Axially and spherically symmetric solitons in warm plasma
Maxim Dvornikov
Abstract and summary · read the original at the source
In one page
A plasmoid is a ball of ionised gas that holds itself together with its own fields instead of a container. Maxim Dvornikov, at Russia’s institute for terrestrial magnetism and the ionosphere, asks under what conditions the equations of plasma physics actually permit one. His route is the nonlinear Schrödinger equation, the standard tool for a packet of Langmuir waves — the collective oscillation of electrons against the ion background. Electron-ion coupling normally makes such a packet collapse. Electron-electron nonlinearities push back, and Dvornikov adds the ones that come from electron pressure in warm plasma, which earlier treatments had left out and which turn out to be the same size as the terms already kept. Solving the resulting equation numerically, he finds standing solutions: rings and spheres of trapped oscillation. The two-dimensional ones are stable; some of the three-dimensional ones are not. He then computes what such an object would look like in the sky — a metre-scale, low-energy plasmoid, and a candidate description of ball lightning.
Why it matters hereChapter 9 is about plasmoids — self-organised balls of plasma that behave like objects rather than like clouds — and this paper is one of the few that derives them from first principles and then says how big, how energetic and how long-lived they can be. Its closing question belongs to chapter 5: what keeps a plasmoid from recombining is an internal energy source or a coherent, superconductor-like state of the plasma itself.
What it claims
01In plasma the nonlinear electron-ion interaction produces modulation instability and drives a Langmuir wave to collapse, while nonlinear electron-electron interactions work the other way and stabilise the evolution of the wave packet — which is what makes stable spatial plasma structures possible at all. Nonlocal electron nonlinearities can arrest the Langmuir collapse under the right conditions.Section I, Introduction, paragraphs 2 and 3
Published and peer-reviewed02Starting from the nonlinear hydrodynamic plasma equations and keeping the electron pressure tensor, the author derives a new nonlinear Schrödinger equation containing nonlocal terms that come from the slowly varying electron density. These pressure terms are the same order of magnitude as the nonlocal terms already known, they matter whenever the electron temperature is not zero, and they do not vanish even in one dimension.Section II B, Eq. 2.18; Section V, Conclusion; Appendix A
Published and peer-reviewed03Solved numerically for the radially symmetric case, the equation has solitonic solutions — localised standing structures of electron oscillation. The two-dimensional, axially symmetric solutions are stable; in three dimensions the solution branches split and some spherically symmetric solitons are unstable, losing electrons rather than holding together.Section III, Figs. 1 to 3; Section V, Conclusion
Published and peer-reviewed04The predicted objects are low-energy plasma structures with an effective radius up to about 1.5 metres, forming in rarefied plasma of around one hundred thousand electrons per cubic centimetre at electron temperatures near one million kelvin — conditions the author notes can exist in the Earth’s ionosphere, and which an ordinary lightning channel can produce locally during a thunderstorm.Section IV, Applications; Fig. 4
Published and peer-reviewed05Stability against decay is set by the ratio of the plasmoid’s electric-field energy to its thermal energy. That ratio rises with soliton energy and reaches one at a critical value — about 1 erg per centimetre in two dimensions and about 215 erg in three — above which the hot electrons no longer escape the plasmoid volume.Section IV, Eq. 4.1 and Fig. 5
Published and peer-reviewed06The model does not yet reach ordinary ball lightning, whose reported energy of ten kilojoules or more and diameter of 20 to 50 centimetres lie outside its predictions, because only the cubic nonlinearity is retained; higher nonlinear terms, important for denser plasma, could account for the smaller size and larger energy. And a low-energy plasmoid with no internal energy source would recombine in milliseconds at atmospheric pressure — unless, as has been suggested, plasma can be brought into a superconducting state, which would prevent the energy loss and give the object a long life.Section IV, final three paragraphs
What to watch
The way in
https://doi.org/10.1017/s002237781100016xPublished in the Journal of Plasma Physics by Maxim Dvornikov of the Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN) at Troitsk, Moscow Region. The manuscript is free to read on arXiv as 1010.0701, but that posting carries arXiv’s non-exclusive distribution licence and the version of record carries the Cambridge University Press core terms — neither is a Creative Commons licence — so this page holds the summary, the claims and the author’s own abstract and sends the reader to the source. The abstract as distributed by the publisher runs the word ‘Abstract’ into the first sentence; it is given below as the paper itself prints it.
How to cite it
Maxim Dvornikov (2011) Axially and spherically symmetric solitons in warm plasma. doi:10.1017/s002237781100016x
Where it sits in the curriculum
Plasmoids, charge clusters and the orbsThe vacuum as a quantum fluid