Advances in ball lightning research

Journal Pre-proof Advances in Ball Lightning Research Mikhail L. Shmatov, Karl D. Stephan PII:

S1364-6826(19)30384-0

DOI:

https://doi.org/10.1016/j.jastp.2019.105115

Reference:

ATP 105115

To appear in:

Journal of Atmospheric and Solar-Terrestrial Physics

Received Date: 27 May 2019 Revised Date:

29 August 2019

Accepted Date: 11 September 2019

Please cite this article as: Shmatov, M.L., Stephan, K.D., Advances in Ball Lightning Research, Journal of Atmospheric and Solar-Terrestrial Physics, https://doi.org/10.1016/j.jastp.2019.105115. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Ltd. All rights reserved.

Advances in Ball Lightning Research

Mikhail L. Shmatov

a

,

Karl D. Stephan

b*

a

Ioffe Institute, 194021 St. Petersburg, Russia

b

Texas State University, San Marcos, Texas 78666

*Corresponding author

Abstract: Ball lightning is a rarely observed phenomenon whose existence is attested to by thousands of eyewitness reports, but which has so far evaded a widely accepted scientific explanation. This review paper summarizes theoretical, observational, and experimental work in the field since approximately 2000. In particular, several situations when mobile phone cameras as well as scientific instruments have been used to capture numerous events that are candidates for ball lightning sightings are considered. We evaluate recent experimental attempts to produce laboratory ball lightning, review what is known about possible ball lightning hazards, and conclude with recommendations for future research in this area.

1. Introduction Science’s ancestor, natural philosophy, began in humanity's wonder at the amazing features of the natural world that can be seen with the unaided eye: the sun, the stars, rain, thunder, lightning, and rarer phenomena such as hail, tornadoes, eclipses, and volcanic eruptions. One by one, these wonders have yielded their secrets to scientific efforts, and we now understand them in terms of objective principles that provide not only detailed explanations, but in many

cases allow accurate predictions and laboratory replications as well. But as of 2019, one natural phenomenon common enough to have been seen by thousands of eyewitnesses still resists not only replication and prediction, but also has refused to yield a widely accepted scientific explanation. That phenomenon is ball lightning. Because observations of ball lightning are very rare compared to sightings of ordinary lightning, most of the observational data we have on ball lightning consists of eyewitness accounts from lay persons who have seen it by chance. While any data set collected in such a manner will include spurious and erroneous material, there are enough common features among the extensive surveys and collections of eyewitness reports (see e.g. Abrahamson et al., 2002; Barry, 1980; Brand, 1923; Grigor’ev, 2006; Grigor’ev et al., 1992; Rayle, 1966; Singer, 1971; Smirnov, 1987, 1988, 1990, 1992; Stakhanov, 1996) to allow the reconstruction of a typical composite ball-lightning sighting, which usually (but not always) happens in the vicinity of an active thunderstorm. This composite relies upon data presented in Rakov and Uman (Rakov and Uman, 2003) which summarizes much of the main statistical data on ball lightning known at that time. Most eyewitnesses do not see the formation of the object, but rather notice it after it has become visible. What they see is usually a spherical or roughly spherical light-emitting object whose size varies from a few cm to a meter or more, with an average diameter of about 20 cm, and whose colors vary from red to yellow, white, blue, and (rarely) green. The object is bright enough to appear brighter than most daylight backgrounds, but usually not much brighter than a typical household incandescent lamp (it should be emphasized, however, that in some situations the object is very bright; see Section 5). Most observers report that the object moves in a mainly horizontal direction at a velocity of up to a few meters per second. The object is typically in

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view for times ranging from 1 s to a minute or more, with most incidents lasting less than 10 s. If the witness still has the object in view at the termination of its existence, it is either vanishes silently or explodes, sometimes noisily and destructively. Most people who see ball lightning have never seen anything quite like it before. The surprise and other strong emotions it can induce tend to impress ball-lightning events strongly on one’s memory. There is evidence from psychological studies that high levels of emotion are associated with “relatively accurate memory for central details but relatively inaccurate memory for peripheral details” (Christianson, 1992). This helps explain why many accounts of ball lightning are from memories that are several decades old, but remain vivid enough to allow the recollection of information such as the object’s size, color, duration, and motion. However, detailed descriptions of its appearance, including small features or interior structures, are comparatively uncommon in such descriptions. In this review, our intention is not to recapitulate the entire history of ball-lightning research or to present an exhaustive bibliography of eyewitness accounts. Both book-length treatments (Barry, 1980; Brand, 1923; Grigor'ev, 2006; Singer, 1971; Smirnov, 1988; Stakhanov, 1996; Stenhoff, 1999) and previous review articles (see e.g. Abrahamson et al., 2002; Charman, 1979; Smirnov, 1987, 1990, 1992) present extensive bibliographies of ball lightning research prior to about the year 2000. Our emphasis in this work is on theoretical, observational, and experimental developments in the field of ball lightning research primarily during the last two decades. We critically review the recent literature with the purpose of discerning directions for future work in this field which are most likely to be fruitful. Research on ball lightning has languished up to now due to, in particular, the extreme difficulty of obtaining instrumented data on the

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phenomenon. But as we will describe below, the popularity of fixed and mobile video recording devices and systematic observations with the use of scientific instruments, in particular, in the gamma-ray range (see e.g. Dwyer et al., 2012, 2015; Enoto, 2017; Shmatov, 2006a, 2019; Umemoto et al., 2016, Wada et al., 2018) may lead to a renaissance of sorts in the study of this heretofore nearly intractable scientific problem. The article is structured as follows. We begin with a review of some recently proposed theoretical models of ball lightning. Next, we review notable recent observations of objects claimed to be ball lightning, and follow that with a review of several recent experimental attempts to produce ball-lightning-like objects in the laboratory. Following a discussion of the potential hazards of ball lightning, we conclude with some proposals for the directions of future research.

2. Recently proposed models of ball lightning It is not our purpose to review the entire record of theoretical ball lightning models, of which there are dozens, as previous reference works (e. g. Stenhoff, 1999) summarize the leading theories adequately up to their respective times of publication. Because ball lightning observations almost always yield more or less reliable quantitative results only for the time of duration of ball lightning and its size and shape, theorists are not burdened by the obligation to make quantitative predictions of other ball lightning parameters except within broad limits. This leads to a situation in which many theories can account for one or two features of ball lightning, but few, if any, can account for the majority of the characteristics that form the core similarities among most observations. The features of ball lightning which an adequate theory should

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account for were most cogently summarized by Rakov and Uman (Rakov and Uman, 2003) in the following eight characteristics:

"(i) ball lightning's association with thunderstorms or with cloud-to-ground lightning; (ii) its reported shape, diameter, and duration, and the fact that its size, luminosity, and appearance generally do not change much during its lifetime; (iii) its occurrence in both open air and in enclosed spaces such as buildings or aircraft; (iv) the fact that ball lightning motion is inconsistent with the convective behavior of a hot gas; (v) the fact that it may decay either silently or explosively; (vi) the fact that ball lightning does not often cause damage; (vii) the fact that it appears to pass through small holes, through metal screens, and through glass windows; (viii) the fact that it is occasionally reported to produce acrid odors and/or leave burn marks, is occasionally described as producing hissing, buzzing, or fluttering sounds, and is sometimes observed to rotate, roll, or bounce off the ground."

Although some researchers would contest the inclusion of some of these criteria, Rakov and Uman contend that an adequate theory should explain at least four of these eight characteristics. Allowing for the possibility that the phenomenon usually termed ball lightning may in fact be a meta-category for more than one type of process (Keul and Diendorfer, 2018), a good theory should at least explain ball lightning's light emission, lifetime, and a few other of its more unusual characteristics.

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2.1. Models using assumptions about oscillation of electrons and ions Several authors proposed ball lightning models using assumptions about oscillations of ions and/or electrons in ball lightning (Alekhin, 2004; Dvornikov, 2010, 2011, 2013; Ostapenko and Tolpygo, 1984; Shmatov, 2001, 2003, 2004a, 2006a, 2015a). The plasmon resonance model proposed by Mayergoyz et al. (Mayergoyz et al., 2005) and the proposal of Miley et al. (Miley et al., 2001) to use an inertial electrostatic device to simulate some aspects of ball lightning are also based on these types of assumptions. There are several definitions of plasmon. Here it is sufficient to present the definition “plasmon is a quantum of plasma oscillations” from an anonymous article in the Physical Encyclopedia (Editor-in-Chief A.M. Prokhorov), Vol. 3, p. 614, Bol. Ros. Encycl., Moscow, Russia (1992) (see also Kittel, 1963). Inertial electrostatic devices are plasma traps for some scenarios of controlled thermonuclear fusion (see e.g. Gu and Miley, 2000; Hirsch, 1967). In many of such traps, the shape of the confined plasma cloud is almost spherical (this results from the use of a spherical grid electrode) and motion of some of the plasma particles can be described approximately as oscillation along radial directions of the cloud (Gu and Miley, 2000; Hirsch, 1967). The assumption of oscillating charged particles has been shown to be compatible with the observational data on the ball lightning lifetime τ bl and volume density ρ E of ball lightning energy ε bl only by the model proposed by Shmatov (2003, 2015a). According to this model, ball lightning has a core consisting of clouds of electrons and almost totally ionized ions which oscillate with respect to each other. The core is surrounded by the so-called depleted layer which isolates it from the atmosphere. The depleted layer of some ball lightning is surrounded by a

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region of luminescence of the air. This layer arises due to the ionization of the air by radiation, mainly UV, from ball lightning. In situations corresponding to relatively long τ bl , the core is spherically symmetrical, its particles oscillate in radial directions and its center can be surrounded by a practically empty region, the densities of particles in which are much less than those in other regions of the core (see Fig. 1).

Fig. 1. Ball lightning with spherically symmetrical core. 1, main region of the core with high densities of electrons and ions; 2, depleted layer; 3, empty region of the core; 4; region of luminescence of the air. Arrows indicate some of the direction of oscillation of the electrons.

