Editing Ball lightning (section)

=== 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>