system
Given the following post, respond as if you're commenting on Reddit:
human
Why particle accelerators are so huge? Wouldn't be possible to crush particles in a smaller and spiral structure?

sorry for the dumb question, my knowledge of electromagnetic fields is restricted.
gpt
The vast majority of accelerators are not that big (they can fit in a garage). It sounds like you're specifically asking about the few very large colliders around the world. So why are *those* so large?

You use a collider rather than a fixed-target machine when you want to reach higher energies. Kinematically, the thresholds for interesting processes are lower with a collider than with a fixed target because with a collider, *all* of the kinetic energies of the two beams is available in the center-of-mass frame (because the center-of-mass frame is the lab frame). In a fixed-target experiment, there's nonzero total momentum in the lab frame, so some of the beam energy is "wasted" on the motion of the center of mass.

So you build a collider when you want to study extremely high-energy processes, which generally means you want the beams to have as much energy as possible too.

And with a collider, you'd prefer it to be circular rather than linear, so the beams will circulate around many times. If the beams circulate some thousands of times before the fill is dumped then each particle has thousands of chances to do something interesting, while in a linear collider it would only have one, so to speak.

But if you want your accelerator to be circular, you need to steer the beam in a circle. For beams at high energies you do this with magnets.

The radius of curvature of the accelerator (ρ), the momentum of the beam (p), and the magnetic field strengths of the main bending magnets (B) are all related to each other by

Bρ = p/q.

That says that the magnetic field times the radius of curvature equals the momentum per unit charge of the beam.

So if p is fixed by your desire for maximum energy, and q is fixed by the type of particle you want in your beam, then the radius of curvature of the accelerator is inversely proportional to the magnetic field strength of the dipoles. But field strengths are practically limited by what technology is available. Superconducting dipole magnets for accelerators can currently give sustained fields on the order of ~ 1 - 10 Tesla. So if your dipole field strength is limited, but you want to maximize the energy of the beam, you need to increase the radius of curvature accordingly. That means that the collider ring needs to be bigger.

If the magnets were stronger, you could have a beam with the same p/q (we call this the "magnetic rigidity" of the beam) at a lower radius. But currently we're limited by the strength of the magnets, so we're stuck with these huge rings, *if* we want to reach the highest possible energies.