Editing Ball lightning (section)

== Proposed scientific explanations ==
There is at present no widely accepted explanation for ball lightning. Several hypotheses have been advanced since the phenomenon was brought into the scientific realm by the English physician and electrical researcher [[William Snow Harris]] in 1843,<ref>{{cite book|last=Snow Harris|first=William|title=On the nature of thunderstorms (originally published in 1843)|publisher=Bastian Books|year=2008|edition=Reprint|pages=34–43|chapter=Section I|isbn=978-0-554-87861-4|chapter-url=https://books.google.com/books?id=XSdHnUv1MKwC}}</ref> and [[French Academy of Sciences|French Academy]] scientist [[François Arago]] in 1855.<ref>François Arago, ''Meteorological Essays'' by, Longman, 1855</ref>

=== Vaporized silicon hypothesis ===
This hypothesis suggests that ball lightning consists of vaporized silicon [[combustion|burning]] through [[oxidation]]. Lightning striking Earth's soil could vaporize the silica contained within it, and somehow separate the oxygen from the silicon dioxide, turning it into pure silicon vapor. As it cools, the silicon could condense into a floating aerosol, bound by its charge, glowing due to the heat of silicon recombining with [[oxygen]]. An experimental investigation of this effect, published in 2007, reported producing "luminous balls with lifetime in the order of seconds" by evaporating pure silicon with an electric arc.<ref name=NGN /><ref>{{cite journal |last1=Paiva |first1=Gerson Silva |author2=Antonio Carlos Pavão |author3=Elder Alpes de Vasconcelos |author4=Odim Mendes Jr. |author5=Eronides Felisberto da Silva Jr. |year= 2007|title= Production of Ball-Lightning-Like Luminous Balls by Electrical Discharges in Silicon|journal=Phys. Rev. Lett.|volume=98 |doi=10.1103/PhysRevLett.98.048501|page=048501 |pmid=17358820 |issue=4 |bibcode=2007PhRvL..98d8501P|url=http://urlib.net/sid.inpe.br/mtc-m17@80/2007/11.12.14.06 }}</ref><ref>{{cite magazine|url=https://www.newscientist.com/article.ns?id=mg19325863.500|title=Lightning balls created in the lab|magazine=New Scientist|date=10 January 2007|quote=A more down-to-earth theory, proposed by John Abrahamson and James Dinniss at the University of Canterbury in Christchurch, New Zealand, is that ball lightning forms when lightning strikes soil, turning any silica in the soil into pure silicon vapour. As the vapour cools, the silicon condenses into a floating aerosol bound into a ball by charges that gather on its surface, and it glows with the heat of silicon recombining with oxygen.}}</ref> Videos and spectrographs of this experiment have been made available.<ref>{{Cite web |url=ftp://ftp.aip.org/epaps/phys_rev_lett/E-PRLTAO-98-047705/ |archive-url=https://web.archive.org/web/20181107032310/http://ftp.aip.org/epaps/phys_rev_lett/E-PRLTAO-98-047705/ |archive-date=2018-11-07 |url-status=dead |title=Index of /Epaps/Phys_rev_lett/E-PRLTAO-98-047705 |access-date=6 April 2007 }}</ref><ref>{{cite journal|last=Slezak|first=Michael|title=Natural ball lightning probed for the first time|url=https://www.newscientist.com/article/dn24886-natural-ball-lightning-probed-for-the-first-time.html#.Utl4i3co6Hu|journal=[[New Scientist]]|volume=221|issue=2953|page=17|access-date=17 January 2014|bibcode=2014NewSc.221...17S|year=2014|doi=10.1016/S0262-4079(14)60173-1|url-access=subscription}}</ref> This hypothesis got significant supportive data in 2014, when the first ever recorded spectra of natural ball lightning were published.<ref name="BLspectrum" /><ref name="BLspectrumvideo" /> The theorized forms of silicon storage in soil include nanoparticles of Si, [[Silicon monoxide|SiO]], and [[Silicon carbide|SiC]].<ref>{{cite journal |last1 = Abrahamson |first1 = John |title = Ball lightning caused by oxidation of nanoparticle networks from normal lightning strikes on soil |journal = Nature |volume = 403 |issue = 6769 |pages = 519–21 |year = 2000 |doi = 10.1038/35000525 |first2 = James |pmid = 10676954 |bibcode = 2000Natur.403..519A |last2 = Dinniss |s2cid = 4387046 }}</ref>
Matthew Francis has dubbed this the "dirt clod hypothesis", in which the spectrum of ball lightning shows that it shares chemistry with soil.<ref name=Francis2014>{{Cite web|url=https://arstechnica.com/science/2014/01/the-dirty-secret-behind-ball-lightning-is-dirt/|title=The dirty secret behind ball lightning is dirt|first=Matthew|last=Francis|date=22 January 2014|website=Ars Technica}}</ref>

