Historical research guide · 0396 · 1999
Ball lightning as a free-force magnetic knot with linked streamers
A. F. Rañada · M. Soler · J. L. Trueba
In one minute
Ball lightning — a glowing sphere that drifts through the air for seconds, sometimes minutes — has no agreed explanation, and Faraday argued it could not be electromagnetic at all, since such a thing would decay instantly. Antonio Rañada, Mario Soler and José Trueba answer him with topology. Their fireball is a ball of air coupled to a magnetic knot: a magnetic field whose lines are closed and threaded through one another. Currents run inside it along short-circuited streamers that follow the lines of the curl of the magnetic field, and the streamers are themselves separate from one another and also linked, so the whole object is thoroughly tangled. That linkage is measurable — it is the helicity integral, the volume integral of the vector potential dotted into the magnetic field — and the authors show it stabilises the system. The streamers run between 16,000 and 19,000 kelvin, where the plasma’s radiated power density has a shoulder and emission is nearly constant, which is how the ball can pour out energy without visibly dimming.
Connection
Chapter 9 is about self-organised plasma objects that hold together far longer than they should, and this is the cleanest statement of why one might: linkage, not confinement, is what keeps the structure alive. The stabilising quantity is the integral of the vector potential dotted into the magnetic field, which is chapter 10’s subject arriving in an atmospheric fireball.
From the source
The model treats a ball lightning as an air ball coupled to a magnetic knot — a magnetic field with linked force lines — that is also a force-free field, one for which the magnetic field crossed into its own curl vanishes, so the Lorentz force is zero.Conference abstract, page 189
Currents flow inside the ball along streamers that are short-circuited and follow the lines of the curl of the magnetic field; the streamers are separated from one another and also linked, so that the system is very tangled indeed.Conference abstract, page 189
The linking of the lines, which can be measured by the helicity integral — the integral of the scalar product of the vector potential and the magnetic field — has a stabilising effect on the system.Conference abstract, page 189
The streamers are hot, in the range 16,000 to 19,000 kelvin, where the curve of power density emitted by the plasma has a shoulder in which the emission is approximately constant — which explains why the ball loses energy by radiation without decreasing its radiance.Conference abstract, page 189
Three effects contribute to the fireball’s stability: the formation in each ball, during a process of Taylor relaxation, of a force-free magnetic field; the Alfvén conditions of magnetohydrodynamics; and the approximate conservation of the helicity integral — and the balls shine while relaxing in an almost quiescent expansion.Companion paper, Rañada, Soler and Trueba, Phys. Rev. E 62, 7181 (2000), abstract
Assuming those linked short-circuited streamers, the lifetime, energy and radiated power of the average observed ball are correctly accounted for, and the model explains why some witnesses feel no heat while others are burnt, and why filaments are seen trailing the ball in some cases.Companion paper, Rañada, Soler and Trueba, J. Geophys. Res. 103 (D18), 23309 (1998), abstract
The way in
https://doi.org/10.1109/plasma.1999.829466How to cite it
A. F. Rañada, M. Soler, J. L. Trueba (1999) Ball lightning as a free-force magnetic knot with linked streamers doi:10.1109/plasma.1999.829466