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In nuclear fusion, the goal is to create and sustain (usually with magnetic fields) a high-temperature and high-pressure environment enough to output more energy than put in.

Tokamaks (donut shape) have been the topology of choice for many years. However, it is very difficult to keep the plasma confined within the walls because of its high surface area (especially in the inner rings).

Why hasn't anyone used spherical magnetic confinement instead (to mimic a star's topology due to gravity)? - Apart from General Fusion

E.g. injecting Hydrogen into a magnetically confined spherical space and letting out the fused energy once a critical stage has been reached?

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    $\begingroup$ Hi and welcome to PSE. Chances are you have read this, but just in case Spherical Tokomak $\endgroup$ – user179430 Dec 24 '17 at 20:38
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    $\begingroup$ I shall read it again :) $\endgroup$ – Valentina Dec 24 '17 at 20:53
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    $\begingroup$ To my knowledge a "spherical TOKAMAK" is just a TOKAMAK. From my point of view the word "spherical" is misleading because the field is also toroidal. $\endgroup$ – common sense Dec 25 '17 at 21:07
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    $\begingroup$ sure hydrogen on hydrogen into deuterium, but the energy released is much smaller and deuterium is trapped in the plasma. It makes no energy logic to trap the energy in the plasma, because emptying the plasma takes away the input energy that was used to make it, and lowers much more the efficiency of getting energy ,imo. There is research on this but it still is in the baby stage, not thinking yet of how to extract the energy. see iflscience.com/physics/… $\endgroup$ – anna v Dec 27 '17 at 10:03
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    $\begingroup$ There is research going on in the UK on MAST (Mega Amp Spherical Tokamak): ccfe.ac.uk/MAST.aspx $\endgroup$ – Pietro Dec 27 '17 at 15:32
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Not an expert, but I believe the answer lies in the hairy ball theorem.

You see, for a magnetic field to turn charged particles back from a surface, the field must be parallel to the surface, which means that to have a fully confining geometry you must have a smooth, everywhere non-zero, and continuous vector field mapped onto a surface.

But the theorem say that you can't do that on a sphere (or topologically equivalent shape).

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    $\begingroup$ @Valentina The hairy ball theorem tells you that any spherical geometry (or indeed in closed and simply-connected geometry, because this is a topological theorem) will leak plasma at at least one point because there has to be a point where the field either points the wrong way (into or out of the notional surface of confinement) or drops to zero intensity. Either way that is a route for plasma to escape. $\endgroup$ – dmckee Dec 25 '17 at 4:54
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    $\begingroup$ @Valentina The point is that you can't control it. There's no way of 'plugging the hole', so to speak, so the forces within the plasma will force it out of this gap that necessarily exists. This might seem odd, because you would think that just applying some additional inwards force at this gap should prevent outflow. But an inwards force is a tangential magnetic field, and the topology of the sphere won't allow one to apply a tangential magnetic field at this point without creating some kind of discontinuity. $\endgroup$ – gj255 Dec 25 '17 at 22:45
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    $\begingroup$ @Valentina Any exit point for the plasma would be a disaster, since the plasma would immediately (by virtue of the internal pressure of the plasma) pass through the exit point and come into contact with the sides of the chamber. Yes, there naturally needs to be some initialising procedure in which the plasma is injected, but once this is done, it's important that there is no way for the plasma to enter or leave the magnetic confinement. $\endgroup$ – gj255 Dec 26 '17 at 0:04
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    $\begingroup$ @Valentina. Good luck confining the air in a balloon with a hole on it. $\endgroup$ – J. Manuel Dec 26 '17 at 7:29
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    $\begingroup$ @Valentina congrats, you've just created a torus. $\endgroup$ – Pureferret Dec 27 '17 at 10:59
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Because that's just one of the many alternative approaches to fusion, and resources are limited.

Nuclear fusion seems very promising, but for all approaches tried so far the challenges have proved to be more numerous and difficult to overcome than initially expected $-$ and the magnetized target fusion that General Fusion has been pursuing is likely no different. One needs to deal with extreme magnetic fields and temperatures, which is hard enough, and at the same time keep a rather fine control in order to maintain stability. That means that too much technology still has to be demonstrated.

Tokamaks and even Stellarators are more mature, developed technologies, so it's natural that efforts concentrate on those designs. That's very expensive research, a long-term investment with returns that are very uncertain $-$ so the alternative approaches have to compete for funding. And once a team has a head start on a given design, there's little incentive for others to follow before it's at least partially proved. That's why these new proposals are mostly being tried each by a single research group.

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Background: confining a plasma requires controlling all of an enormous spectrum of possible instabilities. The tokamak does a good job of stirring the flows so that no individual instability can grow so much that the plasma rushes out and contacts the wall (and thus is quenched). Regarding the particular question of a spherical tokamak: the answer just edited above points out that having a field everywhere tangent to a spherical surface is forbidden by the hairy ball theorem.
Magnetic confinement takes advantage of the fact that a charged particle's path is bent in a (strong) magnetic field; particle trajectories tend to be tight spirals about magnetic field lines owing to the V cross B force (Lorentz force): so particles cannot travel across the field lines unless they are scattered out of their spiraling motion. effectively allowing them to jump to a different line of force. For a spherical tokamak we would require an arrangement of field lines which was everywhere strong and tangent to the surface of the sphere. Such an arrangement would contradict the Hairy Ball theorem (mentioned elsewhere in this topic).

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protected by Qmechanic Dec 25 '17 at 13:25

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