Suppression of Emittance Growth by a Collective Force: Van Kampen Approach

In hadron synchrotrons, external sources of noise affecting the beam induce emittance growth through the mechanism of decoherence. Active feedbacks are often used to suppress this emittance growth. In the presence of beam-beam interactions, it was shown that coherent modes of oscillations with frequencies shifted outside of the incoherent spectrum significantly enhances the efficiency of the emittance growth suppression by active feedbacks. We show that the same enhancement of the emittance growth suppression may be driven by a beam coupling impedance generating a real tune shift larger than the detuning.