Lichtenberg figures are branching electric discharge

Electric discharge

Electric discharge describes any flow of electric charge through a gas, liquid or solid. Electric discharges include:*Electric glow discharge*Electric arc*Electrostatic discharge*Electric discharge in gases*Leader *Partial discharge...

s that sometimes appear on the surface or the interior of insulating materials

Electrical insulation

thumb|250px|[[Coaxial Cable]] with dielectric insulator supporting a central coreThis article refers to electrical insulation. For insulation of heat, see Thermal insulation...

. They are named after the German physicist Georg Christoph Lichtenberg

Georg Christoph Lichtenberg

Georg Christoph Lichtenberg was a German scientist, satirist and Anglophile. As a scientist, he was the first to hold a professorship explicitly dedicated to experimental physics in Germany...

, 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

Electrophorus

An electrophorus is a capacitive generator used to produce electrostatic charge via the process of electrostatic induction. A first version of it was invented in 1762 by Swedish professor Johan Carl Wilcke,...

 to generate high voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 static electricity

Static electricity

Static electricity refers to the build-up of electric charge on the surface of objects. The static charges remain on an object until they either bleed off to ground or are quickly neutralized by a discharge. Static electricity can be contrasted with current electricity, which can be delivered...

 through induction

Electrostatic induction

Electrostatic induction is a redistribution of electrical charge in an object, caused by the influence of nearby charges. Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762. Electrostatic generators, such as the Wimshurst machine, the...

. After discharging a high voltage point to the surface of an insulator, he recorded the resulting radial patterns in fixed dust. 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

Xerography is a dry photocopying technique invented by Chester Carlson in 1938, for which he was awarded on October 6, 1942. Carlson originally called his invention electrophotography...

. This discovery was also the forerunner of modern day plasma physics. Although Lichtenberg only studied 2-dimensional (2D) figures, modern high voltage researchers study 2D and 3D figures (electrical trees) on, and within, insulating materials. Lichtenberg figures are now known to be examples of fractals.

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

Resin

Resin in the most specific use of the term is a hydrocarbon secretion of many plants, particularly coniferous trees. Resins are valued for their chemical properties and associated uses, such as the production of varnishes, adhesives, and food glazing agents; as an important source of raw materials...

, ebonite

Ebonite

Ebonite is a brand name for very hard rubber first obtained by Charles Goodyear by vulcanizing rubber for prolonged periods. It is about 30% to 40% sulfur. Its name comes from its intended use as an artificial substitute for ebony wood...

, or glass

Glass

Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

. The point is positioned very near or contacting the plate. A source of high voltage, such as a Leyden jar

Leyden jar

A Leyden jar, or Leiden jar, is a device that "stores" static electricity between two electrodes on the inside and outside of a jar. It was invented independently by German cleric Ewald Georg von Kleist on 11 October 1745 and by Dutch scientist Pieter van Musschenbroek of Leiden in 1745–1746. The...

 (a type of capacitor

Capacitor

A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

) or a static electricity

Static electricity

Static electricity refers to the build-up of electric charge on the surface of objects. The static charges remain on an object until they either bleed off to ground or are quickly neutralized by a discharge. Static electricity can be contrasted with current electricity, which can be delivered...

 generator, is applied to the needle, typically through a spark gap

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 voltage difference between the conductors exceeds the gap's breakdown voltage, a spark forms,...

. This creates a sudden, small electrical discharge

Electrostatic discharge

Electrostatic discharge is a serious issue in solid state electronics, such as integrated circuits. Integrated circuits are made from semiconductor materials such as silicon and insulating materials such as silicon dioxide...

 to the surface of the plate. This deposits 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

Sulfur or sulphur is the chemical element with atomic number 16. In the periodic table it is represented by the symbol S. It is an abundant, multivalent non-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S8. Elemental sulfur is a bright yellow...

 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.

If the plate receives a mixture of positive and negative charges as, for example, from an induction coil

Induction coil

An induction coil or "spark coil" is a type of disruptive discharge coil. It is a type of electrical transformer used to produce high-voltage pulses from a low-voltage direct current supply...

, 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; for the difference tends to disappear when the experiment is conducted in vacuo

Vacuum

In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

. Riess explains it by the negative electrification of the plate caused by the friction of the water vapour, etc., driven along the surface by the explosion

Explosion

An explosion is a rapid increase in volume and release of energy in an extreme manner, usually with the generation of high temperatures and the release of gases. An explosion creates a shock wave. If the shock wave is a supersonic detonation, then the source of the blast is called a "high explosive"...

 which accompanies the disruptive discharge at the point. This electrification would favor the spread of a positive, but hinder that of a negative discharge. Lichtenberg figures are fully described in his memoir Super nova methodo motum ac naturam fluidi electrici investigandi (Göttinger Novi Commentarii, Göttingen, 1777). It is now known that 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 HV 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.

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 trees. These may ultimately bridge the insulating space, leading to catastrophic failure of the insulating material.

