TWO HUNDRED YEARS of LICHTENBERG FIGURES Summary 1. Introduction When Powder Is Dusted Over a Dielectric Plate After an Electric

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Journal of Electrostatics, 6 (1979) 1--13 1 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

TWO HUNDRED YEARS OF LICHTENBERG FIGURES

YUZO TAKAHASHI Department of Electrical Engineering, Chuo University, Kasuga 1--13--27, Bunkyo-ku, Tokyo (Japan) (Received April 4, 1978)

Summary

Lichtenberg discovered dust figure phenomena of electrical discharges in 1777. His discovery came to the notice of many scientists because it was considered that the figures should show the motion of the electric fluid. Photographic Lichtenberg figures were obtained in the middle of the nineteenth century. Both of these figures, usually called "Lichtenberg figures", have been utilized in the study of electrical discharges. There are many figures, other than Lichtenberg figures, that give a pattern indication of the influence ~r result of a discharge.The era of modern studies of Lichtenberg figures and creepage discharges was opened by Toepler late in the nineteenth century. Some useful figures, such as liquid-crystal Lichtenberg figures and figures by the liquid-development method, have been introduced recently.

1. Introduction

When powder is dusted over a dielectric plate after an electrical discharge has been on it, the power adheres to the surface and appears as a characteristic pattern. Such a pattern can also be obtained on a photographic plate or film by developing in the usual way. Both patterns are called "Lichtenberg figures/ Lichtenberg'sche Figuren"; the former are called "dust figures/Staubfiguren", the latter "photographic Lichtenberg figures". In this paper, photographic Lichtenberg figures are referred to as "photographic figures" for short. Two hundred years have passed since G.Chr. Lichtenberg discovered dust figure phenomena in 1777. His discovery came to the notice of many scientists in those days because of the expected possibility of being able to study the electric fluid. They have been utilized as a method of investigating electrical discharges up to the present. The history of the study of Lichtenberg figures and related figures is surveyed in the present paper. Some examples of Lichtenberg figures are shown in Figs. 1 and 2. Lichten- berg figures are more or less perm_anent records of discharges. It is not easy to measure characteristics of discharges, because they develop and diappear very quickly. When Lichtenberg figures are utilized, the residual charge or the discharge channels can be seen after the discharge has disappeared, and so Lichtenberg figures can be very useful. Since they give information as patterns, rod erectrode /dielectric ,\ (a) plane electrode

Fig. 1. Dust figures in a mixture of 1% SF~ and 99% N2 at atmospheric pressure, applied voltage: 1)< 40 us lightning impulse. (a) Electrode arrangement; (b) negative figure (-25 kV); (c) positive figure, enlarged (+20 kV). By courtesy of Mr. M. Chiba. they are particularly useful in the study of creepage discharges where the length and form of the channel are to be investigated. In the case of dust figures, one can discriminate the polarity of the residual charge using a mixture of certain powders. The form or dimension of Lichtenberg figures depends upon the polarity, magnitude and wave shape of the applied voltage, and also upon the kind and pressure of the gas: positive figures in the air are star-like, and negative moon-like; positive figures develop as trees with increasing applied voltage, while negative ones become fan-shaped figures; positive figures are larger than negative ones at a given applied voltage; the length of figures decrease as the gas pressure is raised; at low pressure, figures are larger than those at atmospheric pressure.

