The neutron temperature example is crucial: you just can't give the cross section of a target alone, the energy of the incoming beam also matters.
Video 1.
How to make a cloud chamber by Suzie Sheehy (2011)
. Source.
Most important application: produce X-rays for X-ray crystallography.
Note however that the big experiments at CERN, like the Large Hadron Collider, are also synchrotrons.
Predecessor to the synchrotron.

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