What is the bending radius of a circular collider?

A circle of circumference L has a radius R = L / 2π. For example, a circle with a circumference of 100 km has a radius of 15.9 km.

If a 100 km circular collider (as that foreseen for the FCC-ee) were a perfect circle, it would have a radius - also called bending radius, because the beam needs to be "bent" by magnetic dipoles to follow the circle - of 15.9 km. Now, circular colliders are made of "arcs" (where the beam is bent indeed) and "straight sections" (in general on both sides of each interaction points). This subtelty is needed to protect the detectors from the synchrotron radiation that would arise from bent beams. In such a configuration, the bending radius of the arcs (i.e., the radius of the corresponding circle) needs to be smaller than the radius of the perfect circle.

For a 100 km FCC-ee, the bending radius in the arcs is expected to be 11 km, as is shown here.

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