69. Can plasma physics explain ball lightning?
Thanks for writing and maintaining such a wonderful resource! I wish
more people did this for their own field of interest.
One question, though, but in a few parts:
Why can't a moving plasma stream generate its own magnetic field
strong enough to contain itself?
One of the problems facing fusion in Tokamak-style plasma containment
devices is the HUGE magnetic fields needed, then the instability of
the plasma itself due to its own magnetic fields.
Yet, as Larmor reported, a plasma is associated with a magnetic field
(I like the 'bootstrap' analogy of yours!).
A possible example from nature may be the (slightly dubious) theories
I have heard about ball-lightning being 'circular lightning' caused
by 'eddy currents' from a lightning strike. Some have observed ball
lightning with enough energy to melt glass that it had drifted
through, and boil water, and even explode with enough force to
flatten a house! They seem to have enough magnetic force to rip metal
objects from their fixtures, yet are stable enough to remain intact
for minutes. (I confess, I even saw one one hot summer's night when
15 years old or so!)
The idea is that rather being a ball as such, it's more a donut shaped helix.
I don't know, but wouldn't the magnetic field always be at
right-angles to the moving ions, and thus they would stabilize each
other, as long as the ions were always moving (and thus a current was
moving)?
Just wanted to ask someone that actually might know, so I can get
back to writing my thesis, like I should.
Reply
A magnetic field of the kind you discuss is theoretically possible, but I think it needs an outside pressure to hold it together.
I once calculated such a field, which involves the same mathematics as Hill's spherical vortex in fluid dynamics. I know this is mathematically far beyond your level, but let me just say that the result is given (including a term B1 which may be omitted) in problem 13, p. 17193, Journal of Geophysical Research, 1994. After deriving it I found that Harold Grad did so first, around 1958. It has field lines somewhat like the Earth's, confined in a sphere.
However, I think such a plasma needs an external pressure to keep it from dispersing, so it might not be a good model for ball lightning. In fact, I vaguely recall a general theorem in mechanics, called the virial theorem, which states, roughly, that an independent mechanical system will not hold together unless the sum-total of attractive forces exceeds that of disruptive forces. "Sum-total" here is taken over the space occupied by the system (e.g. interstellar cloud, planet etc.), with different regions weighed in some specific way, and the primary attractive force is usually gravity, while pressure and magnetic forces are disruptive.
The Earth's magnetosphere can be stable, since the main magnetic source is in the Earth's core, where gravity holds it together. Plasma in containment machines is kept in place by auxiliary coils, embedded in the machine (though I am not familiar with details). However a system which has only plasma (producing pressure) and magnetic fields will not stay together.
Ball lightning remains a mystery, its appearances are too brief and unpredictable for any meaningful study. I have not heard about it producing strong magnetic fields, although ordinary lightning certainly does. If ball lightning occurs immediately afterwards, magnetic effects may perhaps come from the primary stroke.