Ball Lightning
Ball Lightning as a Charge Sink: A Vortex–Magnetic Stabilization Theory
Author: Johnathan McGary
Institution: Ludlow Research Institute, Department of Theoretical Sciences
Date: September 2025
Abstract
Eyewitness videos increasingly show filaments that appear to feed into ball lightning rather than discharge outward, challenging “capacitive bubble” and “combustion nanoparticle” models. I propose a theoretical framework in which ball lightning is a dynamic charge sink: a localized region where counter-streaming atmospheric charges converge, self-organize into a rotating space-charge vortex, and are magnetically stabilized by ring currents. The configuration resembles a warm, collisional force-free plasmoid (spheromak-like) embedded in air at 1 atm. Energy is supplied not by stored charge, but by continuous inflow from storm-scale electric fields and radio-frequency (RF) pumping left by lightning transients. I outline governing equations in a reduced MHD/EHD description, derive scaling estimates for size, fields, and lifetime, and enumerate falsifiable predictions that distinguish this model from microwave-cavity and silicon-vapor hypotheses.
1. Introduction
Ball lightning is reported as a luminous, mobile sphere (∼5–40 cm), lasting 0.5–10 s, often near recent lightning. Puzzles include (i) persistence near metal rails/fences without immediate neutralization, (ii) apparent inward streamers, and (iii) guided motion along invisible paths. Traditional discharge, combustion-colloid, and microwave-standing-wave models address parts of this behavior but struggle to explain inward feeding and field-seeking mobility simultaneously.
This paper advances a charge-sink plasmoid model: storm fields establish counter-polar charge reservoirs; a seed rotation forms a space-charge vortex; azimuthal currents generate a magnetic cage; the ball then persists while it is being fed by ambient gradients and RF transients.
2. Physical Background
2.1 Atmospheric charge environment
Thunderstorms establish strong vertical electric fields near surface (∼10–100 kV·m⁻¹) and leave behind ionized channels, RF bursts (kHz–GHz), and space-charge patches aloft and at ground. Small atmospheric ions at 40–80% RH are typically H3O+(H2O)n\mathrm{H_3O^+(H_2O)_n}H3O+(H2O)n and NO3−/O2−(H2O)n\mathrm{NO_3^-/O_2^-(H_2O)_n}NO3−/O2−(H2O)n with mobilities μ∼1\mu \sim 1μ∼1–2 cm2V−1s−12\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}2 cm2V−1s−1.
2.2 EHD/MHD ingredients
A vertical E\mathbf{E}E with counter-streaming ions + a seed azimuthal asymmetry produces ring currents. Ampère’s law yields a circumferential Bθ\mathbf{B}_\thetaBθ. Cross-fields give E×B\mathbf{E}\times\mathbf{B}E×B drift (charge-sign independent), circularizing flow; collisional viscosity with neutrals damps shear; the system relaxes toward a force-free state ∇×B=αB\nabla \times \mathbf{B} = \alpha \mathbf{B}∇×B=αB (spheromak-like).
3. Proposed Mechanism
3.1 Birth: counter-streaming and rotation
A recent stroke leaves a column with vertical EzE_zEz. Positive ions rise from ground patches; negative ions descend from cloud base. A small azimuthal bias (gust, terrain edge, RF phase) seeds rotation; electrons acquire larger azimuthal drift; a net azimuthal current forms.
3.2 Magnetic self-organization
The current produces Bθ(r)\mathbf{B}_\theta(r)Bθ(r). Magnetic pressure PB=B2/2μ0P_B = B^2/2\mu_0PB=B2/2μ0 and tension oppose radial expansion. The system relaxes toward a near force-free plasmoid with closed field lines; the visible ball is the recombination shell where inflowing charges meet.
3.3 Feeding, not discharging
Because the ball sits near a local potential minimum between charge reservoirs, visible filaments are inward streamers. The glow arises from recombination and line emission within the vortex shell; the core may be dimmer (lower neutral density, higher ionization).
3.4 RF pumping
Lightning leaves broadband RF. A partially ionized sphere with conducting boundary conditions can absorb RF (not purely radiate), sustaining currents for seconds—particularly if the object transiently matches a cavity eigenmode.
4. Mathematical Formulation (reduced, collisional regime)
We treat a warm, partially ionized plasma embedded in neutrals (air) with frequent ion–neutral collisions (MHD with ambipolar diffusion).
Continuity (quasi-neutral ions):
∂n∂t+∇⋅(nv)=Sion−Srec\frac{\partial n}{\partial t} + \nabla \cdot (n\mathbf{v}) = S_{\text{ion}} - S_{\text{rec}}∂t∂n+∇⋅(nv)=Sion−Srec
Momentum (single-fluid with effective viscosity ν\nuν and ion-neutral drag νin\nu_{in}νin):
ρ(∂v∂t+v⋅∇v)=J×B−∇p−ρνin(v−vn)+∇⋅Π\rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla \mathbf{v} \right) = \mathbf{J}\times\mathbf{B} - \nabla p - \rho \nu_{in}(\mathbf{v}-\mathbf{v_n}) + \nabla\cdot\boldsymbol{\Pi}ρ(∂t∂v+v⋅∇v)=J×B−∇p−ρνin(v−vn)+∇⋅Π
Generalized Ohm’s law (collisional, omit Hall at first pass):
E+v×B=ηJ+J×Bne−∇pene\mathbf{E} + \mathbf{v}\times\mathbf{B} = \eta \mathbf{J} + \frac{\mathbf{J}\times\mathbf{B}}{ne} - \frac{\nabla p_e}{ne}E+v×B=ηJ+neJ×B−ne∇pe
Maxwell (quasi-static):
∇×B=μ0J,∇⋅B=0\nabla \times \mathbf{B} = \mu_0 \mathbf{J}, \qquad \nabla \cdot \mathbf{B} = 0∇×B=μ0J,∇⋅B=0
Force-free attractor (relaxed state):
∇×B=αB,α≈const in core\nabla \times \mathbf{B} = \alpha \mathbf{B}, \quad \alpha \approx \text{const in core}∇×B=αB,α≈const in core
Energy balance (steady):
Pin=∫J⋅Eext dV+PRF≈Prad+Pcond+Pchem+Pion-lossP_{\text{in}} = \int \mathbf{J}\cdot \mathbf{E}_{\text{ext}}\, dV + P_{\text{RF}} \quad \approx \quad P_{\text{rad}} + P_{\text{cond}} + P_{\text{chem}} + P_{\text{ion-loss}}Pin=∫J⋅EextdV+PRF≈Prad+Pcond+Pchem+Pion-loss
where PradP_{\text{rad}}Prad is line/continuum emission, PcondP_{\text{cond}}Pcond conductive/convective loss to air, PchemP_{\text{chem}}Pchem exo/endothermic reactions with aerosols, and PRFP_{\text{RF}}PRF net RF absorption.