2. Discovery of Lichtenberg figures

Lichtenberg, who was a Professor of GSttingen University, found his dust figures unexpectedly, and his discovery was reported at the Royal Society of Science of GSttingen on May 3, 1777. Because of his illness, the report was read not by himself but by his teacher, Professor A.G. K~istner. At the public Fig. 2. Photographic Lichtenberg figures in air, applied voltage: 15 ms × 15 min impulse. (a) Negative figure (-15 kV), pressure 0.2 MPa; (b) positive figure (+15 kV), 0.1 MPa; (c) positive figure (+20 kV), 0.6 MPa. meeting on February 21, 1778, Lichtenberg read a report entitled "De nova methodo naturam ac motum fluidi electrici investigandi" (On a new method to investigate the motion of electric fluid.). Part of its text [1] is as follows: "(At that time Lichtenberg made a huge electrophorus of about 2 m in diameter. It was so powerful that a spark of about 40 cm in length could be produced.) ... The occasion of observing this phenomenon (dust figure) was as follows: About the beginning of spring 1777 my electrophorus was just finished. In my room all was still covered with very fine rosin powder that had risen during planing and polishing of the cake and the metal disk, and later it lay on walls and books. When air motion occurred, it deposited on the metal disk of the electrophorus, to my great annoyance. However, it was not until I had hung the disk on the ceiling of the room many times, that the powder deposited on the cake; then I could not cover it uniformly as had occurred on the metal disk, but to my great joy it was arranged like small stars at certain points. These were dull in the beginning and difficult to see; when I sprinkled more dust intentionally, however, they became very clear and often resembled embossed work. Sometimes innumerable stars, the Milky Way and bigger suns appeared. The bows were dull on their concave side, and decorated manifoldly with rays on their convex side. Marvellous small twigs emerged; the twigs produced by frost on window glass resemble them. Small clouds of many various forms and grades of shading and finally different figures of particular shape were seen .... However, a very pleasant play occurred to me, when I saw that these figures could scarcely be destroyed. Even if I wiped off the dust carefully with a feather or a hare's paw, I could nevertheless not prevent that the figures, which were destroyed just before, quickly developed again to some extent anew and still wonderfully. Therefore, I painted a piece of black paper with adhesive paste, laid it down on the figures and pressed it on them lightly. So I succeeded in making several copies of the figures. I have presented these six copies to the Royal Society. This new variety of printing was very favourable for me in order to progress further very quickly, because I had neither pleasure nor time to sketch or destroy all the figures." These figures must have been extraordinarily impressive. Lichtenberg noticed that they appeared where light sparks had gone from the metal disk to the cake of electrophorus. So it was, in this way, that Lichtenberg figures were found. Lichtenberg thought that the figures should show the true nature of electricity or motion of the electric fluid. He confirmed that "+E" figures were star-like, and "-E" figures moon-like. He tried various dusts and cakes; fine sulphur or rosin in a linen pouch was best for powdering; he used also amber, cinnaber, lycopodium, sugar, wheat flour, metal filings, etc. He carried out experiments in vacuum and concluded that both "+E" and "-E" figures were bigger than those in the air. Lichtenberg's discovery aroused great interest in scientists and natural philosophers of the day because of the fine impressive shape of the figures and also because of the expectation that the true nature of the electric fluid could be clarified by the figures. There were "the two-fluids theory" and "the one- fluid theory" of electricity. Scientists expected that the controversy between the theories would come to an end through the study of Lichtenberg figures. Lichtenberg himself, however, remained wary of the theoretical interpretations of his figures and did not take sides. He introduced sumbols of "+" and ..... into the description of electricity instead of "positive" and "negative", as he thought that these symbols could suggest "too much or too little fluid" or "two fluids". Lichtenberg stated that the figures could be utilized to discriminate the polarity of electricity. He proposed an instrument that would be of use to indicate atmospheric electricity. It was composed of a rotating cylinder, driven by clockwork, with a rod on it. If an iron string from a kite would be connected to the rod, the change in atmospheric electricity could be recorded on the cylinder, which was coated with resin. This idea is similar to the klydonograph of our day. However, it is not likely that Lichtenberg constructed this instrument.

3. Georg Christoph Lichtenberg

G.Chr. Lichtenberg was born on July 1, 1742 in Oberramstadt, near Darm- stadt in Germany, as the seventeenth child of a pastor. His body was weak throughout his life, but he was a versatile and prominent thinker. His father passed away when he was nine years old. Georg Christoph, however, was able to study at GSttingen University with the aid of the Lord of Hessen; he specialized in mathematics. In 1770 he was appointed as Professor (Extra- ordinarius) in pure and applied mathematics of G5ttingen University. He later became Ordinarius, and stayed at G5ttingen University until the end of his life. He brought about remarkable changes in geophysics, geodesy and astronomy, and took great interest in experimental physics in his later years. In the field of electricity, the discovery of the phenomenon of Lichtenberg figures is one of the most famous and important, and led to his development of the double electrophorus. In addition, the study of atmospheric electricity and a lightning rod, and the idea of a shielding cage were included in his work. Thus, not only was he a mathematician, but also a Naturforscher (researcher of nature). More- over, Lichtenberg was a literary man. His sense of humour was so fine that his aphorisms and correspondence with his contemporaries are still famous today [2, 3]. His principal reports on the dust figures were read in 1778; it seems that his later study of the figures was not very fruitful. In 1787, he fell down due to nervous collapse and lost much of his vitality; he passed away on February 24, 1799.

