A very fast particle accelerator has many uses, the main one being to collide particles together and see what they are made up of. This improves our understanding of the universe around us, and makes us able to try to replicate the things that we see around us.
We can also use accelerators to make radioactive chemicals called isotopes, which are needed in medicine to diagnose a patient who is ill, or to even treat it (i,e, by chemotherepy).
The most interesting use of a high energy accelerator at the moment (in my opinion) is the suggested use of a proton accelerator being attached to a special type of nuclear reactor, one that uses Thorium instead of Uranium or Plutonium. This type of reactor is very safe by comparison to existing reactors, as you can essentially just “turn off” the reactor, something that you can’t do at the moment.
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