Lowke, Heil, Tam and Murphy (2021) proposed that ball lightning is a cold, highly conducting plasma ball sustained by very large densities (∼1017 cm−3\sim 10^{17}\,\mathrm{cm}^{-3}) of metastable singlet-delta oxygen molecules O2(a1Δg)\mathrm{O_2}(a^1\Delta_g), accumulated by pulsed corona at high-voltage points inside houses or aircraft in ambient thunderstorm fields, with sheath fields replenishing the metastables. The proposal currently imposes the metastable density as an initial condition and treats the energy balance, radiation mechanism, and lifetime only at order-of-magnitude or qualitative level. The open problem is to turn this scenario into a self-consistent, quantitatively predictive theory: grow the metastable density dynamically from pulsed corona discharge, close the energy budget including sheath-field input and conversion to light, predict the emission spectrum and intensity, and derive the steady-state conditions under which a luminous ball of seconds-long lifetime exists as a function of ball size and ambient field.

Background

Ball lightning is a luminous, roughly spherical object, typically reported to persist for seconds and move within houses, aircraft cabins, or open air during thunderstorms; despite centuries of reports (reviewed in the ball-lightning literature since at least Powell's plasma models of the 1960s) no mechanism is generally accepted. One quantitative line of attack is gas-discharge theory. Lowke (1992) showed that metastable oxygen molecules control electrical breakdown in air; Lowke (1996) and Lowke et al. (2012) developed a gas-discharge theory of ball lightning in which the ball is a cold plasma sustained by a corona-like discharge (a weak, localized electrical discharge burning at a conductor in a strong electric field) fed by charges dispersing after a lightning strike. A central chemical actor is singlet-delta oxygen, O2(a1Δg)\mathrm{O_2}(a^1\Delta_g): the lowest electronically excited metastable state of molecular oxygen (about 0.98 eV0.98\,\mathrm{eV} above the ground state), long-lived against radiative decay and efficient at detaching electrons from negative ions. In the model of Lowke, Heil, Tam and Murphy (2021), pulsed corona discharges at sharp metal points in a strong ambient thunderstorm field — Trichel-type negative-corona current pulses, i.e. rapidly repeating discharge pulses at a negatively charged sharp point — accumulate O2(a1Δg)\mathrm{O_2}(a^1\Delta_g) to densities of order 1017 cm−310^{17}\,\mathrm{cm}^{-3}. At such densities, a stable ball-like plasma of electrons, positive and negative ions, and metastables can exist free of electrodes: electron detachment from negative ions by the metastables balances electron attachment (capture of free electrons by oxygen molecules to form negative ions), electron densities are of order 1011 cm−310^{11}\,\mathrm{cm}^{-3}, and because the ball is highly conducting its internal electric field is very low. Strong fields confined to thin boundary layers, called sheaths, at the ball's surface match the ball potential to the ambient potential and can excite further metastables, extending the lifetime beyond the quenching-limited value of roughly 0.1 s0.1\,\mathrm{s}. The authors note that higher excited states of oxygen — O(1D)\mathrm{O}(^1D) atoms and O2(b1Σg+)\mathrm{O_2}(b^1\Sigma_g^+) molecules — and energy transfer from vibrationally excited nitrogen could raise metastable production by up to a factor of ten, but these channels are not modeled. Observational constraints on any such theory are sparse: the only chance-recorded optical spectrum of a natural ball lightning event (Cen, Yuan and Xue 2014) shows atomic emission lines of soil elements rather than molecular oxygen bands, and Yuan et al. (2025) derived from such spectra a pulsed, high-power-density energy core driven, they argue, by intermittent discharge at the base of a previous lightning channel under the ambient thunderstorm field. What the 2021 model itself acknowledges as missing is precisely what a completed theory requires: the calculation imposes 1017 cm−310^{17}\,\mathrm{cm}^{-3} metastables as an initial condition rather than growing them from the corona phase; the energy balance (including the power input of the sheath-field-driven discharge and the efficiency of conversion from stored metastable energy to visible light) is estimated only to order of magnitude; the radiation mechanism — the paper qualitatively assigns the light to binary collisions of O2(a1Δg)\mathrm{O_2}(a^1\Delta_g) in the red near 762 nm762\,\mathrm{nm} and to ternary collisions possibly giving yellow light near 500 nm500\,\mathrm{nm} — is given no quantitative spectrum or intensity; the metastable production rate in the sheaths, its dependence on ball size and ambient field, and the exact conditions under which a steady-state balance yields seconds-long lifetimes are not derived; and reproducible laboratory generation of a long-lived ball without a strong imposed ambient field has not been achieved, with laboratory-creation claims themselves contested (Shmatov and Stephan 2023).

Problem Statement

Complete the metastable-oxygen gas-discharge theory of ball lightning of Lowke et al. (2021) into a self-consistent, quantitatively predictive theory. All of the following jointly serve this single objective, since each supplies a component the others presuppose: (1) replace the imposed initial condition of ∼1017 cm−3\sim 10^{17}\,\mathrm{cm}^{-3} singlet-delta oxygen by a dynamic calculation that grows the metastable density from the pulsed corona phase at high-field conductor points through the establishment of the conducting ball, optionally including the higher oxygen excited states O(1D)\mathrm{O}(^1D) and O2(b1Σg+)\mathrm{O_2}(b^1\Sigma_g^+) and energy transfer from vibrationally excited nitrogen, which the source notes could raise metastable production but does not model; (2) close the energy balance — compute the power input of the sheath-field-driven discharge and the efficiency of conversion of stored metastable energy into visible light, to better than order of magnitude; (3) predict the quantitative emission spectrum and absolute intensity of the ball, and confront the prediction with recorded natural spectra; (4) derive the steady-state condition under which sheath-field replenishment of metastables balances quenching so that a luminous ball of seconds-long lifetime exists, as a function of ball size and ambient field strength. The objective is to establish whether the metastable mechanism can in principle produce the reported phenomenon, for the modeling choices set out above.

References

  1. J. J. Lowke, Wilfried Heil, Eugene Tam, Anthony B. Murphy, 'Toward a theory of ball lightning occurring in houses and aircraft', Journal of Atmospheric and Solar-Terrestrial Physics 214, 105532 (2021). DOI: 10.1016/j.jastp.2020.105532, https://doi.org/10.1016/j.jastp.2020.105532
  2. J. J. Lowke, 'Theory of electrical breakdown in air — the role of metastable oxygen molecules', Journal of Physics D: Applied Physics 25, 202–210 (1992). DOI: 10.1088/0022-3727/25/2/012, https://doi.org/10.1088/0022-3727/25/2/012
  3. J. J. Lowke, 'A theory of ball lightning as an electric discharge', Journal of Physics D: Applied Physics 29, 1237–1244 (1996). DOI: 10.1088/0022-3727/29/5/018, https://doi.org/10.1088/0022-3727/29/5/018
  4. J. J. Lowke, D. Smith, K. E. Nelson, R. W. Crompton, A. B. Murphy, 'Birth of ball lightning', Journal of Geophysical Research: Atmospheres 117 (2012). DOI: 10.1029/2012JD017921, https://doi.org/10.1029/2012JD017921
  5. R. Morrow, 'A general theory for ball lightning structure and light output', Journal of Physics D: Applied Physics 51, 125205 (2018). DOI: 10.1088/1361-6463/aaaf8d, https://doi.org/10.1088/1361-6463/aaaf8d
  6. John Abrahamson, James Dinniss, 'Ball lightning caused by oxidation of nanoparticle networks from normal lightning strikes on soil', Nature 403, 519–521 (2000). DOI: 10.1038/35000525, https://doi.org/10.1038/35000525
  7. Jianyong Cen, Ping Yuan, Simin Xue, 'Observation of the Optical and Spectral Characteristics of Ball Lightning', Physical Review Letters 112, 035001 (2014). DOI: 10.1103/PhysRevLett.112.035001, https://doi.org/10.1103/PhysRevLett.112.035001
  8. Wilfried Heil, Don Smith, 'An Initiation of Ball Lightning in an Aircraft', Journal of Atmospheric and Solar-Terrestrial Physics 225, 105758 (2021). DOI: 10.1016/j.jastp.2021.105758, https://doi.org/10.1016/j.jastp.2021.105758
  9. M. L. Shmatov, K. D. Stephan, 'Questions regarding alleged laboratory creation of ball lightning', Journal of Atmospheric and Solar-Terrestrial Physics 242, 105995 (2023). DOI: 10.1016/j.jastp.2022.105995, https://doi.org/10.1016/j.jastp.2022.105995
  10. Ping Yuan, Tingting An, Jianyong Cen, Rubin Jiang, Shengxin Huang, Zhengshi Chang, Hong Deng, Ruibin Wan, Guorong Liu, Xuejuan Wang, 'The Radiation Power Density of a Natural Ball Lightning Estimated by Its Spectra', Journal of Geophysical Research: Atmospheres 130, e2025JD043587 (2025). DOI: 10.1029/2025JD043587, https://doi.org/10.1029/2025JD043587
  11. A. G. Oreshko, 'Generation of analogues of natural ball lightning in the laboratory', Journal of Atmospheric and Solar-Terrestrial Physics, article 106932 (2026). DOI: 10.1016/j.jastp.2026.106932, https://doi.org/10.1016/j.jastp.2026.106932
  12. A. S. Ivanov, 'Observation of Long-Lived Plasma Formations in a Toroidal air Vortex under Normal Conditions', Proceedings of the Southwest State University. Series: Engineering and Technology 13, 66–74 (2024). DOI: 10.21869/2223-1528-2023-13-4-66-74, https://doi.org/10.21869/2223-1528-2023-13-4-66-74
  13. J. J. Lowke, E. J. Szili, 'Toward a theory of stepped-leaders in lightning', Journal of Physics D: Applied Physics 56, 045201 (2023). DOI: 10.1088/1361-6463/aca103, https://doi.org/10.1088/1361-6463/aca103