=== Electrically charged solid-core model ===
In this model ball lightning is assumed to have a solid, positively charged core. According to this underlying assumption, the core is surrounded by a thin electron layer with a charge nearly equal in magnitude to that of the core. A vacuum exists between the core and the electron layer containing an intense [[electromagnetic field|electromagnetic (EM) field]], which is reflected and guided by the electron layer. The microwave EM field applies a [[ponderomotive force]] (radiation pressure) to the electrons preventing them from falling into the core.<ref>{{cite journal | last1 = Muldrew | first1 = D. B. | year = 1990 | title = The Physical Nature of Ball Lightning | journal = Geophysical Research Letters | volume = 17 | issue = 12 | pages = 2277–2280 | doi = 10.1029/GL017i012p02277 |bibcode = 1990GeoRL..17.2277M }}</ref><ref>{{cite journal | last1 = Muldrew | first1 = D. B. | doi = 10.5194/angeo-28-223-2010 | title = Solid charged-core model of ball lightning | journal = Annales Geophysicae | volume = 28 | issue = 1 | pages = 223–2010 | year = 2010 |bibcode = 2010AnGeo..28..223M | doi-access = free }}</ref>

=== Microwave cavity hypothesis ===
[[Pyotr Kapitsa]] proposed that ball lightning is a glow discharge driven by microwave radiation that is guided to the ball along lines of ionized air from lightning clouds where it is produced. The ball serves as a resonant microwave cavity, automatically adjusting its radius to the wavelength of the microwave radiation so that resonance is maintained.<ref>{{cite journal |author-link1=Pyotr Kapitsa|last1=Капица |first1=П. Л. |year= 1955|script-title=ru:О природе шаровой молнии|journal=Докл. Акад. наук СССР |volume=101 |page=245 |language=ru |trans-title=On the nature of ball lightning}}</ref><ref>{{cite encyclopedia |last1=Kapitsa |first1=Peter L.|author-link1=Pyotr Kapitsa|editor=Donald J. Ritchie |encyclopedia=Ball Lightning: A Collection of Soviet Research in English Translation |title=The Nature of Ball Lightning |edition=1961 |year=1955 |publisher=Consultants Bureau, New York |oclc= 717403|pages=11–16 |isbn=9780835759502}}</ref>

The Handel Maser-Soliton theory of ball lightning hypothesizes that the energy source generating the ball lightning is a large (several cubic kilometers) atmospheric [[maser]]. The ball lightning appears as a plasma caviton at the antinodal plane of the microwave radiation from the maser.<ref>{{cite journal |last1=Handel |first1=Peter H. |author2=Jean-François Leitner |year=1994 |title=Development of the maser-caviton ball lightning theory |journal=J. Geophys. Res. |volume=99 |issue=D5 |page=10689 |url=http://europa.agu.org/?view=article&uri=/journals/jd/93JD01021.xml |archive-url=https://archive.today/20120713173033/http://europa.agu.org/?view=article&uri=/journals/jd/93JD01021.xml |url-status=dead |archive-date=13 July 2012 |bibcode=1994JGR....9910689H |doi=10.1029/93JD01021 |url-access=subscription }}</ref>

