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Behavior of self-confined spherical layer of light radiation in the air atmosphere
Physics Letters A 328 (2004) 189–195 www.elsevier.com/locate/pla
Behavior of self-confined spherical layer of light radiation in the air atmosphere V.P. Torchigin ∗ , A.V. Torchigin Institute of Informatics Problems, Russian Academy of Sciences, Nakhimovsky prospect 36/1, 119278 Moscow, Russia Received 30 January 2004; received in revised form 7 June 2004; accepted 8 June 2004 Available online 21 June 2004 Communicated by F. Porcelli
Abstract Behavior of thin spherical layer of intensive light in an inhomogeneous atmosphere is considered. It is shown that the behavior is similar to puzzling and mysterious behavior of ball lightnings. Under assumption that ball lightning moves along the gradient of atmosphere air density process of ball lightning penetration in a salon of a flying airplane is analyzed. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Jx Keywords: Self-action; Whispering gallery waves; Ball lightning; Propagation; Optical solitons
Ball lightnings (BL) attract attention of many investigators. Now about 10 000 occasions of BL appearance are described and above 2000 papers concerned BLs have been published. Historical surveys appear regularly. Some last of them are in books [1–3]. There is no deficit of hypotheses explained features of BL behavior. Above one hundred hypotheses are known at present. The problem is that all of them are not able to explain the following several generally recognized facts: penetration of BL through window panes, through chimneys and small splits in walls, penetration BLs in salons of flying airplanes, contradiction between BL spectrum which corresponds to a hot body
* Corresponding author.
E-mail address: [email protected] (V.P. Torchigin). 0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.06.022
at the temperature above 5000 K and absence of noticeable IR radiation. These and other properties of BL are very valuable for theorists because they enable to withdraw immediately majority of hypothesizes. For example, since it is found safely that BLs can penetrate through window panes [4,5], ought to withdraw all hypotheses where such words as electrons, ions, clusters, condensate states occur. It is known very well that no particles can penetrate through glass. These thoughts are expressed clearly in [6] where a hypothesis that BL is connected with a strong electrical field formed by atmospheric electricity is proposed. As is known, the field can penetrate though any dielectric, in particular through glass and walls. Puzzling motions of BL are explained by motion of environmental electric field. BL seeks for itself the position where the net action of electrical force vanishes. However, in accor-
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dance with this approach BL can penetrate in rooms through any walls whereas it is known that BL penetrates through holes and splits in walls. It is hard to imagine that the electrical field moves in space in such a way that it forces BL to find out a small split and penetrate through it with changing BL shape. Of even grater difficulties are connected with explanation of BL penetration through chimneys. In 2002 we put forward a hypothesis that BL consists of light radiation emerged at strike of a conventional linear lightning [7]. But as is known the light propagates in straight line at light speed and disappears practically instantly. There are must be some means that force the light to propagate in a limited volume of space. Surprisingly, similar means do exist. Studying whispering gallery light waves in fibers without coating, we found out that their group velocity may be decrease till zero [8]. In this case the wave rotates around the fiber axis and its wave vector is perpendicular to the axis. The same situation takes place in a glass sphere where a whispering gallery light wave circulates along the sphere equator in a thin surface layer [9]. The light wave cannot propagate in a free space owning the total inner reflection on the boundary between glass surface and surrounding space. In this case there is no necessity to have a continuous glass ball. A glass sphere of small thickness is sufficient. Such sphere may be considered as a planar lightguide rolled to the sphere. As is known a thin film planar waveguides are basis of up-to-date integrated optics where, unlike conventional 3D bulk optics, all optical processes are produced in a thin film, that is in two-dimensional space. A thin spherical layer of compressed air may be used instead of the glass spherical layer. As is known the air refraction index increases with increase in the air pressure and total inner reflection may take place at the boundary between the compressed and conventional airs. But what are means which prevent the compressed air from expansion? This is an intense light which circulates within the layer and produces the electrostriction pressure that tends to near air molecules close together. Thus, the intense light confines the compressed air. In turn, the layer of the compressed air shows itself as a thin film lightguide which prevents the light from radiation in free space. We obtain a light bubble comprising of light and air. It was not so hard to show that the air
pressure of several atmospheres is sufficient to confine safely the light radiation in a sphere about several centimeters in diameter [10]. The next step was to show how the light bubble can penetrate through window panes. The problem is that any light, penetrating through a glass, propagates further in straight line and, seemingly, there are no means to force it to not propagate from the light bubble at the opposite side of the glass. It turns out that the problem is solved simply. As light bubble touches the glass surface, the light penetrates inside the glass but is subject to the total inner reflection from the opposite side of the glass. In the same time the light field penetrates in a thin air layer of several wavelengths thickness at the opposite side of the glass. As is known this field cannot excite propagating light waves (the word “total” underlines that all light launched at the opposite side of the glass reflects backwards completely). In the same time the light field in the air region adjacent to the opposite side of the glass produces the electrostriction pressure. As a result, the air density and refraction index increase in the region and next portions of circulating light penetrate in the region. Thus, a small part of the light bubble appears at the opposite