This
figure
was created by irradiating a block of Plexiglas with a 5 million
electron volt electron beam on the left side, rotating it 180 degrees,
and then irradiating it on the right side, thereby creating two
independent
internal charge
layers. The right charge layer was then manually discharged, causing a
3-D "lightning storm" inside the rightmost layer, which then spread
into a
series of discharges between
the two layers. The specimen is lit from below by an array of blue
LED's. Unlike low detail laser crystal art, each Lichtenberg specimen
has a unique and incredibly detailed fractal discharge pattern. As they
branch, the discharge channels become increasingly finer, becoming
hairlike as they finally disappear. The
smallest discharges may ultimately go to the molecular level.
(Actual size: 3" x 3" x 2")
What Are Lichtenberg figures? Lichtenberg figures are branching, tree or fern-like patterns that form as the
result of high voltage discharges on the surface of, or within, electrical insulating materials (dielectrics). The first Lichtenberg figures were actually
2-dimensional patterns formed in dust on the surface of charged insulating 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. The basic principles
involved in the formation of these electrostatic figures later evolved
to become modern xerography and the science of plasma physics. Lichtenberg used electrostatic devices to charge the surfaces
of various insulating materials such as resin, glass, or ebonite. He then
sprinkled a mixture of finely powdered sulfur and red lead (lead
tetroxide) onto the surface. The powdered sulfur was attracted to the
positively charged regions and the red lead to negative regions,
thus making the previously hidden regions of charge clearly visible.
Lichtenberg
also observed 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 round or fan-like. By
carefully placing a piece of paper onto the dusted surface, he was able to
transfer these image to the paper, demonstrating what was later to become
the process of Xerography. Drawings of positive and negative figures actually captured by Lichtenberg are shown below.
Positive Lichtenberg figure
Negative Lichtenberg figure
Later researchers included Gaston Planté (mid 1850's), Thomas Burton Kinraide (late 1800's), Carl Edward Magusson, and Dr. Arthur Von Hippel
(1930's+). These researchers used photographic film to directly capture
the 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 electrical discharges) 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.
This
property was used in klydonographs, special recording instruments
that photographically
recorded the size and shape of Lichtenberg figures that appeared during abnormal electrical surges on power lines.Klydonographs allowed lightning researchers and power system designers to
estimate peak voltages
and polarity
of abnormal transients caused by lightning strikes to power lines.
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 often occur during electrical breakdown processes
within most gases, insulating liquids, and solid dielectrics.
Lichtenberg figures can 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 may form on contaminated insulator surfaces, within
dielectrics due to internal defects or voids, or at points where an
insulator has been physically damaged. Considerable pioneering
research on the detailed
behavior of charge storage within dielectrics was performed by Dr.
Bernhard Gross in the middle of the last century. In
the early 1950's, Dr. Gross discovered that internal Lichtenberg figures could be created
within plastic materials by injecting them with high energy electrons using a linear accelerator (LINAC).
The techniques we use to make our Lichtenberg Figures are build upon
the original theories and techniques discovered by Dr. Gross. The resulting Lichtenberg figures are sometimes called electrical
trees, electron trees, beam trees, or spark trees - we call them Captured Lightning.
How do we create our "Captured Lightning" sculptures?
We have continued to develop and refine irradiation and material
processing techniques to create a truly unique line of 2D and 3D Lichtenberg figure sculptures
that we call "Captured LightningTM".
Our Captured LightningTM sculptures are made from specially cut and polished clear plastic (polymethylmethacrylate, or PMMA),
also called acrylic, or by various trade names such as Lucite, Plexiglas, or Perspex. Acrylic
was selected because of the combination of crystal clarity, and its superior electrical
and mechanical properties. Other clear polymers, such as polycarbonate (PC),
polystyrene (PS) , polyethylene terephthalate (PET), and polyvinyl chloride (PVC) will also work to varying degrees. Some
materials even develop dark, or even black (carbonized), trees.
Our sculptures are created
by injecting acrylic specimens with high velocity electrons.