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The stability of the core is provided by the oscillation of its particles and the atmospheric pressure transferred through the depleted layer (for details, see (Shmatov, 2015a)). The ball max lightning core parameters depend strongly on the maximum value ε osc of the electron kinetic

energy εosc corresponding to its oscillatory motion. The model takes into account the loss of ball lightning core energy ε c , which is the main part of ε bl , due to bremsstrahlung and yields the max of fact that for a spherically symmetrical ball lightning core and the oscillation period with ε osc

the order of 100 keV and greater, other losses of ε c are negligible (see Shmatov, 2003, 2015a max1 max and below). The typical initial values ε osc of ε osc are of the order of 0.1 to 10 MeV

(Shmatov, 2001, 2003, 2004a, 2006a, 2015a, 2019). It is convenient to describe several parameters of the ball lightning core as functions of the parameter max max max γ osc = ε osc /(mc2 ) + 1 ≈ ε osc /(511 keV) + 1 , where m is the rest mass of the electron and c is the max1 max1 max1 = ε osc /(mc2 ) + 1 ≈ ε osc /(511 keV) + 1. velocity of light, or of its initial value γ osc

The oscillatory motion of the particles of the core is disturbed by their random motion. The random motion of the electrons is important mainly as an effect suppressing, in common max with relatively high ε osc , their radiative recombination with the ions of the core. The maximum

max value ε osc,ion of kinetic energy corresponding to oscillatory motion of ions is much less than max max max ε osc = 20mc2 ≈ 10.2 MeV and ε osc . For example, a model situation when ε osc ,ion , averaged

over the ions of N, O and Ar, is about 224 keV, has been described (Shmatov, 2003). Such max max difference of ε osc and ε osc ,ion , asquired by electrons and ions in the same oscillating electric

field, results from the low ratio of m to the rest mass of the ion (see e.g. Shmatov (2003)). The

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typical kinetic energy corresponding to the random motion of the ions can be comparable with max ε osc ,ion and even exceed it, but, in any case, the total kinetic energy of a core ion is also much max less than ε osc . Radiative recombination is accompanied by a quick collisional ionization of the

arising ions and, therefore, results mainly in additional losses of ε c rather than in a decrease in the density ne of the oscillating electrons (Shmatov, 2004a, 2015a). The ability to explain τ bl in the range from several to a few hundred or at least several tens of seconds can be considered as the first requirement to be met by any ball lightning model. For the model proposed by Shmatov, the initial analysis of this ability was performed using the typical time τ rad of the loss of ε c due to bremsstrahlung (Shmatov, 2001, 2003). The energy

dε rad of the bremsstrahlung radiation emitted by the electron with kinetic energy ε k during time dt in plasma containing different ions, the velocities of which are much less than the electron velocity v, equals κ rad (ε k ) ni vdt , where κ rad is the effective stopping averaged over the ions and ni is the density of the ions (see also Berestetskii et al., 1980). The time τ rad was estimated as

τ rad =

max1 ε osc , (dε rad / dt )1

(1)

where (dε rad / dt )1 is dε rad / dt averaged over the first period of the oscillation (Shmatov, 2003). max1 For 1.1 ≤ γ osc , Eq. (1), the approximation ε k ≈ ε osc , a one-dimensional model of plasma

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oscillations and the formula describing κ rad within the framework of the Born approximation (see Berestetskii et al., 1980) yield

τ rad =

max 1 g (γ osc )

Z 2 ni

,

(2)

max1 max1 ) is a function that depends only on γ osc where g (γ osc and Z 2 is the average squared value

of the atomic number Z of the elements the ions of which are present in the core. For ball lightning in the atmosphere of the Earth, Z 2 ≈ 53.44 (Budyko, 1988; Shmatov, 2001, 2003). max1 max1 ≤ 100 , g (γ osc ) is plotted in Fig. 2. Here and below in this Section, it is For 1.1 ≤ γ osc

assumed that ni is constant. This assumption corresponds to many reports about observations of ball lightning which indicate constant or approximately constant diameters (see e.g. Singer, 1971).

max1 max1 Fig. 2. Values of functions g(γ osc ) (dashed line) and g1.1 (γ osc ) (solid line).

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It should be emphasized that in a general case τ rad does not coincide with τ bl . It has max1 max ≈ 10 keV can be been shown that at ε osc of about 50 keV and higher, the value ε osc

considered as corresponding to the end of existence of ball lightning and τ bl can be described as

τ bl ≈

max 1 g1.1 (γ osc )

Z

2

ni

max 1 + τ bl (γ osc = 1.1) ,

(3)

max from its initial value where the first term in the right-hand side is the time of a decrease in γ osc max1 max1 max1 max γ osc ) is a function that depends only on γ osc = 1.1) is the to 1.1, g1.1(γ osc and τ bl (γ osc max time of the decrease in ε osc from 0.1mc2 ≈ 51.1 keV to 10 keV (Shmatov, 2004a, 2006a, max max1 max1 = 1.1) ≈ 0.8 − 2 s. For 1.1 ≤ γ osc ≤ 100 , g1.1(γ osc ) is 2015a). At standard conditions, τ bl (γ osc max ≥ 1.1 , a relative plotted in Fig. 2. The use of Eq. (3) is justified by the fact that at γ osc

contribution of bremsstrahlung into loss of ε c is at least about 82–90 % (for details, see Shmatov, 2015a). The ball lightning core has a positive electric charge arising due to escape of some of the electrons from it (Shmatov, 2003). This charge is important for the stability and, in some situations, the motion of ball lightning, but its value is much less than the charge of all of the ions of the core. Therefore, inside the core ne ≈ Z ni , where Z is the average value of Z. For ball lightning in the atmosphere of the Earth, Z ≈ 7.262 (Budyko, 1988; Shmatov, 2001, 2003).

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Using the aforementioned value of Z 2 and assuming, for the sake of determinacy, that max 1 τ bl (γ osc = 1.1) ≈ 1 s, we can rewrite Eqs. (2) and (3) as

ni ≈

max1 g (γ osc ) 53.44τ rad

ni ≈

max1 g1.1(γ osc ) , 53.44(τ bl − 1 s)

and

max 1 > 1.1 , we can obtain ni corresponding to arbitrarily large respectively. Thus, for any γ osc

values of τ rad and τ bl . However, such ni and other ball lightning core parameters, calculated as its functions, should satisfy several requirements related, in particular, to established parameters of ball lightning and the use of a one-dimensional model. First of all, ni should not be too low and the amplitude Ae of the oscillation of electrons should be at least several times less than the visible radius Rbl of ball lightning under consideration (this requirement should be satisfied, in max particular, at Rbl of several cm; according to a one-dimensional model, Ae ≈ ε osc /( 2πe2 ne ) ,

where e = the absolute value of the electron charge). For example, it is evident that if at any max 1 γ osc and τ bl = 3 s ni were of the order of 1 cm-3 or Ae were of the order of 1 m, the model

would be wrong. The outward pressure in the ball lightning core should equal atmospheric pressure patm . The model should also explain the existence of ball lightning with relatively large max ρ E ≈ neε osc of about 1 kJ/cm3 (see Dmitriev et al., 1981). Several examples demonstrating that

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the requirements of such a kind can be satisfied were presented (Shmatov, 2001, 2003, 2004a, 2015a, 2019). The ball lightning core parameters corresponding to one such example have been obtained when demonstrating that photons of the prolonged gamma-ray emission (or, in other terms, gamma-ray glow) recorded by the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment on January 13, 2012 (Umemoto et al., 2016) could be emitted by ball lightning and generated by annihilation of positrons which arose mainly due to production of the

β + -active isotopes by the sharp gamma-ray flash (see Enoto et al., 2017), accompanying the formation of ball lightning, and production of electron-positron pairs by photons from ball lightning (Shmatov, 2019). The prolonged emission had a duration of about 60 s, its spectrum had the upper boundary ε max ≈ 6.5 − 10 MeV and was a superposition of the continuum and a line identified with an electron-positron annihilation line (Umemoto et al., 2016). Three parameters of the continuum, namely, ε max , the number of its photons detected in the 0.45–0.56 MeV energy range and its duration tc ' ≈ 45 − 60 s in this energy range were explained (the choice of the 0.45–0.56 MeV energy range was determined by available information about the effective area of the detector used by Umemoto et al. (2016)). It has been shown that these parameters correspond to registration of scattered and nonscattered photons from ball lightning max1 ≈ 21 , ni ≈ 4.08 × 1012 cm-3, ne ≈ 2.96 × 1013 cm-3, τ bl ≈ 194 s, with, for example, γ osc

Ae ≤ 0.62 cm (the upper boundary of Ae corresponds to the formation of ball lightning), ball

lightning core radius Rc ≈ 10 cm (it has been assumed that the radius of the empty region was negligible) and R bl ≈ 10 − 12 cm. The distance between ball lightning with such parameters and the detector of the GROWTH experiment was estimated as about 2.2 km. The difference

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between Rbl and Rc results from the existence of the depleted layer and the region of luminescence of the air; it has been assumed that this difference was in the range from several mm to about 2 cm (see also Dmitriev, 1969). Note that in the model situation under consideration, the observable registration of the continuum in the 0.45–0.56 MeV energy range max ends at γ osc ≈ 6 , therefore, τ bl exceeds tc ' significantly (calculations were performed for

tc ' ≈ 50 s). Frequency of oscillation of particles of the core or, in other words, plasma frequency max max1 max ω p , was about 7.43 × 1010 s-1 at γ osc = γ osc = 21, 1.38 × 1011 s-1 at γ osc = 6 and 2.96 × 1011 max = 1.1. The initial amplitude of the oscillating electric field was about 3.3 × 107 V/cm. s-1 at γ osc

The initial value of ρ E was about 48 J/cm3. Earlier, examples with the initial values of ρ E up to about 1–1.4 kJ/cm3 were presented (Shmatov 2001, 2003, 2004a). At such ρ E , the three-dimensional nature of the real oscillations of electrons and ions of the core imposes a restriction on the lower boundary of Rc (Shmatov max 2003, 2004a). For example, at γ osc ≈ 21 , ρ E ≈ 1.4 kJ/cm3, and patm ≈ 105 Pa, Rc should be at

least about 3.2 cm (for details, see Shmatov, 2003). It is worth noting that for plasma ball lightning models using an assumption about random motion of plasma particles, the volume density of kinetic energy of these particles is limited by the rather low value of 1.5 patm which, at conditions close to standard ones, is about 0.15 J/cm3. This results from the dependence of volume density of energy of ideal gas on its pressure (see e.g. Landau and Lifshitz, 1976) and equality of pressures inside and outside of ball lightning. Similar limitations were studied earlier for both other ball lightning models (see e.g.

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Finkelstein and Rubinstein, 1964; Singer, 1980; Shmatov, 2015a) and inertial electrostatic devices (Hirsch, 1967). The importance of the losses of ε bl due to bremsstrahlung was also discussed by Finkelstein and Rubinstein (1964) and Ostapenko and Tolpygo (1984). The quantitative account for the loss of ε c (and, as a result, of ε bl ) due to bremsstrahlung is one of the main differences of the model proposed by Shmatov (2001, 2003, 2015a) from that proposed by Ostapenko and Tolpygo (1984). Other ones are described in (Shmatov 2015a). Several authors, for example, Alekhin et al. ( 2004) and Dvornikov (2010, 2013) proposed ball lightning models which do not take into account the loss of ε bl due to bremsstrahlung. There is an assumption that for the stability of the oscillations of the particles of the ball lightning core, nonlinear effects are necessary (Dvornikov, 2011, 2013). However, examples of the importance of such effects for the ball lightning core parameters which are close to those presented by Shmatov (2001, 2003, 2004a, 2006a, 2015a) were not demonstrated. Some examples presented by Dvornikov (2010, 2011, 2013) were considered earlier by one of the authors of the present work (Shmatov, 2011, 2015a). The initial acceleration of electrons of the ball lightning core results from their attraction to a positive charge injected into the atmosphere, for example, at the stage of the return stroke in the region of propagation of a negative or positive leader, and the effect usually called “cold runaway” or “thermal runaway” (Shmatov, 2001, 2003, 2004a, 2015b). This attraction excites initially many modes of oscillation of electrons, but the emission of radio waves results in quick attenuation of almost all of them except for a spherically symmetrical one and, in some situations, a few others (Shmatov, 2015b). The formation of ball lightning also involves a quick decrease in the density of electrons and ions in the region which becomes the ball lightning core

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(see examples of ni and ne presented above). This occurs due to relatively high temperature and, as a result, high pressure in the plasma arising initially in this region. The formation of ball lightning can be accompanied by a detectable short gamma-ray flash; it is possible that such a flash was already detected by Umemoto et al. (2016). A quantitative example of the initial acceleration of electrons of the core is presented in (Shmatov, 2015b). It has been assumed, in particular, that the maximum strength of electric field in the region of the acceleration is about 10 7 V/cm or higher and the possibility of arising of such electric fields has been considered. The model according to which acceleration of electrons occurs on screening of the strong electric field in the air was used. Note that a similar model explains initial acceleration of electrons of terrestrial gamma-ray flashes with a hard spectrum, i.e., with a significant spectral density at photon energies of several tens MeV (Shmatov, 2015c; see also Tavani, 2011). In the latter case, the acceleration is caused by the strong electric field of negative charge.