side of the glass. Thereafter this part increases gradually. Illustrations of this process are presented in [11–14]. One can see that only light penetrates through the glass and compresses new portions of air located at the opposite side of the glass. The initial air which was in the light bubble before its penetration does not penetrate through the glass. A motion of light bubbles has been studied theoretically in [11–14]. Only the following three properties of light bubbles have been used. First, like a conventional light beam which deflects in a inhomogeneous optical medium from a straight line in the direction where the gradient of the refraction index increases, light bubble moves along the gradient of the refraction index. Because the air refraction index increases linearly with increasing the air density, light bubble moves in the direction where the air density is maximal. The air density is in inverse proportion with the air temperature at constant pressure and light bubble moves in the direction where the air is cooler. Second, unlike a pumped football ball where the air pressure exists in all volume of the ball, the air pressure in a light bubble exists in a thin surface
V.P. Torchigin, A.V. Torchigin / Physics Letters A 328 (2004) 189–195
layer. In this case the deformability of light bubbles increases by (R/w)2 times as compared with that of the football ball where R and w are radius and thickness of light bubble, respectively. For example, if R = 10 cm and w = 10 µm, (R/w) = 106 . In this case a spherical shape of light bubble may be changed by small external forces. Third, light bubble is subject to the effect of selfaction. This means that light bubble, approaching some obstacle, heats it and changes the air temperature field distribution near itself. As a result, various parts of light bubble surface tends to move in various directions and the light bubble shape is deformed. These qualitative considerations occur sufficient to explain many features of light bubble motion. It turns out that it is very simple to explain puzzling motion of light bubbles near the earth surface. The air temperature near the earth surface is greater than that at some distance from the surface (the earth surface absorbs sun radiation and is heated; the air near the earth surface is heated too due to heat conduction). In this case the air density and therefore the air refraction index is smaller near the earth surface than that at some distance from it. As a result, the air refraction index is maximal at some distance from the earth surface. Light bubbles reside at this height which is equal usually about 1 m. To explain penetration of light bubbles through small splits ought to remind that light bubbles may be deformed easily. Approaching the hall which crosssection is smaller than a light bubble diameter, a light bubble heats regions of the wall near the hole. The air adjacent these regions is heated owning heat conduction and regions of the light bubble surface located in this air are subject to forces of repulsion. In the same time the region of light bubble located near the hole axis is subject to forces of attraction to the hole. As a result, the light bubble is deformed in such a way that its shape tends to the shape of the hole. Illustrations of light bubble penetration through a hole are presented in [11–14]. After studying features of light bubble motion, stability and main physical parameters such as the stored energy and lifetime have been analyzed [13]. Initially most difficulties were connected with its lifetime. As is known the life time of conventional sun white light in conventional atmosphere is smaller than 1 millisecond. The lifetime of ball lightnings is greater
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essentially. What is a reason? Analyzing dependence on the air pressure of the molecular light scattering which is responsible for the light lifetime, it was shown that the light scattering decreases at extremely high pressure where air molecules are packed closely. The air compressibility at such pressure is near zero and fluctuations in air density that are responsible for light scattering disappear. As a result, a lifetime of light in a light bubble may be as much as tens seconds that is comparable with the BL lifetime. It is self evident that electrical effects within BL as well as outside it can occur essential influence on BL properties and its behavior. Moreover, such BL properties as generation of low frequency noises in radio receivers, attraction of BL to metal things can be explained easily analyzing an interaction between inner and outer electrical fields. An absence of total charge within BL is a particular case only. The electrostriction pressure that tends to near particles within BL close together is that a phenomenon which cancels forces of mutual repulsion between identical charges and provides BL stability. But consideration of the electrical effects is beyond the scope of the present Letter. The purpose of the present Letter is to give additional proofs of the validity of the hypothesis about light nature of BL. Fortunately, puzzling and mysterious BL behavior can be useful for this purpose because the more puzzling situations are explained on the basis of a hypothesis the more credibility for it. In our opinion, such explanation sometimes may be more conclusive than experimental production of some physical objects that remind BL in its form but differ in their behavior. We are going to consider most puzzling BL behavior connected with BL penetration in a flying airplane. Why do BLs prefer to visit flying airplanes (there are many reports) and is perfectly indifferent to airplanes on the earth surface? Where from such yearning for airplane flight? Everybody who looked in an illuminator of a flying airplane may see small clouds and swarms that run away with large speed may ask why BLs are not blown away the airplane wing although a very strong wind at speed about 1000 km/h blows on the airplane? If BL were composed of some particles, clusters, ions, electron, etc., all of these were blown away immediately. Let us estimate preliminary the velocity at which a light bubble moves in an inhomogeneous atmosphere.
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tial speed dx/dt and initial shift x are equal to zero, we obtain from (2) that the total shift of the light beam is π x = gn R 2 . (3) 2 In this case the speed of shifting is determined by the following expression 2x . T Taking into account (1), we obtain v=
Fig. 1. Direction of coordinate axes relatively the infinite cylindrical layer.
