In
celestial mechanics, the
Lagrangian points (
also
Lagrange points,
[1] L-points, or
libration points) are the points near two large bodies in
orbit where a smaller object will maintain its position relative to the large orbiting bodies. At other locations, a small object would go into its own orbit around one of the large bodies, but at the Lagrangian points the
gravitational forces of the two large bodies, the
centripetal force of orbital motion, and (for certain points) the
Coriolis acceleration all match up in a way that cause the small object to maintain a stable or nearly stable position relative to the large bodies.
— “Lagrangian point”, Wikipedia
I’ve only seen this concept in reference to gravitational fields. I suspect an equivalent may exist for electric fields, which may be useful for developing an improved electrically confined fusion reactor (AKA the sort that school students make every so often as science fair projects, which currently have so many flaws that almost nobody expects them to ever become useful power sources).
Why would it be useful? Let’s begin with the current problem: electrostatic fusion reactors have two grids, one a cathode and the other an anode, to create the electric fields which accelerate the ions enough for nuclear fusion to happen. Unfortunately, fusion is very unlikely compared to the ions simply bouncing off each other, which means even a very spacious grid — 99% empty — isn’t empty enough, and most of the power gets wasted by the few ions which hit the grid each time they fly past.
Some designs try to get around the grid problem. For example Robert Bussard (yes that one) has designed the Polywell reactor which uses a virtual cathode: a cloud of magnetically confined electrons. Another possibility I’ve never had time (and probably resources) to simulate was finding out if the so-called “star mode” of a Farnsworth Fusor, where the ions primarily flow through the gaps in the grids, might be caused by a magnetic field generated by the current flowing between the grids — if it is, you could enhance that field relatively easily, and boost the efficiency. This probably still won’t make it a net power producer (anything I can think of will have been thought of a hundred times already by the professionals), but it might still be interesting for other things.
This brings me to the idea of a Lagrange point as a virtual cathode, where the virtual cathode is the dynamic balance of the electric charges as they move.
It might not be possible at all (gravity is always attractive, unlike electric fields, and this may cause extra problems when you have a plasma field rather than claiming equivalence from a few point-like masses to a a few point-like charges); and even if it is possible at all, it might require a prohibitive power consumption (accelerating a charge produces electromagnetic radiation, slowing the charge down in the process).
Of course, the equivalence of moving electric fields and magnetic fields makes me wonder, again, if a hybrid electric- and magnetic-confinement fusion reactor could do better than either on their own.
Disclaimer: I’m a software engineer, not a doctor of physics. If a proper scientist disagrees with me, trust them.
