Lichtenberg figure
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A Lichtenberg figure (German ''Lichtenberg-Figuren''), or Lichtenberg dust figure, is a branching
electric discharge An electric discharge is the release and transmission of electricity in an applied electric field through a medium such as a gas (ie., an outgoing flow of electric current through a non-metal medium).American Geophysical Union, National Research C ...
that sometimes appears on the surface or in the interior of
insulating materials This is a list of insulation materials used around the world. Typical R-values are given for various materials and structures as approximations based on the average of available figures and are sorted by lowest value.'' R-value at 1 n'' giv ...
. Lichtenberg figures are often associated with the progressive deterioration of high voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within insulating materials often provides engineers with valuable insights for improving the long-term reliability of high-voltage equipment. Lichtenberg figures are now known to occur on or within solids, liquids, and gases during
electrical breakdown Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
. Lichtenberg figures are natural phenomena which exhibit
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
properties.


History

Lichtenberg figures are named after the German physicist
Georg Christoph Lichtenberg Georg Christoph Lichtenberg (1 July 1742 – 24 February 1799) was a German physicist, satirist, and Anglophile. As a scientist, he was the first to hold a professorship explicitly dedicated to experimental physics in Germany. He is remembered for ...
, who originally discovered and studied them. When they were first discovered, it was thought that their characteristic shapes might help to reveal the nature of positive and negative electric "fluids". In 1777, Lichtenberg built a large
electrophorus In electromagnetism, an electrophorus or electrophore is a simple, manual, capacitive, electrostatic generator used to produce charge via the process of electrostatic induction. A first version of it was invented in 1762 by Swedish professor Jo ...
to generate high
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
static electricity Static electricity is an imbalance of electric charges within or on the surface of a material or between materials. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is na ...
through
induction Induction, Inducible or Inductive may refer to: Biology and medicine * Labor induction (birth/pregnancy) * Induction chemotherapy, in medicine * Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell t ...
. After discharging a high voltage point to the surface of an insulator, he recorded the resulting radial patterns by sprinkling various powdered materials onto the surface. By then pressing blank sheets of paper onto these patterns, Lichtenberg was able to transfer and record these images, thereby discovering the basic principle of modern
xerography Xerography is a dry photocopying technique. Originally called electrophotography, it was renamed xerography—from the roots el, ξηρός, label=none ''xeros'', meaning "dry" and -γραφία ''-graphia'', meaning "writing"—to emphasize ...
. This discovery was also the forerunner of the modern day science of
plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...
. Although Lichtenberg only studied two-dimensional (2D) figures, modern high voltage researchers study 2D and 3D figures (
electrical tree In electrical engineering, treeing is an electrical pre-breakdown phenomenon in solid insulation. It is a damaging process due to partial discharges and progresses through the stressed dielectric insulation, in a path resembling the branches of ...
s) on, and within, insulating materials.