In 2017, Researchers from Zhejiang University in Hangzhou, China, proposed that the bright glow of lightning balls is created when microwaves become trapped inside a plasma bubble. At the tip of a lightning strike reaching the ground, a relativistic electron bunch can be produced when in contact with microwave radiation.
<ref>{{cite journal | last=Wu  | first=H. C. | title = Relativistic-microwave theory of ball lightning  | journal = Scientific Reports  | volume = 6  | pages=28263 | date = June 2019  | doi=10.1038/srep28263 | pmid=27328835 | pmc=4916449 | arxiv=1411.4784 | bibcode=2016NatSR...628263W }}</ref> The latter ionizes the local air and the radiation pressure evacuates the resulting plasma, forming a spherical plasma bubble that stably traps the radiation. Microwaves trapped inside the ball continue to generate plasma for a moment to maintain the bright flashes described in observer accounts. The ball eventually fades as the radiation held within the bubble starts to decay and microwaves are discharged from the sphere. The lightning balls can dramatically explode as the structure destabilizes. The theory could explain many of the strange characteristics of ball lightning. For instance, microwaves are able to pass through glass, which helps to explain why balls could be formed indoors.

=== Soliton hypothesis ===
{{Main|Soliton|St. Elmo's fire}}

Julio Rubinstein,<ref>{{cite web|title=Rubinstein, J|url=http://inspirehep.net/author/profile/J.Rubinstein.1|website=Inspire HEP|access-date=6 March 2017}}</ref> [[David Finkelstein]], and James R. Powell proposed that ball lightning is a detached St. Elmo's fire (1964–1970).{{citation needed|date=June 2015}} St. Elmo's fire arises when a sharp conductor, such as a ship's mast, amplifies the atmospheric electric field to breakdown. For a globe the amplification factor is 3. A free ball of ionized{{explanation needed|date=March 2019}} air can amplify the ambient field this much by its own conductivity. When this maintains the ionization, the ball is then a [[soliton]] in the flow of atmospheric electricity.

Powell's kinetic theory calculation found that the ball size is set by the second Townsend coefficient (the mean free path of conduction electrons) near breakdown. Wandering glow discharges are found to occur within certain industrial microwave ovens and continue to glow for several seconds after power is shut off.{{citation needed|date=May 2022}} [[electric arc|Arcs]] drawn from high-power low-voltage microwave generators also are found to exhibit afterglow.{{citation needed|date=May 2022}} Powell measured their spectra, and found that the after-glow comes mostly from metastable [[nitric oxide|NO]] ions, which are long-lived at low temperatures. It occurred in air and in nitrous oxide, which possess such metastable ions, and not in atmospheres of argon, carbon dioxide, or helium, which do not.