Electrons
are tiny, negatively charged particles that orbit the nucleus of the atoms that make up all condensed matter.
An electron beam accelerator is used to accelerate
and focus electrons into a high-energy beam. The energy of the accelerated electrons is measured in millions of electron Volts (or MeV). The
LINAC that we use accelerates electrons to a kinetic
energy
of between three and five MeV. At these energies, electrons leaving the accelerator were traveling at relativistic velocities that are between 98.5% and
99.6% the speed of light.
As the specimen is irradiated
by the beam, electrons are driven
deep inside the acrylic. The penetration depth is determined by
the
electron beam's
initial energy, the material's dielectric properties, and its density.
The higher the electron beam energy, the deeper the penetration. As
the specimen is irradiated, huge numbers
of electrons accumulate inside the acrylic, creating a stranded, cloud-like
layer
of excess negative electrical charge called
a space charge. By
carefully changing the orientation of the specimens and passing them
through the beam in two or more passes, complex 3-dimensional space
charge regions can be produced.
Since acrylic is an excellent dielectric, most of the injected electrons cannot escape, so they accumulate under continued irradiation, causing a huge negative space charge to develop inside the specimen.
As the space charge grows, the resulting electrical field also
increases.
Eventually, the stress from the huge electric field 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 (a process
called ionization). The newly-freed electrons are also accelerated by the
electric field, ionizing even more acrylic
molecules, and creating additional free electrons in a runaway process. Electrically
conductive channels rapidly form within the acrylic as the material undergoes dielectric breakdown.
Once breakdown occurs, the previously trapped charges suddenly rush out, accompanied by a
loud bang(!), as thousands of electrically conductive branches feed current into a brilliant "lightning
bolt" that exits the acrylic. Dielectric breakdown typically occurs within an incredibly short amount of time.
For example, the electrical discharge within a 2 inch square specimens may only last for 20
billionths of a second! The following image shows a 4 inch square specimen as it was being discharged:
(Photo courtesy of Theodore Gray)
The
escaping lightning bolts leave their fingerprints in the acrylic,
forming a permanent "lightning fossil" within. The high current
electrical
discharge current, which may reach hundreds or even thousands of
amperes, causes the acrylic to melt and fracture along each path, and
the higher
current "roots" may even
char slightly.
The
exit point of the discharge appears as a small hole 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. The defect causes a localized concentration of
the electric field, creating a "weak link" where the breakdown process
can begin. Interestingly, even though we've injected a huge negative charge into the
specimens, the electrical breakdown process originates from points which
are electrically positive, and the resulting discharges are
actually "positive" Lichtenberg figures.
Actual discharge current measurements... and a mystery
During
our 2007 production run, we were able to capture the shape of
the current waveform as we discharged a number of 4" x 4" x
3/4" specimens (similar to the specimen above). A special holding
fixture was constructed that had copper foil plates that made physical contact with both of the large surfaces of the
charged acrylic
specimen. A short, heavily insulated wire connected the pair of foil
plates to the pointed tool which was used to discharge the specimen.
The
wire was also passed through the center of an Ion Physics 50 kA
wideband
current transformer
(CT). The current transformer transformed the discharge current pulse
that flowed through the wire
into a voltage signal that was then captured and stored in a high speed
Tektronix digital
storage oscilloscope. The digitized waveform data was subsequently
analyzed using an Excel spreadsheet in order to
recreate the following waveform.
