Historical research guide · 0580 · 2012
Quantum exchange interaction of spherically symmetric plasmoids
Maxim Dvornikov
In one minute
Maxim Dvornikov, working between the University of São Paulo and IZMIRAN in Moscow, is building a physical model of ball lightning out of quantum plasma. In his earlier work a plasmoid is a nano-scale ball of electrons oscillating radially — stable, but only about a billionth of a metre across, far too small to be the glowing sphere people report seeing. This paper supplies the missing step: how those tiny kernels could hold together as one object. Between two perfectly spherical plasmoids no classical force acts at all. But if the ions inside carry a permanent electric dipole — a water ion does, and thunderstorm air is full of water — then the plasmoid’s own oscillating electric field lines up their spins, and the quantum exchange force between the ions of the two structures stops being zero. Dvornikov computes it. In damp air it is far too weak to matter; at the ion density of liquid water it reaches a few percent of a plasmoid’s electromagnetic energy, which is enough to bind.
Connection
Chapter 9 asks what a self-contained luminous plasma sphere actually is, and this is one of the few papers that answers with a composite structure and a number attached: many nano-scale kernels held in one body by a named force, with the ion density it would take to make that force strong enough.
From the source
A plasmoid is modelled as a radial nonlinear oscillation of hot electrons in a plasma of cold singly ionized ions, with the electric field envelope falling off as radius times an exponential in minus the radius over twice the effective size; because the structure is spherically symmetric the magnetic field is identically zero, and no classical force at all acts between two such plasmoids.Section 2, Eqs. 1 and 2, and the paragraph before Eq. 3
The interaction Dvornikov proposes runs through the ions, not the electrons: a singly ionized molecule of an integer-spin neutral carries one uncompensated electron spin, and if that ion has a large permanent electric dipole moment its spin is aligned by the plasmoid’s own oscillating field, so the ion spins are structured and the quantum exchange integral between ions of two different plasmoids is non-zero. The alignment is self-consistent because the spin-flip time is of order a picosecond while observed plasmoid oscillation frequencies do not exceed several megahertz.Section 2, Eqs. 3 to 9; Section 3, final paragraph
The sign of the force is set by the phase difference between the two oscillations. At separations large compared with the plasmoid size the exchange interaction is attractive when the oscillations are in antiphase, that is a phase difference between one half pi and three halves pi, because the ions in the facing segments then keep their spins parallel; at small separation, roughly two to two and a half plasmoid radii apart, attraction instead requires the oscillations to be in phase.Section 3, Eqs. 10 and 11 with Figure 2a, discussion of the root a-nought near 2.45
The magnitude scales as the square of the water-ion number density. In air at 300 kelvin with 100 per cent relative humidity, about two times ten to the twenty-third ions per cubic metre, the exchange energy is only about ten to the minus fourteenth of a plasmoid’s total electromagnetic energy. Raise the density to about ten to the twenty-ninth per cubic metre, the value for liquid water, and it reaches about ten to the minus second — a few per cent, which is enough to make separate kernels coagulate.Section 3, paragraphs 5 to 7; Section 5, second paragraph
The application is a composite ball lightning: separate nano-scale kernels, each a spherically symmetric quantum oscillation of electrons and each created with an arbitrary oscillation phase, self-organize into one plasmoid, most plausibly at the formation stage inside a drop of rain water where the density is high enough. Dvornikov points to observations that a natural plasmoid often divides into several independent objects and that motion of smaller parts inside it is sometimes visible, and to the multi-kernel plasmoid generated in the laboratory by Oreshko and Mavlyudov in 2011.Section 4, paragraphs 3 to 5; Section 5, final paragraph
Dvornikov states the model’s own limits: it describes a low-energy ball lightning with internal structure, it does not explain the reported atmospheric plasmoids carrying up to several megajoules, and he suggests that several distinct kinds of glowing object may be being reported under one name. He names where his results would next be tested — the laboratory plasmoids generated by electric discharges in water.Section 4, final paragraph and the paragraph citing Shabanov 2002 and Versteegh et al. 2008
The way in
https://doi.org/10.1016/j.jastp.2012.08.005How to cite it
Maxim Dvornikov (2012) Quantum exchange interaction of spherically symmetric plasmoids doi:10.1016/j.jastp.2012.08.005