames/second (FPS), and the actual elapsed
time for the clip was only a little longer than three
thousandths of a
second. The speed of the propagating leaders was between
3 x 104 and 6.5 x 105 meters/second. This clip even contains a single frame
which captures the beginning of the return stroke from the Earth going
back up one of the leader channels. Even at the majestic scale
of natural lightning, you can clearly see similarities between the
collection of branching leaders and Lichtenberg figures.
Positive lightning also has a very long lasting "tail" of
follow-through current which typically lasts for several hundred
milliseconds after the initial strike
connects to ground. The combination of long propagation distance (often
many miles from the main storm), very high current (up to 300,000
amperes), and long follow-through current make positive lightning
exceptionally dangerous. It tends to set fire or kill anything, or
anyone, unfortunate enough to be in its path. More of Tom Warner's
fascinating videos can be seen on his YouTube page.
Lichtenberg figures can also be seen at some high energy pulsed
power facilities, especially where deionized water is used as a dielectric to briefly store
large amounts of electrical energy. The photo below is from Sandia National Laboratory's
mighty Z
Machine, the world's most powerful electrical pulse generator. After
the completion of a high energy experiment, the water breaks down from the huge electrical stress,
becoming an electrical conductor that safely dissipates unwanted
residual
energy from the system. The filamentary breakdown paths form Lichtenberg figures that dance across
the water's surface. If you look closely, you'll notice that
many of the paths actually trace out high voltage
electrical field lines along the surface of the water. Although
impressive, this display is only dissipating "left over" energy,
representing only a very small fraction (perhaps 5%) of the energy that was
actually used during the previous pulsed power experiment.
(Click for a higher resolution 840 x 554 pixel image, 561 kB)
Are There Practical Uses for Lichtenberg Figures? Analysis
of
Lichtenberg figures is a powerful tool for diagnosing and subsequently
preventing high
voltage breakdown within solids and along dielectric
interfaces. By examining these figures, experts can diagnose and
prevent future electrical
faults within a variety of devices, such as high voltage transformers,
capacitors, and insulators used by electrical utilities. Historically,
Lichtenberg figures were a powerful tool in measuring the polarity and
magnitude of
transient overvoltages on power lines during direct and indirect
lightning
strikes. These measurements were critical for the development of
reliable electrical power transmission and distribution systems.
Lichtenberg
figures are still used as a forensic clue for identifying the cause of
injury or death of human and animal lightning victims.
In 2009, researchers at Texas A&M University proposed using
3D Lichtenberg figures created within various polymeric materials as
"templates" for growing vascular tissue.
There are significant similarities between branching Lichtenberg
figures and animal circulatory systems - a fact not lost on many
medical researchers. The hope is that, by creating branching 3D
Lichtenberg figures inside a biodegradable polymer, such as polylactic
acid (PLA), scientists could these as "molds" to support the development and growth of vascular tissue. Vascularization
is essential for growing
functional replacement tissues and organs. It's possible that the 18th century technology
of Lichtenberg figures may ultimately play a profound role in organ replacement
therapy during the 21st century!
Captured Lightning Sculptures - fossilized lightning bolts
Captured
Lightning® is indeed an accurate description for our sculptures. Holding a Captured Lightning sculpture is about the closest
you can
come to holding a fossilized lightning bolt. As with snowflakes, every Lichtenberg Figure is unique - a one-of-a
kind treasure, sculpted in exquisite detail by the forces contained within natural lightning.
Two
dimensional photos do not begin to capture the beauty and detail of our 3D
sculptures. Following are a pair of 3-D images that can be rotated 360
degrees so that you can more fully
appreciate the detail within some of our doubly-irradiated sculptures. Once the images have been completely
download, drag your mouse over the image to rotate each for a
full 360
degree view. [Note: because of the large image size, a high speed cable
or DSL Internet connection is recommended].
3D Rotatable Image
3D Rotatable Image
"Heavy Weather"
(Courtesy of Theodore Gray)
"Windblown Lightning"
(Courtesy of Theodore Gray)
Very
few
people have actually seen
or held one of these rare objects, and far fewer have had the
opportunity to own sculptures as beautiful and spectacular as these.
Stoneridge Engineering is proud to be the world's most experienced
provider of these rare
treasures. We
offer a wide selection of 2D and 3D figures ranging in size from
affordable 2 x 2 inch specimens through museum quality figures
as large as 24 inches by 36 inches. Please visit our galleries to see the world's most beautiful Captured Lightning sculptures:
Everyone is a genius at least once a year.
The real geniuses simply have their bright ideas closer together.
– G.C. Lichtenberg
Thunder is good; thunder is impressive. But it is the
lightning that does the work. - Mark Twain
References and Further Reading: 1. Gross, Bernard, "Irradiation Effects in Plexiglas", Journal of Polymer Science, Volume 27, 1958, Issue 115, Pages 135 - 143 2.
Hashishes. Yuzo, "Two Hundred Years of Lichtenberg Figures", Journal of
Electrostatics, Volume 6, Issue 1 , February 1979, Pages 1-13
3. Chadwick, K. H., "The Effect of Light Exposure on the Optical
Density of Irradiated Clear Polymethylmethacrylate", 1972 Phys. Med.