The soliton model of a ball lightning was further developed.<ref name=":0">{{Cite book|chapter = Electron gas oscillations in plasma. Theory and applications|url = https://www.novapublishers.com/catalog/product_info.php?products_id=4460&osCsid=ec1a1f3a9282cfe1dc8d32da111c4b73|title = Advances in Plasma Physics Research|volume = 5|year = 2007|first1 = Maxim|last1 = Dvornikov|first2 = Sergey|last2 = Dvornikov|editor-last = Gerard|editor-first = F.|pages = 197–212|arxiv = physics/0306157|isbn = 978-1-59033-928-2|bibcode = 2003physics...6157D|access-date = 20 December 2018|archive-url = https://web.archive.org/web/20151208193905/https://www.novapublishers.com/catalog/product_info.php?products_id=4460&osCsid=ec1a1f3a9282cfe1dc8d32da111c4b73|archive-date = 8 December 2015|url-status = dead}}</ref><ref name=":1">{{cite journal|title = Formation of bound states of electrons in spherically symmetric oscillations of plasma|url = http://stacks.iop.org/1402-4896/81/i=5/a=055502?key=crossref.abe8a0f48fb80b98d6ac1436a463c132|journal = Physica Scripta|volume = 81|issue = 5|page = 055502|doi = 10.1088/0031-8949/81/05/055502|first = Maxim|last = Dvornikov|arxiv = 1002.0764|bibcode = 2010PhyS...81e5502D |year = 2010|s2cid = 116939689}}</ref><ref name=":2">{{cite journal|title = Axially and spherically symmetric solitons in warm plasma|journal = Journal of Plasma Physics|date = 2011-12-01|issn = 1469-7807|pages = 749–764|volume = 77|issue = 6|doi = 10.1017/S002237781100016X|first = Maxim|last = Dvornikov|arxiv = 1010.0701|bibcode = 2011JPlPh..77..749D |s2cid = 118505800}}</ref> It was suggested that a ball lightning is based on spherically symmetric nonlinear oscillations of charged particles in plasma – the analogue of a spatial Langmuir soliton.<ref>{{cite journal|title = Stable spatial Langmuir solitons|journal = Physics Letters A|date = 2005-02-28|pages = 46–52|volume = 336|issue = 1|doi = 10.1016/j.physleta.2004.11.063|first1 = T. A.|last1 = Davydova|first2 = A. I.|last2 = Yakimenko|first3 = Yu. A.|last3 = Zaliznyak|bibcode = 2005PhLA..336...46D |arxiv = physics/0408023|s2cid = 119369758}}</ref> These oscillations were described in both classical<ref name=":1" /><ref name=":2" /> and quantum<ref name=":0" /><ref name=":3">{{cite journal|last=Dvornikov|first=Maxim|date=2012-02-08|title=Effective attraction between oscillating electrons in a plasmoid via acoustic wave exchange|journal=Proc. R. Soc. A|volume=468|issue=2138|pages=415–428|arxiv=1102.0944|bibcode=2012RSPSA.468..415D|doi=10.1098/rspa.2011.0276|s2cid=28359324|issn=1364-5021}}</ref> approaches. It was found that the most intense plasma oscillations occur in the central regions of a ball lightning. It is suggested that bound states of radially oscillating charged particles with oppositely oriented spins – the analogue of Cooper pairs – can appear inside a ball lightning.<ref name=":3" /><ref name=":5">{{cite journal|last=Dvornikov|first=Maxim|year=2013|title=Pairing of charged particles in a quantum plasmoid|url=http://stacks.iop.org/1751-8121/46/i=4/a=045501?key=crossref.4d16a921f1aef1e1c114d202c136a063|journal=Journal of Physics A: Mathematical and Theoretical|volume=46|issue=4|page=045501|arxiv=1208.2208|bibcode=2013JPhA...46d5501D|doi=10.1088/1751-8113/46/4/045501|s2cid=118523275}}</ref> This phenomenon, in its turn, can lead to a superconducting phase in a ball lightning. The idea of the superconductivity in a ball lightning was considered earlier.<ref name=":7">{{cite journal|title = A model for ball lightning|journal = Nature|date = 1980-03-13|pages = 150–151|volume = 284|issue = 5752|doi = 10.1038/284150a0|first = G. C.|last = Dijkhuis|s2cid = 4269441|bibcode = 1980Natur.284..150D }}</ref><ref name=":8" /> The possibility of the existence of a ball lightning with a composite core was also discussed in this model.<ref name=":4">{{cite journal|last=Dvornikov|first=Maxim|date=2012-11-01|title=Quantum exchange interaction of spherically symmetric plasmoids|journal=Journal of Atmospheric and Solar-Terrestrial Physics|volume=89|issue=2012|pages=62–66|arxiv=1112.0239|bibcode=2012JASTP..89...62D|doi=10.1016/j.jastp.2012.08.005|s2cid=119268742}}</ref>

=== Hydrodynamic vortex ring antisymmetry ===
One theory that may account for the wide spectrum of observational evidence is the idea of [[combustion]] inside the low-velocity region of spherical [[vortex]] breakdown of a natural vortex{{vague|date=July 2012}} (e.g., the '[[Hill's spherical vortex]]').<ref>{{cite journal | last = Coleman | first = PF | year = 1993 | journal = Weather | volume = 48 | issue = 1 | page = 30 | title = An explanation for ball lightning? | doi = 10.1002/j.1477-8696.1993.tb07221.x|bibcode = 1993Wthr...48...27. }}</ref>

