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Is it possible to create (or is it even possible to have exist*), in an arbitrarily hard* vacuum, a formation of charged particles in motion (along a closed path) that is
self-sustaining by being confined by its own magnetic field?
For the simplest case (which wouldn't work as I describe it), imagine
some charged particles traveling in a circle, under the confinement of an external uniform
magnetic field, as is commonly done. However, in this case, the particles have enough speed/kinetic energy and enough density that the electric current of them
moving in a circle generates its own significant magnetic field, so that when the external field is removed, they continue to move in a circle (though a larger one)
and continue to generate their own magnetic field, self-sustainingly (for a while, until synchrotron radiation takes away their kinetic energy).
In a more complex case (which also wouldn't work), the trajectory could be helical, with some sort of return path from one end to the other, to get more turns and
therefore a stronger magnetic field.
However, both of those examples wouldn't work, for a simple reason: magnetic self-repulsion. This is seen in regular wire. If you dump a large capacitor through a
crumpled piece of wire whose ends are fixed, it will spring out into as much of a circle as it can manage between the fixed ends. And in electromagnetic can-/coin-
crushers, the work coil is typically a single-use part, because it blows itself apart with the same magnetic field that crushes the can or coin. In other words, the
magnetic field generated by charged particles moving in a circle or similar trajectory is the opposite of that needed to contain them in that trajectory. For that
reason, I think the charged particles would fly outward upon removal of the external magnetic field, even faster than they would just due to centrifugal release.
Therefore, a more complex configuration would be required to avoid immediate self-destruction, if it's even possible. I suspect it's not, but I'm not sure, which is
why I'm posting this. I feel like it might need some way of twisting a magnetic field in a region of space where there is no source of magnetic field; this might need
external solid matter to redirect the magnetic field, but I guess that's okay, because the soliton can't continue existing without an external device of some sort to
pump it anyway (next paragraph).
Such a more complex design, even if magnetically stable, would still be susceptible to synchrotron losses. Therefore, it will need external pumping to keep
operating (and probably to keep within the very tight tolerances needed for stability). This could be done, in principle, by any method used in particle
accelerators, but at least several of those methods work only on bunches of particles, not a continuous stream, and that bunching would mean the magnetic field
generated by the soliton would be time-varying on a scale comparable to its spatial features, which would mean *very* careful design would be needed.
Anyway, is such a self-sustaining (apart from synchrotron losses) and self-contained electromagnetic soliton even theoretically possible? If not, I will also be glad to
hear about designs using external matter, such as mu-metal, for part of the containment scheme, as long as that part's passive. (Pumping will still have to be
active, of course.) I'd prefer to avoid designs using external permanent magnets, because it's not a new concept to just use two disc magnets with a gap between
them and have the charged particles circulate circularly in that gap.
*Both of these qualifications are mentioned in recognition of the fact that not only is it impossible for a perfect vacuum to be created, it's also impossible for a
perfect vacuum to exist, even if you could create one. (By my understanding, these two impossibilities are not even related to each other.) Similarly, it may be
possible to create one of these solitons, while it's impossible for the soliton that would be created thus to exist. Conversely, it could conceivably be possible for
such a soliton to exist, if it already existed, while its creation by any method is impossible.
[bs0]'s annotation of July 3rd. Discussion of ohmic losses in extremely powerful electric motors. I thought that if the current was flowing through a vacuum, that wouldn't be an issue. Of course, extracting work from the motor will necessitate a commensurate increase in pumping of the soliton. [notexactly, Jul 22 2019]
The relevant physics. [8th of 7, Jul 22 2019]
||Could you explain "closed path"?
||I suspect this is a load of balls. Ball lightning, to be precise.
||Skip that oscillating stone. Hey wait, how many dimensions to catch those pre-existing solitons?
||Technically, ordinary matter is composed of charged
||Maybe we can prove such a configuration is
impossible? Charged particles flowing in a closed
loop must generate a magnetic field which
necessarily has nonzero flux coming through the
loop. In other words, no matter what your loop of
charged particles looks like, it's going to make a
magnetic field that has field lines going through the
loop. This means that no matter what your loop
looks like, it'll experience electromagnetic force
pushing the charged particles on it out away from
the middle of the loop.
||Clearly the goal is a design for a tokomak reactor
which can be garage-built. This is a worthy goal.
||Here's a concept: build your vacuum tubes for the
beamline out of superconductor, so the tube itself
will confine the magnetic field lines to run along the
tube, and any charged particles motion toward the
walls of the tube gets converted into lateral
(spiraling) motion. Put a spark gap generator in
there to get the gas hot, and hope for the best.
||// Could you explain "closed path"? //
||Same meaning as in vector graphics software: a path with no ends but instead goes around and
around, topologically equivalent to a circle.
||// Maybe we can prove such a configuration is impossible? Charged particles flowing in a closed loop
must generate a magnetic field which necessarily has nonzero flux coming through the loop. In other
words, no matter what your loop of charged particles looks like, it's going to make a magnetic field
that has field lines going through the loop. This means that no matter what your loop looks like, it'll
experience electromagnetic force pushing the charged particles on it out away from the middle of
the loop. //
||Indeed, a proof that this is impossible would satisfy me. But we have to pay attention to any proof's
assumptions. Your proof seems like it might assume no magnetic field conductors around the current
path, as well as no time varying component to the current. I suspect that, if anyone has formally
proved this (which is almost certain), they made those same assumptions, meaning that that proof
doesn't rule out a device incorporating those features. (Doesn't mean a device with those features
would work, either, of course.)
||// Here's a concept: build your vacuum tubes for the beamline out of superconductor, so the tube
itself will confine the magnetic field lines to run along the tube, and any charged particles motion
toward the walls of the tube gets converted into lateral (spiraling) motion. Put a spark gap generator
in there to get the gas hot, and hope for the best. //
||Interesting. I might try simulating that, when I get around to learning how to simulate
electromagnetics and charged particle motions, which I need to do anyway for other stuff.