Modern 3D Lichtenberg figures

Modern Lichtenberg Figures can also be created within solid insulating materials, such as acrylic (polymethyl methacrylate or PMMA) or glass by injecting them with a beam of high speed electrons from a linear electron beam accelerator (or Linac

Linear particle accelerator

A linear particle accelerator is a type of particle accelerator that greatly increases the velocity of charged subatomic particles or ions by subjecting the charged particles to a series of oscillating electric potentials along a linear beamline; this method of particle acceleration was invented...

, a type of particle accelerator

Particle accelerator

A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

). 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 25MeV and are moving an appreciable fraction (95 - 99+ percent) of the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 (relativistic

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

 velocities). If the electron beam is aimed towards an acrylic specimen, the electrons easily penetrate the surface of the acrylic, rapidly slowing down 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

Dielectric strength

In physics, the term dielectric strength has the following meanings:*Of an insulating material, the maximum electric field strength that it can withstand intrinsically without breaking down, i.e., without experiencing failure of its insulating properties....

 of the plastic, some portions suddenly become conductive in a process called dielectric breakdown.

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

Lightning is an atmospheric electrostatic discharge accompanied by thunder, which typically occurs during thunderstorms, and sometimes during volcanic eruptions or dust storms...

-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 sparks

Electric spark

An electric spark is a type of electrostatic discharge that occurs when an electric field creates an ionized electrically conductive channel in air producing a brief emission of light and sound. A spark is formed when the electric field strength exceeds the dielectric field strength of air...

 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 beautiful 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. The X-rays darken the acrylic by introducing defects (color centers) in a process called solarization

Solarization

Solarization refers to a phenomenon in physics where a material undergoes a temporary change in color after being subjected to high energy electromagnetic radiation, such as ultraviolet light or X-rays. Clear glass and many plastics will turn amber, green or other colors when subjected to...

. Solarization turns acrylic specimens an amber or brownish color, although older acrylic blends sometimes turn a lime green. The color usually fades over time, and gentle heating, combined with oxygen, accelerates the fading process.

Natural occurrences

Lichtenberg figures may also appear on the skin of lightning

Lightning

Lightning is an atmospheric electrostatic discharge accompanied by thunder, which typically occurs during thunderstorms, and sometimes during volcanic eruptions or dust storms...

 strike victims. These are reddish, fernlike patterns that may persist for hours or days. They are also a useful indicator for medical examiners when determining the cause of death. Lichtenberg figures appearing on people are sometimes called lightning flowers, and they are thought to be caused by the rupture of small capillaries under the skin due to the passage of the lightning current or the shock wave

Shock wave

A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...

 from the lightning discharge as it flashes over the skin. A lightning strike can also create a large Lichtenberg Figure in grass surrounding the point struck. These are sometimes found on golf course

Golf course

A golf course comprises a series of holes, each consisting of a teeing ground, fairway, rough and other hazards, and a green with a flagstick and cup, all designed for the game of golf. A standard round of golf consists of playing 18 holes, thus most golf courses have this number of holes...

s or in grassy meadows. Fulgurite

Fulgurite

Fulgurites are natural hollow glass tubes formed in quartzose sand, or silica, or soil by lightning strikes. They are formed when lightning with a temperature of at least instantaneously melts silica on a conductive surface and fuses grains together; the fulgurite tube is the cooled product...

s may also be created as sand

Sand

Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...

 and soil

Soil

Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

 is fused into glassy tubes by the intense heat of the current.

Electrical treeing

Electrical treeing

Within the field of electrical engineering, treeing is an electrical pre-breakdown phenomenon. It is a damaging process due to partial discharges and progresses through the stressed dielectric insulation, whose path resembles the form of a tree....

 often occurs in high-voltage equipment prior to causing complete breakdown. Following these Lichtenberg figures within the insulation during post-mortem 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.

Fractal similarities

The branching, self-similar patterns observed in Lichtenberg figures exhibit fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

 properties. Lichtenberg figures often develop during the dielectric breakdown of solids, liquids, and even gases. Their appearance and growth appear to be related to a process called diffusion-limited aggregation

Diffusion-limited aggregation

Diffusion-limited aggregation 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 Witten and Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means...

 or 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

Dielectric breakdown model 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 breakdown of solids, liquids, and even gases, explaining the...

(DBM). Although the electrical breakdown mechanisms of air and PMMA are considerably different, the branching discharges turn out to be related. So, it should not be surprising that the branching forms taken by natural lightning also have fractal characteristics.

External links

• What are Lichtenberg Figures and how are they created?
• Lichtenberg Figures, Glass and Gemstones
• 1927 General Electric Review Article about Lichtenberg Figures
• Dielectric Breakdown Model (DBM)
• Making 2D Lichtenberg Figures on wood
• Trap Lightning in a Block.(DIY Lichtenberg Figure at Popular Science)
• Lichtenbergs in acrylic in 3d. 1 2 3 (Requires Quicktime VR to view.)