=== Nanobattery hypothesis ===
Oleg Meshcheryakov suggests that ball lightning is made of composite nano or submicrometer particles—each particle constituting a [[Battery (electrical)|battery]]. A surface discharge shorts these batteries, causing a current that forms the ball. His model is described as an [[aerosol]] model that explains all the observable properties and processes of ball lightning.<ref>{{cite journal |last=Meshcheryakov|first=Oleg |year= 2007|title=Ball Lightning–Aerosol Electrochemical Power Source or A Cloud of Batteries|journal=Nanoscale Res. Lett.|volume=2 |issue=3|pmc=3246378 |doi=10.1007/s11671-007-9068-2|pages=319–330|bibcode = 2007NRL.....2..319M |doi-access=free}}</ref><ref>{{cite arXiv |last=Meshcheryakov |first=Oleg |title=How and why electrostatic charge of combustible nanoparticles can radically change the mechanism and rate of their oxidation in humid atmosphere |eprint=1008.0162 |class=physics.plasm-ph |date=1 August 2010}}</ref>

=== Buoyant plasma hypothesis ===
The declassified [[Project Condign]] report concludes that buoyant charged [[plasma (physics)|plasma]] formations similar to ball lightning are formed by novel physical, electrical, and magnetic phenomena, and that these charged plasmas are capable of being transported at enormous speeds under the influence and balance of electrical charges in the atmosphere. These plasmas appear to originate due to more than one set of weather and electrically charged conditions, the scientific rationale for which is incomplete or not fully understood. One suggestion is that meteoroids breaking up in the atmosphere and forming charged plasmas as opposed to burning completely or impacting as meteorites could explain some instances of the phenomena, in addition to other unknown atmospheric events.<ref>{{cite web|url=http://www.disclosureproject.org/docs/pdf/uap_exec_summary_dec00.pdf |title=Unidentified Aerial Phenomena in the UK, Air Defence Region, Executive Summary |date=December 2000 |page=7|publisher=[[Defence Intelligence|Defence Intelligence Staff]] |website=disclosureproject.org |archive-url=https://web.archive.org/web/20170422214024/http://www.disclosureproject.org/docs/pdf/uap_exec_summary_dec00.pdf |archive-date=22 April 2017 |url-status=dead}}</ref> However, according to Stenhoff, this explanation is considered insufficient to explain the ball lightning phenomenon, and would likely not withstand peer review.<ref>{{cite book |last1=Stenhoff |first1=Mark |last2=James |first2=Adrian |title=Extreme weather : forty years of the Tornado and Storm Research Organisation (TORRO) |date=2016 |publisher=Wiley |location=Hoboken, NJ |isbn=978-1118949962 |pages=227–228 |url=https://books.google.com/books?id=rnhjCwAAQBAJ&pg=PA228}}</ref>

=== Hallucinations induced by magnetic field ===
Cooray and Cooray (2008)<ref>[http://www.el.angstrom.uu.se/meny/artiklar/ball%20lightning.pdf Could some ball lightning observations be optical hallucinations caused by epileptic seizures] {{Webarchive|url=https://web.archive.org/web/20131016080716/http://www.el.angstrom.uu.se/meny/artiklar/ball%20lightning.pdf |date=16 October 2013 }}, Cooray, G. and V. Cooray, ''The open access atmospheric science journal'', vol. 2, pp. 101–105 (2008)</ref> stated that the features of hallucinations experienced by patients having [[epileptic seizure]]s in the [[occipital lobe]] are similar to the observed features of ball lightning. The study also showed that the rapidly changing magnetic field of a close lightning flash is strong enough to excite the neurons in the brain. This strengthens the possibility of lightning-induced seizure in the occipital lobe of a person close to a lightning strike, establishing the connection between epileptic [[hallucination]] mimicking ball lightning and thunderstorms.

