Historical research guide · 0473 · 2024
Electrodynamic model of ball lightning
Anatoly I. Nikitin
In one minute
Ball lightning carries far more energy than anything you could store in a comparable volume of air, and Anatoly Nikitin of the Russian Academy of Sciences asks what sort of object could hold it. His answer is the dynamic electric capacitor: a ring of electrons circling at close to the speed of light, wrapped in a larger cloud of protons whose own orbital motion generates the magnetic field that keeps those electrons in their ring. The protons have to outnumber the electrons for that field to be strong enough, so the whole assembly carries a net positive charge — and that surplus charge is what saves it. It polarises a thin shell of water molecules around the outside, and the pull between shell and charge supplies the inward force that stops the core flying apart. Nikitin then works the numbers: 1900 such capacitors, each half a centimetre across, packed inside a shell of 6.2 cm internal radius, hold 6.36 MJ — about 6.4 billion joules per cubic metre, close to what has been measured in natural ball lightning.
Connection
Chapter 9 treats the self-organised, long-lived ball of charge as a real physical object rather than a curiosity, and this paper is the most explicit published attempt to say what holds one together and where its energy actually sits — not in hot gas but in the ordered kinetic energy of circulating protons, behind a polarised shell. Read it beside Alexander Keul’s survey of what observers have actually recorded at /library/stm-48b6e644d4, and beside J. J. Lowke’s electric-discharge model at /library/stm-72cecea529, which starts from the opposite end of the same question.
From the source
Ball lightning with an energetically active core can be modelled as an ensemble of dynamic electric capacitors: an inner ring of electrons drifting at close to the speed of light, held in orbit by the magnetic field generated by a surrounding population of protons that themselves orbit under the electric attraction of the electron ring, with no material electrodes anywhere in the structure.Introduction, ‘The principle of the dynamic electric capacitor’; Figure 1; Eqs. 1 to 3
The electron ring is stabilised against leaving its plane by the same barrel-shaped magnetic field geometry used in cyclotrons and betatrons — two coaxial current rings give a radial field component whose Lorentz force returns a displaced electron — and the orbit radius is stable provided the axial field falls off more slowly with radius than the inverse first power.Introduction, paragraphs on axial focusing; Figure 2a and 2b
For a worked capacitor of outer radius 0.5 cm holding 100 J of electric field energy, the field between the rings reaches 1.07 times 10¹⁰ V/m, protons orbit at 7.15 times 10⁷ m/s, and the proton count must exceed the electron count roughly tenfold to raise the magnetic field to the 2.84 times 10⁷ A/m needed to confine the electrons — leaving a net positive charge of 1.125 times 10⁻⁴ C and a proton kinetic energy of 3.34 kJ, some 33 times the stored electric field energy.Section ‘Properties of a dynamic electric capacitor’
That surplus positive charge polarises a shell of water molecules around the core, and the force from the gradient of the electric field pulls the shell inward with 3.64 times 10⁸ N for a shell of 6.2 cm internal radius, 1 cm thickness and a core charge of 10⁻² C — enough to balance the centrifugal force of protons carrying about 11.3 MJ, so that the confinement problem is solved by the same excess charge that appeared to make it worse.Section ‘Ball lightning model with an active energy core’
The object is high in energy but low in entropy and low in temperature: charges occupy narrow orbits in an otherwise empty cavity, move without collisions, and therefore strike the shell with only the small radial component of their momentum — which is why an ordered core can be held for seconds where a disordered hot gas, always containing some very fast particles, could not be held at all.Section ‘Ball lightning model with an active energy core’, thermodynamic paragraphs
A multi-element core of 1900 capacitors of 0.5 cm radius fits inside a shell of 6.2 cm internal radius and carries 6.36 MJ of proton kinetic energy at a core energy density near 6.4 times 10⁹ J/m³, comparable with measured energy densities of natural ball lightning, while the shell’s tensile limit — a negative pressure of 7.5 times 10⁴ atmospheres against a molecular pressure of about 1.7 times 10⁴ atmospheres — may be what sets the upper bound on ball lightning energy.Section ‘Ball lightning model with an active energy core’; Figure 5; Conclusion
The way in
https://doi.org/10.15406/paij.2024.08.00344How to cite it
Anatoly I. Nikitin (2024) Electrodynamic model of ball lightning doi:10.15406/paij.2024.08.00344