We normally use particles like protons or electrons. These are charged (positively and negatively respectively) so we use an electric field (effectively a voltage) to move them. Applying a large voltage makes them move faster and if you keep on applying more voltages they go even faster. Eventually they have enough energy for our work and we make them crash into something, or bend them in a magnetic field, the crashing makes different particles (like neutrons), the bending makes light or x-rays.
If you see old TV’s (the really fat ones) they have a particle accelerator in the back which it uses to accelerate electrons onto the screen to make the picture.
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