EUROPEAN PHYSICAL SOCIETY
10th General Conference "Trends in Physics"
Sevilla 9-13, 1996
Abstracts of Contributed Papers, p 10

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CAN LARGE ENERGIES BE STORED IN ORDINARY AIR ?

     Observations of ball lightning seem to indicate that this enigmatic phenomenon could occasionally represent storage of very large energies (up to 10 MJ) in volumes of air of the order of liters at essentially normal density (since ball lightnings are reported to have essentially neutral buoyancy).
     Assuming for the sake of argument that at least some of these observations are accurate, this raises the following two intriguing questions:

i) in what form, if any, could so large energies be stored in air, and

ii) what mechanism, if any, could account for the surprisingly long life-time (of the order of 10 sec) of these objects.

     The answer to question i) must exclude energy stored in the form of ionization, combustible gas, and other forms of chemical energy, since the energies involved would then at most be of the order of tens of eV per atom, wheras the energies quoted above correspond to the order of keV per atom.
     The answer to question ii) must be consistent with the virial theorem, d²J/dt² = W, which is a general relationship connecting the radial moment of inertia J for a dynamic system to a total W of its kinetic, potential and electromagnetic energies. Unless some, so far unknown, form of attraction would be present in ball lightning, the quantity W is positive and the virial theorem then seems to prescribe an accelerated expansion of the system.
     The present communication investigates the possibility that the answer to question i) is charge separation in ordinary air caused by, e g, a lightning stroke or atmospheric electric fields. It is well known that even minute charge displacements from quasi-neutrality can produce very large restoring forces, and can thus provide a form of storage for large quantities of energy. The paper studies the dynamics of violent such transient deviations from charge neutrality, and specifically the possibility of long-lived, spherically-symmetric, radially-oscillating such deviations, the spherical symmetry being of special interest since decay by electromagnetic radiation would then (ideally) not be allowed. Space-time separable, spherically symmetric solutions to the nonlinear electrodynamic equations (Maxwell's equations plus conservation of charge, mass/energy and momentum) are found in exact analytical form with electric field

E(r,t) = (C(t)/r)ⁿ r ^-2.

These solutions either (for n < 0) describe a homogeneous expansion, or (for n > 0) stationary, radial oscillations (in which case C(t) is a common cycloid).
       Interestingly enough, these cycloid solutions - which occur for sufficiently steep charge distributions - are also an answer to question ii). For such radial oscillations with cycloid time-dependence we have, due to recurring vertical cusps, that d²J/dt² > 0 for all times t even though the system is not ever-expanding. Hence this type of electrodynamic self-confinement is not excluded (but actually supported) by the virial theorem, and may be an interesting, potential alternative to magnetic confinement for controlled fusion.

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