Note at once that the velocity may be extremely large. For example, if we assume that a light bubble of 10 cm in diameter is shifted by 1 µm per one light revolution, then the light bubble is shifted by 1 km/s because the light within the light bubble performs 109 revolutions per second. For the sake of simplicity consider an infinite cylindrical layer of compressed air in which an intense light is circulating and supporting the air compression. Let the cylindrical layer of R radius and axis paralleled to the z-axis is located in an inhomogeneous atmosphere which refraction index increases along the x-axis at the rate gn = dn/dx > 0 and does not depend on y, z coordinates (Fig. 1). If the cylindrical layer is located in a homogeneous atmosphere where gn = 0, then the light makes one revolution around the cylinder axis in time T=
2πRn . c
(1)
If the cylindrical layer is located in an inhomogeneous atmosphere where gn > 0, then the light trajectory is not closed. The light shifts additionally at some distance x along the x-axis. In accordance with the eikonal equation the additional shift of light beam in presence of the additional refraction index gradient gn is determined by the following expression d2 x (2) = gn c2 cos(ct/R). dt 2 Let the light beam propagates along the arc beginning at point x = 0, y = −R and ending at point x = 0, y = R. Supposing that at time t = −(π/2)R/c the ini-
gn Rc nD c = , 2 4 where
(4)
v=
(5)
nD = gn D
(6)
is the change in the atmosphere refraction index at distance equaled to the light bubble diameter. For example, if nD = 10−5 , then v = 750 m/s, that is v surpasses the sound speed in air. Ought to underline that light bubble movement is not accompanied by movement of the air compressed within it. Like light bubble movement through a window glass, where only light radiation penetrates through the glass and compresses new air portion located at the opposite side, light bubble movement in the air atmosphere is accompanied by compression of new air portions along direction of the movement and corresponding release of air portions from the opposite light bubble side. Now let us estimate a degree of atmosphere inhomogeneity produced by a flying airplane. An additional air pressure p near a front edge of a wing where the air speed relatively to the airplane is equal to zero and is equal to the airplane speed u relatively the earth is determined by the following expression ρu2 , (7) 2 where ρ is the air density and ρ ∼ = 1 kg/m3. At the airplane speed u = 720 km/h = 200 m/s we have p = 2 × 104 Pa ∼ = 0.2 atmospheres. The air refraction index at the normal atmosphere pressure is determined by the expression n = 1 + n, where n = 2.7 × 10−4 . Since the air density is proportional to the air pressure, then p =
n(p) = 1 +
p n, p0
(8)
V.P. Torchigin, A.V. Torchigin / Physics Letters A 328 (2004) 189–195
where p0 is the air pressure at normal conditions. From (8) we have that an increase in the air pressure by p = 0.2 atmosphere entails increase in the air refraction index by n(p) = 0.2n ∼ = 0.54 × 10−4 . As follows from (5), to provide light bubble motion at the airplane speed it is necessary the following air inhomogeneity nD = u/(c/4) ∼ = 2.66 ×10−6 . Under assumption that p decreases linearly with distance from the airplain we obtain that such decrease takes place at the distance S∼ =
n(p) D = 20D. nD
At D = 0.1 m we obtain that bubbles may catch up the airplane located from them at the distance S = 2 m. Needless to say it is very rough estimations determining the order of magnitude only. But they show that a flying airplane attracts all light bubbles located directly ahead, as well as to the right, left, at the top and bottom in the region of inhomogeneous atmosphere produced by the airplane. Achieving the airplane, light bubble stops in the region where the air density is maximal and moves with this region together and, therefore, with the airplane. No airplane maneuvers can separate the light bubble and airplane. Ought to note that the additional air pressure p near front edge of the wing is proportional to the square of airplane speed u, that is the region from which light bubbles are attracted to the airplane increases with increase in the airplane speed. Besides, the probability for the airplane to meet any BLs is proportional to the airplane speed. Indeed, if the airplane could do several revolutions around the Earth per one second, it could gather all BLs which were met at its trace. Are there any other hypothesizes that explain how BLs can pursue an airplane and moves with it together? As is known the air is rarefied at great height where airplanes fly. Because of this an additional pressure is generated in airplane cabins and saloons to provide normal breath for passengers. Since it is very hard and is not justified economically to keep these rooms hermetic absolutely, there is an air compressor which continuously pumps in the outdoor air. It is natural enough to take the air from that region where the air pressure is maximal that is from the region where BLs can be located. The air is pumped by a turbine compressor and there is a tunnel between the salon and outdoor at any position of turbine blades. Since
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the light bubble layer width is several micrometers only, a split of width smaller than ten micrometers is sufficient for light bubble penetration. The air density gradient is directed into the salon. Moving along the gradient, BL penetrates in the salon. Mechanisms which enable BL to change its shape are considered in [11–14]. One can give recommendation to airplane designers to avoid BL penetration. There must be no splits in the region where additional air pressure is maximal. Consider now puzzling BL motion in a room [4,5]. Usually BL moves along walls near a floor but not near a ceiling. Since a warm air is easier than cool one, the air near a floor is cooler than that near a ceiling and therefore the air refraction index is maximal near the floor. In this case a ball, appearing in a room, moves initially towards the floor which shows itself as an obstruction. Besides, walls of the room are cooler than the air in the middle of the room because the walls are connected with cool ground. Approaching a wall, the ball heats air between the wall and ball. As a result, its motion towards to the wall ceases and the ball begins to move along the wall. Since the air before the ball is cooler than that behind it, the ball continues to move along the room perimeter at some distance from walls. In some cases the ball can find out a door, penetrates though it and leaves the room. There are many evidences supporting this picture. For example, there is a description in [4] an occasion 29 in which a closed trajectory ball lightning in a carriage where builders lived is presented. The trajectory is shown in Fig. 2. Since there is a thermal contact between walls and ground,
Fig. 2. A typical BL trace in a room. 1—eye-witnesses, 2—tables.
