Lichtenberg figure

Lichtenberg figures are named after the German physicist Georg Christoph Lichtenberg, who originally discovered and studied them. At the time, it was thought that their characteristic shapes might help to reveal the nature of positive and negative electric "fluids". Lichtenberg Figures are typically formed by the rapid discharge or redistribution of charges residing on the surface of non-conductors. One way that they can be produced is as follows: A sharp-pointed needle is placed perpendicular to a non-conducting plate, such as of resin, ebonite, or glass, with its point very near to or in contact with the plate, and a high voltage Leyden jar (a type of capacitor) or a static electricity generator is discharged into the needle. 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 seen to attach itself 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 much smaller and has a sharp circular boundary entirely devoid of branches.

If the plate receives a mixed charge, 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 the positive and negative figures seems to depend on the presence of the 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. There is, in all probability, a connection between this phenomenon and the peculiarities of positive and negative brush or streamer discharges in air. Lichtenberg figures are fully described in two memoirs Super nova methodo naturam ac motum fluidi electrici investigandi (Göttingen, 1777-1778).

Modern Lichtenberg Figures can also be created within solid blocks of acrylic plastic (polymethyl methacrylate or PMMA) using a beam of 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 are moving an appreciable fraction (95 - 99+ percent) of the speed of light (relativistic velocities). The electron beam is then aimed towards an acrylic specimen. When the relativistic electrons hit the acrylic, they easily penetrate the surface, slowing down as they collide with the molecules inside the plastic, and finally coming to rest deep inside the specimen. Since acrylic is an excellent electrical insulator, the electrons inside the specimen are temporarily trapped. Under continued irradiation by the beam, the excess electrons form a plane of negative charge inside the specimen. As the charge builds, the effective voltage inside the specimen can reach millions of volts. Ultimately the huge electrical stress exceeds the dielectric strength of the plastic, causing it suddenly become conductive in a process called dielectric breakdown.

Once breakdown occurs, branching tree or fern-like conductive channels are rapidly formed within the plastic, allowing the trapped charge to suddenly rush out in a miniature lightning-like flash and bang. Electrical breakdown of a charged specimen may also be manually triggered by poking the plastic with a pointed conductive object. The powerful electrical spark leaves thousands of permanent branching chains of fractures behind - creating a Lichtenberg figure. Although the internal charge within the specimen is negative, the actual discharge is initiated from the positively charged exterior surfaces of the specimen, and the resulting discharge actually creates a positive Lictenberg figure within. These rare and beautiful objects are sometimes called electron trees, beam trees, or lightning trees. As the electrons rapidly decellerate inside the acrylic, they also generate powerful X-rays. These 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 beautiful lime green. The color usually fades over time, and gentle heating, combined with oxygen, accelerates the fading process.

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.

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.

External links

• What are Lichtenberg Figures and how are they created? (http://205.243.100.155/frames/lichtenbergs.html)
• Lichtenberg Figures, Glass and Gemstones (http://www.orau.org/ptp/collection/Lichtenberg%20figures/Lichtenbergfigures.htm)
• 1927 General Electric Review Article about Lichtenberg Figures (http://americanhistory.si.edu/scienceservice/044138h.htm)
• NASA article on lightning's effects on humans (http://science.nasa.gov/newhome/headlines/essd18jun99_1.htm)
• About Electricity, Lightning, and Lichtenberg Figures (http://volcaniclightning.tripod.com/index.htm)
• Photo of a Lichtenberg Figure on a golf course (http://205.243.100.155/photos/For_Sale/June04/Golfcourse.jpg)
• Dielectric Breakdown Model (DBM) (http://classes.yale.edu/fractals/Panorama/Physics/DLA/DBM/DBM.html)
• Mathematical Description of Diffusion Limited Aggregation (http://classes.yale.edu/fractals/Panorama/Physics/DLA/DBM/DBM2.html)