Lichtenberg figure

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$Modern "3D Lichtenberg Figures" or "Electrical treeing" in a block of clear acrylic. The fractal discharge pattern is believed to extend down to the molecular level. Actual size: 3" × 3" × 2" (76mm × 76mm × 51mm)$

Modern "3D Lichtenberg Figures" or "Electrical treeing" in a block of clear acrylic. The fractal discharge pattern is believed to extend down to the molecular level. Actual size: 3" × 3" × 2" (76mm × 76mm × 51mm)

Lichtenberg figures (Lichtenberg-Figuren, or "Lichtenbergian Dust Figures") are branching electric discharges that sometimes appear on the surface or the interior of insulating materials. They are named after the German physicist Georg Christoph Lichtenberg, 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 order to generate high voltage static electricity through induction. By discharging a high voltage point to the surface of an insulator, he was able to record the resulting radial patterns in fixed dust. By then pressing blank sheets of paper onto these pattens, Lichtenberg was able to transfer and record these images, thereby discovering the basic principle of modern Xerography. 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.

1 Formation
2 Modern 3D Lichtenberg figures
3 Natural occurrences
4 Fractal similarities
5 External links

[edit] 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, ebonite, or glass. The point is positioned very near to, or in contact with, the plate. A source of high voltage, such as a Leyden jar (a type of capacitor) or a static electricity generator, is applied to the needle. This creates a small electrical discharge to the surface of the plate. The electrification of the plate is now tested by sifting over it a mixture of powdered flowers of sulfur and red lead (Pb₃O₄ or lead tetroxide).

The negatively electrified sulfur is attracted to the positively electrified parts of the plate, and the positively electrified red lead to the negatively electrified parts. In addition to the distribution of color thereby produced, there is 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 was positive, a widely extending patch is seen on the plate, consisting of a dense nucleus, from which branches radiate in all directions; if negative, the patch is considerably smaller and has 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, 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. 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 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 at the gas-insulator boundary. Once transferred to the insulator the 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.

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 charring of the underlying material. Over time, branching, tree-like carbonized patterns are formed on the surface of the insulator called electrical trees. These may ultimately bridge the insulating space, leading to catastrophic failure of the insulating material.

[edit] 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, a type of particle accelerator). 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 (relativistic 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 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-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 electrical sparks 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 actual discharge is initiated from the positively charged exterior surfaces of the specimen, so that the resulting discharge actually creates a positive Lichtenberg figure. These rare and 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 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.

[edit] Natural occurrences

Lichtenberg figures may also appear on the skin of lightning victims. These are reddish, fernlike patterns that may persist for hours or days on survivors. They are also a useful indicator for medical examiners when trying to determine the cause of death in a victim. 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 either the passage of the lightning current or the shock wave from the lightning discharge. A lightning strike can also create a large Lichtenberg Figure in the grass surrounding the point hit by the bolt. These are sometimes found on golf courses or in grassy meadows. Fulgurites may also be created as sand and soil is fused into glassy tubes by the heat of the high current lightning discharge.

Electrical treeing also occurs in high-voltage equipment just before breakdown. Following these Lichtenberg figures in the insulation during post-mortem investigation of the broken down insulation can be most useful in finding the cause of breakdown. An experienced High-voltage engineer can see from the direction and the type of trees and their branches where the primary cause of the breakdown was situated and possibly find the cause. Broken-down transformers, High-voltage cables, bushings and other equipment can usefully be investigated in this way; the insulation is unrolled (in the case of paper insulation) or sliced in thin slices (in the case of solid insulations), the results are sketched and photographed and form an archive of the breakdown process.

[edit] Fractal similarities

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