5. Scaling Estimates
Let radius R∼0.05R \sim 0.05R∼0.05–0.15 m; visible shell thickness δ∼0.5\delta \sim 0.5δ∼0.5–5 mm; azimuthal current Iθ∼10I_\theta \sim 10Iθ∼10–300 A (storm-fed).
Magnetic field (loop approximation):
Bθ(r ≈ R)∼μ0Iθ2πR≈1−30 mTB_\theta(r\!\approx\!R) \sim \frac{\mu_0 I_\theta}{2\pi R} \approx 1{-}30\ \text{mT}Bθ(r≈R)∼2πRμ0Iθ≈1−30 mT
This yields magnetic pressure PB∼0.4−360 PaP_B \sim 0.4{-}360\ \text{Pa}PB∼0.4−360 Pa, comparable to small over-pressures in heated air—enough to assist confinement with collisional damping.
E×B drift (upper bound):
vE×B=EB≲104−105 V m−110−2 T∼106−107 m s−1v_{E\times B} = \frac{E}{B} \lesssim \frac{10^4{-}10^5\ \text{V m}^{-1}}{10^{-2}\ \text{T}} \sim 10^6{-}10^7\ \text{m s}^{-1}vE×B=BE≲10−2 T104−105 V m−1∼106−107 m s−1
At 1 atm collisions clip this to cm/s–m/s bulk azimuthal flow—consistent with slow, “deliberate” motion.
Lifetime
If Pin∼102−103 WP_{\text{in}}\sim 10^2{-}10^3\ \text{W}Pin∼102−103 W from ambient fields and RF, and PlossP_{\text{loss}}Ploss similar, a seconds-scale steady state is plausible; termination occurs when EextE_{\text{ext}}Eext collapses or instabilities (kink/sausage) grow.
6. Stability Considerations
Viscous damping with neutrals suppresses small-scale turbulence, aiding spherical symmetry.
Force-free tendency (J∥B\mathbf{J}\parallel \mathbf{B}J∥B) minimizes J×B\mathbf{J}\times\mathbf{B}J×B and internal shear.
Instabilities: Excess current → kink/sausage modes; predicted signatures are sudden brightening (“pop”) versus slow fade (feed starvation).
7. Phenomenology & Predictions (falsifiable)
Inward filaments: High-speed video should show net streamer motion toward the ball, not away.
Field-seeking drift: Motion along ambient ∇E\nabla E∇E and conductor edges; balls “follow” gradients rather than repel from metal per se.
RF absorption lines: Narrowband features (kHz–MHz–GHz) indicating net absorption or mode-locking to environmental RF after nearby strokes.
Spectral content: Mix of atmospheric lines (N₂ bands, O, NOx\mathrm{NO_x}NOx); trace soil/sea salt lines (Na D) if aerosols present—consistent with recombination shell.
Two termination classes: (i) quiet fade (feed loss), (ii) sharp pop (instability)—with distinct acoustic and light curves.
Magnetic footprint: Nearby ferromagnetic sensors (or magnetometers, if present) could register mT-scale transients synchronized with luminosity modulation.
These signatures distinguish the model from microwave-cavity (which predicts strong standing-wave behavior and window interactions) and silicon-vapor combustion (which predicts dominant continuum/oxide spectra and oxygen consumption without strong EM features).
8. Relation to Prior Models
Microwave cavity/plasma bubble: Shares resonance notion, but here the cavity is secondary; the driver is charge inflow + ring current confinement.
Silicon nanoparticle combustion: Explains some colors and persistence; can be a contributing chemistry in the shell but not the driver of confinement or inward streamers.
Electromagnetic knots/solitons: Our model is a collisional, warm-air analogue: a relaxed, near force-free plasmoid continuously powered by environmental currents.
9. Limitations
Strong simplifications (single-fluid, reduced Ohm’s law) in a multi-species, collisional medium; full treatment requires multi-fluid or kinetic collisional modeling with neutral coupling.
RF coupling is environment-specific and remains the least constrained term in the energy budget.
Magnetic field estimates are order-of-magnitude; direct in-situ measurements are rare.
10. Conclusion
Ball lightning can be coherently interpreted as a charge-sink plasmoid: a rotating, magnetically assisted, recombination-bright structure that feeds on ambient charge gradients and transient RF rather than discharging like a capacitor. This unifies inward filaments, field-seeking motion, persistence near conductors, and dual termination modes within one collisional-plasma framework. The model makes clear observational predictions—notably inward streamer directionality and RF absorption features—that can be checked in high-speed imaging and passive EM recordings of future events.
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