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> It's impossible to make a magnet in the shape of a ball that squishes on all sides equally...

Ah, my favorite theorem, The Hairy Ball Theorem!

https://en.m.wikipedia.org/wiki/Hairy_ball_theorem

Can you explain how the Hairy Ball Theorem applies to the spherical magnetic field? My first intuition is that the magnetic field would not be a tangent field because you'd want all of the force lines to point inwards to the center of the sphere. However, based on what you said, it sounds like my intuition is wrong.

To phrase it another way, could you explain why the magnetic field is tangent to the sphere and not normal to it?

There are two things here.

The force magnetic fields apply is always perpendicular to the field: F ~ v × B (right hand rule, and all that). So if you want F to point inward, the one component of B that doesn't matter is its radial component---ie. the tangent component is all that counts. But it's not clear to me that you can't compensate for the restrictions of the hairy ball theorem by having a nonuniform velocity distribution. Of course, there's no "hairy torus" theorem (because it's not true!) and this immediately suggests the tokamak design.

It's also not possible to take a sphere and have the radial magnetic field point inward everywhere (or outward everywhere), because Maxwell's equations prohibit magnetic monopoles.

It's been too long since E&M. I forgot about magnetic fields being normal doh.

And of course, the last point about no magnetic monopoles should be sufficient to make a spherical field impossible.

I'd guess that it has something to do with eddy currents induced within the contained plasma. The HBT probably implies that these can't be perfectly symmetrical, and if they aren't symmetrical the whole thing will fall apart.

Charged particles will spiral along magnetic field lines. Thus, you want to have the field lines only be parallel to the confinement surface, so that the particles will migrate around the surface while doing their smaller-scale spiraling, instead of migrating outwards along field lines that exit the confinement.

great eli5. I attended a lecture by one of the Wendelstein-7X engineers a month ago, and the main reason why they would construct such a thing (took 10 years), from what I figured, was that a tokamak is operated in short pulses, whereas the stellarator runs smoothly.

Wiki: However, stellarators, unlike tokamaks, do not require a toroidal current, so that the expense and complexity of current drive and/or the loss of availability and periodic stresses of pulsed operation can be avoided, and there is no risk of toroidal current disruptions. It might be possible to use these additional degrees of design freedom to optimize a stellarator in ways that are not possible with tokamaks.

What's different about the stellerator magnetic field compared to the donut? And how does that shape help contain fusion better?

The main difference is the plasma circulates.

With the donut, the problem is similar to trying to inflate a balloon that has a weak point in it. Blowing causes the weak point to inflate instead of the balloon.

Plasmas are electrically charged and have their own magnetic field. Trying to squeeze down on the plasma inside the donut shape to cause fusion causes the plasma's own magnetic strength to increase and counter the field being applied to it.

The stellarator works with the plasma's magnetic field instead of against it by spiraling it around in circles.

This is a wonderful ELI5. The doughnut makes it all.

Say why could t you use an electric field instead of a magnetic field?

Apologies if this is a stupid question but aren't they the same thing?

Nope. They are both part of the same thing - the joint electromagnetic field - and they transform into each other in different reference frames, but in a given reference frame, the electric field and magnetic field components behave quite differently.

It blew my mind when I learned how magnetism is a consequence of special relativity.

You can. That's what a Farnsworth fusor does (there are other related designs, but that's the original, and the kind you can build in your garage).

But for complicated reasons, it just isn't efficient enough to actually produce net power output. Of course, neither is any other design right now, but magnetic confinement appears to be the more promising path forward.

Thanks for the explanation. I looked up some of those designs.

Now I'm really puzzled why no one has tried a more naive approach. I'm picturing a hollow metal sphere with a high positive charge with positive ions inside of it. Wouldn't it push them all together and with a high enough charge get them hot enough to fuse?

Counterintuitively, this setup would have zero force inside the sphere. It turns out that being closer to charge on one side of the sphere is always exactly balanced out by the more distant side's greater total charge.

Thanks so much. That was a really great explanation.