Re: Size vs position?
> It has to be a large ring.
> It is not possible to accelerate uncharged particles, such as neutrons. When you accelerate charged particles (or decelerate, as in X-ray machines), energy is radiated away. Circular motion means sideways acceleration, same thing.
> So it has to be a large ring, i.e. small curvature.
The particle is being accelerated by alternating electrical fields along the path, both pushing it and pulling it. It's pulled as it approaches a given field, then when it passes, the field is flipped to start pushing it. If the field didn't flip, then it would start pulling it back and slowing it down again. Assuming a constant distance for the parts which generate the fields, as the particle gains speed, the rate at which the electrical fields alternate must increase in proportion.
If you want to gain a high energy with particle speeds approaching the speed of light, then if you made a linear accelerator, you'd need either an extremely powerful one (very strong electrical fields for quick acceleration) or else a very long one (more fields for longer acceleration).
If instead you use a ring, then the particle(s) being accelerated can make many revolutions, with the rate of alternating the fields increasing with each revolution. As the particle gains speed, it will gain relativistic mass, and strain against the magnetic field keeping it in the ring, which is why you need those big super-cooled super-conducting magnets. The magnetic field is vertical, and as the charged particle travels through it, it experiences a sideways force, which keeps it traveling in a circle.
A ring lets you get more use out of those expensive field generators.