More recent research with [[transcranial magnetic stimulation]] has been shown to give the same hallucination results in the laboratory (termed [[magnetophosphene]]s), and these conditions have been shown to occur in nature near lightning strikes.<ref name="Peer 2010">{{cite journal |author1=Peer, J. |author2=Kendl, A. |doi=10.1016/j.physleta.2010.05.023 |journal=Physics Letters A |volume=374 |title=Transcranial stimulability of phosphenes by long lightning electromagnetic pulses |issue=29 |pages=2932–2935 |year=2010 |arxiv=1005.1153|bibcode = 2010PhLA..374.2932P|s2cid=119276495 }}
* Erratum: {{cite journal |journal=Physics Letters A |volume=347 |issue=47 |pages=4797–4799| doi=10.1016/j.physleta.2010.09.071|title=Erratum and addendum to "Transcranial stimulability of phosphenes by long lightning electromagnetic pulses" [Phys. Lett. A 374 (2010) 2932] |year=2010 |last1=Peer |first1=J. |last2=Cooray |first2=V. |last3=Cooray |first3=G. |last4=Kendl |first4=A. |bibcode = 2010PhLA..374.4797P |doi-access=free }}</ref><ref>[https://www.theregister.co.uk/2010/05/19/ball_lightning_actually_magno_brain_images/ Ball lightning is all in the mind, say Austrian physicists], The Register, 19 May 2010.</ref>
This hypothesis fails to explain observed physical damage caused by ball lightning or simultaneous observation by multiple witnesses. (At the very least, observations would differ substantially.)

Theoretical calculations from [[University of Innsbruck]] researchers suggest that the magnetic fields involved in certain types of lightning strikes could potentially induce visual hallucinations resembling ball lightning.<ref name="Peer 2010" /> Such fields, which are found within close distances to a point in which multiple lightning strikes have occurred over a few seconds, can directly cause the [[neurons]] in the [[visual cortex]] to fire, resulting in [[magnetophosphene]]s (magnetically induced visual hallucinations).<ref>{{cite web |author=Emerging Technology |url=https://www.technologyreview.com/2010/05/11/203417/magnetically-induced-hallucinations-explain-ball-lightning-say-physicists/ |title=Magnetically Induced Hallucinations Explain Ball Lightning, Say Physicists |work=[[MIT Technology Review]] |date=2010-05-11 |access-date=2020-07-06}}</ref>

=== Rydberg matter concept ===
Manykin et al. have suggested atmospheric [[Rydberg matter]] as an explanation of ball lightning phenomena.<ref>{{cite journal | last1 = Manykin | first1 = E. A. | last2 = Ojovan | first2 = M. I. | last3 = Poluektov | first3 = P. P. | s2cid = 96732651 | editor1-last = Samartsev | editor1-first = Vitaly V | doi = 10.1117/12.675004 | title =Rydberg matter: Properties and decay| journal = Proceedings of the SPIE | volume = 6181 | series = SPIE Proceedings | pages = 618105–618105–9 | year = 2006 | bibcode = 2006SPIE.6181E..05M }}</ref> Rydberg matter is a condensed form of highly excited atoms in many aspects similar to electron-hole droplets in semiconductors.<ref>{{cite journal | last1 = Norman | first1 = G. É. | s2cid = 120857543 | doi = 10.1134/1.1355396 | title = Rydberg matter as a metastable state of strongly nonideal plasma | journal = Journal of Experimental and Theoretical Physics Letters | volume = 73 | issue = 1 | pages = 10–12 | year = 2001 |bibcode = 2001JETPL..73...10N }}</ref><ref>{{cite journal | last1 = Manykin | first1 = E. A. | last2 = Zelener | first2 = B. B. | last3 = Zelener | first3 = B. V. | s2cid = 121748296 | doi = 10.1134/S0021364010210125 | title = Thermodynamic and kinetic properties of nonideal Rydberg matter | journal = JETP Letters | volume = 92 | issue = 9 | page = 630 | year = 2011 |bibcode = 2010JETPL..92..630M }}</ref> However, in contrast to electron-hole droplets, Rydberg matter has an extended life-time—as long as hours. This condensed excited [[state of matter]] is supported by experiments, mainly of a group led by Holmlid.<ref>{{cite journal | last1 = Holmlid | first1 = L. | title = Direct observation of circular Rydberg electrons in a Rydberg matter surface layer by electronic circular dichroism | doi = 10.1088/0953-8984/19/27/276206 | journal = Journal of Physics: Condensed Matter | volume = 19 | issue = 27 | page = 276206| year = 2007 |bibcode = 2007JPCM...19A6206H | s2cid = 95032480 }}</ref> It is similar to a liquid or solid state of matter with extremely low (gas-like) density. Lumps of atmospheric Rydberg matter can result from condensation of highly excited atoms that form by atmospheric electrical phenomena, mainly from linear lightning. Stimulated decay of Rydberg matter clouds can, however, take the form of an avalanche, and so appear as an explosion.

