Historical research guide · 0798 · 2010
Formation of bound states of electrons in spherically symmetric oscillations of plasma
Maxim Dvornikov
In one minute
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.
Connection
Chapter 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.
From the source
Spherically 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
Free 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
A 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
For 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’
Bound 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
During 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
The way in
https://doi.org/10.1088/0031-8949/81/05/055502How 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