A pick-up is sensitive to how much a single particle is far from the ideal trajectory (due to betatron oscillations, ie oscillations in the transverse direction). It sends a signal (along a chord) to a kicker magnet, which compensates.
The other particles give "Schottky noise" (ie single particle noise). They contribute more if they are close in frequency to the sampled particle.
Any particle receives a correction which depends on its own signal, and on the other particles' signal. So, there are two competing effects from the kicker: the cooling is linear with the gain G between pick-up and kicker, while the heating due to the kicker is quadratic with G. Since both effects are zero for G=0, there is a range of G for which cooling>heating, and it is possible to find an optimal G which maximizes (cooling-heating).