2.2. Models involving resonant electromagnetic structures In this section we summarize theories that assert ball lightning is the manifestation of a resonant electromagnetic structure. The history of such ideas goes back to (Cerrillo, 1943) and Kapitza (1955, 1961) who claimed that ball lightning could be the result of an electromagnetic standing wave intense enough to break down air (see also Rakov and Uman, 2003). Kapitza (1955, 1961) reached this conclusion under the assumption that the high-energy effects occasionally produced by ball lightning cannot result from energy stored in the object. He was led to conclude that an external energy source was responsible for the observed energy output, and hypothesized that continuous electromagnetic radiation approximately in the UHF to low

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microwave range (300 MHz - 3 GHz) would account for the phenomenon. In 1955, such an assumption was plausible, but investigations since then have failed to identify any such source of continuous radio-frequency radiation, and consequently Kapitsa's theory has been largely abandoned in its original form. However, the idea that plasma itself could serve as a reflecting surface to capture an intense electromagnetic wave inside a spherical object appears to have been proposed first by Dawson and Jones (1969). Their model included a low-density core with an intense peak electric 9

-1

field (~10 V m ) that maintains the object's spherical shape against atmospheric pressure by means of radiation pressure. However, the initiation process for their model was vague and provided no guidance for experimentalists wishing to attempt the production of such an object. Wu (2014, 2016) proposed an extension of the Dawson-Jones model which included an explicit initiation process: the collision of an intense electron bunch with a material object such as soil. Part of the inspiration for Wu's theory comes from the experimental discovery that ordinary lightning reliably produces X-ray bursts (Dwyer and Uman, 2014; Moore et al., 2001). Electrons accelerated by the extreme conditions at the tips of lightning stepped leaders to energies exceeding 1 MeV are responsible for these X-rays and gamma-ray emissions. Wu proposes that a collimated electron bunch containing as many as 10

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electrons could emerge

from the last lightning leader step before it strikes the ground (see Fig. 3). He then shows that as

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Fig. 3. Schematic of Wu's relativistic-microwave theory of ball lightning: electron bunch from lightning leader tip strikes soil, producing intense microwave pulse that creates resonant-cavity plasma bubble ball lightning object.

a consequence, such a concentrated relativistic electron bunch would emit an intense electromagnetic pulse as it strikes the ground or other medium whose dielectric properties differ greatly from air. This pulse would have its energy concentrated in the microwave region (~1 -1

GHz) and reach electric-field intensities as high as 300 MV m . A sustained DC electric field of that magnitude is not possible in ambient atmospheric-1

pressure air, which breaks down at a field of only about 30 MV m . But the electromagnetic pulse arising from the collision of electrons with soil or other dielectric material is of limited physical extent (~1 m or less) and moves with the velocity of light. Wu then shows by means of a numerical simulation that such a pulse encountering plasma can form a bubble: a region of low plasma density surrounded by higher-density plasma.

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As is well known, the plasma frequency ωp (in rad s-1) of a uniform plasma with electron density npe is given by

ωp =

e2 n pe

ε 0 me

(4)

where εo is the permittivity of free space (see e.g. Kittel, 1963; here it is assumed that velocities of plasma electrons are much less than c; the situation when this assumption is not valid was considered by Ivanov et al. (1975) and Shmatov (2001, 2003)). The plasma frequency marks the transition of a plasma from a medium that is primarily transparent to electromagnetic radiation at a frequency above ωp, to one that reflects electromagnetic radiation with frequencies below ωp. Wu uses Eqn. (4) to show that if npe exceeds about 10

10

-3

cm , it will be dense enough to serve

as a reflector of a pulse of GHz-range microwave radiation, thus confining itself to a selfgenerated spherical cavity. Numerical simulations with plasma of the appropriate density and electromagnetic pulses of the appropriate amplitude predict that this phenomenon, which is a soliton-like self-sustaining standing wave, can occur under the right conditions. It is worth noting that small plasma bubbles on the order of microns in diameter have been observed in ultrashort-pulse laser-plasma experiments (Sylla et al., 2012). Wu claims that his theory accounts for several otherwise mystifying aspects of balllightning behavior. Its occurrence near thunderstorms would be accounted for by the need for stepped lightning leaders near the ground to produce electron bunches of sufficient intensity. In particular, since energy in this model is stored primarily in a field and not in an arrangement of physical particles, the object could in principle pass through an intact sheet of glass, as numerous witnesses claim ball lightning has done (see e.g. Brand, 1923; Bychkov et al., 2016; Grigor’ev,

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2006; Grigor’ev et al., 1992; Lowke et al., 2012; Powell and Finkelstein, 1969; Rakov and Uman, 2003; Singer, 1971). Energy storage is accounted for by the electromagnetic energy stored in the intense wave, and could be on the order of kJ. For these reasons, Wu's model of ball lightning does a good job in explaining several of the diverse and unusual properties of ball lightning observed by eyewitnesses. Wu's theory also provides experimental guidance for testing it, if microwave pulses of sufficient intensity can be produced artificially. Unfortunately, Wu estimates that the largest 11

microwave-pulse facility currently available falls short of the 10 -W threshold he estimates for producing microwave bubbles in plasma by about a factor of 10. And even more energy would be required to generate suitable electron bunches to initiate the entire sequence of proposed events. Other aspects of Wu's theory—for example, the ability of a plasma to form a low-loss microwave cavity—are more tractable experimentally and may be tested in the near future. However, a weak point in the theory concerns the question of whether losses in a plasmagenerated cavity could be low enough to store kJ of electromagnetic energy for several seconds, as Wu's theory requires. The problem amounts to the limits on the quality factor or Q of available microwave cavities. The most general definition of Q is the ratio

Q≡

2π (energy stored) energy lost per cycle

(5)

where the cycle referred to is the resonant cycle of the relevant cavity mode. In such a mode with a given Q, the peak amplitude A of the field varies with time as A(t)=A0e

-αt

, in which the

damping coefficient α is given by

α=

ω0 2Q

20

(6)

in which ω0 is the (rad s-1) resonant frequency of the cavity mode (~2π(1 GHz) in this case). One of ball lightning's leading characteristics is that its appearance does not change much over its lifetime (see e.g. (Singer, 1971). Assuming that the energy content of a ball lightning object declines by as much as a factor of 10 during a five-second appearance implies a value for α of -1

10

0.23 s , which for a cavity mode resonating at 1 GHz requires a Q = 1.4 x 10 . Currently the only microwave cavities available that exhibit such high Q values are superconducting cavities designed for particle accelerators, but extreme efforts must be expended for these values to be achieved (Padamsee, 2001). It remains to be shown whether a naturally-occurring phenomenon such as ball lightning is capable of maintaining a high-intensity electromagnetic resonance in the microwave region for such a long period. Regarding the electron-bunch mechanism of Wu's theory, the general association of ball lightning with thunderstorms is well established. But many cases of ball lightning have also been observed in which no ordinary lightning occurred nearby immediately before the object's appearance. In particular, Keul and Diendorfer (Keul and Diendorfer, 2018) correlated over 30 reported ball lightning sightings whose time of occurrence could be estimated accurately, with records of cloud-to-ground (CG) strikes recorded by EUCLID, a European lightning-location system. They found that although many ball lightning objects were sighted within 1 km of a recorded conventional lightning strike, about half occurred at a distance between 1 and 10 km from the reported lightning position. Electron bunches of the type that Wu hypothesizes would lose too much energy over a distance of 1 km or more, so at least in its present form, Wu's theory could not account for these so-called "distant events" in which ball lightning occurs farther than 1 km from a recorded lightning-impact point. This problem should not be regarded as fatal to

21

Wu's theory, however, as there is considerable uncertainty both in Keul and Diendorfer's data and in the details of exactly how such microwave pulses could occur.

2.3. Magnetic-knot model Besides Wu's relativistic-microwave theory of ball lightning, other electromagnetic models have been either developed or expanded since 2000. One such class is the magnetic-knot theory proposed by Rañada et al. (1990). This theory began with a theoretical solution to Maxwell's equations (Rañada, 1990) in which the magnetic field lines form topologically linked curves, like the links of a chain. Fig. 4 shows one example of such a complex of interlinked magnetic-field lines.

Fig. 4. Example of interlinked magnetic field lines along which streamer currents flow in magnetic-knot structure for ball lightning proposed by Ranada. Any two of the lines are linked once. (From Rañada et al (2000), used with permission).

22

Rañada and Trueba (1996) proposed that ball lightning could be explained by such electromagnetic structures, and followed this initial proposal with a more detailed one (Ranada et al., 2000). One aspect of the magnetic fields in the magnetic-knot theory is that they are force-free in the sense that, unlike two bar magnets with adjacent north poles, for example, the fields exert no forces on each other in equilibrium, and are also self-contained in the sense that the energy contained in the field is localized to a roughly spherical region. The force-free aspect of the fields means that any plasma currents present in the structure would not be subjected to destabilizing factors such as the pinch effect, a notable instability in conventional plasmas. Rañada hypothesizes in his model that thin, filamentary plasma currents flow along magneticfield lines and occupy a very small volume of the overall visible object. These currents are prevented from decaying by conservation of the helicity integral, because they represent a minimum-energy state for the corresponding magnetic fields and are limited by thermal diffusion to the air surrounding the thin streamers. While the magnetic-knot theory can account for important features of ball lightning such as energy storage and a "fuzzy" appearance noted by some witnesses (see e.g. Rakov and Uman, 2003; similar terms were also used in the reports published in Abrahamson et al. (2002) and Kolosovskii (1981)), the fact remains that so far magnetic knots are only a theoretical construct and have not been observed directly in the laboratory in air at pressure of about 1 atm and room temperature. Furthermore, it is not clear how an experimentalist would go about creating such an object, given the topological complexity of the structure. Ranada et al. (1998) cite a single experimental observation of Alexeff and Rader (1992), who observed closed loops in high-

23

voltage laboratory spark discharges, but no further experimental work has apparently been pursued along these lines.

