Shape of a particle accelerator

[petrushka.googol]

Is there a preferred shape for a particle accelerator ? eg) like a toroid.

 

Could it be configured as a prism (with a beam originating from the base and moving towards the apex, with fields acting perpendicular to the faces.).

[Klaynos]

Linear accelerators use straight lines, you could put two at an angle to each other. The reason circles are often used is that you can send the particles around and around building up more energy.

[John Cuthber]

Also, the tighter the corners are, the more energy is lost by the beam as it goes round them.

The circular path is the least inefficient in that regard.

[imatfaal]

A cyclotron has a spiral particle beam - with the particle being injected near the middle and exiting at the edge; however the containment is a disc shape

[Enthalpy]

For high energies, the achieveable induction determines the bending radius. That's why it take D=10km in some cases. If one wishes an other shape, he can only add straight portions between the kilometer-radius bends.

 

Which is done actually, since the experiments, collimation, acceleration sections are not within bending magnets hence are on straight paths. But these sections are kept short because the cost additional tunnel length, or at identical length, they reduce the maximum energy.