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the temperature of the wall is smaller than that of the air in the room. In this case the air temperature near wall is smaller than that in the middle of the room and BL tends towards nearest wall. The ball heats air near walls and resides at some distance from the wall. Since the air temperature is greater behind the BL than that in front, BL moves along the wall. Meeting a perpendicular wall which prevents its movement in a straight line, BL heats the wall. As a result, BL turns through 90 degrees. Achieving its entry point and heating the air in the room, BL “sees” that the outdoor air becomes cooler than that in the room. In this case BL leaves the room. In some cases BL can perform several bypasses along the room perimeter (evidence number 45 in [4]). By the way it is marked in some evidences that some signs of burning on the walls are seen. There are many evidences that BL moves not only at unchanged distance from a wall or floor but also by bounces. It can be explained easily. We supposed above that time of transient processes is negligible small and there is a steady-state constantly. If there is some latency, for example, the walls or floor are wet and their heating requires a definite time, an oscillating process can take place. BL approaches a wet floor at the distance which is smaller than that for a dry floor because the feedback comes into play with some delay. In this case the maximal air temperature between BL and the wet floor is greater than that in the former case and BL repelles from the floor. The amplitude of BL oscillations depends on a degree of floor wetness. By the way the same effect takes place at BL penetration through a hole. As is reported in evidence number 100 [4] a ball of 10–15 cm in diameter, passing through a small split in a pane, changed its shape and trembled like a jelly. One can conclude from above descriptions that BL motion is determined by specific conditions in rooms and specific feedbacks. It is hard to imagine that such specific BL motion is controlled by external electrical field as is supposed in [6]. It is very interesting what shape takes large light bubble of several meters diameter? The light bubble equator is located in the layer where the air density is maximal. The top and bottom poles are located in layers where the air density gradient is directed to the equator. As a result, there are forces that tend to flatten light bubble. Since the forces which provide spherical shape of light bubble are in inverse proportion to the square of light bubble diameter, the forces which tend
to flatten BL increases with increase in its diameter but the forces which provide spherical shape to BL decrease and BL is shaped into an ellipsoid. If the distributions of air density gradient are not identical at the top and bottom poles (typical case), the light bubble deformations are not identical also and the light bubble is shaped into a body of revolution reminding a spice or plate. If there is a horizontal component of the air density gradient in the place where the plate is located, the plate is moving in horizontal direction. The plate speed may be great enough. Besides, the speed may be changed in its direction sharply with a change in the direction of the air density gradient. This may explain the great load factor which is demonstrated sometimes by some flying plates. Now consider the question why BL is not indifferent to metallic things. There are many reports that BLs are attracted to metallic objects such as wire fences or telephone lines. When attached to metallic objects BLs generally move along those objects. The point is that all metallic objects offer not only the good electric conduction but also the good heat conduction. Because of 24-hourly temperature changes the temperature of various objects at the earth surface is not identical. In sun day the temperature of upper layer of earth surface is greater than that of layers located more deeply. For example, if a metallic pole is droved in earth, the pole temperature is smaller than that of surrounding air because the heat which the pole obtains from the air propagates downward in the bottom end of the pole. As a result, in the region near the pole the air density gradient is directed to the pole surface. Appearing in the region, BL begins to near the pole. If the air refraction index gradient is not perpendicular to the pole axis then BL, approaching pole and heating the air layer between BL and pole, begin movement along the pole axis at some distance from pole surface. In general, BL obeys the first Newton law of uniform movement. Indeed, if BL moves in some direction in a homogeneous air, BL leaves behind it the air which is warmer than that before of it. This is favorable to further movement. Most if not all physicists are puzzled why BL radiates the light which spectrum corresponds to the temperature of several thousands degrees Celsius and in the same time BL is relatively cold because BL does not burn objects located near it. There is a simple explanation. BL light is not produced
V.P. Torchigin, A.V. Torchigin / Physics Letters A 328 (2004) 189–195
by very hot air but it is scattering of white light which was entrapped in process of BL generation from usual linear lightning. In other words, the light radiation produced by very hot air at the instant of BL generation is conserved in the BL. The very hot air in BL has had time to cool but BL light radiation continues its circulating with initial parameters which correspond to the very hot air. The question now arises why BL color can be various beginning from reddish and ending bluish whereas the color of usual linear lightning is white? There are many reports in which BL colors are various. The matter is that there is not a steady-state between energies of light and compressed air at the moment of BL generation [13]. If initial air energy is greater than that at steady-state, then a part of air energy is transmitted to light and its energy increases. Since total number of photons in light is unchanged in this process, the energy of each photon increases and, therefore, light frequency increases also. In this case the light wavelength is shifted in the blue side of spectrum. If the initial air energy is smaller than that at steady state, the light wavelength is shifted in the red side of spectrum. As for process of BL disappearance that it is fast enough. BL disappears when it becomes instable because of continuous radiation losses (although BL stability is conventional because there is no steadystate due to continuous radiation losses). The air pressure decreases with decreasing light intensity. This entails increasing radiation losses and, therefore, further decreasing the light intensity and so on. In the long run the light ceases to be held by the compressed
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air and is radiated in all sides. The compressed air is no longer held by the light and begins to expand. A small popping or great explosion may be heard. We hope that, taking into account our approach, readers can explain many cases of puzzling BL behavior themselves. Probably, it is timely to recognize that there are perfectly unusual objects of form of light blobs or bubbles in nature. The question how such blobs are generated was partially considered in [14].
References [1] S. Singer, The Nature of Ball Lightning, Plenum, New York, 1971. [2] J.D. Barry, Ball Lightning and Bead Lighting—Extreme Forms of Atmosphere Electricity, Plenum, New York, 1980. [3] M. Stenhoff, Ball Lightning—An Unsolved Problem in Atmospheric Physics, Plenum, New York, 1999. [4] I.P. Stakhanov, The Physical Nature of Ball Lightning, Atomizdat, Moscow, 1996 (in Russian). [5] A.I. Grigor’ev, I.D. Grigor’eva, S.O. Shiryaeva, J. Sci. Explor. 6 (3) (1992) 261. [6] T. Wessel-Berg, Physica D 182 (2003) 222. [7] V.P. Torchigin, Investigated in Russia, Electronic Journal (2003), http://zhurnal.ape.relarn.ru/articles/2002/093.pdf (in Russian). [8] V.P. Torchigin, S.V. Torchigin, Quantum Electron. 33 (10) (2003) 913. [9] S.M. Spillane, T.J. Kippenberg, K.J. Vahala, Nature 415 (2002) 621. [10] V.P. Torchigin, A.V. Torchigin, Laser Phys. 13 (6) (2003) 919. [11] V.P. Torchigin, Lomonosov 2 (2003) 86 (in Russian). [12] V.P. Torchigin, A.V. Torchigin, Khim. Zhizn 1 (2003) 12 (Chemistry and Life, in Russian). [13] V.P. Torchigin, Dokl. Phys. 48 (3) (2003) 108. [14] V.P. Torchigin, A.V. Torchigin, Phys. Scr. 68 (2003) 388.