3. Recent notable quantitative observations of ball lightning and candidate ball lightning objects The great majority of information we have on ball lightning has up to now consisted of eyewitness accounts unaided by quantitative measurements or instrumented recordings. These accounts usually provide only estimates of ball lightning lifetime and size, although there are important exceptions (see e.g. Al’ftan, 1982; Dmitriev, 1969; Dmitriev et al., 1981; Kolosovskii, 1981; Shmatov, 2003; Stephan et al., 2016). In this section, we will review significant recent publications in which objective data in the form of video recordings and spectra were reported. It is worth noting that increasing availability of videorecords of ball lightning was predicted by Cherington (Cherington and Yarnell, 2002). Even with quantitative data such as these reports contain, some ambiguity about the identity of the object in question can remain. In fields such as astronomy, objects of unknown origin tend to persist long enough so that multiple observers can confirm the object's observational characteristics, and come to an agreement on terminology even if no adequate theory is available to account for the observations. This happened with the radioastronomical discovery of what were originally known as quasi-stellar radio sources, or quasars. Several decades elapsed after the discovery of these objects in the 1950s before theorists concluded that they are probably black holes at the centers of galaxies, but during that time there was still a consensus about what the objects should be called (Marziani et al., 2012). The intrinsically short-term nature of ball lightning means that any quantitative observations of it usually cannot be repeated by other observers. This obliges the ball-lightning

24

researcher to classify the observation on his or her own as ball lightning. This classification can be questioned by others, who can also propose alternative explanations in terms of betterunderstood physics of non-ball-lightning phenomena (see e.g. Singer, 1971; Voitsekhovskii and Voitsekhovskii, 1987). These alternative explanations, if accepted, can result in the observation being classed as something other than ball lightning. But because no further observations can be made on the original object, the usual experiment-theory-experiment cycle common to most types of experimental physics cannot be performed, as the original observation or modifications of it cannot be repeated. With these considerations in mind, we have termed some of the objects of the observations discussed below in Subsections 3.2 and 3.3 as "candidate" ball lightning objects, because further experimental and theoretical work may provide a model which will in retrospect either confirm or disconfirm the classification of these objects as ball lightning.

3.1. Incident in New York State, USA, 2008 The question of whether ball lightning produces appreciable amounts of ionizing radiation is a critical one to answer, because some theories predict that ball lightning should produce short-wavelength electromagnetic radiation such as UV, X-rays, and gamma rays, while other theories do not, and this question is extremely important for analysis of hazards associated with ball lightning (see also Section 5). In this regard, an observation that tends to confirm that ball lightning emits ionizing radiation is significant, and one of us (Stephan) has published quantitative measurements relating to an incident which took place in the New York State town of Poughquag on June 23, 2008 (Stephan et al., 2016).

25

The eyewitness to the incident drove to her house during a thunderstorm that lasted until about 9 PM local time. While waiting in her car in front of her house for the rain and lightning to stop, she saw a glowing blue sphere about the size of a canteloupe appear in front of her front door, which was covered in colorless glass. Although the light emitted by the spherical object was blue, the glass in the front door emitted bright light of a different color, which the eyewitness recalled as a fiery yellow. The front door was about 6 meters away from where the eyewitness was sitting in her car. As she watched, the blue sphere moved to her right between her car and the house, and then passed away to the right out of sight. The duration of several seconds, the mainly horizontal motion, and the general behavior of the object seen well qualify it to be classified as ball lightning. Subsequent examination of the glass in the door revealed that it was a type which fluoresces yellow-green on exposure to short-wavelength (253-nm) UV radiation. Quantitative fluorometric measurements of the glass showed that by taking account of the fluorescence efficiency of the glass and the relative brightness of the fluorescence reported by the eyewitness, the ball lightning object must have emitted at least several watts of ionizingradiation power to have produced the fluorescence observed. Because certain types of glass can fluoresce from irradiation by short-wave UV, X-rays and, probably, gamma rays and energetic particles (e.g. beta-rays), this incident by itself does not tell us whether the object was emitting only UV, only X-rays, only gamma rays, some combination of them, or perhaps energetic particles that caused the fluorescence. What it does imply is that the particular object sighted involved a process that produced substantial amounts of electromagnetic (or possibly particulate) emissions capable of causing fluorescence in glass. Therefore, it is unlikely that the mechanism of this ball lightning involved only chemical

26

reactions, as few if any naturally-occurring chemical reactions emit substantial amounts of shortwave UV radiation. Alkemade and Herrman (1979) note that the highest-temperature flames encountered in laboratory spectroscopy reach less than 5000K, at which temperature only 1% or less of the total emitted black-body radiation is in the UV range. Nevertheless, almost any plasma that exists in atmospheric-pressure air will involve chemical reactions (see e.g. Dmitriev, 1969), and so chemical as well as physical processes were no doubt present. Whatever the energy-releasing process was in this ball lightning incident, it was sufficiently energetic to produce ionizing radiation that caused fluorescence of a different color in the glass door.

3.2. Incident in Qinghai Plateau, China, 2012 One of the most-cited recent observational papers on the topic of ball lighting is based on data obtained from an incident that occurred on the Qinghai Plateau of northwestern China in 2012 (Cen et al., 2014). There, researchers were operating an observation station for ordinary lightning research consisting of two video cameras: a 30-fps (frame per second) color camera and a 3000-fps monochrome camera, each equipped for slitless spectroscopy with a diffraction grating over the lens. In the summer of 2012, the researchers recorded a 1.6-second event which they categorized as ball lightning, since the object they photographed appeared to move in a way consistent with other ball-lightning observations. The visible-wavelength spectra recovered from this observation, which had a resolution of about 1.1 nm, are the only such data available so far from an object that was possibly ball lightning. The spectra showed numerous lines due to atoms of Fe, Ca, and Si, in addition to those of the atmospheric gases N and O. While the authors did not draw any definite conclusions from

27

their data regarding positive confirmation of any particular ball-lightning theory, they did mention favorably the Abrahamson-Dinniss soil-lightning-strike theory (Abrahamson and Dinniss, 2000) in connection with their data because iron, calcium, and silicon are commonly found in soils. While Cen and his co-authors did not attempt to extract temperature data from their spectra in any detailed way because their spectral line intensities lacked calibration. Absolute calibration of spectral intensities is not necessary if the so-called “slope” method is used to estimate temperatures of flames from line spectra (Reif et al., 1973). What is necessary for the slope method to yield a good estimate of temperature (on the order of ±10% accuracy) is linearity of the spectrometer’s response and a knowledge of relative calibration, that is, the relative sensitivity of the system with respect to different wavelengths. If the spectrum’s linearity and wavelength response are not known, these factors become interfering variables which degrade the quality of the resulting data. Nevertheless, even with unknown amounts of nonlinearity and sensitivity variation, the slope method is a useful approach to rough estimates of temperature, as the following analysis of the data in Fig. 4 (c) of (Cen et al., 2014) will show. The slope method of spectroscopic temperature measurement is based on an assumed Boltzmann distribution of the density of occupied upper-level energy states in atomic transitions. As shown by Reif et al. (1973), this distribution leads to the following expression for the radiance B(em) of a spectral line, integrated over the wavelength range of the line, for a line with upper-level state multiplicity gq, transition probability Aqp, wavelength ν0, and upper-state energy level Eq:

28

B(em) =

g q Aqp hν 0 n0 l 4π g0

exp(− Eq kT ) (7)

where h = Planck’s constant, l = length of the optical path in a presumably uniform-density and uniform-temperature plasma, n0 = ground-state density, g0 = ground-state multiplicity, k = 8.617 -5

-1

x 10 ev K

= Boltzmann’s constant, and T = temperature.

At a given temperature, transitions

down from higher energy levels will be less intense due to the Boltzmann factor, other things being equal, and this variation of radiance with energy level can be used to estimate the temperature of the region harboring the excited atoms. For different elements with different upper-state energy levels Eq, the only quantities that will vary significantly from line to line are gq, Aqp, ν0, and Eq. Therefore, in a plot in which the x-axis is

 g q Aqpν 0  x = k ln    B(em) 

(8)

and where y = Eq (eV), the spectral lines’ x-values calculated from Eqn. (8) plotted versus their corresponding Eq values on the y-axis should produce points that lie on a straight line whose slope is the temperature T. We selected twelve lines from the spectrum of Fig. 4(c) of (Cen et al. 2014) which were unambiguously identifiable by wavelength, and performed the calculations for the slope method of temperature estimation using the values shown in Table 1. Wavelengths, transition probabilities, multiplicities, and energy levels were obtained from the U. S. National Institute of Standards and Technology atomic spectroscopy databases (https://www.nist.gov/pml/atomic-

29

spectroscopy-databases), and intensities in arbitrary units (a. u.) were measured directly from the figure. Table 1 Spectroscopic data from (Cen et al., 2014) used for slope plot of Fig. 4 Element

Fe Fe Fe Fe Si Si Ca N O N O N

Wavelength Intensity (nm) from Cen (a. u.) 495.7 5.537 526.9 1.157 532.8 1.051 544.6 1.440 568.4 1.681 594.8 3.217 646.2 1.366 746.8 2.097 777.4 4.055 821.6 2.551 844.6 0.292 868 1.555

-1

Aqp (s ) 4.22E7 1.27E6 1.15E6 5.48E5 2.6E6 2.22E6 4.7E7 1.96E7 3.69E7 2.26E7 3.22E7 2.53E7

-

Eq (cm 1

gq

x -1 (eV K )

y (eV)

11 9 7 5 3 5 7 4 5 6 5 6

4644 4315 4293 4171 4244 4214 4573 4400 4413 4422 4621 4.469

5.314 3.215 3.244 3.269 7.139 7.174 4.446 12.01 10.75 11.86 11.00 11.77

)

42815 25899 26140 26339 57515 57798 35819 96800 86625 95532 88631 94881

Fig. 5. Slope-temperature points from Table 1. Line labeled 4828 K is the least-square fit to the four Fe points.

30

As shown by Reif et al. (1973), the temperature of the region observed must be uniform for the slope method to produce a reasonably straight line. The widely scattered points in Fig. 5 imply that the spectral lines of Fig. 4 (c) in (Cen et al., 2014) originated from regions at different temperatures, or at a minimum that the unknown relative calibration of different wavelengths has contributed errors to the plots. In experiments with actual burning spheres of elemental silicon, one of us measured average surface temperatures spectroscopically in the range of 2800-3400 K (Stephan and Massey, 2008). To the extent that the Fe lines in Fig. 5 provide an estimate of temperature, the temperature they indicate of approximately 4800 K appears to be inconsistent with a primarily chemical source of energy for the object in question, although such temperatures can be found in electrical arcs. The positions of points on the y-axis of Fig. 5 are determined by the corresponding upperstate energy levels, which is why points corresponding to atmospheric N and O with Eg values above 10 eV cluster in the upper-right corner of the graph. Although these points are too scattered to apply the slope method of estimating temperature, Cen et al (Cen et al., 2014) say only that the temperature of the object in question is lower than that of an ordinary lightning strike’s stepped leader, namely 15 000 to 30 000 K. The absence of lines of N II or O II corresponding to ions is consistent with this contention, but it appears that the N and O lines in Fig. 4 (c) of (Cen et al., 2014) may arise from a region of the object which is at a higher temperature than the region from which the Fe and Ca lines were emitted. In any event, the data in Fig. 5 imply that the object in question likely contained at least some region(s) in which either the temperature exceeded 3000 K, and possibly much higher, or possibly that storage of energy

31

in metastable states of O2 molecules (Powell and Finkelstein, 1969, 1970) is physically important. Cen et al. (2014) believe that they photographed an occurrence of ball lightning. As we have seen, based upon our current limited knowledge of ball lightning, the data published by Cen et al. (2014) are consistent with that explanation. However, we would like to propose an alternative explanation for the data, one which is made more likely by a subsequent publication concerning the same incident (Wang et al., 2018). It is possible that the object photographed was a power-line arc (flashover) and not what a typical eyewitness observer fairly close to the object would describe as ball lightning. Not all lightning strikes to power lines are absorbed by lightning arrestors and other protective gear. From time to time, lightning will produce an arc to ground (also called a flashover) that persists for seconds or minutes. Typical distribution ground-fault relay settings are in the 240-480 A range (Short, 2014). Hence an arc of a few amperes can sustain itself indefinitely without being interrupted by protection devices. Power-line arcs can last 10-100 s or longer and can travel many meters. One of us published a photographic record and quantitative analysis of an incident near Marfa, Texas which was, in retrospect, probably a power-line flashover that persisted for more than three hours and was probably induced by a lighting strike (Stephan et al., 2011). Although most lightning-induced flashovers occur at the poles that support the lines, flashovers directly to ground may occur if, for example, a lightning channel predisposes the power-line current to follow a direct path to ground rather than through a ground wire on a pole.

