We don’t use a particle accelerator for our work although some people have tried this method in the past but the results weren’t great. There are a lots of different ways to make nuclear fusion work and the one we and lots of other people use is called a tokamak. This involves creating a type of gas called a plasma then containing this with magnets and heating it up until its really hot, hotter than the sun!
The closest thing to a particle accelerator that people are trying at the moment is probably inertial confinement fusion, one of the ways to do this is by shooting a fuel pellet with high powered lasers. Another way to do this is to use shockwaves to collapse a fuel pellet and produce really high pressures in the pellet which causes fusion to happen.
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