When a bunch passes through an electron cloud, the transverse electron density distribution is enhanced and modulated in time as a consequence of the motion of individual electrons under the action of the nonlinear beam field. The effect of this “structured” electron pinch together with the synchrotron motion of beam particles leads to an incoherent emittance growth via the excitation and repeated crossing of resonances, that can give rise to either stochastic “scattering” (“diffusion”) or trapping. We study these effects via a toy model of an idealized pinch, and present applications to the CERN SPS and the GSI SIS100
