It seems that currently, only two types of fusion reactor styles are being used for large scale testing: the Stellarator and the Tokamak. Both of these and a whole bunch of other designs have been developed in the 1950s and '60s. They are based on the idea of confining very hot plasma in a magnetic field, shaped just weirdly enough to not let the plasma escape.
Shaping such a field seems to be extremely complicated and could apparently only recently be achieved using computational optimization on the coil shape. On a side note, these reactors are also massively huge and expensive, probably not unrelated to the design.
Why are we still relying on these half a century old designs? What is stopping us from creating a very simple coil arrangement and just using a control loop to keep the plasma confined? Surely, somebody already thought of this. The designs mentioned before rely on the magnet field to create an inherently stable confinement. But today we can use inherently unstable processes and artificially make them stable by using a control loop.
A viable coil arrangement could potentially consist of 6 coils, distributed around a cube shaped container. The plasma could be induced and heated using light or radiation. If necessary, the coils could be made superconductive. The plasma cloud's shape, size and orientation could be tracked and used to change the field's shape in a way to contain it. The plasma could be compressed by collectively increasing the field strength, further heating it up.
Why doesn't this work?
I'm posting this in the Physics StackExchange because, despite being somewhat of an engineering question, I'm quite sure the underlying physics is what makes the idea impractical.