32

The object recorded by Cen et al. (2014) moved at least an estimated 10 m in a horizontal direction during the time it was visible. In Fig. 6, we have illustrated an alternative scenario which could account for the observed data.

Fig. 6. Alternative explanation for observation in (Cen et al., 2014), consisting of lightninginduced power-line arc (flashover) moving its termination point along the ground.

Suppose an initial lightning strike to a power line (which was in the field of view of the cameras used in (Cen et al., 2014)) induced an initial arc from the power line to the earth, shown terminating at (1) in Fig. 6. The flashover persists after the termination of the lightning discharge. The flashover column itself is excited by 50-Hz AC, so that N and O lines emitted from it are modulated at a 100-Hz frequency (twice for each cycle). In the meantime, the earth at and near the termination point of the flashover is heated to temperatures exceeding 4000 K by the power provided by the arc. Wind or other conditions could cause the arc to move horizontally over most of the 1.6-s duration of the recorded object (points (2), (3) and (4) in Fig.

33

5). At about 1.1 s into the event, the data reported in (Cen et al., 2014) shows that the 100-Hz modulation of the light emission recorded by their high-speed camera abruptly ceases, and the brightness of the object undergoes an exponentially-shaped decline thereafter. This behavior is consistent with cessation of the arc column followed by rapid cooling of the heated earth at the final termination point of the arc (point (4)). While the shape of the object recorded is roughly circular, the events proposed in Fig. 6 would more likely image as an elongated structure. However, the alternative scenario could produce a more nearly circular shape due to foreshortening, obstructions, partial mechanical failure of the power line bringing it closer to ground, or other factors. This alternative explanation accounts easily for regions of widely differing temperature: the flashover arc itself at temperatures exceeding 6000 K, and the earth-contact point, with temperatures in the 3000 5000 K region. The single most persuasive fact in favor of the power-line-arc hypothesis is presented by Wang et al. (2018) who give further analysis of the same incident described by Cen et al. (2014). Wang et al. (2018) describe a measurement which quantifies the light intensity observed during the original incident described by Cen et al. (2014). Using a source of known intensity at the approximate location of the object photographed, the authors estimated that the maximum brightness of the object in its stable state was about 59 000 cd and its maximum optical output power was about 3.7 kW. Estimates of optical power from the likely power-line arc evaluated in (Stephan et al., 2011) range up to about 10 kW, quite comparable to the 3.7 kW estimated in (Wang et al., 2018). The close agreement of estimated optical power between the objects described in the papers by Stephan et al. (2011) and Wang et al. (2018) is one of the strongest pieces of evidence in favor

34

of the hypothesis that both objects were probably power-line flashovers induced by lightning strikes. However, it is worth noting that brightness of light emitted by some ball lightning is very high (see Section 5). The proposal of this alternative hypothesis is not intended as a criticism, but is part of the normal process of analysis, correction, and further observation that science involves. In other fields such as particle physics, publication of results that can be interpreted in more than one way is encouraged in order for others to suggest alternative explanations or to confirm the initial findings. Because quantitative data on ball lightning are so scarce, the process of assessment and interpretation of findings proceeds more slowly than in other fields. But if and when more spectra of suspected ball lightning incidents are obtained, the data reviewed in this section will be a valuable resource against which to compare future data.

3.3. Incident in Mitino, Moscow, 2015 The ubiquity of mobile phones capable of recording good-quality video has led to the possibility that lay persons can make scientifically useful video records of incidents that may be ball lightning. Nikitin et al. (2018b) recently published a description of an incident in the air above a district of Moscow which may be the most well-documented occurrence of ball lightning so far from the viewpoint of video recordings. On 27 July 2015, three different observers in the Mitino district of northwest Moscow noticed a glowing object moving erratically above the apartment buildings and forests of the area. For portions of about 2 min, each observer recorded video of the object with a mobile phone. The object was within simultaneous view of at least two observers during most of the time it was photographed, allowing the researchers to reconstruct both a timeline and a

35

triangulated estimate of geographic position and height above ground level, which ranged between about 30 m and 140 m. For much of the time, the object moved only slightly, remaining -1

within a region of about 12 m by 100 m and moving at a velocity of 5.7 m s or less. Then it -1

rose at an estimated velocity of 15 m s and apparently disappeared into a cloud. The apparent diameter of the object was about 0.75 m. These observations are valuable for several reasons. First, they confirm many of the typical eyewitness accounts of important aspects of ball lightning: its relatively constant brightness over the duration of its lifetime, its erratic and mainly horizontal motion, and its size. At 0.75 m, the object described by Nikitin et al. (2018b) is larger than the average size reported by previous eyewitnesses, and the duration (at least 120 s) is longer than average (see e.g. Carpenter, 1962; Grigor’ev, 2006; Singer, 1971; Smirnov, 1987, 1988, 1990, 1992; Stakhanov, 1996). Nevertheless, the object photographed shows so many of the characteristics of ball lightning that the most likely explanation is that it was an actual ball lightning object, not a balloon or other more common flying object. Note also that Dmitriev et al. (1981) published a report about ball lightning with a diameter of about 1.5 m and lifetime of about 1 minute. A useful analysis can be performed on a photograph (Fig. 3 in (Nikitin et al., 2018b), reproduced here as Fig. 7) with regard to the approximate brightness of the object in question.

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Fig. 7. Mobile-phone image of apparent ball lightning above Moscow. (This image was published in Journal of Atmospheric and Solar-Terrestrial Physics, vol. 179, A. I. Nikitin, A. M. Velichko, T. F. Nikitina, and I. G. Stepanov, p. 99, Copyright Elsevier 2018.)

The sky was cloudy at the time of the incident, and the typical illumination level of a scene under a cloudy daytime sky at summer is in the range of 5000 to 20 000 lux (Kuhling, 1992) or 10 000 to 25 000 lux (Wikipedia, 2018). In the figure, the object appears against a dark background (probably foliage) in the same frame with an apartment building having an area that is painted white. Using ImageJ image-analysis software (available from the U. S. National Institutes of Health at https://imagej.nih.gov/ij/download.html), we found that the relative monochrome-

37

equivalent intensity levels for the white apartment wall and the ball lightning object were 255 and 188, respectively, in the luminance units of ImageJ. Assuming 50% reflectance for the wall, -2

the luminance (in candelas per square meter, cd m ) of a surface with illumination level E (in lux) and reflectance R is

L=

RE

π

(9)

Therefore, if we assume an average value for the illuminance of the scene of 17 500 lx, the -2

luminance of the wall is 2785 cd m . Assuming a linear transfer function for the cameradigitizing and reproduction process, the luminance of the ball lightning object is thus (188/255) x -2

(2785) = 2000 cd m . In a paper on the appearance and visibility of ball lightning, one of us estimated that the typical luminance of ball lightning objects lies in the range of 454 to 4540 cd -2

-2

m (Stephan, 2012). The value of 2000 cd m lies near the middle of this range, and even if lower or upper bounds are assumed for the cloudy-sky illumination levels (5 000 - 25 000 lx), the estimated luminance remains well within the 10:1 range estimated for typical ball lightning objects. This is confirming evidence that the object recorded by the three mobile phone cameras in (Nikitin et al., 2018b) was in fact a likely occurrence of ball lightning. Unfortunately, the data that can be easily extracted from (Nikitin et al., 2018b) is mainly of a nature to confirm other eyewitness accounts, and does not provide a great deal of new quantitative information except to show that the phenomenon can be a stable and long-lasting one. Such a long lifetime poses challenges for many theories that attribute the light emission of ball lightning to an energy storage mechanism contained within the object itself. But as externalenergy theories such as that of Kapitsa (1955, 1961) have largely been discredited because of the

38

absence of any evidence that high-energy electromagnetic fields are present of the type needed for such theories, the Moscow ball lightning incident should be taken into account when any theories of ball lightning are proposed in the future.

3.4. Incident in Mogsokhon, Russia, 2013 On May 27, 2013, ball lightning penetrated through the roof of a wooden house in Mogsokhon village, Buryatiya, Russia (Buyakhaev, 2013; Nikitin et al., 2018a). The explosion accompanying this penetration resulted in the fall of part of one of the house walls and other damage to the house. A woman who worked in the kitchen of the house was seriously injured. The information available in literature (Nikitin et al., 2018a) and online (see e.g. Buyakhaev, 2013) does not allow us to establish the physical nature of the explosion. The explosion might be that of ball lightning itself. However, it is not possible to determine the absence or presence of gas equipment in the damaged house. Therefore, we cannot exclude leakage of flammable gas, used as a fuel, due to the influence of ball lightning on such equipment and subsequent explosion of mixture of the gas with air. For this accident, Nikitin et al. (2018a) estimated ball lightning energy (we denote this parameter as ε bl ) assuming that the house was damaged by the explosion of ball lightning itself. The fallen part of the wall was described as “a flat package of logs”. Equations for calculation of the mass C of a TNT charge necessary for destruction of such a package in the situations when the charge is placed in contact with the package or at some distance from it were used (Nikitin et al., 2018a). For the direct contact of the charge with the wall, Nikitin et al. (2018a) obtained

C = 6.9 kg, while assuming that the explosion occurred in the center of a square room with the side of 4 m, they obtained C = 33 kg. These values of C correspond to the explosion energy

39

releases of about 28 and 132 MJ, respectively, which were used as boundaries of ε bl (Nikitin et al., 2018a). However, the values of C obtained by Nikitin et al. (2018a) are slightly greater than or coincide with the values of C necessary to break all of the logs of the package (Rossal, 1959). According to Rossal (1959), at the direct contact of the charge with the package, the value of C, necessary for breaking all of the logs of the package with parameters, chosen by Nikitin et al. (2018a), is about 6.33 kg. The equation used by Nikitin et al. (2018a) for the situation when the charge is placed at some distance from the package coincides with that for calculation of C necessary to break all of the logs (Rossal, 1959). According to Fig. 1 from the paper by Nikitin et al. (2018a), no log of the fallen part of the wall was broken. Its logs only lost connection with logs with did not fall. Thus, Nikitin et al. (2018a) overestimated the values of C and, thereby, both lower and upper boundaries of ε bl .

4. Some performed and proposed experiments on the formation of ball lightning and its analogues It is evident that more or less reproducible formation of ball lightning in experiments with the use of lightning (ordinary or triggered) or laboratory sources of electricity is highly desirable for both establishing the physical nature of ball lightning and reliable estimation of its danger for humans, animals, aircraft, etc. Since there are many published reports describing formation of ball lightning due to strikes of ordinary lightning to elongated conductors (see e.g. Al’ftan, 1982; Balyberdin, 1966; Grigor’ev, 2006; Singer, 1971; Stakhanov, 1996), several authors discussed the possibility and expedience of reproducing the circumstances, corresponding to such reports, in experiments devoted to the formation of ball lightning. However, many lightning strikes, including those to elongated conductors, do not result in the formation of ball lightning.