Behavior of self-confined spherical layer of light radiation in the air atmosphere V.P. Torchigin ∗ , A.V. Torchigin Institute of Informatics Problems, Russian Academy of Sciences, Nakhimovsky prospect 36/1, 119278 Moscow, Russia Received 30 January 2004; received in revised form 7 June 2004; accepted 8 June 2004 Available online 21 June 2004 Communicated by F. Porcelli
Abstract Behavior of thin spherical layer of intensive light in an inhomogeneous atmosphere is considered. It is shown that the behavior is similar to puzzling and mysterious behavior of ball lightnings. Under assumption that ball lightning moves along the gradient of atmosphere air density process of ball lightning penetration in a salon of a flying airplane is analyzed. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Jx Keywords: Self-action; Whispering gallery waves; Ball lightning; Propagation; Optical solitons
Ball lightnings (BL) attract attention of many investigators. Now about 10 000 occasions of BL appearance are described and above 2000 papers concerned BLs have been published. Historical surveys appear regularly. Some last of them are in books [1–3]. There is no deficit of hypotheses explained features of BL behavior. Above one hundred hypotheses are known at present. The problem is that all of them are not able to explain the following several generally recognized facts: penetration of BL through window panes, through chimneys and small splits in walls, penetration BLs in salons of flying airplanes, contradiction between BL spectrum which corresponds to a hot body
* Corresponding author.
E-mail address: [email protected] (V.P. Torchigin). 0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.06.022
at the temperature above 5000 K and absence of noticeable IR radiation. These and other properties of BL are very valuable for theorists because they enable to withdraw immediately majority of hypothesizes. For example, since it is found safely that BLs can penetrate through window panes [4,5], ought to withdraw all hypotheses where such words as electrons, ions, clusters, condensate states occur. It is known very well that no particles can penetrate through glass. These thoughts are expressed clearly in [6] where a hypothesis that BL is connected with a strong electrical field formed by atmospheric electricity is proposed. As is known, the field can penetrate though any dielectric, in particular through glass and walls. Puzzling motions of BL are explained by motion of environmental electric field. BL seeks for itself the position where the net action of electrical force vanishes. However, in accor-
190
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dance with this approach BL can penetrate in rooms through any walls whereas it is known that BL penetrates through holes and splits in walls. It is hard to imagine that the electrical field moves in space in such a way that it forces BL to find out a small split and penetrate through it with changing BL shape. Of even grater difficulties are connected with explanation of BL penetration through chimneys. In 2002 we put forward a hypothesis that BL consists of light radiation emerged at strike of a conventional linear lightning [7]. But as is known the light propagates in straight line at light speed and disappears practically instantly. There are must be some means that force the light to propagate in a limited volume of space. Surprisingly, similar means do exist. Studying whispering gallery light waves in fibers without coating, we found out that their group velocity may be decrease till zero [8]. In this case the wave rotates around the fiber axis and its wave vector is perpendicular to the axis. The same situation takes place in a glass sphere where a whispering gallery light wave circulates along the sphere equator in a thin surface layer [9]. The light wave cannot propagate in a free space owning the total inner reflection on the boundary between glass surface and surrounding space. In this case there is no necessity to have a continuous glass ball. A glass sphere of small thickness is sufficient. Such sphere may be considered as a planar lightguide rolled to the sphere. As is known a thin film planar waveguides are basis of up-to-date integrated optics where, unlike conventional 3D bulk optics, all optical processes are produced in a thin film, that is in two-dimensional space. A thin spherical layer of compressed air may be used instead of the glass spherical layer. As is known the air refraction index increases with increase in the air pressure and total inner reflection may take place at the boundary between the compressed and conventional airs. But what are means which prevent the compressed air from expansion? This is an intense light which circulates within the layer and produces the electrostriction pressure that tends to near air molecules close together. Thus, the intense light confines the compressed air. In turn, the layer of the compressed air shows itself as a thin film lightguide which prevents the light from radiation in free space. We obtain a light bubble comprising of light and air. It was not so hard to show that the air
pressure of several atmospheres is sufficient to confine safely the light radiation in a sphere about several centimeters in diameter [10]. The next step was to show how the light bubble can penetrate through window panes. The problem is that any light, penetrating through a glass, propagates further in straight line and, seemingly, there are no means to force it to not propagate from the light bubble at the opposite side of the glass. It turns out that the problem is solved simply. As light bubble touches the glass surface, the light penetrates inside the glass but is subject to the total inner reflection from the opposite side of the glass. In the same time the light field penetrates in a thin air layer of several wavelengths thickness at the opposite side of the glass. As is known this field cannot excite propagating light waves (the word “total” underlines that all light launched at the opposite side of the glass reflects backwards completely). In the same time the light field in the air region adjacent to the opposite side of the glass produces the electrostriction pressure. As a result, the air density and refraction index increase in the region and next portions of circulating light penetrate in the region. Thus, a small part of the light bubble appears at the opposite side of the glass. Thereafter this part increases gradually. Illustrations of this