We
found that, for 4" x 4" specimens, the overall discharge
lasts only about 120 nanoseconds (billionths of a second)! For the
specimen below, the
peak current was almost 600 amperes, and was seen to consist of four
separate current peaks. Other specimens showed between three and seven
peaks. This suggests that the electrical tree propagates via a series
of advancing waves. Each peak reflects a surge of newly conducting
channels ("streamers") blasting their way into previously
untapped reservoirs of
charge in the acrylic ahead, followed by a brief pause, then another
surge, etc. Since the
overall discharge propagated a distance of about 4 inches within 80-120
billionths of
a second, the average streamer velocity was between 0.85 and
1.3 million
meters/second (between 526 and 790 miles/second!). However, pauses
between successive surges suggest that streamer velocity during the
growth phase was considerably faster. This creates a paradox, since
even the (slower) average spark
propagation velocity is still approximately 800 times the speed of
sound within
PMMA. This is inconsistent with classical crack propagation theory,
which predicts that the maximum crack propagation speed within a solid
should be limited to the Rayleigh speed (i.e., speed of vibrating
molecules within the material, or 1.614 km/second for PMMA). The
current waveform clearly demonstrates heavy electrical conduction
(apparently through chains of cracks and gas channels within the PMMA)
occurs supersonically, at ~800 times the maximum velocity predicted by
existing materials theory. This is an area ripe for future research. In
any event, the discharge process
certainly creates a powerful shockwave (a loud BANG) and a brilliant,
miniature, blue-white "lightning" flash.
After
the main discharge, there are often tens or hundreds of smaller
secondary electrical
discharges as small pockets of residual charge redistribute
themselves
within the specimen. Larger figures sometimes sparkle and sizzle for
tens of seconds
afterwards, making a sound similar to frying bacon, and intermittent
sparking has been observed 15 - 30 minutes later. These smaller
discharges often sting our fingers when the partially discharged
specimens are handled. Click on the
following image to see some high resolution video taken during our
November, 2007 production run showing 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
Video clip of a huge 18" Lichtenberg figure being created:
Following
is
another video clip of a larger (18" x 18" x 1") specimen being discharged. This was captured during our 2005
production
run. The estimated potential of the internal charge plane was 2.2
million volts. Because of it's larger size, this specimen had
considerably more
stored electrostatic energy, and the discharge was quite loud and very
bright! The actual discharge, although very brief, saturated the
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 tiny chonchoidal
fractures. These
shell-shaped
fractures are characteristic of the way noncrystalline
(amorphous)
materials fracture when stressed beyond their breaking point. Since
these tiny fractures reflect light like small mirrors, illuminating the
figures through the edges causes the entire figure to glow brilliantly
with the reflected color(s) of the external light source.
Lichtenberg figures are fractals
Lichtenberg figures exhibit self-similar branching patterns which
tend
to look similar at various scales of magnification. This property permits Lichtenberg figures to be described and modeled
using a branch of mathematics called Fractal Geometry. Self similarity is a key property of fractals.
Self similarity can easily be seen in the following sequence of zooms
from a 12" x 12" Lichtenberg Figure as the branching become finer and
hairlike, ultimately disappearing.
It has recently been discovered that Lichtenberg figures can be modeled as a process called "Diffusion Limited Aggregation" or DLA. A useful macroscopic model that combines an electric field with DLA is called the Dielectric Breakdown Model or DBM.
The dielectric breakdown model appears to describe the branching growth that
characterize the dielectric breakdown process within solids, liquids, and gases.
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 actually quite similar. So it should not be surprising
that the
branching forms of lightning also have fractal
characteristics. The internal discharges
within charge bearing regions of a thundercloud that feed current into
the main lightning discharge (called J-Streamers and K-Streamers) are quite similar in appearance
to Lichtenberg Figure discharges. This similarity can also be observed during cloud to cloud "anvil crawler" lightning. In fact, holding a Lichtenberg Figure is about the closest
you can
come to holding fossilized lightning in your hand.
Solarization and other effects: During
irradiation, the acrylic is observed to glow a brilliant blue-white
color. Although radiation chemistry studies suggest that this may be luminescence or Cherenkov radiation, the reason(s) are not fully understood. You may also notice that our specimens have a
discharge-free zone along all of the outside edges. This is because PMMA
is not a perfect insulator, so some of
the internal charge can "leak away" to the outside surfaces. This reduces the amount of stored charge along the
perimeter to the point where he electrical field is no longer sufficient to break down the
acrylic. You may also notice that a portion of the acrylic has
an amber or greenish tint. This coloration is called solarization.
Solarization is
thought to be caused by the formation of defects through electron
collisions, high energy x-rays, and temporary trapping of ionic charges
within the molecular structure of
the PMMA.
