It has analogies with static electricity. Static electricity might have a voltage of tens of thousands of volts, but it does little damage when you touch someone as the number of electrons (current) is so small that not much energy is involved.
Similarly with a plasma. The temperature (energy per particle) is very high but the number of particles is small, so the total energy is low. Touching something will cause the energy to leak away (cf. static electricity discharge) converting the hot plasma back to cool gas.
We don't really know how to build this part of the reactor right now, but some metals have the ability to self heal and people think this shield should be possible to build that has a decent lifespan. This is a part of fusion reactors that could be researched right now in parallel with other problems, but there has not yet been funding to build a high level neutron source facility to do the research. This is one fact of many that shows, I think, that national governments are not really interested in fusion energy succeeding.
If it didn't (hypothetically), I imagine it would do some pretty severe damage to the reactor parts specifically. At some point, the vacuum would be broken, air would rush in, and the reaction would _definitely_ stop.
Most of the larger fusors (as far as I'm aware) seem to be refinements of the basic Farnsworth-Hirsch fusor design (https://en.wikipedia.org/wiki/Fusor), which is a relatively simple device. If you have the motivation, you could build one at home with common-ish tools.
And details about the magnets: https://www.osti.gov/etdeweb/servlets/purl/20261539
> The vertical load on coil system is estimated to be 330 tons for the coil weight and 320 tons for vertical disruption load.
With some incredible forces that can be generated by the plasma.
> The lateral loads in tokamak could be generated by plasma disruptions and localized halo current flows through the plasma facing components (PFC) or vacuum vessel. The estimated peak lateral load in KSTAR is about 1.3 MN
I work on a research machine that uses copper coils. It uses 16x 1000 HP train traction motors with 2000 lb flywheels for energy storage to power the confinement field for one second. :)
JET and DIII-D are the largest magnetic confinement fusion research devices made so far and they both use copper coils. They have confining fields of 3.45 T and 2.2 T, respectively. My machine operates at a modest 1 T (for now) and is much smaller. I'm sure the electricity bill that the confining coils that those large machines racked up is substantial.
Besides creating the pressure, that purpose of the magnets is to keep the _few grams_ of plasma away from the walls of the otherwise vacuum chamber.
Look up magnetic levitation, where you keep an object up using just a magnet. Now imagine huge magnets that push against an object from all sides, creating a ton of pressure. (Don't forget to include a whole bunch of fancy math to prevent the object from slipping away like a wet bar of soap you squeeze with your hands.) At no point should the object touch any of the magnets.
Also keep in mind that when you (don't) want to heat something else up it's not the temperature that matters, but the total energy of the object. And the total energy is basically mass x temperature difference. So 1 gram at a million degrees is equivalent to 1 Kg at a thousand degrees, which is a lot less scary.