process are presented in [11–14]. One can see that only light penetrates through the glass and compresses new portions of air located at the opposite side of the glass. The initial air which was in the light bubble before its penetration does not penetrate through the glass. A motion of light bubbles has been studied theoretically in [11–14]. Only the following three properties of light bubbles have been used. First, like a conventional light beam which deflects in a inhomogeneous optical medium from a straight line in the direction where the gradient of the refraction index increases, light bubble moves along the gradient of the refraction index. Because the air refraction index increases linearly with increasing the air density, light bubble moves in the direction where the air density is maximal. The air density is in inverse proportion with the air temperature at constant pressure and light bubble moves in the direction where the air is cooler. Second, unlike a pumped football ball where the air pressure exists in all volume of the ball, the air pressure in a light bubble exists in a thin surface
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layer. In this case the deformability of light bubbles increases by (R/w)2 times as compared with that of the football ball where R and w are radius and thickness of light bubble, respectively. For example, if R = 10 cm and w = 10 µm, (R/w) = 106 . In this case a spherical shape of light bubble may be changed by small external forces. Third, light bubble is subject to the effect of selfaction. This means that light bubble, approaching some obstacle, heats it and changes the air temperature field distribution near itself. As a result, various parts of light bubble surface tends to move in various directions and the light bubble shape is deformed. These qualitative considerations occur sufficient to explain many features of light bubble motion. It turns out that it is very simple to explain puzzling motion of light bubbles near the earth surface. The air temperature near the earth surface is greater than that at some distance from the surface (the earth surface absorbs sun radiation and is heated; the air near the earth surface is heated too due to heat conduction). In this case the air density and therefore the air refraction index is smaller near the earth surface than that at some distance from it. As a result, the air refraction index is maximal at some distance from the earth surface. Light bubbles reside at this height which is equal usually about 1 m. To explain penetration of light bubbles through small splits ought to remind that light bubbles may be deformed easily. Approaching the hall which crosssection is smaller than a light bubble diameter, a light bubble heats regions of the wall near the hole. The air adjacent these regions is heated owning heat conduction and regions of the light bubble surface located in this air are subject to forces of repulsion. In the same time the region of light bubble located near the hole axis is subject to forces of attraction to the hole. As a result, the light bubble is deformed in such a way that its shape tends to the shape of the hole. Illustrations of light bubble penetration through a hole are presented in [11–14]. After studying features of light bubble motion, stability and main physical parameters such as the stored energy and lifetime have been analyzed [13]. Initially most difficulties were connected with its lifetime. As is known the life time of conventional sun white light in conventional atmosphere is smaller than 1 millisecond. The lifetime of ball lightnings is greater
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essentially. What is a reason? Analyzing dependence on the air pressure of the molecular light scattering which is responsible for the light lifetime, it was shown that the light scattering decreases at extremely high pressure where air molecules are packed closely. The air compressibility at such pressure is near zero and fluctuations in air density that are responsible for light scattering disappear. As a result, a lifetime of light in a light bubble may be as much as tens seconds that is comparable with the BL lifetime. It is self evident that electrical effects within BL as well as outside it can occur essential influence on BL properties and its behavior. Moreover, such BL properties as generation of low frequency noises in radio receivers, attraction of BL to metal things can be explained easily analyzing an interaction between inner and outer electrical fields. An absence of total charge within BL is a particular case only. The electrostriction pressure that tends to near particles within BL close together is that a phenomenon which cancels forces of mutual repulsion between identical charges and provides BL stability. But consideration of the electrical effects is beyond the scope of the present Letter. The purpose of the present Letter is to give additional proofs of the validity of the hypothesis about light nature of BL. Fortunately, puzzling and mysterious BL behavior can be useful for this purpose because the more puzzling situations are explained on the basis of a hypothesis the more credibility for it. In our opinion, such explanation sometimes may be more conclusive than experimental production of some physical objects that remind BL in its form but differ in their behavior. We are going to consider most puzzling BL behavior connected with BL penetration in a flying airplane. Why do BLs prefer to visit flying airplanes (there are many reports) and is perfectly indifferent to airplanes on the earth surface? Where from such yearning for airplane flight? Everybody who looked in an illuminator of a flying airplane may see small clouds and swarms that run away with large speed may ask why BLs are not blown away the airplane wing although a very strong wind at speed about 1000 km/h blows on the airplane? If BL were composed of some particles, clusters, ions, electron, etc., all of these were blown away immediately. Let us estimate preliminary the velocity at which a light bubble moves in an inhomogeneous atmosphere.
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tial speed dx/dt and initial shift x are equal to zero, we obtain from (2) that the total shift of the light beam is π x = gn R 2 . (3) 2 In this case the speed of shifting is determined by the following expression 2x . T Taking into account (1), we obtain v=
Fig. 1. Direction of coordinate axes relatively the infinite cylindrical layer.
