What Are Lichtenberg figures?
Our Captured Lightning® sculptures are technically known as "Lichtenberg Figures". Lichtenberg figures are branching, tree-like or fern-like patterns that created by 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, and is reported in his memoir: Super nova methodo naturam ac motum fluidi electrici investigandi (Göttinger Novi Commentarii, Göttingen, 1777). 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 captured by Dr. Lichtenberg are shown below.

Positive Lichtenberg figure	Negative Lichtenberg figure

Later researchers included Gaston Planté (mid 1850's),  Thomas Burton Kinraide (late 1800's), Dr. 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 the peak voltage and polarity of abnormal transients caused when lightning struck 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 various polymers (plastics) by injecting them with high energy electrons using a linear accelerator (LINAC). The techniques that we use to make our Captured Lightning® Sculptures builds upon the original theories and techniques discovered by Dr. Gross. The resulting 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 sculptures. We start with specially cut and polished clear plastic material, (polymethylmethacrylate, or PMMA). This material is commonly called acrylic, or various trade names such as Lucite, Plexiglas, or Perspex. Acrylic was selected because it has a unique combination of optical clarity and superior electrical and mechanical properties. Other clear polymers, such as polycarbonate (PC), polystyrene (PS) , polyethylene terephthalate (PET), and polyvinyl chloride (PVC) also work to varying degrees. Some of these 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 are 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 electrons will penetrate. As the specimen is irradiated, huge numbers of electrons accumulate inside the acrylic, creating a cloud-like layer of excess negative electrical charge called a space charge.  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. 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.

As the space charge grows, the resulting electrical field also increases. Eventually, the electrical stress from the increasing electrical 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). 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. 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(!), and thousands of electrically conductive branches feed current into a brilliant "lightning bolt" that exits the acrylic. Although pictures of the discharge seem to suggest that we are injecting a high voltage into the block, in reality we are removing high voltage already stored within the block. 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 permanent fingerprints in the acrylic, forming a branching "lightning fossil" within. The high current electrical discharges may reach hundreds or even thousands of amperes. The hot plasma 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 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 more positive versus the space charge, and our Captured Lightning® sculptures are actually "positive" Lichtenberg figures.

Actual discharge current measurements... and a paradox
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 with copper foil plates that made physical contact with the large surfaces of the charged acrylic specimen. A heavily insulated wire connected the pair of foil plates to the sharp tool which was used to discharge the specimen. This wire was also passed through the center of an Ion Physics 50 kA wideband current transformer (CT). The current transformer transformed the short discharge current pulse that flowed through the wire into a voltage pulse that could be 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 lasted for only 120 nanoseconds (billionths of a second)! For the specimen shown 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 trees propagated via a series of advancing waves. Each current peak reflects a surge of newly conducting channels ("streamers") blasting their way ahead and into previously untapped reservoirs of charge in the acrylic, 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 8.5 x 10⁵ and 1.3 x 10⁶  meters/second (526 and 790 miles/second!). However, pauses between successive current surges suggest that the peak streamer velocity during growth phases was even faster. Surprisingly, the average streamer velocity within the specimen was comparable to the velocity of positive streamers in air.

However, this creates a paradox, since the measured 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 should be limited to the Rayleigh speed (i.e., the speed of sound) within the material, or 1.614 km/second for PMMA. The current waveform below clearly demonstrates that the chains of cracks and gas channels were fully developed within the acrylic at a rate that's 800 times faster than it should be from classical materials theory. Energy from the intense internal electrical field is apparently converted into electronic breakdown of the PMMA and a "wave" of microcracks that propagate through the charge layer at hypersonic speed. This is an area ripe for future research. In any event, the discharge process creates a powerful shockwave (a loud BANG), a brilliant, miniature, blue-white "lightning" flash, and results in objects of incredible beauty.

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 often 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 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 video camera 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 tiny 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 branching patterns which tend to look similar at various scales of magnification. This self-similar property suggests that Lichtenberg figures can be modeled using a branch of mathematics called Fractal Geometry. Self similarity is a key property of fractals. Our Lichtenberg Figures show a range of fractal patterns depending upon the magnitude of charge injected into the acrylic and how and when the specimens is discharged. Branching figures are technically called "dendritic" or "arborescent" (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 the leftmost figure 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 the center example below. If premature breakdown occurs as we are actively irradiating a specimen, tangled "chaotic" discharges occur. Some specimens show combinations of these basic patterns. 