Formation

Two-dimensional (2D) Lichtenberg figures can be produced by placing a sharp-pointed needle perpendicular to the surface of a non-conducting plate, such as of
resin In polymer chemistry and materials science, resin is a solid or highly viscous substance of plant or synthetic origin that is typically convertible into polymers. Resins are usually mixtures of organic compounds. This article focuses on natu ...
,
ebonite Ebonite is a brand name for a material generically known as hard rubber, and is obtained via vulcanizing natural rubber for prolonged periods. Ebonite may contain from 25% to 80% sulfur and linseed oil. Its name comes from its intended use as a ...
, or
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
. The point is positioned very near or contacting the plate. A source of high voltage such as a
Leyden jar A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typi ...
(a type of
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
) or a
static electricity Static electricity is an imbalance of electric charges within or on the surface of a material or between materials. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is na ...
generator is applied to the needle, typically through a
spark gap A spark gap consists of an arrangement of two conducting electrodes separated by a gap usually filled with a gas such as air, designed to allow an electric spark to pass between the conductors. When the potential difference between the conduct ...
. This creates a sudden, small
electrical discharge An electric discharge is the release and transmission of electricity in an applied electric field through a medium such as a gas (ie., an outgoing flow of electric current through a non-metal medium).American Geophysical Union, National Research ...
along the surface of the plate. This deposits stranded areas of charge onto the surface of the plate. These electrified areas are then tested by sprinkling a mixture of powdered flowers of
sulfur Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula ...
and red lead (Pb3O4 or lead tetroxide) onto the plate. During handling, powdered sulfur tends to acquire a slight negative charge, while red lead tends to acquire a slight positive charge. The negatively electrified sulfur is attracted to the positively electrified areas of the plate, while the positively electrified red lead is attracted to the negatively electrified areas. In addition to the distribution of colors thereby produced, there is also a marked difference in the form of the figure, according to the polarity of the electrical charge that was applied to the plate. If the charge areas were positive, a widely extending patch is seen on the plate, consisting of a dense nucleus, from which branches radiate in all directions. Negatively charged areas are considerably smaller and have a sharp circular or fan-like boundary entirely devoid of branches. Heinrich Rudolf Hertz employed Lichtenberg dust figures in his seminal work proving
Maxwell's Maxwell's, last known as Maxwell's Tavern, was a bar/restaurant and music club in Hoboken, New Jersey. Over several decades the venue attracted a wide variety of acts looking for a change from the New York City concert spaces across the river. Ma ...
electromagnetic wave theories. If the plate receives a mixture of positive and negative charges as, for example, from an induction coil, a mixed figure results, consisting of a large red central nucleus, corresponding to the negative charge, surrounded by yellow rays, corresponding to the positive charge. The difference between positive and negative figures seems to depend on the presence of
air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
; for the difference tends to disappear when the experiment is conducted in
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
. Peter T. Riess (a 19th-century researcher) theorized that the negative electrification of the plate was caused by the friction of the water vapour, etc., driven along the surface by the
explosion An explosion is a rapid expansion in volume associated with an extreme outward release of energy, usually with the generation of high temperatures and release of high-pressure gases. Supersonic explosions created by high explosives are known ...
which accompanies the disruptive discharge at the point. This electrification would favor the spread of a positive, but hinder that of a negative discharge. It is now known that electrical charges are transferred to the insulator's surface through small spark discharges that occur along the boundary between the gas and insulator surface. Once transferred to the insulator, these excess charges become temporarily stranded. The shapes of the resulting charge distributions reflect the shape of the spark discharges which, in turn, depend on the high voltage polarity and pressure of the gas. Using a higher applied voltage will generate larger diameter and more branched figures. It is now known that positive Lichtenberg figures have longer, branching structures because long sparks within air can more easily form and propagate from positively charged high voltage terminals. This property has been used to measure the transient voltage polarity and magnitude of lightning surges on electrical power lines. Another type of 2D Lichtenberg figure can be created when an insulating surface becomes contaminated with semiconducting material. When a high voltage is applied across the surface, leakage currents may cause localized heating and progressive degradation and charring of the underlying material. Over time, branching, tree-like carbonized patterns are formed upon the surface of the insulator called
electrical tree In electrical engineering, treeing is an electrical pre-breakdown phenomenon in solid insulation. It is a damaging process due to partial discharges and progresses through the stressed dielectric insulation, in a path resembling the branches of ...
s. This degradation process is called ''tracking''. If the conductive paths ultimately bridge the insulating space, the result is catastrophic failure of the insulating material. Some artists purposely apply salt water to the surface of wood or cardboard and then apply a high voltage across the surface to generate complex carbonized 2D Lichtenberg figures on the surface.


Fractal similarities

The branching, self-similar patterns observed in Lichtenberg figures exhibit
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
properties. Lichtenberg figures often develop during the
dielectric breakdown Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
of solids, liquids, and even gases. Their appearance and growth appear to be related to a process called
diffusion-limited aggregation Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is app ...
(DLA). A useful macroscopic model that combines an electric field with DLA was developed by Niemeyer, Pietronero, and Weismann in 1984, and is known as the
dielectric breakdown model Dielectric breakdown model (DBM) is a macroscopic mathematical model combining the diffusion-limited aggregation model with electric field. It was developed by Niemeyer, Pietronero, and Weismann in 1984. It describes the patterns of dielectric bre ...
(DBM). Although the electrical breakdown mechanisms of air and PMMA plastic are considerably different, the branching discharges turn out to be related. The branching forms taken by natural lightning also have fractal characteristics.