40

Imyanitov and Tikhii (1967) wrote the following: “It is quite possible that the simplest experiment, similar to that of Franklin, will allow us to reveal the nature of ball lightning. But how to organize this experiment?” Some of the reports about the formation of ball lightning correspond to situations when ordinary lightning strikes an ungrounded antenna or other ungrounded elongated conductor (see e. g. Balyberdin 1966; Grigor'ev 2006, report No. 140). For example, the equipment used in the last experiment of Professor G.-W. Richmann (see e. g. Powell and Finkelstein, 1969, 1970; Richmann, 1956; Shmatov, 2001, 2015b; Singer, 1971) was equivalent to an ungrounded antenna. A chimney lined with soot can serve as an elongated conductor. Therefore, some of the reports about the observation of ball lightning inside or near stoves and fireplaces (Grigor’ev, 2006; Selvaggi et al., 2003; Singer, 1971) may correspond to similar scenarios, although a chimney can also serve simply as an entrance for ball lightning that arose without the influence of lightning on it (Shmatov, 2015b). In any case, the aforementioned information about the ungrounded antennas, etc. allows us to assume that it is expedient to try to observe the formation of ball lightning in situations when ordinary lightning strikes such an antenna (Shmatov, 2009, 2015b). Some of the observational data, for example, Asonov’s report published by Al’ftan (1982) allow us to assume that an antenna can also be grounded through a relatively high 2

resistance of the order of 10 ohm or higher (Shmatov, 2009). To the best of the knowledge of the authors of this paper, the formation of ball lightning was observed only in two specially organized experiments with atmospheric electricity. These experiments were not devoted to ball lightning. The last experiment of Professor G.-W. Richmann was performed during his studies devoted, in particular, to quantitative description of thunderstorm-related phenomena, and caused his death, probably, due to the electrical influence

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of ball lightning (see e. g. Powell and Finkelstein, 1969, 1970; Richmann, 1956; Shmatov, 2001, 2003; Singer, 1971). The second experiment was performed by A.A. Marvin who tried to use ordinary lightning for production of synthetic diamonds (Stakhanov, 1996 p. 148, report No. 117). Ball lightning arose near the sharpened end of a 2-mm-diam, 12-m-long insulated cable, the other end of which was connected to a lightning arrester placed on a geodesic landmark, when lightning struck the landmark. The sharpened end of the cable was placed at the height of 0.5 m above the ground, while the rest of the cable was placed in the ground at the depth of 30 cm. A.A. Marvin observed only one strike of ordinary lightning to the landmark. Reproduction of his experiment and organizing similar experiments with rocket-triggered lightning are desirable. It is worth noting that according to the model described in Section 2.1, in such experiments ball lightning can arise due to strikes of both positive and negative lightning (when lightning is negative, the injection of the positive charge into the air will occur at the stage of the return stroke), while for the experiments with ungrounded antennas, a strike of positive lightning seems to be necessary (Shmatov, 2015b). Note also that the region of the formation of ball lightning in Marvin’s experiment has some similarity to the neighborhood of the defunct leader of cloud-to-ground lightning where the formation of ball lightning is also possible (Shmatov, 2015b). In an experiment with a grounded antenna, both signs of cloud-to-ground lightning may be acceptable. Experiments on the formation of ball lightning with the use of rocket-triggered lightning were performed by Fryberger (1992) and Hill et al. (2010). In the experiments of Fryberger, two rocket-triggered lightning strikes were initiated; ball lightning was neither observed visually nor recorded by video cameras (Fryberger, 1992).

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In the experiments of Hill et al. (2010), eight rocket-triggered lightning strikes were initiated. Two of them produced photographic data considered by the authors of that paper “interesting in the context of ball lightning.” However they “do not claim to have produced ball lightning.” The effects observed by them included emission of light for a duration up to about 648 ms (Hill et al., 2010). To the best of our knowledge, the physical mechanisms of some of these phenomena, for example, those of a glow with the duration of about 0.5 s above pine tree sections, were not established. The data published by Powell and Finkelstein (1969, 1970) allow us to assume that for some of the effects observed by Hill et al. (2010) and by several other researchers, excitation of the metastable states of the O2 molecule was important (see below). Other possible experiments on creation of ball lightning with the use of rocket-triggered lightning were proposed by Egorov and Stepanov (2011), Kikuchi (1999) and Shmatov (2009, 2015b). Egorov and Stepanov (2011) proposed experiments of several kinds, including those with delivery of a flexible conductor to the thundercloud with a rocket or catapult. According to the proposal of Kikuchi (1999), a wire connected to a rocket (or, strictly speaking, a wire one end of which is connected to a rocket), should be grounded through a lumped inductive coil. The coil serves for production of a plasmoid and its confinement by strong mirror-like magnetic fields. The required coil inductance L depends on cloud capacitance C; at C = (1 − 5) × 10−5 F, L should be 1–10 Henry (Kikuchi, 1999). The optimum geometry of the coil was also discussed in (Kikuchi, 1999). The use of the coil corresponds to an MHD (i.e. magnetohydrodynamic) model as well as some other models of ball lightning (Kikuchi, 1999). The proposal of Shmatov (2009, 2015b) is based on his model using an assumption about oscillation of electrons and ions in the ball lightning and also corresponds to other models of

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such a kind (see Section 2.1) and to any other model according to which ball lightning arises due to the injection of an electric charge into the air (see e. g. Brovetto et al., 1976; Stakhanov, 1996). According to this proposal, a wire connected to a rocket should be ungrounded or 2

grounded through the resistance of the order of 10 ohm or higher. In principle, rocket-triggered lightning can also be used in the experiment similar to that performed by A.A. Marvin. Powell and Finkelstein (1969, 1970) performed detailed studies of long-lived luminosities of some pure gases and oxygen-nitrogen mixtures after the influence of microwave discharges. Earlier, luminosities of such a kind were produced in the open atmosphere by J. F. Manwaring with the use of a 75-MHz radiofrequency arc (Powell and Finkelstein, 1969, 1970). In his experiments, a glowing ball lasted for about 0.5 s after RF (i.e. radiofrequency) excitation cutoff (Powell and Finkelstein, 1969, 1970). In the experiments of Powell and Finkelstein (1969, 1970), a 75-MHz RF generator was also used. The luminosities of O2 and air lasted for several hundred ms after RF excitation cutoff (Powell and Finkelstein, 1969, 1970). This was explained by those authors as a result of excitation of b1Σ g + and/or a1∆ g metastable states of the O2 molecule, and the O2 luminosity was the brightest. Electronically excited metastable N2 molecules were previously observed in nitrogen glows lasting for several seconds, but O2 molecules cause a rapid collisional de-excitation of such molecules. The luminosity of N2O lasted for two seconds after RF cutoff (the chemical energy from N2O decomposition was supposed responsible for most light emission) (Powell and Finkelstein, 1969, 1970). Luminosity of air after RF cutoff was also observed in experiments with the use of 2.45GHz microwaves (Ohtsuki and Ofuruton, 1991) and such microwaves with electric discharges

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(Ofuruton et al., 2001). In some of these experiments, the “plasma fire” created by microwaves emerged from a hole in the aluminum foil and lasted for about 1–2 s (Ohtsuki and Ofuruton, 1991). An object emitting visible light during a time of several hundred ms can also be created using a discharge of a high-voltage capacitor through electrodes submerged in a weak aqueous electrolyte (see e. g. Egorov et al., 2004; Egorov and Stepanov, 2011; Friday et al., 2013; Shabanov 2019; Shabanov et al., 2009; Shabanov and Sokolovskii, 2005; Stephan et al., 2013). This type of object was first created in the institute now known as the "Petersburg Nuclear Physics Institute named by B. P. Konstantinov of National Research Center 'Kurchatov Institute'" (Egorov et al., 2004). Since this institute is located in Gatchina, Russia, the object under discussion is often called a “Gatchina plasmoid.” Many of the factors determining the formation and parameters of Gatchina plasmoids were studied experimentally, but several important problems, related, first of all, to the physical mechanism of storage of energy during the relatively long time and the efficiency of the conversion of the energy of the discharge to that of the plasmoid, require additional studies (Egorov et al., 2004; Egorov and Stepanov, 2011; Fantz et al., 2013; Friday et al., 2013; Shabanov, 2019; Shabanov et al., 2009; Shabanov and Sokolovskii, 2005; Stephan et al., 2013; Wurden et al., 2008; Wurden and Wurden, 2011).

The

similarity of lifetimes of such plasmoids and duration of air luminescence after RF excitation cutoff (Ofuruton et al., 2001; Ohtsuki and Ofuruton, 1991; Powell and Finkelstein, 1969, 1970) allows us to assume that storage of energy in Gatchina plasmoids is partly or even mainly provided by excitation of the metastable levels of O2 molecules (see also Stephan et al., 2013). Additional studies, related in particular to the dependence of the parameters of plasma on composition and pressure of gas in which the plasma arises, are also desirable for establishing

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the physical nature of effects described by Oreshko (2015), who interpreted the appearance of light-emitting regions in experiments with powerful electric discharges, accompanied by intensive radiowave radiation, as the formation of ball lightning. The information about the motion of these regions with the velocities of about 5×108 cm/s = 5000 km/s and their penetration through obstacles (Oreshko, 2015) allows us to assume that the motion of this region corresponds to motion of regions of strong excitation of air by electric current or/and radiowaves, rather than to directed motion of particles of plasma clouds (see also Mitchell et al., 2008; Ofuruton et al., 2001; Ohtsuki and Ofuruton, 1991; Powell and Finkelstein, 1969, 1970; Stephan, 2006).

5. Hazards associated with ball lightning

5.1. Contactless influence of ball lightning on humans and objects and some effects accompanying direct contact

It is well known that the direct influence of ball lightning on a human being can cause injury or death (see e.g. Barry, 1980; Dmitriev et al., 1986; Grigor’ev, 2006; Imyanitov and Tikhii, 1967; Selvaggi et al., 2003; Shmatov, 2003; Singer, 1971; Smirnov, 1987, 1988, 1992). However, the validity of any model of ball lightning is not established yet. Therefore, sometimes it is difficult even to classify the rendezvous with ball lightning as dangerous or safe and to optimize the treatment of a human being injured by ball lightning (Shmatov, 2003). From this point of view, the problem of the radiation hazard from ball lightning is most important. Carpenter (1962) was probably the first to discuss the hypothesis that radiation from ball

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lightning can be hazardous, although the first models according to which ball lightning emits ionizing radiation were proposed much earlier (see e.g. Brand 1923; Bottlinger 1928). The assumption under consideration is in agreement with several reports about biological and physical effects that were or could be caused by ball lightning and is consistent with several models of ball lightning, but there is no general consensus as to the degree to which radiation from ball lightning is hazardous ( see e.g. Carpenter, 1962; Cowgill, 1886; Garfield, 1976; Shmatov, 2003, 2006 a, b, 2009; Stakhanov, 1996). Stakhanov (1996) mentioned a letter informing him about the appearance of symptoms of radiation sickness, in particular about the loss of hair and teeth after the passage of ball lightning near the author of the letter, but was unsure about the reliability of the facts reported. In 1886, Cowgill published a brief paper about an accident that happened near Maracaibo, Venezuela and resulted in the appearance of symptoms similar to those of radiation sickness, in particular, in a violent vomiting and the formation of black blotches on skin (Cowgill, 1886). The accident was accompanied by a vivid dazzling light, a loud humming noise, a smoky appearance, and a peculiar smell (Cowgill, 1886). In the literature on ball lightning, this accident was mentioned for the first time by Garfield (1976). The sufferers did not report an observation of a fiery ball or similar object, but this does not contradict the assumption that they were injured by ball lightning, because it is possible that they could not see the object due to its dazzling light (Shmatov, 2003, 2006a) or for some other reason. Electron paramagnetic resonance (EPR) studies of tooth enamel provide the possibility to estimate the dose of gamma irradiation received by a human body (Bougai et al., 2002; Galstian et al., 2004; Tipikin et al., 2016). Such studies along with EPR studies of nails and hair (Tipikin et al. 2016) can be used for diagnostics and optimization of treatment of sufferers injured by ball

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lightning, at least in the situations when symptoms similar to those of radiation sickness appear (Shmatov, 2006a, 2009). Probably, in some extreme situations EPR studies of bones (see e.g. Tipikin et al. 2016) can also be expedient. The influence of ionizing radiation on human beings can be accompanied by a so-called “X-ray hangover” (this effect is similar to the influence of alcohol; (Kireev, 1960; Kurshakov, 1963)), frightening dreams (Kurshakov 1963), high-order cognitive impairment and progressive dementia (Robbins et al., 2011). If the assumption about the ionizing-radiation hazard of some ball lightning is correct, the aforementioned effects, especially the last one, can serve as an additional factor with regard to the danger of ball lightning, because these effects can cause an unserious attitude to the information obtained from the victim(s) and, thereby, delay or even prevent proper treatment (see also (Shmatov, 2009) and bibliography therein). Bychkov et al. (2004) published a report of R.P. Yaptune about the contactless influence of ball lightning on small lead shot in hunting cartridges with cardboard cases in Ust’-Eniseisk District, Taimyr Peninsula, USSR, in 1979. Ball lightning melted the small shot (Bychkov et al. 2004). This effect was explained as a result of heating lead by high-energy photons from ball lightning (Shmatov, 2006b, 2009). The fact that the influence of ball lightning on the cartridges did not initiate detonation of fulminate of mercury in their percussion caps supports the assumption that the cartridges were influenced by high-energy photons rather than by radiowaves. The temperature of self-ignition and explosion of fulminate of mercury is 130 to 150 C (Kondrikov, 1972), while pure lead melts at 327.3 C (see e.g. Gol’din et al., 1983). However, the high-energy photons would heat the percussion caps relatively weakly due to the small fraction of high-Z elements in fulminate of mercury (its chemical formula is Hg(OCN)2 (Kondrikov, 1972)) and other components of their initiating explosive (Shmatov, 2006b, 2009).

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Radiowaves would probably ignite the percussion caps due to heating of their metal parts. The event was accompanied by the death of three men in the two years after their observation of ball lightning, along with problems with the eyesight of the observers and injuries of their dog (Bychkov et al. 2004). This information is in agreement with the assumption about the radiation hazard of ball lightning, but other explanations are also possible (Shmatov, 2006b, 2009). An important report about biological and physical effects related to the contactless influence of ball lightning was also presented by E.A. Asonov and published by Al’ftan (1982) (see also Shmatov, 2003). After observation of ball lightning from the distance of about 3–4 m and more, E.A. Asonov suffered from a general indisposition for half a year (Al’ftan, 1982). Ball lightning also damaged some parts of his camera (Al’ftan, 1982). The camera was placed on a tripod and the minimum distance between the camera and the ball lightning was about 30– 50 cm (Al’ftan, 1982). The effects observed by E.A. Asonov could be due to the influence of high-energy photons from ball lightning (Shmatov, 2003). The event took place near Sosnovo, USSR, in August 1978 (Al’ftan, 1982). Note that the model of Shmatov predicts very high radiation hazard from ball lightning with high ε bl of the order of 1 MJ and greater and low or even negligible radiation hazard from ball lightning with low ε bl of the order of 100 J (Shmatov, 2003). According to several reports, ball lightning sometimes turns on or turns off electric equipment, for example, incandescent lamps (Brand, 1923; Imyanitov and Tikhii, 1967). This could result from ionization of air in switches by high-energy photons from ball lightning (Shmatov, 2003). Such ionization can be dangerous, first of all, for the electric and electronic equipment of aircraft. Note that in recent years, a similar problem of radiation hazards from terrestrial gamma-ray flashes for the crews, passengers and electronic equipment of aircraft has

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been discussed (see e. g. (Dwyer et al., 2010, 2012; Shmatov, 2015c; Tavani et al., 2013; Xu et al., 2012). It is assumed that ball lightning can initiate ordinary lightning and release of electric charge accumulated on the ground (Imyanitov and Tikhii, 1967; Powell and Finkelstein, 1969, 1970; Smirnov, 1992; Stakhanov, 1996). The problems of the possibility and potential danger of the last effect seem to require additional studies. In any case, initiation of ordinary lightning due to ionization of air by high-energy photons from ball lightning is probably possible (Shmatov, 2003). The model considered in Section 2.1 allows us to assume that termination of gamma-ray glow with upper boundary of the spectrum of about 20 MeV by ordinary lightning discharge that started about 15 km away from the gamma-radiation detector (Wada et al., 2018) resulted from max 1 attraction of leader of ordinary lightning to ball lightning with γ osc ≈ 41 which was a source of

the glow. Such attraction probably increases the danger of ball lightning and seems to be related, at least partly, to ionization of the air by high-energy photons from ball lightning. The very high brightness of light emitted by some ball lightning can be considered as one more dangerous factor of the contactless influence of ball lightning on humans. For example, E.A. Asonov described the light from ball lightning as dazzling and brighter than that of a 20-kW xenon lamp (Al’ftan, 1982). He reported an almost immediate negative influence of ball lightning on his sight, using a term that could be translated as “growing dark in the eyes,” but after eye treatment there was complete recovery of sight in 2–3 weeks after the event (Al’ftan, 1982). The effect of ball lightning on vision in this case was probably caused by the very bright visible light, but the contribution of UV radiation seems also to be possible. According to the report presented by N.A. Konkina and published by Grigor’ev (2006), during her encounter with

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ball lightning she was afraid to open her eyes because she thought that she would become blind due to the extreme brightness of the light (Grigor’ev, 2006; the bright light probably accompanied explosion of ball lightning at its contact with the ground). Very bright light from ball lightning can also result in direct contact of humans with ball lightning, loss of control while driving, and other secondary effects. There are a number of reports of human casualties, including death, due to direct contacts with ball lightning (Akkuratov 1982; Barry, 1980; Dmitriev et al., 1986; Grigor’ev, 2006; Imyanitov and Tikhii, 1967; Likhosherstnykh, 1983, Selvaggi et al., 2003; Shmatov, 2003; Singer, 1971; Smirnov, 1988, 1990, 1992). The influence of electrical energy seems to be the main dangerous factor of direct contact, although the information presented by Akkuratov (1982), Likhosherstnykh (1983) and Dmitriev et al. (1986) about the influence of ball lightning on five mountaineers, one of which died immediately or almost immediately, allow us to assume that in some situations thermal burns caused by ball lightning are also mortally dangerous. The wounds of the mountaineers were unusual (Akkuratov, 1982; Likhosherstnykh, 1983). According to Likhosherstnykh (1983), these wounds could be caused by explosion of liquid in the tissues due to the influence of induced currents. It was also assumed that the explosion of such a kind could also be caused by fast heating of tissue by high-energy photons (Shmatov, 2009). It should be noted that compatibility of these assumptions, especially of the last one, with long-term survival of four mountaineers requires additional studies.

5.2. Hazard of electric pulses generated by ball lightning and electric field in the vicinity of ball lightning

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The ability of ball lightning to kill humans by means of an electrical impulse can be considered established. The death of Professor G.-W. Richmann is one of the examples of such a kind (Powell and Finkelstein, 1969, 1970; Shmatov, 2001, 2003; Singer, 1971). It should be noted, however, that opinions differ about ball lightning parameters and physical effects related to this ability. Using the data presented by Lee (1977), Smirnov (1988) has assumed that lethal injury from a short electric pulse to a human being is possible when the energy ε pulse of the pulse is equal to or greater than 2 kJ. This assumption and the fact that the electric field Ebls near a ball lightning surface cannot exceed the electric field Ebr ≈ 25 − 30 kV/cm corresponding to breakdown of air (see e. g. Grigor’ev et al., 2016; Smirnov, 1992 and below; here it is assumed that conditions are sufficiently close to standard ones) imply that the electric charge of ball lightning is not dangerous for humans. According to Smirnov (1990, 1992), the danger of ball lightning for humans is related to the initiation of “an electric explosion”, i.e. a powerful electric discharge. A similar assumption was also made by Stakhanov (1996). According to the model proposed by Shmatov (Shmatov, 2003), the ability of some ball lightning to generate an electric pulse with ε pulse ≥ 2 kJ results from the periodical transformation of kinetic energies of the oscillating electrons into the energy of the “macroscopic” electric field. Grigor’ev et al. (2016) used the assumption according to which an electric pulse is mortally dangerous at

ε pulse = 0.1 − 1 J (Manoilov, 1985). This assumption corresponds to the high danger of the electrical charge of some ball lightning (Grigor’ev 2016). Although the real lower boundary of the mortally dangerous value of ε pulse for electric pulses which could be generated by ball lightning remains unclear, it is evident that direct contact with ball lightning is highly undesirable.

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It should be noted that several authors proposed or mentioned ball lightning models with s

Ebl >>Ebr (see e.g. Nikitin et al., 2018a; Shabanov, 2019; Zaitsev and Zaitsev, 1991). In particular, Nikitin et al. (2018a) presented a model example with a positive ball lightning charge

Q = 10−2 C and ball lightning radius of 6 cm. These values correspond to the energy ε blf of electric field of ball lightning of at least about 7.5 × 109 J and Ebls ≈ 2.5 × 108 V/cm which is sufficient not only for breakdown of air but also for cold runaway (see e.g. Dwyer et al., 2012; Shmatov, 2015b and bibliography therein) and, as shown below, even for a physically important tunnel ionization of molecules and atoms of the air. Nikitin et al. (2018a) assume that in such a situation the breakdown does not occur due to the following. According to their model, ball lightning has a charged core and a cover (i.e. spherical layer), surrounding the core and arising due to attraction of polarizable material, for example, water, to the core. Attraction of the cover to the core provides the stability of ball lightning, while “low conductivity of an interval between the charged core and its cover” limits the current, passing through the cover, “by values of 10−3 − 10−2 A” and, thereby, “suppresses the possibility of spark channel formation” (Nikitin et al., 2018a). However, even if such cover could exist and electrons, arising in the air due to tunnel and collisional ionization (see, e.g. Landau and Lifshitz, 1974; Raizer, 2009), would not penetrate through its surface, it would be quickly coated by the electrons with a several fold decrease in Ebls and release of energy of the order of 0.1ε blf . For example, it is possible to show that the rate RtH of tunnel ionization of hydrogen atoms at the distances from zero to 1 cm from the outer surface of the cover would be in the range of about 3.5 × 1010 − 3.7 × 1012 s-1 (see e.g. Landau and Lifshitz, 1974), while at standard conditions, the 1-cm-thick layer of air around this surface contains about 1.4 × 1022 molecules. 53

The rates of tunnel ionization of N2, O2 and Ar are different from RtH . The detailed analysis of the rates of tunnel ionization of the components of the air should take into account their excitation and is outside the scope of this paper. However, the fact that the values RtH presented above are large demonstrates that tunnel ionization of air is sufficient for a quick release of electrons the absolute value of the total electric charge of which exceeds Q. It should be emphasized that prediction of the possibility of the stabilization of ball lightning by the cover mentioned above (Nikitin et al., 2018a, see also Zaitsev and Zaitsev, 1991 and Shabanov, 2019) is based on this principally mistaken assumption. Namely, it is assumed that the electric charges, arising in the different regions of inner and outer surfaces of the cover, are influenced only by the electric field of the core and do not interact with each other (Nikitin et al., 2018a; see also Zaitsev and Zaitsev, 1991). It is easy to show that this results in the important overestimation of the inward force, acting on the shell.

