The idea of stohastic cooling is due to Simon van der Meer (Nobel Prize 1984).
At some point in the lattice appropriate pick-up mechanisam detects the beam. Precisely tuned amplifier delivers an electro-magnetic kick to the SAME particles, somewhere later in the lattice, reducing the emittance.
Main constraint on this process is the bandwidth of the amplifier, as there are many particles circylating the ring at high velocities. Present limit is in the order og GHz and extension into the optical range is in the process.
This kind of cooling mechanism helped in detection of W and Z particles in CERN.