Spherical Electromagnet Formed By Six Coils For Plasma Containment and Nuclear Fusion

Question

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.

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.

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.

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

Update to question on 2024/06/21 The following OpenSCAD drawing came out of all the conversation from this question. The 12 rods represent electrodes for creating arcs of plasma and the coils are for manipulating the plasma. I understand that no one thinks it will work but it is fun to think about and I hope to experiment with a working model in the future. Thanks to all for the dialog.

Answer 1

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.