Note at once that the velocity may be extremely large. For example, if we assume that a light bubble of 10 cm in diameter is shifted by 1 µm per one light revolution, then the light bubble is shifted by 1 km/s because the light within the light bubble performs 109 revolutions per second. For the sake of simplicity consider an infinite cylindrical layer of compressed air in which an intense light is circulating and supporting the air compression. Let the cylindrical layer of R radius and axis paralleled to the z-axis is located in an inhomogeneous atmosphere which refraction index increases along the x-axis at the rate gn = dn/dx > 0 and does not depend on y, z coordinates (Fig. 1). If the cylindrical layer is located in a homogeneous atmosphere where gn = 0, then the light makes one revolution around the cylinder axis in time T=
2πRn . c
(1)
If the cylindrical layer is located in an inhomogeneous atmosphere where gn > 0, then the light trajectory is not closed. The light shifts additionally at some distance x along the x-axis. In accordance with the eikonal equation the additional shift of light beam in presence of the additional refraction index gradient gn is determined by the following expression d2 x (2) = gn c2 cos(ct/R). dt 2 Let the light beam propagates along the arc beginning at point x = 0, y = −R and ending at point x = 0, y = R. Supposing that at time t = −(π/2)R/c the ini-
gn Rc nD c = , 2 4 where
(4)
v=
(5)
nD = gn D
(6)
is the change in the atmosphere refraction index at distance equaled to the light bubble diameter. For example, if nD = 10−5 , then v = 750 m/s, that is v surpasses the sound speed in air. Ought to underline that light bubble movement is not accompanied by movement of the air compressed within it. Like light bubble movement through a window glass, where only light radiation penetrates through the glass and compresses new air portion located at the opposite side, light bubble movement in the air atmosphere is accompanied by compression of new air portions along direction of the movement and corresponding release of air portions from the opposite light bubble side. Now let us estimate a degree of atmosphere inhomogeneity produced by a flying airplane. An additional air pressure p near a front edge of a wing where the air speed relatively to the airplane is equal to zero and is equal to the airplane speed u relatively the earth is determined by the following expression ρu2 , (7) 2 where ρ is the air density and ρ ∼ = 1 kg/m3. At the airplane speed u = 720 km/h = 200 m/s we have p = 2 × 104 Pa ∼ = 0.2 atmospheres. The air refraction index at the normal atmosphere pressure is determined by the expression n = 1 + n, where n = 2.7 × 10−4 . Since the air density is proportional to the air pressure, then p =
n(p) = 1 +
p n, p0
(8)
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where p0 is the air pressure at normal conditions. From (8) we have that an increase in the air pressure by p = 0.2 atmosphere entails increase in the air refraction index by n(p) = 0.2n ∼ = 0.54 × 10−4 . As follows from (5), to provide light bubble motion at the airplane speed it is necessary the following air inhomogeneity nD = u/(c/4) ∼ = 2.66 ×10−6 . Under assumption that p decreases linearly with distance from the airplain we obtain that such decrease takes place at the distance S∼ =
n(p) D = 20D. nD
At D = 0.1 m we obtain that bubbles may catch up the airplane located from them at the distance S = 2 m. Needless to say it is very rough estimations determining the order of magnitude only. But they show that a flying airplane attracts all light bubbles located directly ahead, as well as to the right, left, at the top and bottom in the region of inhomogeneous atmosphere produced by the airplane. Achieving the airplane, light bubble stops in the region where the air density is maximal and moves with this region together and, therefore, with the airplane. No airplane maneuvers can separate the light bubble and airplane. Ought to note that the additional air pressure p near front edge of the wing is proportional to the square of airplane speed u, that is the region from which light bubbles are attracted to the airplane increases with increase in the airplane speed. Besides, the probability for the airplane to meet any BLs is proportional to the airplane speed. Indeed, if the airplane could do several revolutions around the Earth per one second, it could gather all BLs which were met at its trace. Are there any other hypothesizes that explain how BLs can pursue an airplane and moves with it together? As is known the air is rarefied at great height where airplanes fly. Because of this an additional pressure is generated in airplane cabins and saloons to provide normal breath for passengers. Since it is very hard and is not justified economically to keep these rooms hermetic absolutely, there is an air compressor which continuously pumps in the outdoor air. It is natural enough to take the air from that region where the air pressure is maximal that is from the region where BLs can be located. The air is pumped by a turbine compressor and there is a tunnel between the salon and outdoor at any position of turbine blades. Since
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the light bubble layer width is several micrometers only, a split of width smaller than ten micrometers is sufficient for light bubble penetration. The air density gradient is directed into the salon. Moving along the gradient, BL penetrates in the salon. Mechanisms which enable BL to change its shape are considered in [11–14]. One can give recommendation to airplane designers to avoid BL penetration. There must be no splits in the region where additional air pressure is maximal. Consider now puzzling BL motion in a room [4,5]. Usually BL moves along walls near a floor but not near a ceiling. Since a warm air is easier than cool one, the air near a floor is cooler than that near a ceiling and therefore the air refraction index is maximal near the floor. In this case a ball, appearing in a room, moves initially towards the floor which shows itself as an obstruction. Besides, walls of the room are cooler than the air in the middle of the room because the walls are connected with cool ground. Approaching a wall, the ball heats air between the wall and ball. As a result, its motion towards to the wall ceases and the ball begins to move along the wall. Since the air before the ball is cooler than that behind it, the ball continues to move along the room perimeter at some distance from walls. In some cases the ball can find out a door, penetrates though it and leaves the room. There are many evidences supporting this picture. For example, there is a description in [4] an occasion 29 in which a closed trajectory ball lightning in a carriage where builders lived is presented. The trajectory is shown in Fig. 2. Since there is a thermal contact between walls and ground,
Fig. 2. A typical BL trace in a room. 1—eye-witnesses, 2—tables.
