Formation of bound states of electrons in spherically symmetric oscillations of plasma
Maxim Dvornikov
Abstract and summary · read the original at the source
In one page
Maxim Dvornikov asks how a ball of glowing plasma can hold itself together long enough to be seen. His answer starts with a shape. If the electrons in a plasma oscillate purely in and out along the radius, the motion generates no magnetic field at all, so the ball cannot radiate its energy away — which would account for how steady natural spherical plasmoids look. That buys stability, but it raises a second problem: free oscillations of that kind need frequencies above the plasma’s own Langmuir frequency, far higher than anything the atmosphere supplies. So Dvornikov looks for a mechanism that works at the beginning of a plasmoid’s life. A test electron oscillating slowly emits ion acoustic waves, and the wake it leaves behind screens its own repulsion. Under conditions he spells out with numbers, the net force between two electrons turns attractive and beats the ordinary Debye-Hückel screening. That is the same bookkeeping that makes a Cooper pair in a metal — so the plasmoid can hold a superconducting phase while it forms.
Why it matters hereChapter 9 needs a physical reason a plasmoid holds together and where the energy that sustains it comes from, and this paper supplies both in one move: a radial breathing mode that cannot radiate, and a phonon-mediated attraction that pairs electrons the way superconductivity pairs them. It also reaches into chapter 12, because Dvornikov’s own discussion ends by pointing at nuclear reactions as the internal source that would keep such a structure alive once the driving field is switched off.
What it claims
01Spherically symmetric oscillations of electrons in plasma have no magnetic field, so a plasmoid built from that motion loses no energy to radiation — which explains the relative stability of spherical plasmoids generated in natural conditions.Introduction, second paragraph; Section 2.1, Electromagnetic potentials in the system of radially oscillating particles
Published and peer-reviewed02Free spherically symmetric oscillations require excitation above the electron plasma frequency, which is ten to the twelve to ten to the thirteen per second for densities of ten to the fifteen to ten to the seventeen per cubic centimetre and is very difficult to reach in natural conditions, while forced oscillations are possible at frequencies below it.Section 2.2, Classical plasma hydrodynamics; Section 4, Discussion
Published and peer-reviewed03A test electron in forced radial oscillation emits ion acoustic waves and is surrounded by a cloud of phonons that shields its repulsive potential; the resulting wake potential is attractive, and the effective interaction between two electrons can transcend the Debye-Hückel screening potential.Section 3, Equations 10, 11 and 16
Published and peer-reviewed04For a plasma of electrons and singly ionised nitrogen atoms at a temperature of one thousand kelvin and a number density of ten to the fifteen per cubic centimetre, with the two electrons one Debye length apart and an oscillation amplitude a tenth of that distance, the interaction energy exceeds the energy of oscillation for driving frequencies between about ten to the sixth and ten to the tenth per second — a range reachable in atmospheric plasma.Section 3, paragraph beginning ‘To form a bound state with another electron’
Published and peer-reviewed05Bound states of electrons formed by this exchange are the plasma analogue of Cooper pairs and can put the plasma inside a spherical plasmoid into a superconducting state, supplying the smooth transition from an externally driven structure to one with self-sustained oscillations; Dvornikov proposes this as the mechanism underlying ball lightning.Section 4, Discussion
What to watch06During the superconducting stage of a plasmoid’s evolution an internal source of energy must appear, because recombination of charged particles has to be compensated by fresh ionisation; Dvornikov points to the proposal that nuclear reactions serve as that energy source.Section 4, Discussion, final paragraph
What to watch
Read it · abstract
Abstract
We study spherically symmetric oscillations of electrons in plasma in the frame of classical electrodynamics. Firstly, we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Secondly, we consider both free and forced spherically symmetric oscillations of electrons. Finally, we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Hückel potential. We suggest that oscillating electrons can form bound states at the initial stages of the spherical plasma structure evolution. The possible applications of the obtained results for the theory of natural plasmoids are examined.
The way in
https://doi.org/10.1088/0031-8949/81/05/055502Published as Physica Scripta 81, 055502 (2010) by Maxim Dvornikov, then at the Universidad Técnica Federico Santa María in Valparaíso and at IZMIRAN near Moscow. The manuscript is free to read on arXiv as 1002.0764, but that posting carries arXiv’s non-exclusive distribution licence rather than a Creative Commons licence, and the journal version is under the IOP Publishing copyright, so this page holds the summary, the claims and the author’s own abstract and sends the reader to the source.
How to cite it
Maxim Dvornikov (2010) Formation of bound states of electrons in spherically symmetric oscillations of plasma. doi:10.1088/0031-8949/81/05/055502
Where it sits in the curriculum
Plasmoids, charge clusters and the orbsLattice confinement fusion