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 Lightning^TM". Our Captured Lightning^TM 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.  

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 1   Gallery 2

Everyone is a genius at least once a year.
The real geniuses simply have their bright ideas closer together.
– G.C. Lichtenberg

Other Links: