The electron-ion model of Fedosin (2024) describes ball lightning as a self-closed fragment of a linear-lightning channel: a shell of rapidly circulating electrons generates a strong magnetic field that confines positive air ions rotating in the interior, while the interior positive charge retains the electron shell; bead lightning is a chain of such shells-and-cores stabilized by inter-bead magnetic attraction against electrostatic repulsion. The published work computes only quasi-stationary equilibrium parameters (maximum size, energy, charge, magnetic field) and explicitly defers the dynamics. The open problem is the quantitative, time-dependent completion of this model: (i) the formation phase - charge separation and closure of the circulating electron current in a curved lightning branch when the main stroke current stops, with ionization and recombination kinetics - and the disappearance phase, treated with full ionized-plasma physics; (ii) replacement of the limiting bead-current estimate (electron speed taken as v→cv\to c) by values including relativistic corrections and realistic current-flow conditions in a partially ionized shell; and (iii) a quantitative collisional, radiative, and discharge loss budget from which observed lifetimes and decay modes follow. A secondary, explicitly posed but contested sub-question asks what forces could stabilize micron-scale electron-dominated charge clusters (so-called Exotic Vacuum Objects) and allow them to form chains.

Background

Ball lightning is a luminous, roughly spherical object, typically 10–40 cm across and lasting seconds to tens of seconds, reported near thunderstorms and electrical equipment for centuries; despite extensive case collections it remains an unsolved problem in atmospheric physics (Boerner 2023). Bead lightning is a related phenomenon in which the afterglow of a linear-lightning channel fragments into a chain of persistent glowing beads that can be seen for up to a few seconds. A plasmoid is a self-contained plasma structure carrying its own magnetic field; millimeter-to-decimeter plasmoids with thin charged surface shells have been produced in laboratory discharges (Shabanov 2019), and one fortuitous spectroscopic observation of natural ball lightning exists (Cen, Yuan and Xue 2014). Many competing models are on the table: the relativistic-microwave theory, in which the ball is a discharge plasma sustained by self-trapped microwave radiation, with long-term losses and stability analyzed by Stephan (2016); a hot highly charged sphere of air (Broka 2018); a free-electron creation hypothesis (Boerner 2023); a topological-soliton model verified with three-dimensional time-dependent simulations of the Gross-Pitaevskii equation, the mean-field nonlinear Schrödinger equation of condensates (Zhe Li 2026); and magnetohydrodynamic (MHD) channel-decay accounts of bead formation (Ludwig and Saba 2005). The electron-ion model of Fedosin (2024) proposes that ball lightning is a small piece of linear lightning closed on itself: relativistic electrons circulate in an outer shell, their current produces a strong azimuthal magnetic field (the pinch effect - self-compression of a current channel by its own magnetic field - is invoked during formation), and this field confines positively charged air ions rotating inside, while the interior charge holds the shell. In equilibrium the model yields a maximum ball radius of order 20 cm, energy content of order 10 kJ, net positive charge, and kilogauss-scale internal magnetic fields; bead lightning stability follows from magnetic attraction between neighboring bead currents exceeding their electrostatic repulsion and wind pressure. The published treatment is deliberately static: the author states that the dynamic aspects of formation and disappearance, including charge recombination, are described only briefly 'since they require a separate article involving entire apparatus of ionized plasma physics', that the bead-current formula is a limiting estimate obtained by taking the electron speed at v→cv\to c, and that 'more precise current values could be determined if we take into account relativistic corrections and conditions of current flow in ionized plasma and in outer shell of bead lightning'. Losses (shell-electron impact ionization regenerating electrons, discharge into surrounding air, energy leakage through the still-conductive channel) are discussed only qualitatively. The paper also poses, as explicitly unanswered questions within an analogy between ball lightning and micron-scale negatively charged electron clusters called Exotic Vacuum Objects (EVOs, reported in cold-fusion-adjacent literature and reviewed by Hubler 2022), what forces could let such electron-dominated clusters remain spherical against electrostatic repulsion and how they could form chains.