(Click for larger image) Densely Dendritic Discharges (higher charge density)

(Click for larger image) Dendritic Discharges (lower charge density)

(Click for larger image) Chaotic Discharges (prematurely discharged)

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, branching tree limbs, and the arteries, veins, and capillaries within your body.

It has recently been discovered that Lichtenberg figures can be modeled using 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. 

Solarization and other effects:
During irradiation, the acrylic glows a brilliant blue-white color. Although radiation chemistry studies suggest that this may be a combination of 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 "leaks away" to the outside surfaces. This reduces the amount of stored charge along the perimeter to the point where the 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 the temporary trapping of ionic charges within the molecular structure of the PMMA. Solarization normally occurs only in the region between the surface that was irradiated by the electron beam and the discharge layer.  During irradiation, the electrons were initially traveling at about 99% of the speed of light. As they penetrate the specimen, they collide with acrylic molecules, 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 this 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 (250 - 400 nm). This causes solarized regions to appear initially as a lime green or amber color. Some electrons may become trapped for months, perhaps years, afterwards, forming color centers which contribute to the solarization.

Many irradiated specimens initially turn a bright lime green color which, over a period of minutes to hours, fades to an amber color. This may take months, or even years, to fade away. The fading process can be accelerated by gently heating the block in the presence of oxygen, or by placing the specimen in bright light or ultraviolet light. Most older Lichtenberg figures may no longer show any solarization, but some show slight "fogging" from irradiation damage. Some specimens show little initial solarization, while a small number of specimens appear to permanently retain their amber color. Most specimens also exhibit slight changes in refractive index, especially near the Lichtenberg discharge region. These behavioral differences are thought to be due to variations in the acrylic blends used by various manufacturers, permanent irradiation-induced changes to the polymeric structure of the acrylic, and residual mechanical stresses near the discharge fractures. Residual stresses within a sculpture 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 polarizer.

Natural Lichtenberg figures - fulgurites and lightning discharges
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 channel 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", or "keraunographic markings". Although the exact causes are 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 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 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.

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 often quite similar. So it should not be surprising that the branching forms of natural lightning also have fractal characteristics.  This similarity can also be observed during "anvil crawler"  and horizontal "spider lightning".  Spider lightning follows a positively charged cloud layer, and the slowly propagating discharges can crawl across the sky for 30-40 miles - literally spanning from horizon to horizon.

Similar shapes occur when thunderstorms generate conductive leaders that propagate downward from a charged cloud to the ground below. When one of these connects with an unfortunate object on the ground, a high current surge rushes through the completed path as a Cloud-to-Ground (CG) lightning strike. An exceptional example downward propagating positive leaders was recently 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 rare positive lightning bolt. Positive lightning is a significantly rarer (and considerably more dangerous) form of lightning versus negative lightning. The "slow motion" video (below) shows the air breaking down, forming glowing conductive plasma paths (called leaders) that fan downward  from a huge reserve of positive charge within the cloud above. The glowing positive leaders tips smoothly propagate, unlike negative lightning which progresses in a series of jumps (called stepped leaders). Once one of the descending leaders finally connects with the Earth below, it 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), so the actual elapsed time in the following clip was only a little longer that three thousandths of a second. The estimated speed of the propagating leaders was between 30,000 and 650,000 meters/second. This clip even has a single frame which captures the beginning of the return stroke from the Earth going back up the leader channel. And, even at the majestic scale of natural lightning, you can easily 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 often lasts for many hundreds of 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 YouTube.

Lichtenberg Figures can also be seen 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)

Holding a Lichtenberg Figure is about the closest you can come to holding fossilized lightning in your hand - Captured Lightning® is indeed an apt description. 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, and 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 visit our galleries to see the world's most beautiful Lichtenberg figures:

Gallery 1     Gallery 2     Special Eye Candy Page

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

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, 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", Dielectrics and Electrical Insulation, IEEE Transactions on, 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 Revew: Instruments for Lightning Measurements (Includes Klydonograph and Lichtenberg Figures)
13. Watson, Alan and Dow, Julian, "Emission Processes Accompanying Megavolt Electron Irradiation of Dielectrics", Journal of Applied Physics, December 1968, Volume 39, Issue 13, pp. 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, Pages:519 - 522 vol.2
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
17. Brown, R. G., "Time and Temperature Dependence of Irradiation Effects in Solid Dielectrics",  Journal of Applied Physics, September 1967, Volume 38, Issue 10, pp. 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 
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)

Download a one-page condensed explanation (377 kB PDF file)
Download a one-page explanation in German (translated by Harry Meier)

Purchase your very own Lichtenberg Figures