=== Vacuum hypothesis ===
In December 1899, Nikola Tesla theorized that the balls consisted of a highly rarefied hot gas.<ref name="Tesla, Nikola 1978"/>

===Electron-ion model===
Fedosin presented a model in which charged ions are located inside the ball lightning, and electrons rotate in the shell, creating a magnetic field.<ref>{{Cite journal |last=Fedosin |first=Sergey G. |date=2024-10-19 |title= Electron-ion model of ball and bead lightning |journal= Journal of Atmospheric and Solar-Terrestrial Physics |volume= 265|issue= |pages= 106374|language=en|doi= 10.1016/j.jastp.2024.106374 |s2cid= 273448290 |bibcode=  2024JASTP.26506374F |arxiv=2410.18132 }}</ref>

The long-term stability of ball lightning is ensured by the balance of electric and magnetic forces. The electric force acting on the electrons from the positive volume charge of the ions is the centripetal force that holds the electrons in place as they rotate. In turn, the ions are held by the magnetic field, which causes them to rotate around the magnetic field lines. The model predicts a maximum diameter of 34 cm for ball lightning, with the lightning having a charge of about 10 microcoulombs and being positively charged, and the energy of the lightning reaching 11 kilojoules.<ref>{{Cite journal |last1=Fedosin |first1=Sergey G. |last2= Kim |first2=A. S.| date=2001 |title= The physical theory of ball lightning | url=https://applphys.orion-ir.ru/appl-01/01-1/01-1-e.htm |journal= Applied Physics (Russian Journal) |volume= 1|issue= |pages= 69–87|language=en|doi= 10.5281/zenodo.14005316 |s2cid= 20073308 }}</ref>

The electron-ion model describes not only ball lightning, but also bead lightning, which usually occurs when linear lightning disintegrates. Based on the known dimensions of the beads of bead lightning, it is possible to calculate the electric charge of a single bead and its magnetic field. The electric forces of repulsion of neighboring beads are balanced by the magnetic forces of their attraction. Since the electromagnetic forces between the beads significantly exceed the force of the wind pressure, the beads remain in their places until the moment of extinction of the bead lightning.

=== Electrochemical model ===
In the electrochemical model (based on work by Stakhanov <ref>{{cite book |last1=Stakhanov |first1=I.P. |title=The Physical nature of ball lightning (CEGB Translation, CE8244) |date=1979 |publisher=Atomizdat |location=Moscow |url=https://naturalplasmas.com/files/The_Physical_Nature_of_Ball_Lightning.pdf}}</ref> and later modified by Turner<ref name=turner1994>{{cite journal |last1=Turner |first1=D.J. |title=The structure and stability of ball lightning |journal=Philos. Trans. R. Soc. London A |date=1994 |volume=347 |issue=1682 |url=https://naturalplasmas.com/files/The-Structure-and-Stability-of-Ball-Lightning.pdf}}</ref><ref name=turner2002>{{cite journal |last1=Turner |first1=D.J. |title=The fragmented science of ball lightning |journal=Philos. Trans. R. Soc. London A |date=2002 |volume=360 |issue=1790 |url=https://royalsocietypublishing.org/doi/10.1098/rsta.2001.0921}}</ref>) a lightning ball is an air plasma surrounded by several chemically active layers. It is fuelled by nitrogen oxidation producing the ions H<sub>3</sub>O<sup>+</sup> and NO<sub>2</sub><sup>-</sup>. On hydration these ions can combine, refrigerating the plasma surface. The aerosols of nitrous acid so produced are then further oxidized to nitric acid. They grow in size and restrict the inflow of air, thus holding the plasma together.
 