Problem Statement

The electron-ion model of ball and bead lightning (Fedosin 2024) exists so far only as a quasi-stationary equilibrium calculation. The open problem is its quantitative, time-dependent completion: (1) Formation dynamics - starting from a curved, current-carrying branch of a linear-lightning channel at stroke termination, derive or simulate the transient charge separation: closure of the circulating electron current when the main lightning current stops, ionization and recombination kinetics, and the electromagnetic evolution of the channel fragment into the electron-shell / positive-ion-core configuration, using full ionized-plasma physics in the generally three-dimensional geometry of a curved channel. (2) Refined currents - replace the limiting bead/ball electron-current estimate obtained by taking the electron speed as v→cv\to c with values incorporating relativistic corrections and realistic current-flow conditions in the partially ionized outer shell, and quantify how the predicted size, energy, charge, and magnetic-field parameters change. (3) Loss and lifetime balance - model quantitatively the collisional, radiative, and discharge loss channels together with regeneration by shell-electron impact ionization, so that the observed lifetimes (seconds to tens of seconds for ball lightning; up to about 2.5 s for beads) and the decay modes (quiescent decay versus explosive energy release upon contact with conductors) follow from the model rather than being assumed. Together, (1)-(3) form one consistent framework that follows formation, quasi-equilibrium (recovering the published equilibrium parameters as a limiting state), and disappearance, and that confronts the predicted observables with the observational statistics and laboratory plasmoid experiments cited in the source work. A demonstration, grounded in the physics of realistic transport rather than in the failure of one particular approach, that the equilibrium configuration is dynamically unattainable or unsustainable would also resolve the problem. Secondary and conditional on contested phenomenology: the source also poses, within the analogy between ball lightning and micron-scale Exotic Vacuum Objects, the questions of what forces could maintain an electron-dominated charge cluster in spherical shape against electrostatic repulsion and how such clusters could form chains; this sub-question rests on charge-cluster reports lacking independent reproduction and is separable from the primary core.

References

  1. Fedosin, S. G. (2024). Electron-ion model of ball and bead lightning. Journal of Atmospheric and Solar-Terrestrial Physics 265, 106374. doi:10.1016/j.jastp.2024.106374 (preprint arXiv:2410.18132). https://arxiv.org/abs/2410.18132
  2. Oreshko, A. G. (2025). Answers to "Questions regarding alleged laboratory creation of ball lightning" from the standpoint of plasma physics and electrodynamics. Journal of Atmospheric and Solar-Terrestrial Physics 277, 106674. doi:10.1016/j.jastp.2025.106674. https://doi.org/10.1016/j.jastp.2025.106674
  3. Oreshko, A. G. (2026). Generation of analogues of natural ball lightning in the laboratory. Journal of Atmospheric and Solar-Terrestrial Physics, article 106932 (volume not yet assigned). doi:10.1016/j.jastp.2026.106932. https://doi.org/10.1016/j.jastp.2026.106932
  4. McGruder, C. H., III (2025). General Relativity Explains Why Ball Lightning Does Not Fall. Journal of Modern Physics 16, 1222-1231. doi:10.4236/jmp.2025.169063. https://doi.org/10.4236/jmp.2025.169063
  5. Hubler, G. K. (2022). A Possible Heuristic Explanation of Exotic Vacuum Objects (EVO's, Charge Clusters). Journal of Condensed Matter Nuclear Science 36(1), 30-37. doi:10.70923/001c.72586. https://doi.org/10.70923/001c.72586
  6. Stephan, K. D. (2016). Extension of Relativistic-Microwave Theory of Ball Lightning Including Long-term Losses And Stability. arXiv:1608.00450. https://arxiv.org/abs/1608.00450
  7. Ludwig, G. O. and Saba, M. M. F. (2005). Bead lightning formation. Physics of Plasmas 12, 093509. doi:10.1063/1.2048907. https://doi.org/10.1063/1.2048907
  8. Broka, C. A. (2018). Ball Lightning as a Hot, Highly Charged, Sphere of Air. arXiv:1811.12309. https://arxiv.org/abs/1811.12309
  9. Boerner, H. (2023). The Role of Free Electrons in Ball Lightning Creation. arXiv:2304.01784. https://arxiv.org/abs/2304.01784
  10. Li, Zhe (2026). A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation. arXiv:2605.09851. https://arxiv.org/abs/2605.09851
  11. Shabanov, G. D. (2019). On the possibility of making natural ball lightning using a new pulse discharge type in the laboratory. Physics-Uspekhi 62(1), 92-107. doi:10.3367/UFNe.2018.03.038318. https://doi.org/10.3367/UFNe.2018.03.038318
  12. Cen, J., Yuan, P. and Xue, S. (2014). Observation of the Optical and Spectral Characteristics of Ball Lightning. Physical Review Letters 112, 035001. doi:10.1103/PhysRevLett.112.035001. https://doi.org/10.1103/PhysRevLett.112.035001