The main difference between collider and fixed target accelerators lies in the way particles are accelerated and made to collide. In a fixed target accelerator, particles are accelerated in a straight line towards a stationary target, whereas in a collider, two beams of particles are accelerated in opposite directions and made to collide at a point.
Colliders are generally considered better for studying high energy particle collisions. This is because they can achieve higher collision energies by accelerating particles in both directions, resulting in a higher probability of producing rare and high energy collisions.
In a collider accelerator, particles are steered using magnetic fields created by powerful magnets. The magnets are arranged in a circular path to keep the particles moving in a circular orbit, and smaller magnets are used to focus and steer the beams towards each other at the collision point.
Examples of collider accelerators include the Large Hadron Collider (LHC) at CERN and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. Examples of fixed target accelerators include the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory and the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab.
Collider accelerators have the advantage of being able to achieve higher collision energies, making them better for studying high energy particle interactions. However, they also have higher costs and technical challenges associated with creating and controlling two beams of particles. Fixed target accelerators, on the other hand, are less expensive and technically simpler, but they can only achieve lower collision energies and are limited in the types of particles they can accelerate and study.