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the temperature of the wall is smaller than that of the air in the room. In this case the air temperature near wall is smaller than that in the middle of the room and BL tends towards nearest wall. The ball heats air near walls and resides at some distance from the wall. Since the air temperature is greater behind the BL than that in front, BL moves along the wall. Meeting a perpendicular wall which prevents its movement in a straight line, BL heats the wall. As a result, BL turns through 90 degrees. Achieving its entry point and heating the air in the room, BL “sees” that the outdoor air becomes cooler than that in the room. In this case BL leaves the room. In some cases BL can perform several bypasses along the room perimeter (evidence number 45 in [4]). By the way it is marked in some evidences that some signs of burning on the walls are seen. There are many evidences that BL moves not only at unchanged distance from a wall or floor but also by bounces. It can be explained easily. We supposed above that time of transient processes is negligible small and there is a steady-state constantly. If there is some latency, for example, the walls or floor are wet and their heating requires a definite time, an oscillating process can take place. BL approaches a wet floor at the distance which is smaller than that for a dry floor because the feedback comes into play with some delay. In this case the maximal air temperature between BL and the wet floor is greater than that in the former case and BL repelles from the floor. The amplitude of BL oscillations depends on a degree of floor wetness. By the way the same effect takes place at BL penetration through a hole. As is reported in evidence number 100 [4] a ball of 10–15 cm in diameter, passing through a small split in a pane, changed its shape and trembled like a jelly. One can conclude from above descriptions that BL motion is determined by specific conditions in rooms and specific feedbacks. It is hard to imagine that such specific BL motion is controlled by external electrical field as is supposed in [6]. It is very interesting what shape takes large light bubble of several meters diameter? The light bubble equator is located in the layer where the air density is maximal. The top and bottom poles are located in layers where the air density gradient is directed to the equator. As a result, there are forces that tend to flatten light bubble. Since the forces which provide spherical shape of light bubble are in inverse proportion to the square of light bubble diameter, the forces which tend
to flatten BL increases with increase in its diameter but the forces which provide spherical shape to BL decrease and BL is shaped into an ellipsoid. If the distributions of air density gradient are not identical at the top and bottom poles (typical case), the light bubble deformations are not identical also and the light bubble is shaped into a body of revolution reminding a spice or plate. If there is a horizontal component of the air density gradient in the place where the plate is located, the plate is moving in horizontal direction. The plate speed may be great enough. Besides, the speed may be changed in its direction sharply with a change in the direction of the air density gradient. This may explain the great load factor which is demonstrated sometimes by some flying plates. Now consider the question why BL is not indifferent to metallic things. There are many reports that BLs are attracted to metallic objects such as wire fences or telephone lines. When attached to metallic objects BLs generally move along those objects. The point is that all metallic objects offer not only the good electric conduction but also the good heat conduction. Because of 24-hourly temperature changes the temperature of various objects at the earth surface is not identical. In sun day the temperature of upper layer of earth surface is greater than that of layers located more deeply. For example, if a metallic pole is droved in earth, the pole temperature is smaller than that of surrounding air because the heat which the pole obtains from the air propagates downward in the bottom end of the pole. As a result, in the region near the pole the air density gradient is directed to the pole surface. Appearing in the region, BL begins to near the pole. If the air refraction index gradient is not perpendicular to the pole axis then BL, approaching pole and heating the air layer between BL and pole, begin movement along the pole axis at some distance from pole surface. In general, BL obeys the first Newton law of uniform movement. Indeed, if BL moves in some direction in a homogeneous air, BL leaves behind it the air which is warmer than that before of it. This is favorable to further movement. Most if not all physicists are puzzled why BL radiates the light which spectrum corresponds to the temperature of several thousands degrees Celsius and in the same time BL is relatively cold because BL does not burn objects located near it. There is a simple explanation. BL light is not produced
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by very hot air but it is scattering of white light which was entrapped in process of BL generation from usual linear lightning. In other words, the light radiation produced by very hot air at the instant of BL generation is conserved in the BL. The very hot air in BL has had time to cool but BL light radiation continues its circulating with initial parameters which correspond to the very hot air. The question now arises why BL color can be various beginning from reddish and ending bluish whereas the color of usual linear lightning is white? There are many reports in which BL colors are various. The matter is that there is not a steady-state between energies of light and compressed air at the moment of BL generation [13]. If initial air energy is greater than that at steady-state, then a part of air energy is transmitted to light and its energy increases. Since total number of photons in light is unchanged in this process, the energy of each photon increases and, therefore, light frequency increases also. In this case the light wavelength is shifted in the blue side of spectrum. If the initial air energy is smaller than that at steady state, the light wavelength is shifted in the red side of spectrum. As for process of BL disappearance that it is fast enough. BL disappears when it becomes instable because of continuous radiation losses (although BL stability is conventional because there is no steadystate due to continuous radiation losses). The air pressure decreases with decreasing light intensity. This entails increasing radiation losses and, therefore, further decreasing the light intensity and so on. In the long run the light ceases to be held by the compressed
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air and is radiated in all sides. The compressed air is no longer held by the light and begins to expand. A small popping or great explosion may be heard. We hope that, taking into account our approach, readers can explain many cases of puzzling BL behavior themselves. Probably, it is timely to recognize that there are perfectly unusual objects of form of light blobs or bubbles in nature. The question how such blobs are generated was partially considered in [14].
References [1] S. Singer, The Nature of Ball Lightning, Plenum, New York, 1971. [2] J.D. Barry, Ball Lightning and Bead Lighting—Extreme Forms of Atmosphere Electricity, Plenum, New York, 1980. [3] M. Stenhoff, Ball Lightning—An Unsolved Problem in Atmospheric Physics, Plenum, New York, 1999. [4] I.P. Stakhanov, The Physical Nature of Ball Lightning, Atomizdat, Moscow, 1996 (in Russian). [5] A.I. Grigor’ev, I.D. Grigor’eva, S.O. Shiryaeva, J. Sci. Explor. 6 (3) (1992) 261. [6] T. Wessel-Berg, Physica D 182 (2003) 222. [7] V.P. Torchigin, Investigated in Russia, Electronic Journal (2003), http://zhurnal.ape.relarn.ru/articles/2002/093.pdf (in Russian). [8] V.P. Torchigin, S.V. Torchigin, Quantum Electron. 33 (10) (2003) 913. [9] S.M. Spillane, T.J. Kippenberg, K.J. Vahala, Nature 415 (2002) 621. [10] V.P. Torchigin, A.V. Torchigin, Laser Phys. 13 (6) (2003) 919. [11] V.P. Torchigin, Lomonosov 2 (2003) 86 (in Russian). [12] V.P. Torchigin, A.V. Torchigin, Khim. Zhizn 1 (2003) 12 (Chemistry and Life, in Russian). [13] V.P. Torchigin, Dokl. Phys. 48 (3) (2003) 108. [14] V.P. Torchigin, A.V. Torchigin, Phys. Scr. 68 (2003) 388.