4. Electrical figures

Lichtenberg figures -- dust and photographic -- are figures in which the distribution of residual charge due to the discharge or the discharge channels is recorded through powdering or through a direct photochemical effect. The figures remain more or less permanently after the discharge. Sometimes, surface discharge channels themselves are referred to as Lichtenberg figures, but that is wrong. After the discharge has disappeared, the channels do not remain, and nothing has been recorded; Lichtenberg figures must be recorded. Some effects or results of discharges can be made visible by methods other than dust figures and photographic figures, and the pattern records that remain for a certain period can be obtained. An example is a trace on the skin struck by lightning. All such figures, including Lichtenberg figures, are called "electrical figures/elektrische Figuren ". If a coin or a medal is used as an electrode, reflected figures can be obtained; they are termed "elektrische Bilder or elektrische Abbildungen (electrical pictures)". Riess referred to elektrische figuren and elektrische Bilder as "elektrische Zeichnungen (electrical sketches)" altogether [4, 5]. Electrical figures can be classified by the way that the effect of the discharge is to be made visible. The classification given by K. Przibram [6] is described in the following, where some families are added by the present author. Classification of electrical figures

(D In gas or liquid (a) Accumulating figures/Anlagerungsfiguren There is a difference between accumulation of the alien substance at discharged places and that at the other places. This non-uniformity results in a pattern. (~) Dust figures/Staubfiguren (1) Lichtenberg figures in the original sense, i.e. figures obtained through powdering after the discharge. Riess [4] got such figures using tobacoo smoke instead of powder. (2) Figures by liquid~levelopment method [7, 8] ; this uses liquid toner containing colloidal particles for electrophotography. (3) Kundt's dust circle [9] ; if powder covering a plane electrode is blown out by a spark, a circle appears on the powder layer. (4) Holtz's figure in liquid [10, 11]. Three-dimensional figures can be formed. These may result from the current flow. (~) Cases where the alien substance is liquid or vapour (1) Aldini's oil figures [12] ; an oil layer spreads out if it is struck by a discharge. Toriyama [ 13] noticed the undulation of residual oil on a dielectric plate removed from an oil vessel after a discharge in oil. C2) Breath figures [4, 5, 14] are obtained by breathing on the dielectric surface, the pattern appearing due to selective condensation. Frost figures [15, 16] are formed when the plate is taken out of a cryogenic vessel after a discharge. (3) Silvered figures [17] can be seen if molten silver is used. (b) Denudation figures/Entbl~ssungsfiguren These are formed if a surface layer of the plate is removed by a discharge. Lichtenberg figures in a wide sense, that is the case of powdering before the discharge. Such figures can also be obtained on a plate coated with soot [18] or on a silvered glass plate [19]. (c) Relief figures (~) On a hard solid (1) Priestley's rings [20] remain behind on a metal surface after a spark. B. Franklin had observed them in 1751. (2) Riess' feste BiIder (solid pictures) [4, 5] due to erosion of metal surface. This process is similar to that of modem discharge machining. (~) On a soft solid or a liquid surface (1) Priestley's traces of sparks on various materials [ 20], including a cabbage leaf. (2) Relief figures on a liquid surface (dielectric liquid [21] or water). The duration of the figures is short. (3) Relief figures on resin was reported by van der Willingen in 1862 possibly for the first time [6]. Heat-developed figures, obtained by Blake [22] (probably for the first time) by gentle heating when selective melting occurs. (d) Discoloration figures (a) On metal (Franklin and Priestley [20] ; on mica, glass and potassium iodide paper (Riess [4, 5] ). Priestley's rings on a metal surface have rainbow colours resulting from oxidation. Figures on potassium iodide paper are due to electrolysis. (~) Tracking (7) Figures of withered grass at a point struck by lightning (5) Figures on the skin struck by lightning (e) Photographic Lichtenberg figures. Their research history will be described in § 5.2. (~) Liquid-crystal Lichtenherg figures are obtained on liquid crystals [ 23, 24]. (e) Priestly [20] referred to Lane's observation of phosphorescent figures that remain after a discharge on solid materials.

(II) In solid (three-dimensional figures) (a) Lightning tube and fulgurite in sand or rock struck by lightning (b) Tree in dielectric solid; three-dimensional figures of discharge channels in glass have been known since the middle of the nineteenth century [25]. Holtz observed figures in a binding agent between two glass plates [26], but they are two-dimensional.

We can find more detailed classifications, morphology, and research history of these figures in reviews of Riess [4, 5], Wiedemann [27], Lehmann [25], Holtz [28] and Przibram [6]. Among these various figures, dust figures and photographic figures are in widest use in the study of discharges, though some others (for example, heat- developed figures, liquid-crystal Lichtenberg figures, figures by the liquid- development method and frost figures) are sometimes utilized. The reason is that dust figures and photographic figures are excellent in clarity, resolution, durability, reproducibility and are easy to obtain. Therefore "Lichtenberg figures" usually mean the two kinds mentioned above, although some others are occasionally referred to as Lichtenberg figures. E. Chladni, influenced by Lichtenberg's discovery, found other impressive figures in 1787" Chladni figures of quartz sand on a plate due to its acoustic vibration modes. They are also called Staubfiguren.

