Morrow's unified theory of ball lightning (J. Phys. D: Appl. Phys. 51, 125205, 2018) proposes that a lightning strike creates a long-lived quasi-neutral plasma ball with essentially zero internal electric field, surrounded by an expanding shell of positive ions whose space-charge field drives negatively charged particles inward, and that the observed light of ball lightning comes from soil- or fuel-derived particles that acquire large negative charges in the strike, are trapped and burn inside the ball for seconds at a total output of order 1 W. The plasma-structure side of this theory is computed, but the particle side is asserted rather than derived or tested. The open problem is to establish that mechanism quantitatively: model how dust and debris particles acquire and carry the required negative charge during a lightning strike, so that the assumed charge values are derived and validated rather than postulated; determine the particle size, composition, and ignition conditions under which they ignite and burn stably once driven through the surrounding positive-ion shell's inward space-charge field and trapped inside the plasma ball, including whether, and under what conditions, they can produce stable laboratory ball lightning; and model how particle burnout couples to plasma decay to terminate the event.

Background

Ball lightning is a luminous, roughly spherical object, typically 10–50 cm across, that appears during thunderstorms, floats freely for several seconds, and sometimes leaves behind a residue of dust or an odor of burning; despite centuries of reports (including the 2012 Qinghai event whose optical spectrum was recorded fortuitously by Chinese researchers; Cen, Yuan and Xue 2014), no accepted quantitative explanation exists. A plasma is an ionized gas containing free electrons and positive and negative ions; its behavior is governed by particle continuity equations coupled to the electric field produced by its own net charge (the space-charge field). One long lineage of theories treats ball lightning as an electric-discharge phenomenon: Lowke, Uman and Liebermann (1969) and Lowke (1996) modeled it as a glowing plasma sustained by the field of excess electric charge, including so-called 'phantom plasma balls' — plasma structures that persist for seconds but radiate almost no light, and hence cannot by themselves explain the luminosity of most reports. A second lineage explains the light chemically: Abrahamson and Dinniss (2000) proposed that a lightning strike vaporizes soil into silicon nanoparticles that form chains and burn while glowing, and Paiva et al. (2007) produced seconds-lived luminous balls in the laboratory by electric arcing through silicon wafers; Porter et al. (2014) later measured the electric charge carried by such silicon-arc luminous bodies. Morrow (2018) unified the two lineages computationally. Solving the coupled continuity equations for positive ions, negative ions and electrons, he found that any initial ion ball with an excess of positive ions — independent of the initial ion density over four orders of magnitude, and for small minority negative-ion fractions — evolves within about 1 s into a plasma ball whose central density equals the reciprocal of the ion neutralization coefficient (the rate coefficient for mutual neutralization of positive and negative ions) and whose internal electric field is zero, surrounded by a departing sphere of positive ions whose space-charge field, acting near and around the plasma ball, points inward and drives negative ions and negatively charged particles toward the center. He then proposed that burning particles from the soil, knocked loose and highly negatively charged by the lightning strike itself, are driven into this electrostatic trap, burn there, and provide the observed light: literature burnout times of 5–10 s for coal particles match observed ball-lightning lifetimes, a few hundred burning particles would radiate about 1 W, and the brown dust sometimes reported after extinction would be the combustion residue. The computations, however, take the particle charges as assumed inputs, and the published abstract itself frames the particle side as a proposition rather than a derivation: the connection with burning-particle theories is 'the proposition that the burning particles are highly-charged which is very likely after a lightning strike,' the 5–10 s coal burnout time is invoked 'as an example,' and laboratory generation appears as 'suggestions ... for the generation of ball lightning in the laboratory' — specifically experiments with coal dust, silicon fibers, or exploding wires. What therefore remains open is the quantitative mechanism by which particles acquire these charges, the particle size/composition/ignition conditions needed for stable burning once trapped inside the plasma ball, the burning behavior of soil-derived particles (silicon, iron, calcium) in the plasma-ball environment where they are trapped, and the interplay of particle burnout and plasma decay at termination. Independent work since 2018 has sharpened the observational targets — Yuan et al. (2025) derived the first radiation power densities from the spectra of a natural ball lightning event, finding emission from neutral oxygen (O I) around 37.4×10737.4\times10^{7} W/m2^2 with persistent neutral silicon (Si I) and iron (Fe I) emission near 3×1073\times10^{7} W/m2^2, the soil-element lines being directly relevant to a burning-particle mechanism — but has not filled the particle-side gaps.

Problem Statement

Within Morrow's unified plasma-ball theory of ball lightning — in which a lightning-produced ion ball evolves into a zero-internal-field plasma ball surrounded by a positive-ion shell whose space-charge field traps negatively charged particles — establish, quantitatively, the charged burning-particle mechanism that would make the theory a complete physical account of natural ball lightning. Concretely: (1) model the mechanism by which soil- and fuel-derived dust particles acquire and retain the large negative charges assumed in the theory during a lightning strike, so that the required charge-to-mass values are derived rather than postulated; (2) determine the particle sizes, compositions, and ignition conditions under which such particles ignite and burn stably once driven through the inward space-charge field region and trapped inside the plasma ball — including whether, and under what conditions, they can produce stable laboratory ball lightning; (3) characterize the burning behavior and burnout times of soil-derived particles (silicon, iron, calcium) in the actual in-ball environment in which they are trapped, replacing the example coal-literature burnout times with values for the actual particle population; and (4) model the termination of the event, i.e. the interplay between particle burnout and plasma decay that ends the luminosity within the observed seconds-scale lifetimes and leaves the reported residual dust. These four questions are linked parts of one objective — a validated quantitative lifecycle of the burning charged particle inside the lightning-produced plasma ball. A well-supported negative result on any part — a quantitative result establishing that a required condition cannot be met — resolves that part. Consistent with the source's own framing, the resulting mechanism should be compatible with the seconds-scale observed ball-lightning lifetimes (cf. the 5–10 s example coal-particle burnout time) and with a light output of order 1 W from a few hundred burning particles; the observed spectral line content, including Si and Fe lines from soil elements, and the reported terminal dust residue remain descriptive observational context. The absolute radiation power densities reported by Yuan et al. (2025) for their particular natural event — an event those authors attribute to small-gap intermittent discharge — are contextual motivation, not a mandatory reproduction target.

References

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