There are several different ways to design these accelerators, each with its benefits and drawbacks. Here's a quick list of the major accelerator design choices:

Accelerators can be arranged to provide collisions of two types:

Fixed target: Shoot a particle at a fixed target.

Colliding beams: Two beams of particles are made to cross each other.

Accelerators are shaped in one of two ways:

Linacs: Linear accelerators, in which the particle starts at one end and comes out the other.

Synchrotrons: Accelerators built in a circle, in which the particle goes around and around and around...