5.3. Some expected problems related to space missions

Ball lightning can be dangerous for some space missions. Carpenter (1962) was the first to discuss this possibility when he mentioned that “the atmospheres of Jupiter and Saturn might provide environments where an encounter with ball lightning could be disastrous to an exploratory Aero-Space force.” The possibility of existence and potential danger of ball lightning in the atmospheres of Venus, Jupiter, Mars and Titan was discussed by Shmatov (Shmatov, 2004a, 2004b) within the framework of the model described in Section 2.1. The high atmospheric pressure near the surface of Venus and the low atomic numbers of the main components of the atmosphere of Jupiter were considered as very favorable for the existence of

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ball lightning (Shmatov, 2004b). However, it is now clear that for the aforementioned model, estimates of the expected properties of ball lightning in the atmosphere of Jupiter and other celestial bodies with the atmospheres containing large amount of hydrogen should be augmented by an analysis of the problem of the collisional transfer of kinetic energy of electrons of the ball lightning core to ions. An analysis of this problem is performed only for ball lightning in the atmosphere of the Earth, and the conclusions about the low importance of such a transfer are based partly on the fact that the atomic numbers of the main components of air are greater than unity (Ostapenko and Tolpygo, 1984; Shmatov, 2004b, 2015a). Lightning has been detected on Jupiter, its satellite Io, Venus, Uranus, and Saturn (see e.g. Iudin et al., (2018) and bibliography therein). The dust storms on Mars were considered as a possible reason for lightning (Chameides et al., 1979). The potential danger of ball lightning in the atmospheres of other celestial bodies for space missions is related, in particular, to the possibility of damage to balloons and parachutes (Shmatov, 2004a, 2004b).

6. Conclusions One of the main goals of this review is to provide guidance for future investigations by pointing out critical problems that need to be solved. In mature areas of science where there is a consensus about the basic nature of the phenomenon under study, critical problems are fairly easy to identify by means of the interplay between theories and experimental and observational results. When a theory cannot account for the salient features of an experiment or observation, the theory needs to be modified until its predictions are in substantial agreement with observed empirical data. If a promising theory needs experimental verification, experiments should be performed to verify or contradict the theory. This process assumes a certain degree of consensus

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among the interested parties: agreement on basic definitions of what data qualifies as the proper subject of study, for example, and a recognition of which theories best account for the data at a given time. By these criteria, the study of ball lightning is still immature. As we have seen, alternative explanations not involving ball lightning can be found for some of the most prominent recently published observational data in this field. And even in the limited scope of this review, we have examined at least six distinct recently proposed theories which have few overlapping features. These theories cannot all be correct, but the lack of reliable quantitative data on ball lightning makes it difficult to reject any of these theories out of hand. Theorists are often tempted to propose models which can account for only a selected number of ball lightning observations, and often ignore other observations or data which cannot be accounted for by their theory. In a situation where theories abound and empirical data is scarce, the best course is to concentrate effort on producing more and better-quality observations, and if possible, experiments directed at producing a phenomenon that in all essential respects behaves like ball lightning. While many experimenters claimed to have produced ball lightning in the laboratory (Egorov et al., 2004; Golka, 1994; Ito et al., 2009; Jones, 1910; Oreshko, 2015; Rice-Evans, 1982; Ritchie, 1963; Shabanov, 2019), attempts to reproduce these experiments have either failed or shown that the phenomenon, while reproducible, did not have more than one or two of the essential characteristics of natural ball lightning (Stephan et al., 2013; Stephan and Massey, 2008). Several of the theories described above furnish some guidance as to how one might go about developing an experiment to produce ball lightning. The theories of Shmatov (Shmatov,

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2003, 2015b), Rañada (Rañada et al., 2000), and Wu (2016), among others, give some indication of how experimental production of ball lightning might be achieved. Unfortunately, reproducing in the laboratory the typical conditions in a thunderstorm which give rise to ordinary lightning, not to mention ball lightning, would require the production of large electric fields over distances of at least hundreds of meters, which is at present essentially impossible. But if the special conditions that produce ball lightning can be identified with the aid of either theoretical or additional observational studies, perhaps the goal of producing ball lightning in the laboratory which behaves in all essential respects like ball lightning in nature, can be achieved. On the observational side, synthetic programs which collect and analyze multiple ball lightning sightings and correlate them with each other and with lightning-detection network data may provide new insights into conditions or mechanisms that produce ball lightning. Two studies published since 2000 are notable in this regard. The first study describes an unusual incident in Neuruppin, Germany in 1994 in which over 30 observers reported multiple ball lightning objects all correlated in time with a single 370kA positive cloud-to-ground discharge that occurred at 1608 UTC that evening (Bäcker et al., 2007). Two large ball lightning objects were each sighted by more than one observer to float in the air for several seconds, and at least six smaller such objects were sighted inside houses and other buildings by various residents. The reports were collected by one of the authors of the paper (Bäcker), who was the meteorologist on duty at the town's weather station when the incident occurred, and who fielded many of the initial phone calls reporting the incidents immediately afterwards. The chief points of interest in that paper from a theoretical view are the locations of the simultaneous objects, which were ascertained in (Bäcker et al., 2007) with a precision of less

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than 1 km in many cases. For those sightings which could be located with this degree of precision, the distance from the sighting point to the ground termination of the 370-kA positive stroke ranged from 3.8 km to 11.2 km. In other words, the process that gave rise to these multiple objects involved action over a large distance, ranging from 4 to 11 km or more. Besides the ball lightning objects, numerous eyewitness accounts of corona flashes at the time indicate that the entire region may have been subjected to a short intense electric field capable of producing ground-based negative leaders. A second more extensive study of 34 ball lightning sightings in Europe used data from the European Cooperation for Lightning Detection (EUCLID) network to identify ordinary lightning discharges that occurred in close time relationship with ball lightning sightings whose time was well established by other means (Keul and Diendorfer, 2018). Of these sightings, 85% came with the time of the observation known within an accuracy of 5 min or better. The researchers divided their cases into two categories: close events, in which the distance between the lightning location site provided by EUCLID and the ball lightning sighting was less than 1 km, and distant events, where the distance was between 1 and 10 km (Keul and Diendorfer, 2018). The mean distance for the 17 close events was 0.42 km, and the mean distance in the 17 distant-event cases was 5.7 km. This data clearly shows that while ball lightning can occur within less than 1 km of a near-simultaneous ordinary lightning flash, a substantial number of such events happen more than 1 km away, thus confirming the lesson from the Neuruppin event that it is not necessary for lightning to strike in the immediate vicinity for ball lightning to occur. Keul and Diendorfer also found that the percentage of positive strokes in the EUCLID data that were correlated with ball lightning was 54% (Keul and Diendorfer, 2018), much higher than the overall statistical average for typical ordinary lightning of about 10% (Rakov and Uman,

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2003). Studies such as (Keul and Diendorfer, 2018) and (Bäcker et al., 2007), which correlate individual sightings of ball lightning with others and with objective quantitative data, promise to elucidate aspects of the ball lightning problem that a single observation cannot. However, observations of single events such as the multiple-camera sighting of an apparent ball lightning object near Moscow (Nikitin et al., 2018b) can be analyzed to extract quantitative data on ball lightning brightness and motion. A fruitful line of inquiry in this regard would be to mount a systematic solicitation for well-documented ball lightning sightings, together with sufficient background and circumstantial data (time, location, etc.) to allow correlation with records of lightning-detection networks and other objective data. A concerted effort to procure photographic records of ball lightning may seem quixotic in view of the phenomenon's rarity. But despite the abundance of conventional and high-speed photographic studies of ordinary lightning, there are relatively few photographs or video records that portray the ground and surroundings of a cloud-to-ground lightning flash. Because many sightings indicate that ball lightning often appears within 100 meters or so of ground level, airborne reconnaissance using unmanned aerial vehicles (UAVs) flying at low altitudes during lightning activity might provide considerable data on ball lightning, as well as throwing light on certain damage mechanisms and other phenomena of ordinary lightning which are still poorly understood (Stephan, 2019). According to Imyanitov (1988), “even outside the thunderclouds, in the clouds ball lightning are one hundred times more frequent than near the ground” (see also Shmatov, 2015b). An attempt to confirm this statement with the use of UAVs flying at high altitudes is highly desirable. A high-speed infrared camera was successfully used for studies of discharges generated by artificial clouds of charged water (Kostinskiy et al., 2015a, 2015b, 2016). The use of similar cameras, including those carried by UAVs, to search for ball lightning

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in clouds may be effective. Studies involving observations in visible, infrared, x-ray and gammaray ranges with different locations of visible and infrared cameras and detectors of high-energy photons are also highly desirable (see also Ashby and Whitehead, 1971; Fryberger, 1992; Shmatov, 2006, 2019). The increasing number of potential eyewitnesses equipped with mobile phones featuring video cameras increases the chances that significant ball lightning events can be captured digitally by multiple observers, if researchers can obtain the data together with enough background information to make it useful. Social-media applications such as a free downloadable data-capture system for the use of the general public might be very helpful here, although it is evident that an analysis revealing fakes will be necessary. Ball lightning can be a difficult topic to deal with, even for editors of scientific journals. A recent survey by us of the number of papers in the online Scientific Citation Index Expanded which show up under the search term "ball lightning" showed that the majority of papers (231 out of 455) were published in journals that are categorized in some way as "multidisciplinary." In an era of ever-increasing specialization, a topic such as ball lightning which does not have an agreed-upon subject area as its home gets neglected, not through malevolent intent, but simply because publications on the topic are scattered so widely among disparate fields of physics, chemistry, meteorology, geophysics, and even engineering. This situation reflects the reality that there are few if any tightly associated groups of researchers who work in a coordinated way on problems associated with ball lightning. Notwithstanding this relative lack of attention, the authors of this review believe that the scientific community owes it to itself and to the culture at large to overcome the challenges of ball lightning research and get to the bottom of what is still largely an ongoing mystery. It is our

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hope that this update will encourage more workers to attack the problems associated with ball lightning with renewed vigor and resources, so that the problem of how ball lightning forms and exists—along with any new physics that may be needed—can at last be solved.

7. Acknowledgments We would like to thank the anonymous referees for useful comments on the initial version of this paper. One of us (Stephan) acknowledges the support of the Julian Schwinger Foundation through Grant No. JSF-16-04-0000.

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Advances in Ball Lightning Research: Highlights • • • •

Ball lightning research made significant progress since 2000 Fluorescence caused by ball lightning quantified Ball lightning captured by 3 simultaneous video recordings Several new plasma-based theories proposed