Solarization is usually confined only to the portion of the acrylic
that was in the direct path of the decelerating electrons. Electrons within the beam are initially traveling at
~99% of the speed of light. As they collide with acrylic molecules, they rapidly come 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 their energy in the form of heat and powerful X-rays. As the acrylic absorbs electrons and x-rays, various physical and chemical reactions occur that alter its optical properties. Although
the specific causes of solarization are not fully understood, there
is evidence that irradiation creates unstable, or longer-lived
"metastable", compounds that preferentially absorb light at the blue end of
the spectrum. This causes solarized regions to appear as an amber or lime green color.
While much of the solarization fades over a period of hours, the remainder may take months, or even years, to fade.
The fading
process can be accelerated by gently heating the block in the
presence of oxygen. Most
older Lichtenberg figures no longer show any solarization,
but they may still show a bit of
"fogging" above the discharge layer. Some exceptional specimens show
virtually no initial solarization, while other specimens retain
their color indefinitely. Most specimens also exhibit
slight changes in their refractive index, especially near the Lichtenberg discharge region. These
differences are
thought to be due to variations in the acrylic blend used
by various manufacturers, permanent irradiation-induced changes to the
structure of the acrylic, or residual mechanical stresses near the discharge fractures.
Natural Lichtenberg figures and fulgurites
Occasionally, nature also creates "fossilized lightning". Called fulgurites,
these
are hollow, 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 channel of 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 humans who have been struck by lightning. The
unfortunate 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
The
medical term for this phenomenon is "arborescent lightning burn" or
"arborescent erythema". Although their cause is subject to
some debate,
lightning flowers appear to be the result
of damage to small capillaries under the skin, perhaps caused by the
flow of electrical current
from the stroke, or 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
two days later. A small Lichtenberg figure
has
also been observed at the point
where a high voltage spark penetrated the skin of an unfortunate (but
surviving) local electrical experimenter who took an accidental "hit"
from 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 how similar the above figure appears to the Lichtenberg figure within this specimen (lit from below 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. This
phenomenon can also be seen on a much larger scale at some high energy pulsed
power facilities, where deionized water is often used as a dielectric to briefly store
large amounts of electrical energy. The famous photo below is from Sandia National Laboratory's
mighty Z
Machine, the world's largest pulse generator. After
the completion of a high energy experiment, the water breaks down from the electrical stress,
becoming an electrical conductor that safely dissipates unwanted
residual
energy from the system, and forming Lichtenberg figures that dance along
the water's surface. If you look closely, you'll notice that
many of the radial 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)
Most
of the acrylic Lichtenberg figures shown on our web site were produced
by
irradiating various acrylic shapes using a 5 MeV Continuous Wave (CW)
LINAC - a 150 kW high power electron beam accelerator called a Dynamitron. A few were created using pulsed linear accelerators at significantly higher beam energies (10
- 15 MeV). Lichtenberg figures are completely
safe - they have been electrically discharged and have no residual radioactivity or X-radiation.
And, as with snowflakes, every Lichtenberg Figure is a one-of-a kind treasure.
Following
are a pair 3-D images that can be rotated 360 degrees so that you can fully
enjoy the beauty of our doubly-irradiated Lichtenberg figures. The irradiation process
results in very complex discharges within and
between the two charge layers. Please wait for the images to
completely
download, then drag your mouse to rotate the images for a full 360
degree view. (Warning: you'll need a Cable or DSL connection to view these since
they are each ~6 MB files and will take quite some time to fully load.)
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. Far fewer have ever owned one.
Stoneridge Engineering is proud to be the world's most experienced provider for these beautiful and rare
treasures. We
offer a wide selection of 2D and 3D figures ranging in size from
affordable 2 inch specimens through museum quality figures
as large as 24 inches by 36 inches. Please view our galleries to see the world's most beautiful Lichtenberg figures: Gallery 1Gallery 2
Everyone is a genius at least once a year.
The real geniuses simply have their bright ideas closer together.
– G.C. Lichtenberg