Historical research guide · 0860 · 2024

Verification of validity of the electrodynamic model of ball lightning

Anatoly I. Nikitin

In one minute

This is the sequel Anatoly Nikitin wrote to his own model of ball lightning, and it asks the hard question about it: would such an object actually hold together? The picture is a core of circling protons and electrons — dynamic electric capacitors — sealed inside a thin shell of polarised water. Four forces act on that shell. Two push out, the centrifugal force of the orbiting protons and the Coulomb repulsion of the core’s surplus charge; two push in, the pull of the polarised shell on that same charge, and plain atmospheric pressure. Nikitin writes the balance down, differentiates it, and finds every term of the derivative negative, which means the equilibrium is stable for any combination of size, charge and shell thickness. He then shows why the size stays constant in the wild: the object must shed energy and charge at matched rates. Break that match one way and it collapses; break it the other and it explodes.

Connection

Chapter 9 treats the self-organised, long-lived ball of charge as a real object with an engineering description, and this is the paper that supplies the stability analysis that description needs — not a sketch of what a plasmoid might be, but a force balance you can differentiate. It is the direct continuation of the model sheet at /library/stm-90f3c174b1, and its closing pages reach the observation that chapter 9 keeps returning to: to stay aloft, a heavy charged sphere needs either the atmospheric electric field or its own buoyancy, and a hundred-metre object at aircraft altitude works out to a very thin shell around a very large volume.

From the source

Four forces act on the shell of ball lightning in the electrodynamic model — the centrifugal force of the orbiting protons and the Coulomb force of the core’s uncompensated charge push outward, while the gradient force on the polarised shell and atmospheric pressure push inward — and setting their sum to zero gives the equilibrium condition for the object as a whole.Analysis of the stability conditions of ball lightning; Equations 1 to 5
That equilibrium is stable rather than marginal: differentiating the force balance with respect to the internal radius, and using the constancy of the shell volume together with the work done against the compressing forces, leaves a derivative in which every term is negative — so the system is in stable equilibrium for any values of the geometry factor, the charge, the shell thickness and the radius.Analysis of the stability conditions of ball lightning; Equations 6 to 10
The observed constancy of ball lightning’s size follows from a matched pair of losses: the radius and shell thickness stay fixed only if the object sheds stored proton energy and surface charge at rates tied together by one bracket, so that the radiated power equals that bracket multiplied by the current leaking from the shell.Estimation of the stability time of ball lightning; Equations 11 to 14
Which way the object fails depends on how much charge it carries, because the stretching force changes as the square of the charge while the compressing force changes only linearly with it: at small charge a disturbed object collapses, at large charge it explodes — and the paper points to dashcam footage of an explosion on impact with a car and to video of a bright flash followed by extinction half a second later as the two cases.Estimation of the stability time of ball lightning; Equations 16 and 17; Figures 1 and 2
Charge leaks away slowly enough for the object to live: with the conductivity of air near the ground at 3.5 times ten to the minus fourteen per ohm-metre, the charge falls by a factor of e in 253 seconds, so an average 25-second lifetime costs only about ten per cent of the charge, and a core carrying half a hundredth of a coulomb leaks about 20 microamperes into the atmosphere.Estimation of the stability time of ball lightning; Equations 15 and 18
Above a critical stored energy of 16.9646 joules the curves of shell thickness against charge develop a minimum, so there is a thinnest possible shell and a charge that achieves it — and for the minimum-shell case the computed outer radius tracks the sizes reported for observed ball lightning of 10, 1000 and 2300 megajoules, while millimetre-scale objects of 100 to 1000 joules come out as entirely possible.Balance of forces in ball lightning, Equations 19 to 31; Figures 3 and 4; the section on thrifty ball lightning

The way in

https://doi.org/10.15406/paij.2019.08.00345

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Physics and Astronomy International Journal 8(3), 156–161, received 27 September 2024, published 4 October 2024 by MedCrave Group. The article carries its own licence line at the foot of page 156 — ‘©2024 Nikitin et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially’ — and the licence link on the publisher’s page for this article resolves to CC BY-NC 4.0; both were read on 2026-09-08. The full text is reproduced below from the publisher PDF, cleaned of running heads, the citation footer and the reference-number superscripts the extraction left inline. The four figures are not reproduced; their captions are kept, because each one names what the surrounding paragraph is calculating or observing. The paper is set with subscripts and superscripts that the extraction flattened, so the equations are reset here in plain notation with the usual raised digits, and inequalities are written out in words because the page is MDX; every equation was checked against a rendering of the printed page. The reference list is kept in full. TWO TRANSCRIPTION NOTES. First, the DOI: the article’s own citation footer prints 10.15406/paij.2024.08.00345, but that string does not resolve, while the registered identifier 10.15406/paij.2019.08.00345 does resolve to this article, so the resolving one is kept above. Second, equation 25 is reproduced exactly as printed, with R raised to the third power; the sentence immediately following it states the two limiting cases as 16 pi sigma a R over k and 32 pi sigma R squared over k, which follow from the same substitution with R raised to the second power. Nothing has been altered — the printed form stands and the reader can see both. Author affiliation: the V. L. Talrose Institute for Energy Problems of Chemical Physics at the N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences.

How to cite it

Anatoly I. Nikitin (2024) Verification of validity of the electrodynamic model of ball lightning doi:10.15406/paij.2019.08.00345

Where it sits in the curriculum

Plasmoids, charge clusters and the orbs