Constructual law

Lichtenberg figures are examples of natural phenomena which exhibit
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
properties. The emergence and evolution of these and the other tree-like structures that abound in nature are summarized by the
constructal law Adrian Bejan is an Romanian-American, American professor who has made contributions to modern thermodynamics and developed his constructal law. He is J. A. Jones Distinguished Professor of Mechanical Engineering at Duke University and author of ...
. First published by Duke professor
Adrian Bejan Adrian Bejan is an American professor who has made contributions to modern thermodynamics and developed his constructal law. He is J. A. Jones Distinguished Professor of Mechanical Engineering at Duke University and author of the books Design i ...
in 1996, the constructal law is a first principle of physics which summarizes the tendency in nature to generate configurations (patterns, designs) that facilitate the free movement of the imposed currents that flow through it. The constructal law predicts that the tree-like designs described in this article should emerge and evolve to facilitate the movement (point-to-area) of the electrical currents flowing through them.


Natural occurrences

Lichtenberg figures are fern-like patterns that may appear on the skin of
lightning strike A lightning strike or lightning bolt is an electric discharge between the atmosphere and the ground. Most originate in a cumulonimbus cloud and terminate on the ground, called cloud-to-ground (CG) lightning. A less common type of strike, ground- ...
victims and typically disappear in 24 hours. A lightning strike can also create a large Lichtenberg figure in grass surrounding the point struck. These are sometimes found on
golf course A golf course is the grounds on which the sport of golf is played. It consists of a series of holes, each consisting of a tee box, a fairway, the rough and other hazards, and a green with a cylindrical hole in the ground, known as a "cup". Th ...
s or in grassy meadows. Branching root-shaped "
fulgurite Fulgurites (), commonly known as "fossilized lightning", are natural tubes, clumps, or masses of sintered, vitrified, and/or fused soil, sand, rock, organic debris and other sediments that sometimes form when lightning discharges into ground. ...
" mineral deposits may also be created as
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class of s ...
and
soil Soil, also commonly referred to as earth or dirt, is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Some scientific definitions distinguish ''dirt'' from ''soil'' by restricting the former te ...
is fused into glassy tubes by the intense heat of the current.
Electrical treeing In electrical engineering, treeing is an electrical pre-breakdown phenomenon in solid insulation. It is a damaging process due to partial discharges and progresses through the stressed dielectric insulation, in a path resembling the branches of ...
often occurs in high-voltage equipment prior to causing complete breakdown. Following these Lichtenberg figures within the insulation during post-accident investigation of an insulation failure can be useful in finding the cause of breakdown. An experienced high-voltage engineer can see from the direction and the shape of trees and their branches where the primary cause of the breakdown was situated and possibly find the initial cause. Broken-down transformers, high-voltage cables, bushings and other equipment can usefully be investigated in this manner. The insulation is unrolled (in the case of paper insulation) or sliced in thin slices (in the case of solid insulating materials). The results are then sketched or photographed to create a record of the breakdown process.