5. Research history of Lichtenberg figures

Some electrical figures, fulgurite and phosphorescent figures for instance, had been known before Lichtenberg's discovery. Lichtenberg's dust figures were the first, however, to be utilized for studying the motion of the electric fluid, or discharge channels in a modern sense. The majority of electrical figures were found under the influence of Lichtenberg's discovery: they had not been found until it was recognized that the motion of the electric fluid or discharge channels could be recorded. It should, therefore, be said that the era of electrical figures was opened by Lichtenberg.

5.1. Dust figures Following Lichtenberg's discovery in 1777, a lot of scientists began such experiments in the expectation that the true nature of the electric fluid could be clarified by Lichtenberg figures. Lichtenberg himself did not give any explanation as to why the figures were formed. T. Cavallo noticed the following facts in 1779 [29]. The powder particles are electrified while they are shaken in a linen pouch before sprinkling; therefore they adhere to the plate selectively, resulting in figures. Lichtenberg, who thought that the electric fluid flowing through the electrode and the cake should cause the figures, did not agree with him. He felt probably that the role of the powder is stressed too much in Cavallo's conclusion. We can now say that both opinions are right in view of modern theory. Lichtenberg figures are of particular use in the study of creepage discharges. J.A. de Luc got dust figures of creepage discharges in 1786--1787 [30] ; these maybe the first such figures. In 1788, de Villarsy introduced a mixture of sulphur and minium, and discovered the following facts[ 31]. Yellow sulphur is electrified negatively and red lead positively while they are shaken in a linen pouch; therefore, positions of positive residual charge on the plate change to yellow and negative ones become red after the powdering. Thus the polarities of charge can be discriminated in dust figures; this mixture remains in wide use.

5.2 Photographic Lichtenberg figures Photography has been known widely since daguerreotype was reported at the Academy of Paris in 1839. Various experiments on photography were carried out after that time by scientists in many countries. E. Becquerel reported the effects of a chemical ray from an electric spark on silver chloride paper and silver bromide paper in 1840 [32]. This is probably the first description of the effect of a light discharge on photographic materials. B. Silliman et al. published a paper in 1842 on daguerreotype of a light discharge registered through a lens [33]. They wrote that the experiments were carried out in 1840. Pinaud in 1851 was possibly the first [34] to record discharge channels creeping directly on a daguerreotype plate and silver iodine paper. He noticed that positive figures have pointed heads while negative ones are round. In 1862, O.N. Rood obtained figures on wet collodion plates [35]. Characteristics of a surface discharge depend upon the resistivity of the surface. Therefore, figures on a dry plate are far more important in the study of discharges than those mentioned above. Jamin presented Ducretet's figures on a dry plate at the Academy of Paris in 1884 [36] ; they are possibly the first such figures. Thereafter, many figures on dry plates were reported in many countries. Figures were described by words in reports printed in those days. Some~ times they were printed also, but as woodcuts or lithographs. E.-S. Trouvelot's paper in 1888 [37] was possibly the first to contain figures printed by auto- type with a net screen, which was invented in 1880. Photographic figures are called Lichtenberg figures nowadays, though they were not discovered by Lichtenberg. The term was used in Germany as early as by G. Sieben in 1889 [38]. In 1919 P.O. Pedersen adopted this usage into English [39]. C.E. Magnusson in the U.S.A. stated in 1928 that "... the photographic records are generally referred to as Lichtenberg figures although photographic Lichtenberg figures would be more specific" [40]. In French, one rarely refers to Lichtenberg in connection with electrical figures. Photographic figures are easier to obtain than dust figures if a dark chamber is provided. Since the nineteenth century it has been discussed whether the figures are caused by a light of the discharge or by other effects such as the high field and bombardment by charged particles, etc. [35, 41]. There is no established theory of this point at present.