Biol. 17, Pages 88-93 4.
Chadwick, K. H., and Leenhouts, H. P., "Fading of
radiation-induced optical density in polymethylmethacrylate on oxygen
diffusion", Phys. Med. Biol. 15 No 4 (October, 1970), Pages 743-744
5. L. Niemeyer, L. Pietronero*, and H. J. Wiesmann, "Fractal Dimension
of Dielectric Breakdown", Phys. Rev. Lett. 52, Pages 1033–1036 (1984) 6.
Gardner, Donald G., et. al., "Radiation-induced changes in the index of
refraction, density, and dielectric constant of poly(methyl
methacrylate)", Journal of Applied Polymer Science, Volume 11, Issue 7,
July 1967, Pages 1065-1078 7.
Akishin, A.A.; Tseplyaev, L.I., "Edge effect in radiation-charge
dielectric materials", Physics and Chemistry of Materials Treatment, v
31, n 1, Jan.-Feb. 1997, p 30-1. A similar paper is also contained
within the book "Effects of Space Conditions on Materials", Akishin, A.
I., Nova Science Publishers, 2001, ISBN 1590330285
8. Fothergill, J.C.; Dissado, L.A.; Sweeney, P.J.J., "A
discharge-avalanche theory for the propagation of electrical trees. A
physical basis for their voltage dependence", Dielectrics and
Electrical Insulation, IEEE Transactions on, Volume 1, Issue 3 , June
1994, Pages 474 - 486
9. R. A. Galloway, T. F. Lisanti and M. R. Cleland, "A new 5 MeV –300
kW Dynamitron for radiation processing", Radiation Physics and
Chemistry, Volume 71, Issues 1-2, September-October 2004, Pages 551-553
10. Sessler, G.M.. "Charge distribution and transport in polymers",
IEEE Transactions on Dielectrics and Electrical Insulation, Volume 4 ,
Issue 5 , Oct. 1997
Pages 614 - 628 11. Karczmarczuk, Jerzy, "Dendrites in Nature and in Computer", Foton 84/SPECIAL ISSUE, Spring 2006 12.
C. M. Foust, General Electric Review: Instruments for Lightning
Measurements (Includes Klydonograph and Lichtenberg Figures), Volume
34, #4, April, 1931, Pages 235-246
13. Watson, Alan and Dow, Julian, "Emission Processes Accompanying
Megavolt Electron Irradiation of Dielectrics", Journal of Applied
Physics, December 1968, Volume 39, Issue 13, pages 5935-5940
14. Fujimori, S., "Fractal properties of breakdowns", Properties and
Applications of Dielectric Materials, 1988. Proceedings, Second
International Conference on Properties and Applications of, 12-16
Sept. 1988, Volume 2, Pages 519 - 522
15. Domart, Yves, M. D., Garet, Emmanuel, M.D., "Lichtenberg Figures
Due to a Lightning Strike", New England Journal of Medicine, Volume
343:1536, November 23, 2000, Number 21, Images in Clinical Medicine
16. H. Hiraoka, "Radiation Chemistry of Poly(methacrylates)", Radiation Chemistry, March 1977, pages 121-130
17. Brown, R. G., "Time and Temperature Dependence of Irradiation
Effects in Solid Dielectrics", Journal of Applied Physics,
September 1967, Volume 38, Issue 10, pages 3904-3907
18. Yu. S. Deev, M. S. Kruglyi, V. K. Lyapidevskii and V. I. Serenkov,
"Mechanism underlying the formation of dendritic or tree-like channels
in a dielectric irradiated with charged particles", Atomic
Energy, Volume 29, Number 4, October, 1970, pages 1037-1040
19. Ebert, Ute and
Arrayas, Manuel, "Pattern Formation in Electric Discharges", p. 270 -
282 in: Coherent Structures in Complex Systems, eds.: D. Reguera et
al., Lecture Notes in Physics 567 (Springer, Berlin 2001)
20. Yu.N.
Vershinin, S.V. Barakhvostov, "Electron Processes in the Pulse
Breakdown of Solid Dielectrics", 3rd International Conference on
“Technical and Physical Problems in Power Engineering”, (TPE-2006), May
29-31, 2006 - Gazi University, Ankara, Turkey (covers detonation theory of high field breakdown in solid dielectrics) 21.
Vershinin, Yu. N., "Parameters of Electronic Detonation in Solid
Dielectrics", Technical Physics, Vol. 47, No. 12, 2002, pages 1524–1528.
Translated from Zhurnal TekhnicheskoÏ Fiziki, Vol. 72, No. 12,
2002, pp. 39–43, ISSN: 10637842 22. N, I, Kuskova, "Spark Discharges in Condensed Media", Technical Physics, Volume 46, Number 2, 2001, pages 182-185
23. Theodore Gray, "Theo Gray's Mad Science: Experiments You Can Do At Home - But Probably Shouldn't", Black Dog & Leventhal Publishers, 2009, ISBN 978-1579127916
24. Jen-Huang Huang, Jeongyun Kim, et al, "Rapid Fabrication of
Bio-inspired 3D Microfluidic Vascular Networks", Journal of Advanced
Materials, Volume 21,Issue 35, pages 1-5, DOI: 10.1002/adma.200900584
