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Several years ago I have proposed an open source spherical magnetic vessel to contain plasma for nuclear fusion which can be seen by following this link.
A photo of it is seen below.
Photo of model, 25-hedron?

A question here asks why the torus is used instead of a sphere to contain plasma.

My understanding is that too much heat is lost with a torus to sustain fusion because the plasma is stretched out around the reactor which exposes a lot of surface area. So if it were possible to make a spherical magnetic container that should help.

The accepted answer cites the hairy ball theorem which states that a sphere will always leak flux somewhere because it is not possible to map a smooth non-zero, and continuous vector field onto its surface.

The device I propose gets around this problem by constantly moving the opening in the magnetic field so that by the time the plasma has reached this opening, the opening has moved to a different location. The plasma tries to follow the opening which causes it to rotate in pitch, roll, and yaw so that it cuts across the magnetic field lines of the coil which induces current and a secondary magnetic field in the plasma. And since the plasma is rotating in three different axes, it also cuts across its own magnetic field which should cause compression.

Model with colored paper strips

Same model, different angle

Each of the six coils is powered individually.
Six separate signals from a computer are fed to six channels of amplification which are then fed to the coils. The interplay of the magnetic fields induced by the six coils is what makes the field rotate in pitch, roll, and yaw at the same time.
Or if powered as shown by the paper models above then the plasma would be expelled.

Perhaps these devices could be clustered as shown below.

Beehive-like stacked 3D model

Or perhaps a track could be made as shown below which might be another way to impart spin to the plasma.

Double helix stacking arrangement

Does this help address the concerns about using a spherical container to hold and manipulate plasma for fusion reactors?

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I think you might still have a problem of plasma leaking from the moving opening. Think of the magnetic containment of the plasma sort of like a balloon:
Intuitively, if you had a balloon with a hole in it, air would leak out no matter if the hole moves or not. The plasma/gas inside the reactor/balloon fills the contained volume, so there will always be particles ready to escape near the new position of the opening regardless if it moves or not.

Edit
As pointed out by @probably_someone, moving the hole fast enough can probably mitigate leakage. I would expect the leakage timescales to be similar to the hydrodynamical time scales, i.e. the governing velocity is the ion-acoustic speed $c_{\rm s}\sim\sqrt{T_{\rm electron}/m_{\rm ion}}$, where $T_{\rm electron}$ is the electron temperature and $m_{\rm ion}$ is the mass of the ions. For a $T_{\rm electron}\sim100\rm\,keV$ fusion plasma, that comes up to $c_{\rm s}\sim1\%$ the speed of light.

In the case of the balloon, disregarding how to practically move a hole around at or above the speed of sound, that might actually significantly reduce leakage. But the gas+balloon analogy is, per usual, a bad oversimplification -- sorry for bringing it up.

With the plasma, you have the problem of moving around a hole in the magnetic field at around $1\%$ the speed of light. The usual magnetic field strengths in magnetic confinement fusion is in the order of $B\sim1\rm\,T$. That would induce an electric field on the order of $E\sim c_{\rm s}B\sim1\rm\,MV/m$. This electric field will be pointing in opposite directions at the front and back of the hole with respect to the direction of the hole's motion.

Generally the electric field direction which pulls electrons out (they are much faster at responding that the heavier ions) out will be driving a current of electrons out from the confinement. Unlike the magnetic fields, the electrons are not confined by the electric field lines, which bend back into the plasma, and I would suspect that they gain enough energy to escape. The core will be slowly be depleted of electrons, thus accumulating a net positive charge, which may end up with the plasma breaking out from the magnetic confinement due to the electrostatic repulsion between the ions.

All this is not even considering the practical difficulties of manipulating a ${\sim}1\rm\,T$ field around at about $1\%$ the speed of light. You would need extremely powerful power sources to drive the coils to change their magnetic fields that fast. Considering that a current tokamak like JET draws about $500\rm\,MW$ of power just to have a static magnetic field, I would say that this spherical design isn't technically feasible either.

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  • $\begingroup$ I was thinking about this the other day, and I came to the conclusion that you probably can prevent fluid from escaping a container with a hole in it, if you move the hole much faster than some threshold speed (whether this is the speed of sound of the fluid, or the typical velocity of the fluid's constituents, or something else, I'm not sure). Basically, move the hole so fast that the time it takes to pass through it is much larger than the time interval in which it allows passage at a certain spot. That speed is almost certainly much higher than would be practical, in any case. $\endgroup$ – probably_someone Nov 26 '19 at 14:01
  • $\begingroup$ Device has four objectives. 1. Pull the plasma to the part of vessel opposite the current position of the opening. Think swinging an open sack of rocks. The rocks don't fall out. 2. Get the plasma to spin and cut across magnetic lines of flux from step 1. Or the field can spin - it doesn't mater. Think stator in squirrel cage ac motor. 3. Induce current in the plasma from step 2. Think rotor in squirrel cage ac motor. 4. Current in plasma from step 3 induces a magnetic field in the plasma to compress it (self attraction). Now it doesn't matter if the vessel has a leak. Think ball lightning. $\endgroup$ – John Shearing Nov 26 '19 at 15:49
  • $\begingroup$ @JohnShearing "Think swinging an open sack of rocks. The rocks don't fall out." - Rocks in a sack aren't moving in random directions at up to thousands of kilometers per second. The constituents of a plasma are. $\endgroup$ – probably_someone Nov 26 '19 at 15:54
  • $\begingroup$ @JohnShearing I'm also confused, in step 2, about how you would get the plasma to cut across the magnetic field lines from 1. The main point of magnetic confinement fusion is that the plasma has a really hard time moving across magnetic field lines, so if you give the plasma enough energy to cut across those field lines, then what keeps the plasma from also cutting across the "main" confinement field lines? $\endgroup$ – Andréas Sundström Nov 26 '19 at 16:22
  • $\begingroup$ What I am asking is can we get more types of forces involved and exploit the out of phase nature of the forces as they interact? Like the way light bounces back and forth between mirrors to make a laser from well timed flashes of light or how an ac motor works. I wonder if these have analogies for plasma. The device above is intended to facilitate exploring those analogies. Playing with devices and ideas that are not likely to work can still produce things which are completely unexpected and at times more valuable than what was originally intended. Thanks for thinking about this with me. $\endgroup$ – John Shearing Nov 26 '19 at 17:58

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