5. 3.Modern studies A number of reports on the morphology of Lichtenberg figures appeared in the nineteenth century. Most of the phenomenological knowledge of today was obtained in this period. For example, back figures that are formed in the wave tail of the applied voltage was reported by Riess [4, 5]. After that, however, scientists paid less attention to Lichtenberg figures, because the main stream of electrical science flowed along galvanism and electromagnetism. Thus, experiments on Lichtenberg figures became unimportant in the study of the true nature of electricity. Lichtenberg figures were often demonstrated as some- thing like jugglery, since they were impressive anyhow. The era of modern research on Lichtenberg figures was opened by M. Toepler around 1898 [42--44]. He measured creepage discharges quanti- tatively with the aid of Lichtenberg figures, and classified modes of the discharges. Thereafter, the important achievements of P.O. Pedersen (since 1919) [39], F.H. Merril and A. yon Hippel (1939) [45], E. Nasser (since 1959) [46, 47], and so on, appeared. Pedersen applied Lichtenberg figures to the measure- ment of very short time intervals. Nasser measured streamer development with a photographic film put between point and plane electrodes. W. Rogowski et al. got Lichtenberg figures on a colour film [48].

5.4 Lichtenberg figures in a dielectric liquid Reports on Lichtenberg figures in a dielectric liquid did not appear until the latter half of the nineteenth century. Though W. Holtz described figures in a liquid [10, 11], it is doubtful whether they were due to discharges or not. S. Doubrava in 1879 [49] and Przibram in 1918 [50] referred to dust figures and photographic figures in a liquid, respectively, but very briefly. The beginning of the study of Lichtenberg figures in a dielectric liquid was related to the development of high-voltage power transmission and high-tension 10 oil insulation. In 1924, S. Mochizuki published a paper written in Japanese which described photographic figures in transformer oil in detail and contained several printed pictures [51]. This is possibly the first paper on the subject. In a European language, E. Marx referred to photographic figures in oil and published one printed picture in 1930 [52]. A detailed paper of H. Staack in German appeared in the next year [53]. Y. Toriyama published a paper in 1930 that described dust figures in liquid in detail for the first time [13, 54].

5.5 Industrial applications of Lichtenberg figures There have been few industrial applications of Lichtenberg figures. The klydonograph, developed by J.F. Peters of Westinghouse in 1924 [55], is the most important. This instrument has a rod electrode placed on a moving film, and may be used to give an indication of the time of occurrence, the polarity and magnitude of voltage surges on transmission lines. Lichtenberg had proposed an apparatus similar to the klydonograph, as mentioned in § 2. There are some applications of Lichtenberg figures or electrical figures, such as those to recorders, current measuring devices with a paper gap and electrical discharge machining. W. Thomson (Lord Kelvin) referred to the spark recorder in connection with his siphon recorder in 1873 [56].

5. 6 The latest researches Lichtenberg figures in SF6, the most important insulating gas of today, were published by Toriyama in 1961 [57]. Figures in H2, 02 and CO2 were reported by E. Reitlinger about 1860 [58, 59]. Przibram described Lichtenberg figures in C12 in 1918 [50], and Merril and von Hippel described ones in CC12 and CC12F~ in 1939 [45]. Figures in vacuum had been investigated already by Lichtenberg as mentioned in § 2. Lichtenberg figures in gases compressed at a pressure of several atmospheres were reported by Pedersen in 1929 [39], possibly for the first time. Lichtenberg figures in liquid nitrogen, which is of importance in connection with cryogenic power transmissions, were published by the present author in 1972 [16, 60, 61]. M. Chiba et al. investigated those in detail [15, 16, 62]. Hane et al. reported figures on a colour film in liquid nitrogen in 1974 [63]. Some new method of Lichtenberg figures have been developed recently by Japanese research workers: liquid-crystal Lichtenberg figures by M. Sone et al. in 1971 [23, 24] and figures by the liquid-development method by H. Kishida et al. in the same year [7, 8]. The former can give information by a change in colour; the latter are dust figures in a wide sense. In this method, however, liquid toner which contains colloidal particles for electrophotography is used instead of powder; no dark room is necessary, and the resolution is good. Lichtenberg figures will be of use in estimating three-dimensional distributions of space charge in a solid. If one slices a dielectric block that has trees and powders on the cut, figures due to the space charge can be observed [64]. 11

6. Conclusions

Lichtenberg figures have been evaluated very differently during the past two centuries. Once they were looked upon as a decisive proof of the motion of the electric fluid, and then as a subject of entertaining demonstration. They are very useful, however, because the residual charge or discharge channels can be made visible by them. They will also be utilized in the study of discharges in the future. Some new families have recently been added to the figures. Lichtenberg figures usually give only qualitative information. Quantitative data can be obtained by adequate contrivance or application together with other measuring methods.

Acknowledgements

The author is very much indebted to the late Professor H. Prinz of Technische Universitit Miinchen and the Alexander yon Humboldt-Stiftung for kind support during his stay in West Germany. Thanks are due to Mr. M. Chiba of University of Tokyo who allowed the reproduction of pictures.

References

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