These processes require very delicately balanced chemical and electrical conditions in the surrounding air which explains the rarity of the phenomenon. With optimal reaction conditions, the weight of the droplets formed can more than offset the buoyancy force of the hot plasma. At the same time, the net positive charges, both on the outside of the ball and on the Earth's surface (during a thunderstorm), can sometimes balance the ball in the air a meter or less above the ground.

Ball movement can be driven by electrical fields but also, since the air in-flow is restricted by the number and mean diameter of the surface particles, it will respond to local humidity differences. Furthermore, the air in-flow provides a very effective surface tension to the ball.<ref name="turner1994"/> This explains such apparently anomalous behaviors as squeezing through relatively small holes and bouncing. In its final form, the model <ref name="turner2002"/> can explain all the known characteristics of ball lightning. 
Thermodynamic considerations <ref>{{cite journal |last1=Turner |first1=D. |title=Vapor Phase Electrochemistry: The Missing Science |journal=Journal of Scientific Exploration |date=2023 |volume=37 |issue=3 |pages=390-428 |url=https://doi.org/10.31275/20232707}}</ref> refute the fallacy that rapid charge neutralisation precludes ball lightning from being a plasma.

=== Other hypotheses ===
Several other hypotheses have been proposed to explain ball lightning:

* Spinning electric [[dipole]] hypothesis. A 1976 article by V. G. Endean postulated that ball lightning could be described as an [[electric field]] vector spinning in the [[microwave]] frequency region.<ref>{{cite journal | last1 = Endean | first1 = V. G. | s2cid = 4194750 | title = Ball lightning as electromagnetic energy | doi = 10.1038/263753a0 | journal = Nature | volume = 263 | issue = 5580 | pages = 753–755 | year = 1976 |bibcode = 1976Natur.263..753E }}</ref>
* [[Electrostatic]] Leyden jar models. Stanley Singer discussed (1971) this type of hypothesis and suggested that the electrical recombination time would be too short for the ball lightning lifetimes often reported.<ref>{{cite book|last=Singer|first=Stanley|title=The Nature of Ball Lightning|location=New York|publisher=Plenum Press|year=1971}}</ref>
* Smirnov proposed (1987) a [[fractal]] [[aerogel]] hypothesis.<ref>Smirnov 1987, ''Physics Reports'', (Review Section of ''Physical Letters''), 152, No. 4, pp. 177–226.</ref>
* [[Mikhail Zelikin|M. I. Zelikin]] proposed (2006) an explanation (with a rigorous mathematical foundation) based on the hypothesis of [[plasma (physics)|plasma]] [[superconductivity]]<ref name=":8">{{cite journal | last1 = Zelikin | first1 = M. I. | s2cid = 123066140 | title = Superconductivity of plasma and fireballs | doi = 10.1007/s10958-008-9047-x | journal = Journal of Mathematical Sciences | volume = 151 | issue = 6 | pages = 3473–3496 | year = 2008 | doi-access = free }}</ref> (see also<ref name=":3" /><ref name=":5" /><ref name=":7" />).
* A. Meessen presented a theory at the 10th International Symposium on Ball Lightning (June 21–27, 2010, Kaliningrad, Russia) explaining all known properties of ball lightning in terms of collective oscillations of free electrons. The simplest case corresponds to radial oscillations in a spherical plasma membrane. These oscillations are sustained by parametric amplification, resulting from regular "inhalation" of charged particles that are present at lower densities in the ambient air. Ball lightning vanishes thus by silent extinction when the available density of charged particles is too low, while it disappears with a loud and sometimes very violent explosion when this density is too high. Electronic oscillations are also possible as stationary waves in a plasma ball or thick plasma membrane. This yields concentric luminous bubbles.<ref>{{cite journal|url=http://www.meessen.net/AMeessen/Ball-Lightning-Theory.pdf|title=Ball Lightning: Bubbles of Electronic Plasma Oscillations|journal=Journal of Unconventional Electromagnetics and Plasmas|last1=Meessen|first1=A.|volume=4|pages=163–179|year=2012|access-date=17 April 2019|archive-date=17 April 2019|archive-url=https://web.archive.org/web/20190417133352/http://www.meessen.net/AMeessen/Ball-Lightning-Theory.pdf|url-status=dead}}</ref>