In insulating materials

Modern Lichtenberg figures can also be created within solid insulating materials, such as acrylic (polymethyl methacrylate or
PMMA PMMA may refer to: * para-Methoxymethamphetamine, a stimulant drug * Philippine Merchant Marine Academy The Philippine Merchant Marine Academy ( fil, Akademiya sa Bapor Pangkalakalan ng Pilipinas) also referred to by its acronym PMMA) is a ma ...
) or glass by injecting them with a beam of high speed
electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
from a linear electron beam accelerator (or
Linac A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear be ...
, a type of
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...
). Inside the Linac, electrons are focused and accelerated to form a beam of high speed particles. Electrons emerging from the accelerator have energies up to 25 MeV and are moving at an appreciable fraction (95 - 99+ percent) of the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
( relativistic velocities). If the electron beam is aimed towards a thick acrylic specimen, the electrons easily penetrate the surface of the acrylic, rapidly decelerating as they collide with molecules inside the plastic, finally coming to rest deep inside the specimen. Since acrylic is an excellent electrical insulator, these electrons become temporarily trapped within the specimen, forming a plane of excess negative charge. Under continued irradiation, the amount of trapped charge builds, until the effective voltage inside the specimen reaches millions of volts. Once the electrical stress exceeds the
dielectric strength In physics, the term dielectric strength has the following meanings: *for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and beco ...
of the plastic, some portions suddenly become conductive in a process called
dielectric breakdown Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
. During breakdown, branching tree or fern-like conductive channels rapidly form and propagate through the plastic, allowing the trapped charge to suddenly rush out in a miniature
lightning Lightning is a naturally occurring electrostatic discharge during which two electric charge, electrically charged regions, both in the atmosphere or with one on the land, ground, temporarily neutralize themselves, causing the instantaneous ...
-like flash and bang. Breakdown of a charged specimen may also be manually triggered by poking the plastic with a pointed conductive object to create a point of excessive voltage stress. During the discharge, the powerful
electric spark An electric spark is an abrupt electrical discharge that occurs when a sufficiently high electric field creates an ionized, electrically conductive channel through a normally-insulating medium, often air or other gases or gas mixtures. Michael F ...
s leave thousands of branching chains of fractures behind - creating a permanent Lichtenberg figure inside the specimen. Although the internal charge within the specimen is negative, the discharge is initiated from the positively charged exterior surfaces of the specimen, so that the resulting discharge creates a positive Lichtenberg figure. These objects are sometimes called ''electron trees'', ''beam trees'', or ''lightning trees''. As the electrons rapidly decelerate inside the acrylic, they also generate powerful
X-rays An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 Picometre, picometers to 10 Nanometre, nanometers, corresponding to frequency, ...
. Residual electrons and X-rays darken the acrylic by introducing defects (color centers) in a process called
solarization The Sabatier effect, also known as pseudo-solarization (or pseudo-solarisation) and erroneously referred to as the Sabattier effect, is a phenomenon in photography in which the image recorded on a negative or on a photographic print is wholly o ...
. Solarization initially turns acrylic specimens a lime green color which then changes to an amber color after the specimen has been discharged. The color usually fades over time, and gentle heating, combined with oxygen, accelerates the fading process.


On wood

Lichtenberg figures can also be produced on wood. The types of wood and grain patterns affect the shape of the Lichtenberg figure produced. By applying a coat of electrolytic solution to the surface of the wood, the resistance of the surface drops considerably. Two electrodes are then placed on the wood and a high voltage is passed across them. Current from the electrodes will cause the surface of the wood to heat up, until the electrolyte boils and the wooden surface burns. Because the charred surface of the wood is mildly conductive, the surface of the wood will burn in a pattern outwards from the electrodes. The process can be dangerous, resulting in deaths every year from electrocution.


See also

*
Crown shyness Crown shyness (also ''canopy disengagement'', ''canopy shyness'', or ''inter-crown spacing'') is a phenomenon observed in some tree species, in which the crowns of fully stocked trees do not touch each other, forming a canopy with channel-like ...
*
Dielectric breakdown model Dielectric breakdown model (DBM) is a macroscopic mathematical model combining the diffusion-limited aggregation model with electric field. It was developed by Niemeyer, Pietronero, and Weismann in 1984. It describes the patterns of dielectric bre ...
*
Fractal curve A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectif ...
*
Kirlian photography Kirlian photography is a collection of photographic techniques used to capture the phenomenon of electrical coronal discharges. It is named after Semyon Kirlian, who, in 1939, accidentally discovered that if an object on a photographic plate is ...
*
Lightning burn Lightning injuries are injury, injuries caused by a lightning strike. Initial symptoms may include heart asystole and respiratory arrest. While the asystole may resolve spontaneously fairly rapidly, the respiratory arrest is typically more prolon ...
*
Patterns in nature Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foa ...
* Diffusion limited aggregation


References


External links

{{Commons category, Lichtenberg figures
What are Lichtenberg Figures and how are they created?




* ttps://web.archive.org/web/20021129224345/http://classes.yale.edu/Fractals/Panorama/Physics/DLA/DBM/DBM.html Dielectric Breakdown Model (DBM)
Trap Lightning in a Block
(DIY Lichtenberg Figure at Popular Science) * Lichtenbergs in acrylic in 3d

(Requires QuickTime VR to view.)


Lichtenberg wood burning With a Welder
Electricity Electrical breakdown Lightning Dielectrics Fractals