There are quite a few designs out there that accelerate different particles up to different energies so we can study different physics.
They have a few main features in common. Firstly if you want to accelerate something, it needs to have a charge. At ISOLDE in Cern, extreme heat or lasers can be used to ionise atoms by removing electrons. Electric and magnetic fields then do the rest. If your atoms are in a 1+ state, having a negatively-charged metal plate in front of them accelerates them down the beam pipe.
Different shaped magnets can be used to steer the beam around corners, and the beam can be ‘focussed’ (a bunch of particles with the same charge will repel away from each other). The beam pipe needs to be pumped down to a really good vacuum (one 10 billionth of atmospheric pressure is just about acceptable) otherwise your particles hit air molecules.
In a linear accelerator, a radio signal changes the plates between positive and negative as the particles go past. This is so they get attracted by the plate in front of them and repelled by the plate behind them at the same time.
The cool thing about ISOLDE is that we do this with atoms that are radioactive! They get made by another CERN accelerator.
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